DETAILED ACTION
A request for continued examination under 37 CFR 1.114, including the fee set forth in 37 CFR 1.17(e), was filed in this application after final rejection. Since this application is eligible for continued examination under 37 CFR 1.114, and the fee set forth in 37 CFR 1.17(e) has been timely paid, the finality of the previous Office action has been withdrawn pursuant to 37 CFR 1.114. Applicant's submission filed on July 8th, 2025 has been entered.
This action is in response to the amendments filed on July 8th, 2025. A summary of this action:
Claims 23-26, 28, 30, 37-41, 43-51 have been presented for examination.
Claims 23-26, 28, 30, 37-41, 43-51 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea of both a mathematical concept and mental process without significantly more.
Claims 44, 46, 48, and 50-51 is/are rejected under 35 U.S.C. 103 as being unpatentable over Liepa et al., US 2008/0259077 in view of Co, US 2015/0154796 and in view of Siemens, “World-class finite element analysis (FEA) solution for the Windows desktop”, copyright 2008, URL: www(dot)plm(dot)automation(dot)siemens(dot)com/en_gb/Images/fe%20finite%20element%20analysis%20for%20windows%20fs%20W%205_tcm642-53789(dot)pdf and in further view of Zhang et al., “Remanufacturing-oriented geometric modelling for the damaged region of components”, 2015
Claims 45 is/are rejected under 35 U.S.C. 103 as being unpatentable over Liepa et al., US 2008/0259077 in view of Co, US 2015/0154796 and in view of Siemens, “World-class finite element analysis (FEA) solution for the Windows desktop”, copyright 2008, URL: www(dot)plm(dot)automation(dot)siemens(dot)com/en_gb/Images/fe%20finite%20element%20analysis%20for%20windows%20fs%20W%205_tcm642-53789(dot)pdf and in further view of Zhang et al., “Remanufacturing-oriented geometric modelling for the damaged region of components”, 2015 and in further view of Scratchapixel, “Ray Tracing: Rendering a Triangle”, accessed via WayBack Machine with an archive date of May 2015, URL: www(dot)scratchapixel(dot)com/lessons/3d-basic-rendering/ray-tracing-rendering-a-triangle/barycentric-coordinates
Claims 47 and 49 is/are rejected under 35 U.S.C. 103 as being unpatentable over Liepa et al., US 2008/0259077 in view of Co, US 2015/0154796 and in view of Siemens, “World-class finite element analysis (FEA) solution for the Windows desktop”, copyright 2008, URL: www(dot)plm(dot)automation(dot)siemens(dot)com/en_gb/Images/fe%20finite%20element%20analysis%20for%20windows%20fs%20W%205_tcm642-53789(dot)pdf and in further view of Zhang et al., “Remanufacturing-oriented geometric modelling for the damaged region of components”, 2015 and in further view of Fu et al., “An Improved Texture Mapping Model Based on Mesh Parameterization in 3D Garments”, 2014
Claim 23 and dependents thereof not rejected under § 102/103, in view of the amendments. The closest combination of prior art is the one previously of record for dependent claim 29 (Final Act. 69-72), but this does not fairly teach what is now recited in the present independent claim, including the feature of “wherein each integer facet identifier is mapped onto a spiral of unit squares about an origin, wherein each triangle in a respective unit square is discrete and separated from a boundary of the respective unit square, and wherein each triangle in the respective unit square does not touch other triangles in the respective unit square;” as recited in ordered combination.
The next closest references are listed in the conclusion section below, but while they do teach mapping facets to unit squares, they do not do so in the manner claimed, when read in view of instant fig. 12-13, in particular “wherein each triangle in a respective unit square is discrete and separated from a boundary of the respective unit square, and wherein each triangle in the respective unit square does not touch other triangles in the respective unit square” as recited in the claims.
This action is non-final
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Response to Arguments/Amendments
Regarding the § 101 Rejection
Maintained, updated as necessitated by amendment. Remarks are for the newly added steps, so see the rejection below for how they are considered in the § 101 rejection.
Regarding the § 102/103 Rejection
With respect to claim 23, and dependents thereof, the rejection is withdrawn in view of the amendments which incorporated the subject matter of the claim tree of 42.
With respect to claim 44, rejection maintained and updated below as necessitated by amendment.
With respect to the remarks, regarding Liepa for performing of the modifications, see ¶ 60: “In addition, after a detail model 402 has been conformed to a destination 404, the user can proceed to modify the destination 404 Surface in any way, and the conformed detail models 402 may dynamically and automatically (and without user input) update based on a construction history of the conformation operation. The user may also modify the input detail model 402 geometry and the conformed detail models 402 may update accordingly (e.g., dynamically and without user input)." – and ¶¶ 76 and 79, as were relied upon. In particular, note that it is to the “input detail model” and “the destination 404”, i.e. the modifications are to the original model formats.
¶ 70 to clarify: “Thus, rather than merely mapping the detail model 402 to a mesh representation of the destination 404, embodiments of the present invention map the detail model 402 to the actual original destination 404. In addition, steps 1002-1006 may be performed dynamically and interactively in real time as the detail model 402 is manipulated with respect to the surface (e.g., as described above in the user interface).”
Liepa anticipates this, and Liepa teaches a hybrid modeling process because Liepa’s modeling process has both mesh and NURBs data (see Liepa, as relied upon).
See Appeal 2024-000206: “Under the broadest reasonable interpretation, however, the Examiner finds that Liepa' s mapping is an example of the claimed communicating in view of disclosures in Appellant's specification, which teaches: "This disclosure provides a mapping between the natural parameterization of the mesh and a u, v parameterization, of the type used in boundary representation models, by combining the integer identifier of the facet with the facet parameters." Id. at 22 (citing [instant] Spec. ¶ 81). According to the Examiner, Liepa's teachings are similar to the teachings in this specification passage because Liepa communicates the mesh to the B-rep model "such that the mesh and B-rep models are mapped to each other” – and see ¶ 81: “This disclosure provides a mapping between the natural parameterization of the mesh and au, v parameterization, of the type used in boundary representation models, by combining the integer identifier of the facet with the facet parameters. The use of a modified parameterisation allows [i.e. a latent property/advantage of using such a mapping] a user input made in a boundary representation model to be mapped to data held only in mesh format, using the same mechanisms as classic surfaces.”
To further clarify, in the ‘206 appeal: “Appellant does not dispute these findings in the Reply Brief. We agree with the Examiner that the broadest reasonable interpretation of "communicating" encompasses mapping in light of the specification's teaching that "[t]his disclosure provides a mapping between the natural parameterization of the mesh and a u, v parameterization, of the type used in boundary representation models." Spec. ¶ 81, quoted in Ans. 22 (emphasis by Examiner).”
Besides that, even if Liepa did not teach this, see Zhang as discussed in Appeal 2023-001298, starting on page 7, including: “We are not convinced by Appellant's argument because Zhang's geometric modelling method performing "direct" Boolean operations on the original CAD solid model and triangle mesh model at least suggests "applied directly to the mesh data" as recited in claim 1. See Zhang, p. 803, col. 2, ¶ 1, Ans. 19” – wherein POSITA would have been motivated to combine Liepa’s hybrid modeling system that maps mesh data to NURBs data with Zhang’s “novel method to perform Boolean operations on the triangulated approximation surfaces and exact parameter surfaces is also presented.” (Zhang, abstract) because “This paper presents a novel geometric modelling method to obtain the geometric model by performing the direct Boolean operations on the original CAD solid model and the triangle mesh model of the damaged part. Although the CAD model and the triangle mesh model are two different types of boundary representation, as the former is an exact surface representation and the latter is a discrete approximation, this paper implements their direct Boolean operations. This method can avoid reconstructing the scanned mesh surface so the efficiency and accuracy of geometric modelling gets a lot of improving” (Zhang, § 5).
As a further point of clarity, MPEP § 2173.05(g): “A functional limitation must be evaluated and considered, just like any other limitation of the claim, for what it fairly conveys to a person of ordinary skill in the pertinent art in the context in which it is used. A functional limitation is often used in association with an element, ingredient, or step of a process to define a particular capability or purpose that is served by the recited element, ingredient or step…When a claim limitation employs functional language, the examiner’s determination of whether the limitation is sufficiently definite will be highly dependent on context (e.g., the disclosure in the specification and the knowledge of a person of ordinary skill in the art)…” – i.e. the limitation at issue is a purely functional limitation stating the function/desired result of the application of the modeling operations; and instant disclosure ¶ 81 discloses what provides the functionality.
¶ 82 to clarify: “However, the method does enable components of the CAD application to communicate points on meshes using the same mechanism as the CAD applications uses for classic surfaces, so that it is possible to have a hybrid boundary representation model which incorporates mesh data without expensive and computing intensive conversion of the data format.”
These remarks imply some distinctive claim construction is required on a purely functional limitation (in a similar manner as was previously implied about the “communicating” limitation in the ‘206 appeal), but such is an unreasonable interpretation, and the instant specification makes clear what “enable[s]” the functionality claimed, and Liepa teaches this feature, as found by PTAB Appeal 2024-000206 in affirming the Examiner’s answer in view of ¶ 81 as previously pointed to.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 23-26, 28, 30, 37-41, 43-51 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea of both a mathematical concept and mental process without significantly more.
Step 1
The claims are directed towards the statutory category of a process.
Step 2A – Prong 1
The claims recite an abstract idea of both a mental process and mathematical concept.
As an initial matter, the Examiner notes that, in view of the previous definition of “parameterization” relied upon in Appeal 2024-000206 at page 7 ¶ 2 and page 9, ¶ 1, the Examiner notes that there is a simpler manner to describe this mathematical concept to a person not skilled in the mathematics of advanced geometry, although that is its proper mathematical definition per the textbook of record.
It is akin to Projecting/mapping, in the context of geometry, traces its roots back to cartography from centuries ago, long before the invention of the computer. For example, many people are familiar with the Mercator projection, or at least its results, as world maps have commonly been produced for centuries using such a projection, e.g. latitude and longitude coordinates place on a 2D world map are mathematically projected from the 3D lines on a 3D spherical Earth into a 2D plane, e.g. by the Mercator projection. E.g. the maps drawn by Amerigo Vespucci (his first name is the origin of the name America such as in United States of America) used a projection as well.
E.g., see University of Virginia Library, Article on “Lewis and Clark, The Maps of Exploration”, accessed Jan. 2026, URL: explore(dot)lib(dot)virginia.edu/exhibits/show/lewisclark/novusorbis/overview3. “Wright published “A Chart of the World on Mercator’s Projection” in 1600 based on his projection of a globe engraved by the English globe maker Emery Molyneux in 1592. It was the first map to use Wright’s improvements on Mercator’s projection. This map, sometimes called the “Wright-Molyneux Map,” also was published in The Principall Navigations, Voiages, Traffiques and Discoveries of the English Nation (London, 1598-1600), compiled by Richard Hakluyt.Considered a sixteenth-century cartographic landmark, the Wright-Molyneux Map is alluded to in Shakespeare’s Twelfth Night, when Maria says teasingly of Malvolio: “He does smile his face into more lynes, than is in the new Mappe, with the augmentation of the Indies…”
To be clear, see ¶ 83, and note this is really just a coordinate transformation mathematical calculation between a 3D space (e.g. x, y, z; or any other coordinate plane in 3D) to a 2D coordinate system, but becomes a parameterization as its parametrizing it with a bijective mapping (see Merriam Webster Dictionary, Definition of “bijection”, accessed electronically Jan. 23rd, 2026, URL: merriam-webster(dot)com/dictionary/bijective: “a mathematical function that is a one-to-one and onto mapping”). E.g., note page 114 of the Siggraph book cites to “G. Mercator. Nova et aucta orbis terrae descriptio ad usum navigantium emendate accommodata. Duisburg, 1569” – which, given the date and name, is presumably Mercator’s 1569 publication on his projection. Also pages 15-16, paragraph split between the pages: “Other interesting parameterizations are those that are globally conformal like the stereographic projection for the hemisphere, and it was shown by Riemann [1851] that such a parameterization exists for any surface that is topologically equivalent to a disk and any simply connected parameter domain.”
Further, note ¶ 83 discusses the use of a “barycentric coordinate system”. To more clearly understand the plain meaning of this, see Wolfram MathWorld, “Barycentric Coordinates”, Jan. 23rd 2026, URL: mathworld(dot)wolfram(dot)com/BarycentricCoordinates(dot)html: “Barycentric coordinates are triples of numbers (t_1,t_2,t_3) corresponding to masses placed at the vertices of a reference triangle DeltaA_1A_2A_3. These masses then determine a point P, which is the geometric centroid of the three masses and is identified with coordinates (t_1,t_2,t_3). The vertices of the triangle are given by (1,0,0), (0,1,0), and (0,0,1). Barycentric coordinates were discovered by Möbius in 1827 (Coxeter 1969, p. 217; Fauvel et al. 1993)….” – and note, their discovery, and presumably use, was long before computers, i.e. math that is reasonably performed mentally when applied to triangles, and a fundamental basic tool of scientific and engineering work, e.g. in the derivations of Einstein for the theory of relativity. E.g. Ungar, Abraham Albert. "An introduction to hyperbolic barycentric coordinates and their applications." Mathematics Without Boundaries: Surveys in Interdisciplinary Research. New York, NY: Springer New York, 2014. 577-648. § 1 : “A barycenter in astronomy is the point between two objects where they balance each other. It is the center of gravity where two or more celestial bodies orbit each other. In 1827 M¨obius published a book whose title, Der Barycentrische Calcul, translates as The Barycentric Calculus. The word barycenter means center of gravity, but the book is entirely geometrical and, hence, called by Jeremy Gray [15], M¨obius’s Geometrical Mechanics. The 1827 Mobius book is best remembered for introducing a new system of coordinates, the barycentric coordinates…Barycentric coordinates are commonly
used in Euclidean geometry [47], convex analysis [28], and non-relativistic
quantum mechanics [2]. Evidently, Einstein addition is tailor made for the adaptation
of barycentric coordinates for use in hyperbolic geometry [42, 43], hyperbolic
convex analysis and, perhaps, relativistic quantum mechanics [3].” As summarized in § 2, e.g. “Accordingly, the restricted Einstein addition is a commutative group operation, as Einstein noted in [6]; see [7, p. 142]…. Einstein addition (3) of relativistically admissible velocities, with n = 3, was introduced by Einstein in his 1905 paper [6] [7, p. 141] that founded the special theory of relativity, where the magnitudes of the two sides of Einstein addition (3) are presented.” – i.e. it was a math concept used in the mental discoveries of Einstein such as the theory of relativity, before computers were invented, and MPEP § 2106.04(b): “Diamond v. Chakrabarty, 447 U.S. 303, 309, 206 USPQ 193, 197 (1980). "Likewise, Einstein could not patent his celebrated law that E=mc2; nor could Newton have patented the law of gravity." Id. Nor can one patent "a novel and useful mathematical formula," Parker v. Flook, 437 U.S. 584, 585, 198 USPQ 193, 195 (1978);”
This is a math concept that has its origins from long before computers, and one of “the basic tools of scientific and technological work” (MPEP § 2106.04(I)). Projecting for maps from 3D to 2D using mathematics was performed mentally as a long-standing practice in cartography. The use of barycentric coordinate systems for triangles (¶ 83) is a math concept that also predates the invention of a computer, with uses in countless fields of endeavor, and one simple enough that for a small collection of triangles a person is readily able to do mentally, or use a computer as a tool to do it quickly with a large collection of triangles (MPEP § 2106.05(f))
To further clarify on this, ¶ 81 of the disclosure: “This disclosure provides a mapping between the natural parameterization of the mesh and a u, v parameterization, of the type used in boundary representation models” – to clarify on what POSITA would have understood for this (MPEP § 2111.01(I and III)), see:
Datta, Ranadev, and C. Guedes Soares. "NURBS based scheme for automatic quadrilateral mesh generation for FE and BEM analysis." Marine Systems & Ocean Technology 7.1 (2012): 29-35. § 2.2, last two paragraphs, discussing how NURB surfaces are, by mathematical definition per equation 4, mapped to a “unit square” in R2 (two dimensional space), specifically note the “u” and “v” coordinates for this.
Hua, Tienyong, and Ibrahim Zeid. "A free-form mesh generator for three-dimensional surfaces." International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Vol. 97690. American Society of Mechanical Engineers, 1993. Abstract, § 2 ¶¶ 1-2: “Parametric surface representation is realized by using a continuous, vector-valued function P(u, v) of two parameters, ii and n. In most cases, u and v intervals are [0,1 ]. That makes the parametric surface maps into a unit square in the parametric space. The free-form surface mesh generation concept is described as follows. An analytic or synthetic surface can always's be transformed into its parametric space which is a two-dimensional space of u and v.” and see § 3.4, including its subsection “B-spline Surface”, noting B-splines are in the “u, v” parametric space as part of their definition (by equation)
To further clarify, Grimm, Cindy M. "Parameterization using manifolds." International Journal of Shape Modeling 10.01 (2004): 51-81. Abstract and § 1 including: “There are many surface representations, such as meshes and implicit surfaces, that lack a “built-in” parameterization, such as the one provided by spline surfaces. The primary use of a surface parameterization in graphics is as a texture map. A parametric surface equation is also useful for calculating differential geometry entities such as geodesics and principal curvature. These metrics can then be used for applications such as feature extraction, shape classification, and comparisons of 3D objects. Parameterization is essentially the problem of flattening a surface (or piece of a surface) to the plane without folding or creasing it. This creates a mapping from the surface to the plane. Current approaches with meshes have focused on finding “nice” mappings that distribute distortions in well-behaved ways…” then see pages 5-6 paragraph split between the pages: “Several papers describe surface construction techniques using manifolds 15,16,35,36,31. Grimm’s approach 16 begins with a mesh and builds a manifold with one chart per mesh element. The approach in Navau and Garcia’s first paper 36 builds a manifold for a planar mesh by mapping the boundary of the mesh to the unit square. Charts and embedding functions can then be built on the unit square. We adopt this approach for planar meshes”
In other words, as the Examiner had previously stated, and was stated in Appeal 2024-000206: “The Examiner adds that "the alleged improvement is to address 'a problem as facet meshes cannot be parameterized in the same way as a boundary representation model,"' and "[t]his is a problem in the mathematical concepts of meshes and B-rep [boundary representation] models."… We do not agree that the extracting and deriving steps recite an improvement to technology because, as correctly found by the Examiner, "the judicial exception alone cannot provide the improvement."” – i.e. B-rep mathematical representations, by their mathematical definition, have a u, v parameterization for the math equation definition them, consistent with ¶ 81 statement: “a u, v parameterization, of the type used in boundary representation models”, and what is lacking is a math concept to get the mesh mathematical representation from a 3D coordinate system into this 2D coordinate system, to which is the math concept of mesh parameterization is twice applied, once to a natural parameterization, then to a modified parameterization, so as to allegedly solve the mathematical problem of getting these two mathematical representations into the same coordinate system, and the problem herein disclosed (as discussed in the appeal) is a mathematical problem, not a technological one.
Such a purely mathematical concept is not eligible subject matter without additional elements that meaningfully integrate the math concept itself into a practical application (MPEP § 2106.04(d)) or amount to significantly more than the abstract idea itself (MEPP § 2106.05), no matter how narrow the abstract idea is. MPEP § 2106.04(I): “The Supreme Court’s concern that drives this "exclusionary principle" is pre-emption. Alice Corp., 573 U.S. at 216, 110 USPQ2d at 1980. The Court has held that a claim may not preempt abstract ideas, laws of nature, or natural phenomena, even if the judicial exception is narrow (e.g., a particular mathematical formula such as the Arrhenius equation). See, e.g., Mayo, 566 U.S. at 79-80, 86-87, 101 USPQ2d at 1968-69, 1971 (claims directed to "narrow laws that may have limited applications" held ineligible); Flook, 437 U.S. at 589-90, 198 USPQ at 197 (claims that did not "wholly preempt the mathematical formula" held ineligible). This is because such a patent would "in practical effect [] be a patent on the [abstract idea, law of nature or natural phenomenon] itself." Benson, 409 U.S. at 71- 72, 175 USPQ at 676. The concern over preemption was expressed as early as 1852. See Le Roy v. Tatham, 55 U.S. (14 How.) 156, 175 (1852) ("A principle, in the abstract, is a fundamental truth; an original cause; a motive; these cannot be patented, as no one can claim in either of them an exclusive right.").”
See MPEP § 2106.04: “...In other claims, multiple abstract ideas, which may fall in the same or different groupings, or multiple laws of nature may be recited. In these cases, examiners should not parse the claim. For example, in a claim that includes a series of steps that recite mental steps as well as a mathematical calculation, an examiner should identify the claim as reciting both a mental process and a mathematical concept for Step 2A Prong One to make the analysis clear on the record.”
To clarify, see the USPTO 101 training examples, available at https://www.uspto.gov/patents/laws/examination-policy/subject-matter-eligibility.
The mathematical concept recited in claim 23 is:
A method of defining a point on a mesh representation of a part of a product for additive manufacturing …, the method comprising: - a math concept with an intended use. See Appeal 2024-000206, pages 7-8: “After carefully considering Appellant's arguments, we agree with the Examiner that the preamble and limitations the Examiner identifies recite mathematical concepts… We consider the preamble and limitations identified by the Examiner in tum. First, the portion of the preamble identified by the Examiner as reciting a mathematical concept recites, "A method of defining a point on a mesh representation." Appellant does not argue that the preamble is limiting, and we determine that it is not, so it cannot impart patent eligibility to the claim. See Digitech Image Tech. LLC v. Electronics for Imaging, Inc., 758 F.3d 1344, 1351 (Fed. Cir. 2014) (Intended use in a preamble is not sufficient to render patent eligible a claim directed to an abstract idea.).” and page 11: “We do not address the preamble further because, as we explain above, there is no evidence in this record supporting that the preamble is limiting.”
obtaining, by the data processing system, a natural representation of each triangle of the mesh data representation, the natural representation comprising an integer facet identifier of each facet and associated facet parameters, the facet parameters comprising a pair of u, v parameters;… obtaining, by the data processing system, a modified representation for each triangle of the mesh data representation of the part comprising a combination of the integer facet identifier and the facet parameters, - math calculations in textual form. See Appeal 2024-000206 pages 6-10 to clarify on the BRI, include seeing the citations to the instant disclosure. In this case, the term “obtaining” is merely being used as a textual placeholder for calculating. E.g. ¶¶ 81-84, e.g. akin to the “extracting” and “deriving” (¶¶ 5, 22, 28). See fig. 14 as well, # 60-61. The only supporting words under § 112(a) for written description support for obtaining are terms like “deriving”, “extracting”, and the like previously considered in the prior Appeal, thus showing the interchangeably of these terms for when used in these particular steps.
wherein each integer facet identifier is mapped onto a spiral of unit squares about an origin, wherein each triangle in a respective unit square is discrete and separated from a boundary of the respective unit square, and wherein each triangle in the respective unit square does not touch other triangles in the respective unit square; - math relationships/equations in the mathematical field of geometry.
E.g. see fig. 12-13, this is merely an act of mapping to form the math relationships between triangles and unit squares in geometry. ¶ 86 of the instant disclose.
The mathematical concept recited in claim 44 is:
A method of defining a point on a mesh representation of a part of a multipart product for additive manufacturing - rejected under a similar rationale as above
obtaining a natural representation of each facet of the mesh data comprising an integer identifier of each facet and associated facet parameters comprising a pair of u, v parameters; - rejected under a similar rationale as above
… obtaining a modified representation of each facet of the mesh data comprising a combination of the integer identifier and the facet parameters…- rejected under a similar rationale as above
This claims merely nests the math calculations into limitations that require the performance of the calculation itself to perform additional limitations, akin to “calculate X, then obtain X data” but worded as “obtain X including calculate X”.
Under the broadest reasonable interpretation, the claim recites a mathematical concept – the above limitations are steps in a mathematical concept such as mathematical relationships, mathematical formulas or equations, and mathematical calculations. If a claim, under its broadest reasonable interpretation, is directed towards a mathematical concept, then it falls within the Mathematical Concepts grouping of abstract ideas. In addition, as per MPEP § 2106.04(a)(2): “It is important to note that a mathematical concept need not be expressed in mathematical symbols, because "[w]ords used in a claim operating on data to solve a problem can serve the same purpose as a formula." In re Grams, 888 F.2d 835, 837 and n.1, 12 USPQ2d 1824, 1826 and n.1 (Fed. Cir. 1989). See, e.g., SAP America, Inc. v. InvestPic, LLC, 898 F.3d 1161, 1163, 127 USPQ2d 1597, 1599 (Fed. Cir. 2018)”
See MPEP § 2106.04(a)(2).
To clarify, see the USPTO 101 training examples, available at https://www.uspto.gov/patents/laws/examination-policy/subject-matter-eligibility.
The mental process recited in claim 23 is:
obtaining, by the data processing system, a natural representation of each triangle of the mesh data representation, the natural representation comprising an integer facet identifier of each facet and associated facet parameters, the facet parameters comprising a pair of u, v parameters;… obtaining, by the data processing system, a modified representation for each triangle of the mesh data representation of the part comprising a combination of the integer facet identifier and the facet parameters – a mental process, when applied to a small set of data, when read in view of ¶ 83, wherein this is merely doing a coordinate transformation of triangles into a barycentric coordinate system, which is a math concept that was performed prior to the invention of the computer, thus a mental process as well. See Example 45, claim 1, discussion of the use of the Arrhenius equation in the 1800s in the prong one analysis, and see the above evidence showing a similar historical fact.
wherein each integer facet identifier is mapped onto a spiral of unit squares about an origin, wherein each triangle in a respective unit square is discrete and separated from a boundary of the respective unit square, and wherein each triangle in the respective unit square does not touch other triangles in the respective unit square; - a mental process of drawing, such as with pen and paper, in view of fig. 12-13 and its accompanying description, wherein a person simply observes a collection of triangle integer identifiers (e.g. on paper as a table, as it is just the “integer facet identifier” that is being mapped per the claim), and then proceeds to draw out a map, or mentally visualize in their own mind, to arrive at a joint drawing akin to fig. 12, with fig. 13 for the interior of each unit square. ¶¶ 86-87 of the instant disclosure go into no particular detail about what this is to do in the technology of CAD, but rather provide a bare conclusory assertation of “The spiral and structural arrangement of the integer facet identifiers shown in Fig. 12 is an efficient way of operating the method” without specifying how such an improvement would be provided.
The mental process recited in claim 44 is:
obtaining a natural representation of each facet of the mesh data comprising an integer identifier of each facet and associated facet parameters comprising a pair of u, v parameters; - rejected under a similar rationale as above
… obtaining a modified representation of each facet of the mesh data comprising a combination of the integer identifier and the facet parameters…- rejected under a similar rationale as above
providing, by the data processing system, a representation of the modified multipart product…– as this is a mental process, such as a person observing on the display of a computer, or on a print-out from a computer (e.g. fig. 7-8), or on pen-and-paper drawings, graphical depictions of the selected parts, and mentally visualizing them together. This would be akin to the mental process performed by a mechanic or engineer faced with the task of trying to determine whether a new part (e.g. a bolt), such as in a part catalog, would work with an existing design so they mentally visualize, in their own mind, the bolt combined with the existing design (e.g. a door hinge, a bike, etc.), so as to mentally observe the product, wherein such observation would used for a mental judgement as to whether or nor the bolt will work with the new design.
To clarify, the claim recites with no particularity how this representation is to be provided, or what this representation is, but rather merely expresses the data formats it is to be done with, and a desired result.
wherein the mesh data is treated as a surface in the hybrid boundary representation model, wherein the hybrid boundary representation model has a mixture of the mesh data and the classic geometric representation data, – a mental process, given the generality recited, but for the mere instructions to do this on a computer and in a computer enviroment. For example, a person would readily be able to observe, such as on a display of a computer, printouts from a computer, or the like, a visual representation of mesh data and a visual representation of a B-rep model (e.g. instant fig. 7, or a much simpler model, and mentally visualize the mesh as a surface in the B-rep model. One would readily be able to use physical aids in this process, e.g. use paper, and print out the B-rep model (fig. 7 # 15), and then print-out, on a sheet of translucent paper, the mesh (fig. 7, # 16), and then achieve this limitation by aligning the translucent paper laid on top of the paper representation of the B-rep model, thus combining the two and resulting in fig. 7.
To clarify, the claim does not recite how this step is accomplished in a particular manner that would preclude this from being a mental process, but for mere instructions to do this on a computer. Furthermore, the claim does not recite with any particularity what the product is, i.e. this may readily be applied to a much simpler product with much simpler parts, e.g. a product such as two LegoTM bricks, wherein one brick is in the first format and the other brick is in the second format, wherein a person would readily be able to mentally visualize in their own mind these two bricks together with both formats (i.e. visualizing one as a simple, coarse mesh with a few elements, and the other by a classic geometry representation, e.g. lines), or use physical aids such as discussed above.
To add, this abstract idea recited herein is akin to the dynamic document (this would be the provided representation in the instant claims) and the underlying XML documents (this would be the obtained mesh data and classic geometric representation in the instant claims) of Intellectual Ventures I v. Capital One Fin. Corp., 850 F.3d 1332, 121 USPQ2d 1940 (Fed. Cir. 2017). MPEP § 2106.05(f): “Intellectual Ventures I v. Capital One Fin. Corp., 850 F.3d 1332, 121 USPQ2d 1940 (Fed. Cir. 2017), the steps in the claims described "the creation of a dynamic document based upon ‘management record types’ and ‘primary record types.’" 850 F.3d at 1339-40; 121 USPQ2d at 1945-46. The claims were found to be directed to the abstract idea of "collecting, displaying, and manipulating data." 850 F.3d at 1340; 121 USPQ2d at 1946. In addition to the abstract idea, the claims also recited the additional element of modifying the underlying XML document in response to modifications made in the dynamic document. 850 F.3d at 1342; 121 USPQ2d at 1947-48. Although the claims purported to modify the underlying XML document in response to modifications made in the dynamic document, nothing in the claims indicated what specific steps were undertaken other than merely using the abstract idea in the context of XML documents. The court thus held the claims ineligible, because the additional limitations provided only a result-oriented solution and lacked details as to how the computer performed the modifications, which was equivalent to the words "apply it". 850 F.3d at 1341-42; 121 USPQ2d at 1947-48 (citing Electric Power Group., 830 F.3d at 1356, 1356, USPQ2d at 1743-44 (cautioning against claims "so result focused, so functional, as to effectively cover any solution to an identified problem")).”
In particular, note in the opinion of Intellectual Ventures I v. Capital One Fin. Corp: “…IV next submits that the specific combination of PRTs, MRTs, and a dynamic document overcomes the previous problem of the "incompatibility of XML documents with different 'XML syntax[es]' and different 'XML formats, relational database schemes, and messages formats.'" Appellants' Br. 40 (citing J.A. 168, 1388). In particular, IV argues that the claims set forth a unique solution to a problem with contemporary XML documents. Id. at 45. But the claims do not recite particular features to yield these advantages. Although the claims purport to modify the underlying XML document in response to modifications made in the dynamic document, this merely reiterates the patent's stated goal itself. Nothing in the claims indicate what steps are [**1948] undertaken to overcome the stated incompatibility problems with XML documents to propagate those modifications into the XML document. Indeed, the claim language here provides only a result-oriented solution, with insufficient detail for how a computer accomplishes it. Our law demands more. See Elec. Power Grp., 830 F.3d at 1356 (cautioning against claims "so result focused, so functional, as to effectively cover any solution to an identified problem")…” – the Examiner is noting this case because of the similarity in what is claimed in the instant claims, in the context of CAD/CAE systems, wherein a similar idea was found to be abstract in Intellectual Ventures I v. Capital One Fin. Corp in the context of XML documents.
In the presently claimed invention, there is one distinction from IV – it does not provide a technological solution to incompatibles between the data structures, but rather a purely mathematical solution to the math problem, because this not a technological problem at all, but rather a mathematical problem (as discussed in detail above) rooted in the mathematical nature of the data itself, not in the data structure of how the data is implemented in a technological manner on the computer. MPEP § 2106.05(a): “Examples that the courts have indicated may not be sufficient to show an improvement in computer-functionality… vii. Providing historical usage information to users while they are inputting data, in order to improve the quality and organization of information added to a database, because "an improvement to the information stored by a database is not equivalent to an improvement in the database’s functionality," BSG Tech LLC v. Buyseasons, Inc., 899 F.3d 1281, 1287-88, 127 USPQ2d 1688, 1693-94 (Fed. Cir. 2018); and”
Should further clarification be sought, and given the instant disclosure describes avoiding a conversion of a data format into another format (¶¶ 58, 61, 63, 65, 66, etc.), in view of MPEP § 2106.07(I): “When evaluating a claimed invention for compliance with the substantive law on eligibility, examiners should review the record as a whole (e.g., the specification, claims, the prosecution history, and any relevant case law precedent or prior art) before reaching a conclusion with regard to whether the claimed invention sets forth patent eligible subject matter.” See, as was cited to and quoted in part (pages 4-5, the block quote) in Ex parte Desjardins Appeal 2024-000567, so see the opinion of AI Visualize, Inc. v. Nuance Commc'ns, Inc., 97 F.4th 1371, 2024 U.S.P.Q.2d 632 (Fed. Cir. 2024): “…In other words, the asserted claims are directed to converting data and using computers to collect, manipulate, and display the data. We reached a similar conclusion in Hawk Tech. Sys., LLC v. Castle Retail, LLC, 60 F.4th 1349 (Fed. Cir. 2023). Hawk considered patent claims involving "viewing multiple simultaneously displayed and stored video images on a remote viewing device of a video surveillance system." Id. at 1352 . The patent holder emphasized that the claims required converting video [*1379] data using certain parameters in such a manner that the data could be manipulated and displayed to conserve bandwidth and preserve the data quality. Id. at 1357. But "converting information from one format to another . . . is an abstract idea." Id…”
Under the broadest reasonable interpretation, these limitations are process steps that cover mental processes including an observation, evaluation, judgment or opinion that could be performed in the human mind or with the aid of physical aids but for the recitation of a generic computer component. If a claim, under its broadest reasonable interpretation, covers a mental process but for the recitation of generic computer components, then it falls within the "Mental Process" grouping of abstract ideas. A person would readily be able to perform this process either mentally or with the assistance of physical aids. See MPEP § 2106.04(a)(2).
To clarify, see the USPTO 101 training examples, available at https://www.uspto.gov/patents/laws/examination-policy/subject-matter-eligibility. In particular, with respect to the physical aids, see example # 45, analysis of claim 1 under step 2A prong 1, including: “Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited calculation, the use of such physical aid does not negate the mental nature of this limitation.”; also see example # 49, analysis of claim 1, under step 2A prong 1: “Moreover, the recited mathematical calculation is simple enough that it can be practically performed in the human mind. Even if most humans would use a physical aid, like a pen and paper or a calculator, to make such calculations, the use of a physical aid would not negate the mental nature of this limitation.”
As such, the claims recite an abstract idea of both a mental process and mathematical concept.
Step 2A, prong 2
The claimed invention does not recite any additional elements that integrate the judicial exception into a practical application. Refer to MPEP §2106.04(d).
The following limitations are merely reciting the words "apply it" (or an equivalent) with the judicial exception, or merely including instructions to implement an abstract idea on a computer, or merely using a computer as a tool to perform an abstract idea, as discussed in MPEP § 2106.05(f), including the “Use of a computer or other machinery in its ordinary capacity for economic or other tasks (e.g., to receive, store, or transmit data) or simply adding a general purpose computer or computer components after the fact to an abstract idea (e.g., a fundamental economic practice or mathematical equation) does not integrate a judicial exception into a practical application or provide significantly more”:
The recitations of “a data processing system” in the independent claims are considered as mere instructions to use a computer, and generic computer components, as a tool to implement the abstract idea. Fig. 1 and accompanying description in ¶¶ 48-49 further demonstrates the generic nature of this data processing system, and ¶ 51: “For example the data processing system 21 in this example may correspond to a computer, workstation, and/or a server. However, it should be appreciated that alternative embodiments of a data processing system may be configured with corresponding or alternative components such as in the form of a mobile phone, tablet, controller board or any other system that is operative to process data and carry out functionality and features described herein associated with the operation of a data processing system, computer, processor, and/or a controller discussed herein.” See Appeal ‘206, page 14: “Accordingly, we sustain the Examiner's§ 101 rejection of claim 23 and claims 24-30 and 33-43, which Appellant does not argue separately. See 37 C.F.R. § 41.37(c)(l)(iv).”
The following limitations are adding insignificant extra-solution activity to the judicial exception, as discussed in MPEP § 2106.05(g):
… communicating the point to a hybrid boundary representation model of the part of the product, the method comprising:…obtaining, by a data processing system, a mesh data representation relating to a part of the product comprising scanning, with a scanner, a physical sample of the part, wherein the mesh data representation comprises a plurality of triangles each representing a facet;… communicating, by the data processing system, the modified representation for each triangle of the mesh data representation to the hybrid boundary representation model; - mere data gathering and data transmission. See Appeal ‘206, pages 12-14: “As for the "obtaining," "communicating," and "storing" limitations, we agree with the Examiner that they recite insignificant extra-solution activity, rather than technological improvements… We agree with the Examiner that each of the aforementioned additional limitations recites insignificant extra-solution activity. One hallmark of insignificant extra-solution activity is "necessary data gathering and outputting." MPEP § 2106.05(g) (emphasis omitted)…. As such, we agree with the Examiner that all of the additional limitations constitute insignificant extra-solution activity…” – see example 45, claim 3, prong 2 and step 2B for its analysis, note at prong 2 its citation to MPEP § 2106.05(b)(III): “Whether its involvement is extra-solution activity or a field-of-use, i.e., the extent to which (or how) the machine or apparatus imposes meaningful limits on the claim. Use of a machine that contributes only nominally or insignificantly to the execution of the claimed method (e.g., in a data gathering step or in a field-of-use limitation) would not integrate a judicial exception or provide significantly more. See Bilski, 561 U.S. at 610, 95 USPQ2d at 1009 (citing Parker v. Flook, 437 U.S. 584, 590, 198 USPQ 193, 197 (1978)), and CyberSource v. Retail Decisions, 654 F.3d 1366, 1370, 99 USPQ2d 1690 (Fed. Cir. 2011) (citations omitted) ("[N]othing in claim 3 requires an infringer to use the Internet to obtain that data. The Internet is merely described as the source of the data. We have held that mere ‘[data-gathering] step[s] cannot make an otherwise nonstatutory claim statutory.’" 654 F.3d at 1375, 99 USPQ2d at 1694 (citation omitted)). See MPEP § 2106.05(g) & (h) for more information on insignificant extra-solution activity and field of use, respectively.”
Claim 44: deriving, by the data processing system, a second data relating to one or more second parts of the multipart product in a second format, wherein the second format comprises a classic geometric representation; … receiving, by the data processing system, instructions of a first selection of at least one first part of the one or more first parts of the multipart product comprising mesh data; receiving, by the data processing system, instructions of a second selection of at least one second part of the one or more second parts of the multipart product comprising classic geometric representation data; - mere data gathering
The limitation of generating and transmitting, by the data processing system, manufacturing instructions for the additive manufacturing of the product using the hybrid boundary representation model is considered as a token post solution activity as well as mere instructions to “apply it” given the lack of restriction of how these instructions are to be generated or how it is to be transmitted, and this limitation does not even require the act of manufacturing to be performed, and even if it did it would be akin to the cutting of hair with scissors in MPEP § 2106.05(g and f) of In re Brown. To clarify, see ¶ 68, including its generic description of simply using a “printer” to do this, e.g. “a 3d printer”, but with no particular details set forth on what this machine even is, but rather merely conveying the use of a generic, off-the-shelf, printer/3D printer to be used in its ordinary capacity, with no particular detail as to what the manufacturing instructions are or how they are generated (¶¶ 16-17), and see ¶ 65: “At the end of the design process for the product, which may include the design process for any equipment with which it must interact, manufacturing instructions may be generated 59, suitable for a machine that is to manufacture the products, or parts thereof.”- which is simply expressing a desired result of these instructions for how they are to be intended to be generated.
The limitations of applying, by the data processing system, a modelling operation to modify one or more of the selected at least one first part and the selected at least one second part to form a modified multipart product, wherein, when the modelling operation is applied to modify the at least one first part, the modelling operation is made without modification to a format of the mesh data…, and wherein, when the modelling operation is applied to modify the at least one second part, the modelling operation is made without modification to a format of the classic geometric representation data…wherein offsetting, shelling, or thickening operations and detailing is applied directly to the mesh data
These are akin to MPEP § 2106.05(f): “Intellectual Ventures I v. Capital One Fin. Corp., 850 F.3d 1332, 121 USPQ2d 1940 (Fed. Cir. 2017)…” as was discussed above, include seeing in the opinion: “IV maintains that because the invention relates to a specialized computer language—XML—and renders otherwise incompatible documents compatible through a unique dynamic document based on MRTs and PRTs … IV's characterization, however, does not change the result… IV's identification of the '081 patent 's specific data structures and objects (PRTs and MRTs) also does not change our analysis under this step. In particular, IV argues that the '081 patent creates these specific data structures to interrelate various XML documents in a particular way to ensure compatibility of otherwise incompatible documents. IV maintains that these structures provide a concrete solution through a component that detects modifications to the dynamic document and in response thereto, propagates those changes back to the underlying XML document. We disagree… Although these data structures add a degree of particularity to the claims, the underlying concept embodied by the limitations merely encompasses the abstract idea itself of organizing, displaying, and manipulating data of particular documents… The PRTs and MRTs are, at bottom, broadly [***8] defined labels for generic data types that transfer data from one type of electronic document to another—here, the so-called dynamic document. The resulting dynamic document, in turn, is nothing more than an interface for displaying and organizing this [**1947] underlying data. These features, therefore, do not alter our conclusion that the claimed invention is directed to the abstract concept of collecting, displaying, and manipulating data of particular documents…The claims, according to IV, specify how to manage and modify XML documents of varying formats and syntax in a way that departed from convention. It argues that the patent accomplishes this by creating a "dynamic document" based upon the MRTs and PRTs, so the system can modify multiple sets of XML data components at once through a user interface… Indeed, as the district court observed, IV set forth particular definitions for these terms that describe them as generic data structures… IV next submits that the specific combination of PRTs, MRTs, and a dynamic document overcomes the previous problem of the "incompatibility of XML documents with different 'XML syntax[es]' and different 'XML formats, relational database schemes, and messages formats.'"… Although the claims purport to modify the underlying XML document in response to modifications made in the dynamic document, this merely reiterates the patent's stated goal itself. Nothing in the claims indicate what steps are [**1948] undertaken to overcome the stated incompatibility problems with XML documents to propagate those modifications into the XML document. Indeed, the claim language here provides only a result-oriented solution, with insufficient detail for how a computer accomplishes it. Our law demands more. See Elec. Power Grp., 830 F.3d at 1356 (cautioning against claims "so result focused, so functional, as to effectively cover any solution to an identified problem").
To clarify, see ¶ 75: “As can be understood from the embodiments of this disclosure performance improvements may be achieved by avoiding conversion between formats, whilst maintaining design intent. The various portions of the model can be represented in their natural formats and edited using the appropriate tools.” And ¶ 14: “Modifications may be applied to any of the parts of the product, but the modifications are made to representations in the same format as the representation was originally generated” and ¶ 65: “If modifications are required 56, the designer determines which part and what format of data is available for that part (mesh or classic geometry) and the designer works 57 on each part in need of modification in the format in which that data is held.” And ¶ 66: “Modifications to the meshes can be made using downstream functions in the model which are able to operate on faceted models. Modifications to the classic geometry features are carried out using downstream functions which are compatible with classic geometry models because the different data formats are modelled separately.” And ¶ 61: “Using a conventional CAD model, the workflow described above requires conversion of the outer shape to a curved-surface model before proceeding, because current modelling operations, such as offsetting and Booleans, do not work on a mixture of facets and classic surfaces” – i.e. neither the claims nor the specification provide any details on how the computer implements the modifications to achieve the claimed result, akin to “…Intellectual Ventures I v. Capital One Fin. Corp.,…Although the claims purported to modify the underlying XML document in response to modifications made in the dynamic document, nothing in the claims indicated what specific steps were undertaken other than merely using the abstract idea in the context of XML documents. The court thus held the claims ineligible, because the additional limitations provided only a result-oriented solution and lacked details as to how the computer performed the modifications, which was equivalent to the words "apply it". 850 F.3d at 1341-42; 121 USPQ2d at 1947-48 (citing Electric Power Group., 830 F.3d at 1356, 1356, USPQ2d at 1743-44 (cautioning against claims "so result focused, so functional, as to effectively cover any solution to an identified problem"))” As discussed in MPEP § 2106.05(f) and above
In addition, should it be found that the recitations of wherein the mesh data is treated as a surface in the hybrid boundary representation model, wherein the hybrid boundary representation model has a mixture of the mesh data and the classic geometric representation data are not part of the abstract idea, then the Examiner submits these would be rejected under a similar rationale as discussed in Intellectual Ventures I v. Capital One Fin. Corp, specifically these recitations being akin to the discussion of the “dynamic document” (i.e. “The resulting dynamic document, in turn, is nothing more than an interface for displaying and organizing this [**1947] underlying data”) and its features.
Furthermore, should it be considered that the recitations of “treated as a surface” is the how the alleged improvement is provided, then the Examiner notes for the consideration ¶¶ 58, and 78-84 in the instant disclosure, and the decision in Appeal 2024-000206.
A claim that integrates a judicial exception into a practical application will apply, rely on, or use the judicial exception in a manner that imposes a meaningful limit on the judicial exception, such that the claim is more than a drafting effort designed to monopolize the judicial exception. See MPEP § 2106.04(d).
MPEP 2106.04(II)(A)(2) “…Instead, under Prong Two, a claim that recites a judicial exception is not directed to that judicial exception, if the claim as a whole integrates the recited judicial exception into a practical application of that exception. Prong Two thus distinguishes claims that are "directed to" the recited judicial exception from claims that are not "directed to" the recited judicial exception…Because a judicial exception is not eligible subject matter, Bilski, 561 U.S. at 601, 95 USPQ2d at 1005-06 (quoting Chakrabarty, 447 U.S. at 309, 206 USPQ at 197 (1980)), if there are no additional claim elements besides the judicial exception, or if the additional claim elements merely recite another judicial exception, that is insufficient to integrate the judicial exception into a practical application. See, e.g., RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) ("Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract"); Genetic Techs. Ltd. v. Merial LLC, 818 F.3d 1369, 1376, 118 USPQ2d 1541, 1546 (Fed. Cir. 2016) (eligibility "cannot be furnished by the unpatentable law of nature (or natural phenomenon or abstract idea) itself."). For a claim reciting a judicial exception to be eligible, the additional elements (if any) in the claim must "transform the nature of the claim" into a patent-eligible application of the judicial exception, Alice Corp., 573 U.S. at 217, 110 USPQ2d at 1981, either at Prong Two or in Step 2B” and MPEP § 2106(I): “Mayo, 566 U.S. at 80, 84, 101 USPQ2dat 1969, 1971 (noting that the Court in Diamond v. Diehr found “the overall process patent eligible because of the way the additional steps of the process integrated the equation into the process as a whole,”” – and see MPEP § 2106.05(e).
To further clarify, MPEP § 2106.04(II)(A)(1): “Alice Corp., 573 U.S. at 216, 110 USPQ2d at 1980 (citing Mayo, 566 US at 71, 101 USPQ2d at 1965). Yet, the Court has explained that ‘‘[a]t some level, all inventions embody, use, reflect, rest upon, or apply laws of nature, natural phenomena, or abstract ideas,’’ and has cautioned ‘‘to tread carefully in construing this exclusionary principle lest it swallow all of patent law” See also Enfish, LLC v. Microsoft Corp., 822 F.3d 1327, 1335, 118 USPQ2d 1684, 1688 (Fed. Cir. 2016) ("The ‘directed to’ inquiry, therefore, cannot simply ask whether the claims involve a patent-ineligible concept, because essentially every routinely patent-eligible claim involving physical products and actions involves a law of nature and/or natural phenomenon").”
As a point of clarity, RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) ("Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract"); Genetic Techs. Ltd. v. Merial LLC, 818 F.3d 1369, 1376, 118 USPQ2d 1541, 1546 (Fed. Cir. 2016) (eligibility "cannot be furnished by the unpatentable law of nature (or natural phenomenon or abstract idea) itself." discussed in MPEP § 2106.04(II)(A)(2) as well as MPEP § 2106.04(I): “Synopsys, Inc. v. Mentor Graphics Corp., 839 F.3d 1138, 1151, 120 USPQ2d 1473, 1483 (Fed. Cir. 2016) ("a new abstract idea is still an abstract idea") (emphasis in original).
The claimed invention does not recite any additional elements that integrate the judicial exception into a practical application. Refer to MPEP §2106.04(d).
Step 2B
The claimed invention does not recite any additional elements/limitations that amount to significantly more.
The following limitations are merely reciting the words "apply it" (or an equivalent) with the judicial exception, or merely including instructions to implement an abstract idea on a computer, or merely using a computer as a tool to perform an abstract idea, as discussed in MPEP § 2106.05(f), including the “Use of a computer or other machinery in its ordinary capacity for economic or other tasks (e.g., to receive, store, or transmit data) or simply adding a general purpose computer or computer components after the fact to an abstract idea (e.g., a fundamental economic practice or mathematical equation) does not integrate a judicial exception into a practical application or provide significantly more”:
The recitations of “a data processing system” in the independent claims are considered as mere instructions to use a computer, and generic computer components, as a tool to implement the abstract idea. Fig. 1 and accompanying description in ¶¶ 48-49 further demonstrates the generic nature of this data processing system, and ¶ 51: “For example the data processing system 21 in this example may correspond to a computer, workstation, and/or a server. However, it should be appreciated that alternative embodiments of a data processing system may be configured with corresponding or alternative components such as in the form of a mobile phone, tablet, controller board or any other system that is operative to process data and carry out functionality and features described herein associated with the operation of a data processing system, computer, processor, and/or a controller discussed herein.” See Appeal ‘206, page 14: “Accordingly, we sustain the Examiner's§ 101 rejection of claim 23 and claims 24-30 and 33-43, which Appellant does not argue separately. See 37 C.F.R. § 41.37(c)(l)(iv).”
The following limitations are adding insignificant extra-solution activity to the judicial exception, as discussed in MPEP § 2106.05(g):
… communicating the point to a hybrid boundary representation model of the part of the product, the method comprising:…obtaining, by a data processing system, a mesh data representation relating to a part of the product comprising scanning, with a scanner, a physical sample of the part, wherein the mesh data representation comprises a plurality of triangles each representing a facet;… communicating, by the data processing system, the modified representation for each triangle of the mesh data representation to the hybrid boundary representation model; - mere data gathering and data transmission. See Appeal ‘206, pages 12-14: “As for the "obtaining," "communicating," and "storing" limitations, we agree with the Examiner that they recite insignificant extra-solution activity, rather than technological improvements… We agree with the Examiner that each of the aforementioned additional limitations recites insignificant extra-solution activity. One hallmark of insignificant extra-solution activity is "necessary data gathering and outputting." MPEP § 2106.05(g) (emphasis omitted)…. As such, we agree with the Examiner that all of the additional limitations constitute insignificant extra-solution activity…” – see example 45, claim 3, prong 2 and step 2B for its analysis, note at prong 2 its citation to MPEP § 2106.05(b)(III): “Whether its involvement is extra-solution activity or a field-of-use, i.e., the extent to which (or how) the machine or apparatus imposes meaningful limits on the claim. Use of a machine that contributes only nominally or insignificantly to the execution of the claimed method (e.g., in a data gathering step or in a field-of-use limitation) would not integrate a judicial exception or provide significantly more. See Bilski, 561 U.S. at 610, 95 USPQ2d at 1009 (citing Parker v. Flook, 437 U.S. 584, 590, 198 USPQ 193, 197 (1978)), and CyberSource v. Retail Decisions, 654 F.3d 1366, 1370, 99 USPQ2d 1690 (Fed. Cir. 2011) (citations omitted) ("[N]othing in claim 3 requires an infringer to use the Internet to obtain that data. The Internet is merely described as the source of the data. We have held that mere ‘[data-gathering] step[s] cannot make an otherwise nonstatutory claim statutory.’" 654 F.3d at 1375, 99 USPQ2d at 1694 (citation omitted)). See MPEP § 2106.05(g) & (h) for more information on insignificant extra-solution activity and field of use, respectively.”
Claim 44: deriving, by the data processing system, a second data relating to one or more second parts of the multipart product in a second format, wherein the second format comprises a classic geometric representation; … receiving, by the data processing system, instructions of a first selection of at least one first part of the one or more first parts of the multipart product comprising mesh data; receiving, by the data processing system, instructions of a second selection of at least one second part of the one or more second parts of the multipart product comprising classic geometric representation data; - mere data gathering
The limitation of generating and transmitting, by the data processing system, manufacturing instructions for the additive manufacturing of the product using the hybrid boundary representation model is considered as a token post solution activity as well as mere instructions to “apply it” given the lack of restriction of how these instructions are to be generated or how it is to be transmitted, and this limitation does not even require the act of manufacturing to be performed, and even if it did it would be akin to the cutting of hair with scissors in MPEP § 2106.05(g and f) of In re Brown. To clarify, see ¶ 68, including its generic description of simply using a “printer” to do this, e.g. “a 3d printer”, but with no particular details set forth on what this machine even is, but rather merely conveying the use of a generic, off-the-shelf, printer/3D printer to be used in its ordinary capacity, with no particular detail as to what the manufacturing instructions are or how they are generated (¶¶ 16-17), and see ¶ 65: “At the end of the design process for the product, which may include the design process for any equipment with which it must interact, manufacturing instructions may be generated 59, suitable for a machine that is to manufacture the products, or parts thereof.”- which is simply expressing a desired result of these instructions for how they are to be intended to be generated.
The limitations of applying, by the data processing system, a modelling operation to modify one or more of the selected at least one first part and the selected at least one second part to form a modified multipart product, wherein, when the modelling operation is applied to modify the at least one first part, the modelling operation is made without modification to a format of the mesh data…, and wherein, when the modelling operation is applied to modify the at least one second part, the modelling operation is made without modification to a format of the classic geometric representation data…wherein offsetting, shelling, or thickening operations and detailing is applied directly to the mesh data
These are akin to MPEP § 2106.05(f): “Intellectual Ventures I v. Capital One Fin. Corp., 850 F.3d 1332, 121 USPQ2d 1940 (Fed. Cir. 2017)…” as was discussed above, include seeing in the opinion: “IV maintains that because the invention relates to a specialized computer language—XML—and renders otherwise incompatible documents compatible through a unique dynamic document based on MRTs and PRTs … IV's characterization, however, does not change the result… IV's identification of the '081 patent 's specific data structures and objects (PRTs and MRTs) also does not change our analysis under this step. In particular, IV argues that the '081 patent creates these specific data structures to interrelate various XML documents in a particular way to ensure compatibility of otherwise incompatible documents. IV maintains that these structures provide a concrete solution through a component that detects modifications to the dynamic document and in response thereto, propagates those changes back to the underlying XML document. We disagree… Although these data structures add a degree of particularity to the claims, the underlying concept embodied by the limitations merely encompasses the abstract idea itself of organizing, displaying, and manipulating data of particular documents… The PRTs and MRTs are, at bottom, broadly [***8] defined labels for generic data types that transfer data from one type of electronic document to another—here, the so-called dynamic document. The resulting dynamic document, in turn, is nothing more than an interface for displaying and organizing this [**1947] underlying data. These features, therefore, do not alter our conclusion that the claimed invention is directed to the abstract concept of collecting, displaying, and manipulating data of particular documents…The claims, according to IV, specify how to manage and modify XML documents of varying formats and syntax in a way that departed from convention. It argues that the patent accomplishes this by creating a "dynamic document" based upon the MRTs and PRTs, so the system can modify multiple sets of XML data components at once through a user interface… Indeed, as the district court observed, IV set forth particular definitions for these terms that describe them as generic data structures… IV next submits that the specific combination of PRTs, MRTs, and a dynamic document overcomes the previous problem of the "incompatibility of XML documents with different 'XML syntax[es]' and different 'XML formats, relational database schemes, and messages formats.'"… Although the claims purport to modify the underlying XML document in response to modifications made in the dynamic document, this merely reiterates the patent's stated goal itself. Nothing in the claims indicate what steps are [**1948] undertaken to overcome the stated incompatibility problems with XML documents to propagate those modifications into the XML document. Indeed, the claim language here provides only a result-oriented solution, with insufficient detail for how a computer accomplishes it. Our law demands more. See Elec. Power Grp., 830 F.3d at 1356 (cautioning against claims "so result focused, so functional, as to effectively cover any solution to an identified problem").
To clarify, see ¶ 75: “As can be understood from the embodiments of this disclosure performance improvements may be achieved by avoiding conversion between formats, whilst maintaining design intent. The various portions of the model can be represented in their natural formats and edited using the appropriate tools.” And ¶ 14: “Modifications may be applied to any of the parts of the product, but the modifications are made to representations in the same format as the representation was originally generated” and ¶ 65: “If modifications are required 56, the designer determines which part and what format of data is available for that part (mesh or classic geometry) and the designer works 57 on each part in need of modification in the format in which that data is held.” And ¶ 66: “Modifications to the meshes can be made using downstream functions in the model which are able to operate on faceted models. Modifications to the classic geometry features are carried out using downstream functions which are compatible with classic geometry models because the different data formats are modelled separately.” And ¶ 61: “Using a conventional CAD model, the workflow described above requires conversion of the outer shape to a curved-surface model before proceeding, because current modelling operations, such as offsetting and Booleans, do not work on a mixture of facets and classic surfaces” – i.e. neither the claims nor the specification provide any details on how the computer implements the modifications to achieve the claimed result, akin to “…Intellectual Ventures I v. Capital One Fin. Corp.,…Although the claims purported to modify the underlying XML document in response to modifications made in the dynamic document, nothing in the claims indicated what specific steps were undertaken other than merely using the abstract idea in the context of XML documents. The court thus held the claims ineligible, because the additional limitations provided only a result-oriented solution and lacked details as to how the computer performed the modifications, which was equivalent to the words "apply it". 850 F.3d at 1341-42; 121 USPQ2d at 1947-48 (citing Electric Power Group., 830 F.3d at 1356, 1356, USPQ2d at 1743-44 (cautioning against claims "so result focused, so functional, as to effectively cover any solution to an identified problem"))” As discussed in MPEP § 2106.05(f) and above
In addition, should it be found that the recitations of wherein the mesh data is treated as a surface in the hybrid boundary representation model, wherein the hybrid boundary representation model has a mixture of the mesh data and the classic geometric representation data are not part of the abstract idea, then the Examiner submits these would be rejected under a similar rationale as discussed in Intellectual Ventures I v. Capital One Fin. Corp, specifically these recitations being akin to the discussion of the “dynamic document” (i.e. “The resulting dynamic document, in turn, is nothing more than an interface for displaying and organizing this [**1947] underlying data”; also “And the recited dynamic document provides little more than an unspecified set of rules for displaying and organizing MRTs in a user interface akin to the generic interfaces we have elsewhere explained impart no inventive concept.”) and its features.
Furthermore, should it be considered that the recitations of “treated as a surface” is the how the alleged improvement is provided, then the Examiner notes for the consideration ¶¶ 58, and 78-84 in the instant disclosure, and the decision in Appeal 2024-000206.
In addition, the above insignificant extra-solution activities are also considered as well-understood, routine, and conventional activities, as discussed in MPEP § 2106.05(d):
obtaining, by a data processing system, a mesh data representation relating to a part of the product comprising scanning, with a scanner, a physical sample of the part, wherein the mesh data representation comprises a plurality of triangles each representing a facet; - and the similar recitations in claims 33 and 36 - this is similar to the example in MPEP § 2106.05(d)(II) of: “iv. Storing and retrieving information in memory… v. Electronically scanning or extracting data from a physical document…”; in addition, see ¶ 61 of the instant specification: “The full conventional process is illustrated graphically in Figs. 6a to 6e. …The physical product 10 is scanned, as shown in Fig.6b and the scanned data is imported into a CAD system, where it is converted, i.e. surfaces are constructed which match the scan data, as shown in the image of Fig.6c…” – and for more evidence, see
Yu, TzuYi, and Alan Shih. "Surface Reconstruction and Mesh Generation Using Reverse Engineering Approach." 43rd AIA A Aerospace Sciences Meeting and Exhibit. 2005. §§ II-III, in particular § III tables 1-2 and ¶ 1: “For reverse engineering, there are many different type of scanner hardware available. They varies from optical scanning, laser scanning, to contact scanning. In this study, two types of scanners are utilized.
communicating, by the data processing system, the modified representation for each triangle of the mesh data representation to the hybrid boundary representation model; - this is considered similar to the example WURC activity as discussed in MPEP § 2106.05(d)(II) of: “i. Receiving or transmitting data over a network, e.g., using the Internet to gather data, Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362 (utilizing an intermediary computer to forward information); TLI Communications LLC v. AV Auto. LLC, 823 F.3d 607, 610, 118 USPQ2d 1744, 1745 (Fed. Cir. 2016) (using a telephone for image transmission); OIP Techs., Inc., v. Amazon.com, Inc., 788 F.3d 1359, 1363, 115 USPQ2d 1090, 1093 (Fed. Cir. 2015) (sending messages over a network); buySAFE, Inc. v. Google, Inc., 765 F.3d 1350, 1355, 112 USPQ2d 1093, 1096 (Fed. Cir. 2014) (computer receives and sends information over a network);”
generating and transmitting, by the data processing system, manufacturing instructions for the additive manufacturing of the product using the hybrid boundary representation model- this is considered similar to the example WURC activity as discussed in MPEP § 2106.05(d)(II) of: “i. Receiving or transmitting data over a network, e.g., using the Internet to gather data, Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362 (utilizing an intermediary computer to forward information); TLI Communications LLC v. AV Auto. LLC, 823 F.3d 607, 610, 118 USPQ2d 1744, 1745 (Fed. Cir. 2016) (using a telephone for image transmission); OIP Techs., Inc., v. Amazon.com, Inc., 788 F.3d 1359, 1363, 115 USPQ2d 1090, 1093 (Fed. Cir. 2015) (sending messages over a network); buySAFE, Inc. v. Google, Inc., 765 F.3d 1350, 1355, 112 USPQ2d 1093, 1096 (Fed. Cir. 2014) (computer receives and sends information over a network);” – also, see:
¶ 60 of the instant disclosure
Arisoy et al., “DESIGN AND TOPOLOGY OPTIMIZATION OF LATTICE STRUCTURES USING DEFORMABLE IMPLICIT SURFACES FOR ADDITIVE MANUFACTURING”, 2015, abstract and § 1
Zhang et al., “Remanufacturing-oriented geometric modelling for the damaged region of components”, abstract and § 1
AutoCAD2k10, Youtube Video: “3d printing (AutoCAD 2010)”, Mar. 17th, 2009, URL: youtube(dot)com/watch?v=Om3pCkRqid4 – AutoCAD software, in view of this evidence and the other YouTube videos produced above, had many of the modeling features presently claimed, e.g. in this video: “0:00 - 3D printing functionality is integrated 0:02 - into AutoCAD 2010 with dramatically 0:04 - improved output for stereo lithography 0:07 - files and easy access to 3D printing 0:10 - services produce STL files using the 0:13 - traditional STL out or export commands 0:15 - as well as the new 3D print command all 0:18 - of these methods for producing STL files”
Siemens, "Parasolid: The world's leading production-proven 3D modeling kernel", copyright 2011. Accessed via the Siemens website (Year: 2011) – see page 10, ¶ 4: “Manufacturing. Parasolid delivers comprehensive modeling capabilities for tapering, blending, thickening, outlining and identification that support a wide range of manufacturing processes, including 3D machining, molding, casting, turning and numerical control (NC) toolpath generation. Parasolid also is an ideal platform for exchanging solid models across manufacturing supply chains, including sharing models with bundled CNC and inspection/metrology applications.“ as well as page 3, ¶ 2; page 5 ¶ 1; page 6, ¶ 2;
Besl et al., “Hybrid Modeling for Manufacturing using NURBS, Polygons, and 3D Scanner Data”, 1998 abstract, and § 1 including ¶ 1.
applying a modelling operation to one or more of the selected first and second parts;… and wherein offsetting, shelling, or thickening operations and detailing is applied directly to the mesh data;… - applying such operations is considered WURC in view of Siemens, "Parasolid: The world's leading production-proven modeling kernel", copyright 2011, page 7: “Parasolid delivers a range of methods that enable CAD users to create thin-walled parts using simple inputs, including: • Thickening of sheet models • Hollowing of solid models • General offsetting Each of these methods provides powerful functionality, including automatic self-intersection removal and together form a comprehensive suite of tools that accelerate the design of plastic moldings, castings, pressings and panels.” And page 8: “Model simplification”: “Parasolid can be used to identify and remove model details, including holes, blends and arbitrary faces to support downstream operations – such as finite element analysis and CAM – where certain model details can be safely ignored…”
deriving, by the data processing system, a second data relating to one or more second parts of the multipart product in a second format, wherein the second format comprises a classic geometric representation; … this is considered similar to the example WURC activity as discussed in MPEP § 2106.05(d)(II) of: “iii. Electronic recordkeeping, Alice Corp. Pty. Ltd. v. CLS Bank Int'l, 573 U.S. 208, 225, 110 USPQ2d 1984 (2014) (creating and maintaining "shadow accounts"); Ultramercial, 772 F.3d at 716, 112 USPQ2d at 1755 (updating an activity log); iv. Storing and retrieving information in memory, Versata Dev. Group, Inc. v. SAP Am., Inc., 793 F.3d 1306, 1334, 115 USPQ2d 1681, 1701 (Fed. Cir. 2015); OIP Techs., 788 F.3d at 1363, 115 USPQ2d at 1092-93; additionally, see the instant disclosure, ¶¶ 56, 60-61, 68. Also see Owen et al., “FACET-BASED SURFACES FOR 3D MESH GENERATION”, § 1: “Computational simulations of physical processes modeled using finite element analysis frequently employ complex automatic mesh generation techniques… Solid models or boundary representation (b-rep) models are most frequently employed, typically provided through a commercial computer aided design (CAD) package or third party library…In recent years, facetted models have become more important as an alternative geometry representation from NURBS representations. Complete 3D geometric models can be represented as a simply connected set of triangles. In many cases, facetted models may be preferred or may be the only representation available” and see §§ 2.2-2.4
receiving, by the data processing system, instructions of a first selection of at least one first part of the one or more first parts of the multipart product comprising mesh data; receiving, by the data processing system, instructions of a second selection of at least one second part of the one or more second parts of the multipart product comprising classic geometric representation data - this is considered similar to the example WURC activity as discussed in MPEP § 2106.05(d)(II) of: “iii. Electronic recordkeeping, Alice Corp. Pty. Ltd. v. CLS Bank Int'l, 573 U.S. 208, 225, 110 USPQ2d 1984 (2014) (creating and maintaining "shadow accounts"); Ultramercial, 772 F.3d at 716, 112 USPQ2d at 1755 (updating an activity log); iv. Storing and retrieving information in memory, Versata Dev. Group, Inc. v. SAP Am., Inc., 793 F.3d 1306, 1334, 115 USPQ2d 1681, 1701 (Fed. Cir. 2015); OIP Techs., 788 F.3d at 1363, 115 USPQ2d at 1092-93;… i. Recording a customer’s order, Apple, Inc. v. Ameranth, Inc., 842 F.3d 1229, 1244, 120 USPQ2d 1844, 1856 (Fed. Cir. 2016);”, also see Siemens, "Parasolid: The world's leading production-proven modeling kernel", copyright 2011, page 7: “…Direct modeling is an extremely powerful editing capability that allows regions of a model to be manipulated and/or replaced; it is particularly useful when applications need to make complex model adjustments independent of any model history….”, additionally, see the instant disclosure, ¶¶ 56, 60-61, 68
wherein the mesh data is treated as a surface in the hybrid boundary representation model, wherein the hybrid boundary representation model has a mixture of the mesh data and the classic geometric representation data and similar such recitations:
First, the Examiner notes the a “collection of facets” as recited in this claim is not a particular data structure, but rather a mathematical construct of geometry. See ¶ 22: “the mesh data representation comprising a plurality of triangles each representing a facet”, ¶¶ 53, 55-56, 83-84, including in ¶ 53: “A vertex represents a point in space….A facet is a triangular region of a plane. A mesh is a connected collection of facets.” – i.e. a collection of connected triangles on a plane, described by the trigonometric mathematical relationships (see Mackay Radio & Tel. Co. v. Radio Corp. of America, as discussed in MPEP § 2106.04(a)(2)(I)(A)) between the “three vertices” [i.e. the corners] (¶ 83) of each triangle – i.e. this limitation is simply storing data that is mathematical in nature, with no particular technological data structure (e.g. using XML) for how it is stored
Second, having a collection of facets for mesh data is WURC - ¶¶ 55-57 and 61, including in ¶ 61: “The full conventional process is illustrated graphically… Thus, the exterior surface 15 of the shell 10 is naturally represented by facets…”, also see Owen et al., “FACET-BASED SURFACES FOR 3D MESH GENERATION”, § 1 ¶ 3: “In recent years, facetted models have become more important as an alternative geometry representation from NURBS representations. Complete 3D geometric models can be represented as a simply connected set of triangles. In many cases, facetted models may be preferred or may be the only representation available” and § 3: “…The method used to store and evaluate the facet data can vary according to the source of those data…”
Third, hybrid models combing different data formats are WURC. This is a term of art.
E.g., see newly cited:
Geomagic, User Guide, Nov. 2013, URL: engineering(dot)pitt(dot)edu/contentassets/52314f399aba40fa86709314a569641c/geomagicdesignx2014userguide(dot)pdf – for a user guide for commercially available software; then see § 1.1 ¶ 1: “Thank you for choosing Geomagic Design X, the most comprehensive 3D Scan-To-CAD Software Solution. 3D Systems, Inc. is the leader in providing technologies that make 3D scanning a powerful tool for a variety of applications including manufacturing, R&D, quality inspection, medical research, civil engineering and more, and is now presenting the future of 3D scanning software technology with its next generation 3D scan data processing platform, Geomagic. Geomagic Design X makes the process of creating parametric CAD models from real world parts faster and easier by utilizing a design process and user interface that are instantly familiar to CAD users.” Then, see the section on “True Hybrid Modeler” on page 11: “Geomagic Design X is a truly comprehensive 3D scan data processing application that offers parametric solid modeling capabilities, NURBS surfacing capabilities, and a hybrid modeling process that utilizes both capabilities for the creation of parametric CAD models that contain freeform features.” – as discussed further starting on page 47 in the section: “Reverse Modeling Process” including “The Reverse Modeling process is the process of creating an optimal 3D model from 3D scan data (Point Cloud or Mesh), that is generated during the Scan Data Processing phase. This process is the core of Reverse Design, where optimized mesh and 3D features, such as 3D curves, 3D surfaces, and 3D solid bodies, are created by using various modeling methods… The Mesh Modeling method creates an optimized mesh that contains important information by
applying various geometric and mathematical operations. The Feature Modeling method creates 3D geometric feature shapes based on extracted design intent and elements from 3D scan data The Fitting Surface Modeling method creates fitted freeform surfaces on complex freeform feature shapes. The Hybrid Modeling method creates a complex feature model from 3D scan data by using the Feature Modeling method in conjunction with the Fitting Surface Modeling method” – then, see § 4.2 for more details, in particular its discussion of “Hybrid modeling”, including that it is “useful for designing a new product from a mock-up or clay model” then see §§ 4.2.2-4.2.3, in particular see “Surface fitting technology” note on page 71: “Surface Fitting Technology is a unique technique in the Reverse Design process that provides
an effective way to easily and quickly create 3D freeform surface bodies from a freeform mesh
shape. It creates surface patches by projecting uniform points within curve loops constructed
on a freeform mesh shape, and fitting to the projected points. A 3D freeform surface body is
created by connecting fitted surface patches. This technique is usually used for creating a highly accurate 3D freeform surface body from 3D scan data” [instant disclosure; ¶ 58: “As set out in more detail below, this disclosure addresses the problem by using a model which defines a new surface type to represent a mesh.”] – then, see § 4.2.4, including the figure for “Creating a complex 3D Model by using the Hybrid Modeling method”
Also, note the discussion starting on page 26 of the 3D sketch, including: “3D Sketch uses spline curves which can be drawn anywhere (3D Sketch) in 3D space or drawn directly on a mesh (Mesh 3D Sketch). 3D Sketch is commonly used for the path of a loft or sweep body. 3D Mesh Sketch is mainly used for generating a curve network on a mesh. Then surfaces can be generated within the network boundaries.”
AutoCAD2k10, YouTube Video: “AutoCAD 2010 - New features (Mesh Modeler)”, May 12th, 2009, URL: youtube(dot)com/watch?v=IpVZ_L72Hx0 – “3:00 - context as in this example this 3:02 - motorcycle was modeled 100% inside 3:05 - AutoCAD using mesh and solids another 3:08 - section will show that the converted 3:10 - mesh can allow any of the solid 3:12 - operations like in this case 3:14 - shell within a few hours a proficient 3:17 - user can come up with a model like this 3:20 - which would have taken an important 3:22 - amount of time before or would have just 3:24 - been impossible to create in 3:28 - alet for for a better visualization of” – see the demonstration in the video for clarification at this time frame
Kurland, AutoCAD 2013 3D Tutorials, 2012 copyright, URL: www(dot)andrew(dot)cmu(dot)edu/course/48-568/PDFs/3D_AutoCAD(dot)pdf – see §§ 8.2-8.3; § 10.1, then see § 11.14 on page 120, include seeing its figures, note the visible mesh in the top-most figure.
E.g. see previously cited:
Lai et al., “Blending of mesh objects to parametric surface”, 2015, § 2, last two paragraphs, including: “Hybrid modeling catches the attention of researchers since a hybrid modeling scheme benefits from mixing the different representations. Adzhiev et al. [17] studied a hybrid system of volumetric data, voxel, and implicit surface functions. The method depends on the conversion between voxels and implicit surfaces. Constructive solid geometry (CSG) has been extended in the work of [18] by using a hybridized CSG tree structure called The HybridTree. Blending or Boolean operations between implicit surfaces and meshes are dependent on the associated field functions. The NURBS-based hybridize element proposed by [19] was used to solve the compatibility problem between element surfaces in FEA and CFD simulations. Specific hybrid elements with mesh elements joining a NURBS surface with a watertight boundary was proposed by [20] but the method does not offer a generic hybrid element definition. Martin et al. [21] mixed mesh elements and NURBS elements in volumetric models as a kind of hybrid structure, but the gaps were filled only by an infinite refinement on the mesh side. Modeling free form solid by using Extended Simplicial Chains and PN-Triangles was studied by [22]. The solid resulting from Boolean operation contained trimmed patches.” Besl, “Hybrid Modeling for Manufacturing using NURBS, Polygons, and 3D Scanner Data”, 1998. See § 3, ¶¶ 1-4, then § 5: “A hybrid surface model IS collection of planar polygon sets (always equivalent to a triangle mesh) and NURBS surface sets. The quality of hybrid surface model is related to how well it obeys approximate continuity constraints.”
Pernot et al., “A HYBRID MODELS DEFORMATION TOOL FOR FREE-FORM SHAPES MANIPULATION”, 2008, abstract: “This paper addresses the way models mixing various types of geometric representations (e.g. NURBS curves and patches, polylines, meshes),…”, then § 1: “For two decades, some attempts have been carried out to try to overcome the limits inherent to the low level manipulations of the underlying mathematical models. Today, the challenge lies in the definition and simultaneous manipulation of potentially non-manifold models mixing various types of geometric representations. The final aim is to propose a shape manipulation approach which is completely independent of the underlying geometric representations”, e.g. figure 1, then see § 2 including ¶ 1 and subsection “Mixing models of different continuities”: “Among the possible combinations, the coupling between surfaces and meshes is certainly the most interesting one in terms of potential applications. One application concerns the use of subdivision surfaces together with NURBS surfaces”
Zhang et al., “Remanufacturing-oriented geometric modelling for the damaged region of components”, 2015, Abstract then see § 3.2.3. See § 1 ¶ 3 and § 2.2 (1) as well, along with fig. 2
Freytag, “B-rep SE: Simplicially Enhanced Boundary Representation”, Abstract, § 1.2.
The claimed invention is directed towards an abstract idea of both a mathematical concept and a mental process without significantly more.
Regarding the dependent claims
Claim 24 recites addition steps in the math concept, including the use of a formula in textual form. See Appeal ‘206, page 9, for its discussed on ¶¶ 83 and 88 of the instant disclosure. The “identifying” steps are part of the math concept, i.e. establishing the mathematical variables representation the geometrical math relationships of a triangle; and furthermore people are readily able to perform such identifications, e.g. when applying the Pythrogrean theorem
Claim 25 - a mental step/process, such as a person mentally visualizing an update to a representation of the part, e.g. an engineer mentally visualizing a design change to a part, or a fashion designer mentally visualizing a design change (e.g. the product being a dress, and the part being straps of the dress, wherein the designer mentally visualizes what different straps would be best suited for the dress).
Claim 26 recites an insignificant extra-solution activity of mere data gathering (via the user input), followed by an insignificant extra-solution activity of mere data transmission as well as part of the mere instructions to use a computer as a tool to implement the abstract idea of the mental process of a mental observation of a point on the mesh (to clarify, the use of a facet identifier and a unique point for identifying a point on the mesh is akin to the mental act of observing a map for a specific region, e.g. US Interstate I-95 and the unique point of mile marker 35, and observing where that point is on the map), wherein this may readily be performed with a simple mesh, e.g. fig. 12-13.
The insignificant extra-solution activity is additionally considered as well-understood, routine, and conventional activity, similar to the examples in MPEP § 2106.05(d)(II) of: “i. Receiving or transmitting data over a network, e.g., using the Internet to gather data,… i. Recording a customer’s order, Apple, Inc. v. Ameranth, Inc., 842 F.3d 1229, 1244, 120 USPQ2d 1844, 1856 (Fed. Cir. 2016);”
Claims 28 is merely further limiting the abstract idea as discussed in detail for similar limitations in claim 23 above
Claim 30 recites another portion of the math concept in the form of mathematical relationships/equations in geometry in textual form. To clarify on the BRI of the term “affine transformation”, while the instant disclosure (¶ 26) does not define what this term is, see Eck, Hobart and William Smith Colleges, Math 204: Linear Algebra, Fall 2020, Reading Guides for Math 204, Chapter 16: “Affine Transformations”, accessed via URL: math(dot)hws(dot)edu/eck/math204/guide2020/16-affine-maps(dot)html:
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Claim 37 recites an insignificant extra-solution activity of mere data gathering followed by mere data transmission and generally linking to a particular field of use wherein these are considered WURC in view of MPEP § 2106.05(d)(II): “i. Receiving or transmitting data over a network, e.g., using the Internet to gather data, Symantec, 838 F.3d at 1321, 120 USPQ2d at 1362 (utilizing an intermediary computer to forward information); TLI Communications LLC v. AV Auto. LLC, 823 F.3d 607, 610, 118 USPQ2d 1744, 1745 (Fed. Cir. 2016) (using a telephone for image transmission); OIP Techs., Inc., v. Amazon.com, Inc., 788 F.3d 1359, 1363, 115 USPQ2d 1090, 1093 (Fed. Cir. 2015) (sending messages over a network); buySAFE, Inc. v. Google, Inc., 765 F.3d 1350, 1355, 112 USPQ2d 1093, 1096 (Fed. Cir. 2014) (computer receives and sends information over a network); but see DDR Holdings, LLC v. Hotels.com, L.P., 773 F.3d 1245, 1258, 113 USPQ2d 1097, 1106 (Fed. Cir. 2014)… iii. Electronic recordkeeping, Alice Corp. Pty. Ltd. v. CLS Bank Int'l, 573 U.S. 208, 225, 110 USPQ2d 1984 (2014) (creating and maintaining "shadow accounts"); Ultramercial, 772 F.3d at 716, 112 USPQ2d at 1755 (updating an activity log); iv. Storing and retrieving information in memory, Versata Dev. Group, Inc. v. SAP Am., Inc., 793 F.3d 1306, 1334, 115 USPQ2d 1681, 1701 (Fed. Cir. 2015); OIP Techs., 788 F.3d at 1363, 115 USPQ2d at 1092-93;”, also see the instant disclosure, ¶¶ 56, 60-61
See MPEP § 2106.05(h): “For instance, a data gathering step that is limited to a particular data source (such as the Internet) or a particular type of data (such as power grid data or XML tags) could be considered to be both insignificant extra-solution activity and a field of use limitation.”
Claim 38 is rejected under a similar rationale as claim 37.
Claim 39 recites: “…generating the physical sample of the part” – this is an insignificant extra-solution activity performed as part of the data gathering - to clarify, MPEP § 2106.05(g): “i. Performing clinical tests on individuals to obtain input for an equation… iii. Presenting offers to potential customers and gathering statistics generated based on the testing about how potential customers responded to the offers; the statistics are then used to calculate an optimized price…” – the generating of the physical sample as recited in claim is considered similar to the acts of “Presenting offers to potential customers…” and “Performing clinical tests on individuals…” – as the generation of the physical sample is, as claimed, solely for the purpose of performing mere data gathering using the physical sample, similar to how presenting the offer was used for “gathering statistics”, and similar to how performing the clinical tests was used such to “obtain input for an equation”
To clarify on the BRI of claim 39, ¶ 64 of the disclosure: “The first stage is for the designer [a person] to generate 50 the physical model, for example from wood or clay. When the designer is happy with the form of the physical model, the model is scanned 51 and the scanned data…”
Claim 39 is additionally considered as well-understood, routine, and conventional activity as discussed in MPEP § 2106.05(d) when claim 39 is taken in view of ¶ 64 and in further view of ¶ 61 of the instant disclosure, wherein this is also similar to the example in MPEP § 2106.05(d)(II): “v. Electronically scanning or extracting data from a physical document” as the physical document would have been generated such as to be scanned
Claim 40 is reciting addition steps in the mathematical concept and further limiting the mathematical concept in geometry (note which limitations in particular it has antecedent basis back to)
Claim 41 is specifying a further portion of the mathematical concept
Claim 43 recites additional steps in the mathematical concept for similar reasons as the limitations it further limits as discussed above
Claims 45-51 rejected under similar rationales as their parallel dependent claims discussed above.
The claimed invention is directed towards an abstract idea of both a mathematical concept and a mental process without significantly more.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 44, 46, 48, and 50-51 is/are rejected under 35 U.S.C. 103 as being unpatentable over Liepa et al., US 2008/0259077 in view of Co, US 2015/0154796 and in view of Siemens, “World-class finite element analysis (FEA) solution for the Windows desktop”, copyright 2008, URL: www(dot)plm(dot)automation(dot)siemens(dot)com/en_gb/Images/fe%20finite%20element%20analysis%20for%20windows%20fs%20W%205_tcm642-53789(dot)pdf and in further view of Zhang et al., “Remanufacturing-oriented geometric modelling for the damaged region of components”, 2015
Claim 44
A method of defining a point on a mesh representation of a part of a multipart product for additive manufacturing and communicating the point to a hybrid boundary representation model of the part of the multipart product, the method comprising: (Liepa, abstract: “A method, apparatus, and article of manufacture provide the ability to map a detail model to a destination while preserving the shape of the detail model. A destination surface (that is a smooth surface) is obtained. The destination surface is tessellated to generate a mesh representation of the destination surface. A parameterization of the mesh representation is then generated. Reverse mapping is conducted from a point of a detail model surface to a point of the destination surface via the parameterization and mesh representation [points are communicated between a mesh and a B-rep model].” and see figure 1 this uses a “computer”; as to the surface being a part of a product: ¶ 7;
as to the B-rep model ¶ 41: “Such geometry is referred to as a detail model and can be a spline surface (including NURBS [Non-Uniform Rational B-Spline] and Bezier surfaces), subdivision surface, implicit surface, algebraic surface, procedural surface, mesh surface, solid, volume, curve, point, multiple surfaces, collections of contiguous surfaces, and any other surface(s ), curve(s ), point(s), solid(s) or volume(s).”, also see ¶ 43: “The destination surface can be a spline surface (including NURBS [Non-Uniform Rational B-Spline]and Bezier surfaces), subdivision surface, implicit surface, algebraic surface, procedural surface, mesh surface, boundary surface ( of a solid or volume), curve, multiple surfaces, collections of contiguous surfaces, and any other surface(s) or curve(s)” – these are examples of a B-rep model, see ¶ 54 of the instant specification)
[a] deriving, by a data processing system, a first data relating to one or more first parts of the multipart product in a first format, wherein the first format comprises mesh data, and wherein the deriving of the first data comprises [a1] obtaining a natural representation of each facet of the mesh data comprising an integer identifier of each facet and associated facet parameters comprising a pair of u, v parameters; [b] deriving, by the data processing system, a second data relating to one or more second parts of the multipart product in a second format, wherein the second format comprises a classic geometric representation; [c] receiving, by the data processing system, instructions of a first selection of at least one first part of the one or more first parts of the multipart product comprising mesh data; [d] receiving, by the data processing system, instructions of a second selection of at least one second part of the one or more second parts of the multipart product comprising classic geometric representation data;
Liepa, abstract, and ¶¶ 12-13, then see ¶¶ 41-44: “To begin use of the Conform Rig tool, the user first selects the geometry to be modified, or conformed at step 302. Such geometry is referred to as a detail model and can be spline surface (including NURBS Non-Uniform Rational B-Spline and Bezier surfaces), subdivision surface, implicit Surface, algebraic Surface, procedural Surface, mesh Surface, Solid, Volume, curve, point, multiple surfaces, collections of contiguous Surfaces, and any other Surface(s), curve(s), point (s), solid(s) or volume(s)… At step 306, one or more surfaces, or a single mesh, or a single curve on any Surface (isoparms, trim boundaries, curves-on-Surface, trim mesh, patch precision lines), or a locator point on a Surface is selected as the destination. The destination is the geometry onto which the detail models are to be mapped… The destination Surface can be a spline Surface (including NURBS Non-Uniform Rational B-Spline and Bezier Surfaces). Subdivision Surface, implicit surface, algebraic Surface, procedural Surface, mesh Surface, boundary Surface (of a Solid or Volume), curve, multiple Surfaces, collections of contiguous Surfaces, and any other Surface(s) or curve(s). All Such Surface(s) can be tessellated (e.g., the tessellation of a mesh is the mesh itself)… Once the user has elected to proceed, the Conform operation takes the detail model geometry and, as if it was a thick stamp, applies it onto the destination surface at step 308.” e.g., ¶ 46: “In FIG.4, the detail model 402 is the round feature on the right and the destination 404 is the half-cylinder surface on the left.” – i.e. this receives first and second data of the destination model and the detail model in different model formats, wherein the user then performs selections with the received geometry data – to clarify on the BRI of classic geometry representation, see ¶ 54 of the instant disclosure
to clarify on the products modelled, see ¶ 7 for the examples: “In 3D modeling, animation, effects, and rendering applications, it is desirable to place and display one object (referred to as a detail model) onto another object (referred to as a destination). For example, a company logo may be copied or placed onto the front hood of an automobile or the side of a shoe. In another example, a semi-soft rubber disc may be wrapped around a cylindrical Surface. With Such an application/effect, it may be desirable for the detail model to conform to a curved destination surface yet retain its detail model proportions.”)
with respect to [a1]; see Liepa, ¶¶ 62-63: “…In this regard, the destination 404 surface may be obtained in response to the user selecting the destination at step 306 of FIG. 3…At step 1002, the destination surface 404 is tessellated to create/ generate a mesh representation of the (smooth) destination surface 404.”; as to this being a triangular mesh see ¶ 14: “The mapping is defined from the flattened triangles to the triangles of the destination surface tessellation, and then as a projection ( or a closest point determination) from the tessellation triangles to the destination surface.”, as to the facet, see ¶ 53 of the instant specification: “A facet is a triangular region of a plane.”, e.g. Liepa’s “triangles” then ¶ 64: “: “At step 1004, a new parameterization of the tessellated destination 404 (i.e., the mesh) is generated. The new parameterization is unrelated to the ( original) intrinsic parameterization, and provides a new UV coordinate for every vertex [of every triangle] of the mesh. Mesh parameterization can be interpreted as a flattening operation. For example, if the UV coordinate is a point on the XY-plane, since every mesh vertex has a new UV coordinate that can be mapped to an XY position, the result is a flattening of the curved mesh surface ”
and as to this [a1] including an identifier, see ¶ 66: “At step 1006, a reverse mapping is defined from the new parameterization to the destination surface (e.g., via the parameterization and mesh representation). In this regard, step 1006 may be viewed as a process wherein the detail model 402 is overlayed onto the flattened mesh and for every point of the detail model surface 402 ( e.g., each point of the detail model 402 may be mapped to a point of the destination surface which may be a point on or in the vicinity of the destination surface), the appropriate triangle of the flattened [previously parametrized] mesh is identified. With the triangle, embodiments work backwards and identify the triangle on the original unflattened mesh which in turn is utilized to identify the actual point on the original destination surface 404.” as the triangle is identified in both the parameterized and the original meshes, a skilled person would have inferred that there was an identifier associated with each triangle
[e] applying, by the data processing system, a modelling operation to modify one or more of the selected at least one first part and the selected at least one second part to form a modified multipart product, wherein, when the modelling operation is applied to modify the at least one first part, the modelling operation is made without modification to a format of the mesh data and comprises obtaining a modified representation of each facet of the mesh data comprising a combination of the integer identifier and the facet parameters, and wherein, when the modelling operation is applied to modify the at least one second part, the modelling operation is made without modification to a format of the classic geometric representation data;
Liepa, as cited above, then see Liepa ¶¶ 41,43, 66, and 75, in particular see 66-67: “At step 1006, a reverse mapping is defined from the new parameterization to the destination surface (e.g., via the parameterization and mesh representation)… In other words, the mapping proceeds from the detail model to the flattened destination 404 version to the curved destination 404 version, to the original destination 404 surface. Such a reverse mapping is enabled based on the mappings ( e.g., the generation of the new parameterization 1004 may result in the use of a mapping to/from the tessellated destination surface from/to the flattened tessellated destination surface) ( e.g., the tessellated destination surface may produce/result in a mapping to/from the mesh representation from/to the original destination surface) obtained during the steps 1002 and 1004.” – i.e. the mapping/modified parameterization is communicated to both the detail model and the destination surface, wherein either one of these, or both of them, are a B-rep model as per ¶ 41 and ¶ 43”
Then, see Liepa, ¶ 44: “Once the user has elected to proceed, the Conform operation takes the detail model geometry and, as if it was a thick stamp, applies it onto the destination surface at step 308.” Which is an example of a modelling operation, for other example modeling operations see ¶ 47: “In FIG. 4, the top of the detail model 402 has been stretched. Embodiments of the invention may provide an option to modify/change how the detail model 402 stretches. In this regard, both the thickness and footprint may operate independently of each other (or together) and a user may establish/control Such a setting and operation”, ¶ 48: “404. Using the various buttons 406, 408, 410, and 412 at the bottom of the modeling window, the user may elect to be in translate 406, rotate 408, scale 410, or elevate 412 mode. Each mode may update and perform the desired operation dynamically in real time” – see ¶¶ 49-54 for more clarification on this, as well as ¶ 58, and ¶ 60: “In addition, after a detail model 402 has been conformed to a destination 404, the user can proceed to modify the destination 404 Surface in any way, and the conformed detail models 402 may dynamically and automatically (and without user input) update based on a construction history of the conformation operation. The user may also modify the input detail model 402 geometry and the conformed detail models 402 may update accordingly (e.g., dynamically and without user input).”, and see figures 4-9 for visual examples, also see ¶ 76)
To further clarify, Liepa, ¶¶41-46 as discussed above, then see ¶¶ 63-71, include seeing: ¶ 71: “Accordingly, the detail model 402 is mapped to the original Smooth Surface in a highly accurate manner while preserving the shape of the detail model 402 (e.g., without altering the shape of the detail model 402). Thus, rather than merely mapping the detail model 402 to a mesh representation of the destination 404, embodiments of the present invention map the detail model 402 to the actual original destination 404.” And ¶ 67: “...In other words, the mapping proceeds from the detail model to the flattened destination 404 version to the curved destination 404 version, to the original destination 404 Surface. Such a reverse mapping is enabled based on the mappings (e.g., the generation of the new parameterization 1004 may result in the use of a mapping to/from the tessellated destination surface from/to the flattened tessellated destination Surface) (e.g., the tessellated destination Surface may produce/result in a mapping to/from the mesh representation from/to the original destination Surface) obtained during the steps 1002 and 1004...”, – i.e. there is an original detail model, and the mapped/conformed “detail model” is a representation of the original detail model that is attached/mapped to the “original destination surface” via the “parameterization” discussed in ¶¶ 63-71 in detail (see the instant disclosure, ¶¶ 80-84; see Appeal 2024-000206 for its discussion of Liepa on this feature, including page 18) wherein Liepa clarifies in ¶ 66: “In this regard, step 1006 may be viewed as a process wherein the detail model 402 is overlayed onto the flattened mesh and for every point of the detail model surface 402 (e.g., each point of the detail model 402 may be mapped to a point of the destination surface which may be a point on or in the vicinity of the destination Surface),” – i.e. each model is treated as a surface to the other model in the attachment, by the mapping. See ¶ 43 for additional clarification: “It may be noted that the process for selecting the detail model Surface, selecting a tool to perform the conform operation, the user selecting the destination Surface, and the displaying of the detail model Surface mapped to the destination Surface may be performed in any temporal order.”, and see ¶¶ 41 and 43 for the NURBs surface and other similar such surfaces, as well as meshes
Wherein, as a result of this mapping modeling operations are applied in the form the data is held without changing the data format of the original models - ¶ 60: “In addition, after a detail model 402 has been conformed to a destination 404, the user can proceed to modify the destination 404 Surface in any way, and the conformed detail models 402 may dynamically and automatically (and without user input) update based on a construction history of the conformation operation. The user may also modify the input detail model 402 geometry and the conformed detail models 402 may update accordingly (e.g., dynamically and without user input).” – i.e. the input models themselves are modified, and the mapping provides for the updating of the conformed model when either input model is modified – to further clarify on this point, ¶ 76: “Embodiments of the invention may also provide the ability to translate 406 a copy of a detail model 402 along a destination surface 404, and to rotate 408, scale 410, and elevate 412. This can be achieved by inserting additional transformations in the mapping chain…” and ¶ 79: “embodiments of the invention solve the problem of creating a copy of the detail model that conforms to a curved destination Surface yet retains the original detail model proportions” and ¶ 70 to clarify: “Thus, rather than merely mapping the detail model 402 to a mesh representation of the destination 404, embodiments of the present invention map the detail model 402 to the actual original destination 404. In addition, steps 1002-1006 may be performed dynamically and interactively in real time as the detail model 402 is manipulated with respect to the surface (e.g., as described above in the user interface).” - in other words, when the use applies modeling operations so as to “manipulate[]”/”modify” the input models, these operations are directly applied to the original model in its original formation without modifying the original model, and instead the mapped conformed models are dynamically updated in the joint representation of Liepa via the mapping of Liepa
in addition to the above, should it be found that Liepa does not anticipate this feature of the “…modelling operations are applied in the form in which the data is held…”, see view of Liepa ¶¶ 63-71 in detail, the instant disclosure, ¶¶ 80-84 including in ¶ 81: “The use of a modified parameterisation allows a user input made in a boundary representation model to be mapped to data held only in mesh format, using the same mechanisms as classic surfaces.”; See Appeal 2024-000206: “Under the broadest reasonable interpretation, however, the Examiner finds that Liepa' s mapping is an example of the claimed communicating in view of disclosures in Appellant's specification, which teaches: "This disclosure provides a mapping between the natural parameterization of the mesh and a u, v parameterization, of the type used in boundary representation models, by combining the integer identifier of the facet with the facet parameters." Id. at 22 (citing [instant] Spec. ¶ 81). According to the Examiner, Liepa's teachings are similar to the teachings in this specification passage because Liepa communicates the mesh to the B-rep model "such that the mesh and B-rep models are mapped to each other” – and see ¶ 81: “This disclosure provides a mapping between the natural parameterization of the mesh and au, v parameterization, of the type used in boundary representation models, by combining the integer identifier of the facet with the facet parameters. The use of a modified parameterisation allows [i.e. a latent property/advantage of using such a mapping] a user input made in a boundary representation model to be mapped to data held only in mesh format, using the same mechanisms as classic surfaces.”, then see MPEP § 2145(II): “Prima Facie Obviousness Is Not Rebutted by Merely Recognizing Additional Advantages or Latent Properties Present But Not Recognized in the Prior Art”: “Mere recognition of latent properties in the prior art does not render nonobvious an otherwise known invention. In re Wiseman, 596 F.2d 1019, 201 USPQ 658 (CCPA 1979)… "The fact that appellant has recognized another advantage which would flow naturally from following the suggestion of the prior art cannot be the basis for patentability when the differences would otherwise be obvious." Ex parte Obiaya, 227 USPQ 58, 60 (Bd. Pat. App. & Inter. 1985)” - To further clarify, in the ‘206 appeal: “Appellant does not dispute these findings in the Reply Brief. We agree with the Examiner that the broadest reasonable interpretation of "communicating" encompasses mapping in light of the specification's teaching that "[t]his disclosure provides a mapping between the natural parameterization of the mesh and a u, v parameterization, of the type used in boundary representation models." Spec. ¶ 81, quoted in Ans. 22 (emphasis by Examiner).”
[f] providing, by the data processing system, a representation of the modified multipart product comprising the selected at least one first part in the first format and the selected of the at least one second part in the second format, wherein the mesh data of the first format is a collection of facets, wherein the mesh data is treated as a surface in the hybrid boundary representation model, wherein the hybrid boundary representation model has a mixture of the mesh data and the classic geometric representation data, (Liepa, as was cited and discussed above, i.e. it maps the original mesh model to the original NURBs model via the parameterization process of Liepa in ¶¶ 61-67, so as to form a representation of both parts in each of their respective formats, or to put it simply, ¶ 44: “Once the user has elected to proceed, the Conform operation takes the detail model geometry and, as if it was a thick stamp, applies it onto the destination surface at step 308. Such a "stamp" may be required to initially lie parallel to the X-Y plane. In this regard, the reference plane may default to the X-Y plane, and can later be changed by the user” and ¶ 79: “In summary, given a three dimensional detail model that is defined over a reference plane, embodiments of the invention solve the problem of creating a copy of the detail model that conforms to a curved destination surface yet retains the original detail model proportions.” – e.g. fig. 5-7, wherein modifications operate on the original models/input models, and the representation is “update[d] accordingly (e.g. dynamically and without user input)” to account for user manipulations/modifications (¶¶ 60, ,76, 79, etc. as cited and discussed extensively above)
Liepa does not explicitly teach: the identifier being an integer
Liepa, in view of Co teaches: integer identifier (Co, ¶ 22: “…A triangle record may include an integer triangle identifier and an integer mesh identifier…”)
Also, see Appeal 2024-000206 discussion of claim 23 subpart “a. extracting” and “deriving” for its res judicata effect on this § 103
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the teachings from Liepa on “A method, apparatus, and article of manufacture provide the ability to map a detail model to a destination while preserving the shape of the detail model” (Liepa, abstract) with the teachings from Co on “converting data stored as triangle meshes to octree cubes in a compressed state” (Co, ¶ 22) The motivation to combine would have been that this would have “allow[ed] for faster intersection testing” (Co, ¶ 22).
While Liepa does not explicitly teach the following feature, Liepa in view of Siemens teaches: and wherein offsetting, shelling, or thickening operations and detailing is applied directly to the mesh data; (Liepa, as was discussed above including ¶ 60: “In addition, after a detail model 402 has been conformed to a destination 404, the user can proceed to modify the destination 404 Surface in any way, and the conformed detail models 402 may dynamically and automatically (and without user input) update based on a construction history of the conformation operation. The user may also modify the input detail model 402 geometry and the conformed detail models 402 may update accordingly (e.g., dynamically and without user input).”
In view of Siemens, page 1, then see page 2: “Geometry modeling and editing Femap provides extensive geometry creation and editing tools that enable engineers to effectively, efficiently create geometry for analysis, including… Solids – create blocks, cylinders, cones and spheres, extrude and revolve, Boolean operations, explode and stitch, fillet and chamfer, shell thicken and remove face…” – also, page 4: “Meshing and mesh editing”: “Benefit from flexible mesh controls and extensive editing capabilities:” “Extrude, revolve, sweep – extrude, revolve or sweep curves, elements or element faces” [example of detailing] and “Edit element – change element connectivity, modify order of element. Scale, translate, rotate or align elements. Modify offsets, orientation and reverse normal of planar elements. Modify element property or type. Modify planar element material angle, plate thickness and shell properties. Adjust beam warping. Add or remove coefficients of thermal expansion for rigid elements”- to clarify, the Examiner notes shelling is an example of hollowing, as it shells the object, i.e. creates a hollow space inside the object as it turns it into a shell.
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the teachings from Liepa, as modified by Co above, on “In Summary, given a three dimensional detail model that is defined over a reference plane, embodiments of the invention solve the problem of creating a copy of the detail model that conforms to a curved destination Surface yet retains the original detail model proportions” (Liepa, ¶ 79) with the teachings from Siemens on features of “Femap® software is an advanced engineering analysis environment for simulation of complex engineering problems” (Siemens, summary).
The motivation to combine would have been that “…Using Femap engineers can simulate the performance of their products virtually to determine their performance and behavior, reducing the need for testing and prototypes..” (Siemens, page 1, summary). Additional motivations to combine are listed n the “Benefits” section on page 1: “Significantly speed up the design process by bringing simulation closer to design and reducing time to- market Reduce the need for costly prototypes and testing, saving time and money Perform failure analysis that improves product performance and reliability, reducing costly recalls Evaluate and optimize designs to minimize material use, investigate use of alternative materials and perform trade-off studies to evaluate differing designs Standalone engineering analysis environment that can exchange data with any CAD system and simulate using all major commercial solvers”
Additional motivations to combine are: “Femap provides extensive geometry creation and editing tools that enable engineers to effectively, efficiently create geometry for analysis” (page 2), and “Benefit from flexible mesh controls and extensive editing capabilities:” (page 4).
In addition, the Examiner also notes that as per ¶ 61 these types of modeling operations are “conventional”/”current modelling operations”, as also demonstrated by Siemens as discussed above, as well as the previously relied upon Siemens, “Parasolid: The world’s leading production-proven 3D modeling kernel”, copyright 2011, as was discussed in Appeal 2023-001298 on pages 8-9 – as such, see MPEP § 2143(I)(A) for its discussion of “Anderson’s-Black Rock, Inc. v. Pavement Salvage Co., 396 U.S. 57, 163 USPQ 673 (1969)” in example 1, and the KSR rationale of “A) Combining prior art elements according to known methods to yield predictable results” is also readily applicable.
While Liepa does not explicitly teach the following feature, Liepa in view of Zhang teaches:
[g] and generating and transmitting, by the data processing system, manufacturing instructions for the additive manufacturing of the modified multipart product using the hybrid boundary representation model. (Liepa, as was cited above for a method of modeling products wherein two different model data formats are mapped to each other but kept in their original format [i.e. Liepa is not converting the data formats of the original models];
As taken in view of Zhang, abstract: “The accurate additive manufacturing technology provides an effective and efficient means for remanufacturing or repairing high value and damaged engineering components. Important work to implement this technology is to construct the geometric model of the damaged or worn region, which lays the foundation for the computation of the tool path [example of manufacturing instructions] and the virtual digit repair” and Zhang § 1 ¶ 1 including: “Mechanical products usually may suffer from various damages, such as wear, impact dents and cracks, after a period of service time, which affects the normal work of the product. As a result, the damaged part has to be replaced or repaired. Replacing a damaged part with a new part will cause the cost increase and the waste of resources, especially for some complex precision components. Remanufacturing is a typical green manufacturing mode for saving cost and reducing consumption of resources. However, the traditional way of repairing damaged parts mainly depends on the skill level of workers and their repair experience. As a result, it is very difficult to repair the complex precision parts (e.g. more than IT6 precision) in high quality and efficiency. In recent years, the rapid development of the digital laser sampling and cladding technology, such as laser-based Direct Metal Deposition (DMD) technology, provides a new solution for remanufacturing or repairing the damaged parts. In the DMD process, the path traced by the laser beam is regulated through Computer Numeric Controls (CNC), so a reference geometric model of the defective region must be available [1]. The geometric modelling of the damaged region lays the foundation for subsequent path planning of the laser cladding tool and machining tool.” – e.g. Zhang fig. 2 and § 2.2, wherein similar to Liepa this is also doing hybrid modelling with a “mesh model” and a “NURBS-based B-rep model” - and see fig. 7 to clarify
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the teachings from Liepa, as modified above, on “A method, apparatus, and article of manufacture provide the ability to map a detail model to a destination while preserving the shape of the detail model” (Liepa, abstract, and see fig. 1 along with its accompanying description) with the teachings from Zhang on “…Important work to implement this technology is to construct the geometric model of the damaged or worn region, which lays the foundation for the computation of the tool path and the virtual digit repair...” (Zhang, abstract, see § 2.1 ¶ 2 to clarify as well as figure 2 and § 2.2)
The motivation to combine would have been that “The accurate additive manufacturing technology provides an effective and efficient means for remanufacturing or repairing high value and damaged engineering components…” Additional motivations to combine include: “This method can avoid reconstructing the scanned mesh surface so the efficiency and accuracy of geometric modelling gets a lot of improving.” (Zhang, § 5 ¶ 1). An additional motivation to combine would have been that “…Recently, the development of the reverse engineering technology provides a feasible solution to the issue [4]… The cloud data can be converted to a set of triangular meshes, which forms the geometrical boundary of the damaged region. On the other hand, the CAD solid model of the damaged part represents the design requirements for the geometry and topology of the defect-free part. In addition, the CAD model of the damaged part is usually available” (Zhang, § 2.1, ¶ 1) – i.e. Zhang would have provided a technique to obtain a mesh model from “scanning” (fig. 2) as while the “CAD model…is usually available”, the mesh model may not be “available” without such “Digitization” (fig. 2).
Should it be found that Liepa alone does not teach limitation [e], see Zhang as discussed in Appeal 2023-001298, starting on page 7, including: “We are not convinced by Appellant's argument because Zhang's geometric modelling method performing "direct" Boolean operations on the original CAD solid model and triangle mesh model at least suggests "applied directly to the mesh data" as recited in claim 1. See Zhang, p. 803, col. 2, ¶ 1, Ans. 19” – wherein POSITA would have been motivated to combine Liepa’s hybrid modeling system that maps mesh data to NURBs data with Zhang’s “novel method to perform Boolean operations on the triangulated approximation surfaces and exact parameter surfaces is also presented.” (Zhang, abstract) because “This paper presents a novel geometric modelling method to obtain the geometric model by performing the direct Boolean operations on the original CAD solid model and the triangle mesh model of the damaged part. Although the CAD model and the triangle mesh model are two different types of boundary representation, as the former is an exact surface representation and the latter is a discrete approximation, this paper implements their direct Boolean operations. This method can avoid reconstructing the scanned mesh surface so the efficiency and accuracy of geometric modelling gets a lot of improving” (Zhang, § 5).
Regarding Claim 46.
Liepa, as taken in combination above, teaches:
The method of claim 44, further comprising:
communicating, in response to a position request consequent to a user input receiving instructions of a selection of a point on the mesh representation of the part of the multipart product, the integer identifier and a unique point together to the hybrid boundary representation model to identify the point on the mesh representation. Liepa, see ¶ 62: “…In this regard, the destination 404 surface may be obtained in response to the user selecting the destination at step 306 of FIG. 3…”, to clarify, ¶ 43: “Once a destination has been selected, the user may be prompted to accept the conform destination or to finalize the conform operation. In the case of the destination being a surface curve or a surface point, the detail model will still be mapped onto the surface to which these entities belong. The curve or point merely acts as a constraint on the placement of the detail model…The destination surface can be a spline surface (including NURBS [Non-Uniform Rational B-Spline] and Bezier surfaces), subdivision surface, implicit surface, algebraic surface, procedural surface, mesh surface, boundary surface ( of a solid or volume), curve, multiple surfaces, collections of contiguous surfaces, and any other surface(s) or curve(s). [examples of B-rep models]”, and see ¶ 75 for the modified parameterization as cited above)
also, see ¶ 71 to further clarify: “As described above, step 1006 maps each point of the detail model onto the flattened mesh, to the curved mesh, to the original destination surface 404. For example, a point (x,y,z) in the detail model 402 may be mapped into reference space to identify reference coordinates (r,s,t), such that (x,y, z)=rR1 +sR2 +tR3” and ¶66, as taken in view of Co above for the integer identifier
Regarding Claim 48.
Liepa, in combination as discussed above, teaches:
The method of claim 44, further comprising:
generating a physical sample of the part. (Liepa, in view of Zhang, in particular Zhang fig. 2 for its “Scanning” process to generate the “mesh model” from a generated physical sample of a part [see the photograph])
The motivation to combine would have been that “This method can avoid reconstructing the scanned mesh surface so the efficiency and accuracy of geometric modelling gets a lot of improving.” (Zhang, § 5 ¶ 1). An additional motivation to combine would have been that “…Recently, the development of the reverse engineering technology provides a feasible solution to the issue [4]… The cloud data can be converted to a set of triangular meshes, which forms the geometrical boundary of the damaged region. On the other hand, the CAD solid model of the damaged part represents the design requirements for the geometry and topology of the defect-free part. In addition, the CAD model of the damaged part is usually available” (Zhang, § 2.1, ¶ 1) – i.e. Zhang would have provided a technique to obtain a mesh model from “scanning” (fig. 2) as while the “CAD model…is usually available”, the mesh model may not be “available” without such “Digitization” (fig. 2).
Regarding Claim 50.
Co teaches:
The method of claim 44, wherein an integer value of the integer identifier is different for each triangle of the mesh data such that the integer value of the integer identifier of a first triangle of the mesh data is a first integer value and the integer value of the integer identifier of a second triangle of the mesh data is a second integer value that is different from the first integer value. (Co, ¶ 4: “Each triangle record of the list of triangle records includes an integer triangle identifier and an integer mesh identifier.”, as clarified in ¶ 41: “The triangular records from each grid cell of the second 3D grid cell may be encoded as a list of integers. This list of integers may include the number of triangles in the cell as well as the integer mesh identifiers and integer triangle identifiers for all of the triangles of that grid cell of the second 3D grid. Thus, grid cell of the second 3D grid including one or more triangles of the portion of the triangular mesh may be associated with 2n+1 integers.” – as such, a skilled person would have inferred that the integer triangle identifiers for each triangle are different values, as they identify a particular triangle and there is a plurality of “integers”)
The rationale to combine is the same as was discussed above for the independent claims.
Regarding Claim 51.
Liepa, in view of Co teaches:
The method of claim 44, wherein the natural representation comprises three pieces of data for each triangle of the mesh data including the integer identifier and the pair of u, v parameters; And wherein the obtaining the modified representation includes determining a unique point from the pair of u, v parameters such that the modified representation comprises two pieces of data for each triangle of the mesh data including the unique point and the integer identifier. (Liepa, as cited above, teaches this, include seeing ¶ 75: “For example, after the mesh representing the destination surface is parameterized (i.e., at step 1004), the flattened mesh can be resealed in UV space so that it has the same area as the unflattened mesh [example of deriving a modified parameterization, as this is modifying the first parameterization]. As a result, the mapping from the detail model to the destination surface can be approximately size preserving.”
As taken in view of Liepa, ¶¶ 66-67: “…In this regard, step 1006 may be viewed as a process wherein the detail model 402 is overlayed onto the flattened mesh and for every point of the detail model surface 402 ( e.g., each point of the detail model 402 may be mapped to a point of the destination surface which may be a point on or in the vicinity of the destination surface), the appropriate triangle of the flattened mesh is identified [example of a unique point from the u, v coordinates, because this is “each point” that is mapped and each point is a unique point]. With the triangle, embodiments work backwards and identify the triangle on the original unflattened mesh which in turn is utilized to identify the actual point on the original destination surface 404… In other words, the mapping proceeds from the detail model to the flattened destination 404 version to the curved destination 404 version, to the original destination 404 surface.”, see ¶¶ 69-71 to further clarify
As to the integer identifier, this would have been obvious when Liepa ¶ 64 as cited above was taken in view of Co ¶ 22 and ¶ 39 as were cited above
The rationale to combine is the same as was discussed above for the independent claims.
Claims 45 is/are rejected under 35 U.S.C. 103 as being unpatentable over Liepa et al., US 2008/0259077 in view of Co, US 2015/0154796 and in view of Siemens, “World-class finite element analysis (FEA) solution for the Windows desktop”, copyright 2008, URL: www(dot)plm(dot)automation(dot)siemens(dot)com/en_gb/Images/fe%20finite%20element%20analysis%20for%20windows%20fs%20W%205_tcm642-53789(dot)pdf and in further view of Zhang et al., “Remanufacturing-oriented geometric modelling for the damaged region of components”, 2015 and in further view of Scratchapixel, “Ray Tracing: Rendering a Triangle”, accessed via WayBack Machine with an archive date of May 2015, URL: www(dot)scratchapixel(dot)com/lessons/3d-basic-rendering/ray-tracing-rendering-a-triangle/barycentric-coordinates
Regarding Claim 45.
While Liepa modified above, does not explicitly teach the following feature, Liepa, as taken in combination above, and in further view of Scratchapixel teaches:
The method of claim 44, wherein the obtaining of the modified representation comprises: identifying first, second, and third vertices of each facet; identifying first and second axes of each facet; and defining a unique point within the facet based a combination of an origin, a constant multiple of the first axis, and a constant multiple of the second axis, where the constant multiples are greater than or equal to zero and a combination of the constant multiples is less than or equal to one. (Liepa, in view of Co as discussed above for the modified representation, in further view of Scratchapixel, pages 1-2, the paragraph and equations split between the pages: “You can also simply use two coordinates (let's say u and v) [e.g., Liepa, ¶ 64 “UV coordinate”] to express the coordinates of P [a unique point] in a two dimensional coordinate system defined by its origin (A) and the edge AB and AC [the axes of the triangle] (pretty much like expressing 2D points in the orthogonal two-dimensional coordinate system defined by an x- and y-axis. The only difference in our case is that AB and AC are not necessarily orthogonal and that the origin of this coordinate system is A [the axes were identified based on identified vertices A, B, and C]). Anyway, just to say that you can define a position [a unique point] inside the triangle with the equation P=A+u∗AB+v∗AC (where u≥0 and v≥0 and u+v≤1) [the sum, including that the constants are =>0 and the sum of the constants <=1] This equation can read as, "starts from A, move a little bit in the direction of AB, then a little bit in the direction of AC and you will find P". Now if you develop this equation you can write: …” – to clarify on the BRI of this limitation, see the instant specification ¶ 83
Also, see Appeal 2024-000206 discussion of claim 24 for its res judicata effect on this § 103
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the teachings from Liepa, as modified above, on a system “A method, apparatus, and article of manufacture provide the ability to map a detail model to a destination while preserving the shape of the detail model” wherein this includes “A parameterization of the mesh representation is then generated” (Liepa, abstract) wherein this is into “a new UV coordinate” system (¶ 64 of Liepa) with the teachings from Scratchapixel on using “Barycentric coordinates” for a “triangle” (Scratchapixel, ¶ 1). The motivation to combine would have been that “If the barycentric coordinates are used to compute the position of a point located on the triangle using the triangle vertices, we can interpolate any other data defined at the triangle's vertices (like for example the color) in the exact same way. In other words, barycentric coordinates are used to interpolate vertex data across the triangle's surface (the technique can be applied to any data type, float, color, etc.)…” (Scratchapixel, page 4, ¶ 1).
Claims 47 and 49 is/are rejected under 35 U.S.C. 103 as being unpatentable over Liepa et al., US 2008/0259077 in view of Co, US 2015/0154796 and in view of Siemens, “World-class finite element analysis (FEA) solution for the Windows desktop”, copyright 2008, URL: www(dot)plm(dot)automation(dot)siemens(dot)com/en_gb/Images/fe%20finite%20element%20analysis%20for%20windows%20fs%20W%205_tcm642-53789(dot)pdf and in further view of Zhang et al., “Remanufacturing-oriented geometric modelling for the damaged region of components”, 2015 and in further view of Fu et al., “An Improved Texture Mapping Model Based on Mesh Parameterization in 3D Garments”, 2014
Regarding Claim 47.
While Liepa modified above, does not explicitly teach the following feature, Liepa, as taken in combination above, and in further view of Fu teaches:
The method of claim 44, wherein the modified representation comprises an affine transformation of internal facet parameters of each facet. (Fu, § III.B, section titled “Mesh Parameterization”, ¶ 2: “…Our goal is to find a single parameterization of the entire
mesh, a piecewise linear mapping from the 3D mesh to the 2D plane, described by assigning 3D coordinates to each vertices. For triangle t , this 2D coordinates can be denoted as ut = {u0t , u1t , u2t} . Given this setup, the unique affine transformation P : U → T between the vertexes of triangle U and T is determined. First, the eigenvalue metric space [15] in the affine transformation of triangles can be defined in (3)…”)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the teachings from Liepa, as modified above, on a system “A method, apparatus, and article of manufacture provide the ability to map a detail model to a destination while preserving the shape of the detail model” wherein this includes “A parameterization of the mesh representation is then generated” (Liepa, abstract) with the teachings from Fu on “an efficient and simple mesh parameterization method is presented in this paper” (Fu, abstract). The motivation to combine would have been that Fu’s technique was “efficient and simple”.
Regarding Claim 49.
While Liepa modified above, does not explicitly teach the following feature, Liepa, as taken in combination above, and in further view of Fu teaches:
The method of claim 44, wherein the obtaining of the modified representation includes a transformation from the natural representation of each triangle of the mesh data to the modified representation of each triangle of the mesh data that preserves points, straight lines and planes(Liepa, ¶ 75: “For example, after the mesh representing the destination surface is parameterized (i.e., at step 1004), the flattened mesh can be resealed in UV space so that it has the same area as the unflattened mesh [example of deriving a modified parameterization, as this is modifying the first parameterization]. As a result, the mapping from the detail model to the destination surface can be approximately size preserving.”
As taken in view of Liepa, ¶ 8, as clarified in ¶ 65: “Shape preserving mapping is one technique that may be used to perform such a flattening… As used herein, a shape preserving map is a function that preserves angles…”
so that points lying on a line before the transformation still lie on the line after the transformation, a midpoint of a line segment before the transformation is still the midpoint after the transformation and parallel lines before the transformation remain parallel lines after the transformation. (Liepa, ¶ 75, as taken in view of ¶¶ 8 and 65 of Liepa, as taken in further view of Fu § III.B, section titled “Mesh Parameterization”, ¶ 2: “…Our goal is to find a single parameterization of the entire mesh, a piecewise linear mapping from the 3D mesh to the 2D plane, described by assigning 3D coordinates to each vertices. For triangle t , this 2D coordinates can be denoted as ut = {u0t , u1t , u2t} . Given this setup, the unique affine transformation P : U → T between the vertexes of triangle U and T is determined. First, the eigenvalue metric space [15] in the affine transformation of triangles can be defined in (3)…”
To clarify on the BRI, ¶ 84 of the instant specification: “For efficient translation between the two parameterizations, the external parameterization should be an affine transformation of the internal facet parameters of each facet, i.e. [that is] points, straight lines and planes are preserved in the transformation, so that all points lying on a line initially, still lie on a line after transformation, the midpoint of a line segment is still the midpoint after transformation and parallel lines remain parallel after transformation” – in view of the instant specification ¶ 84, this limitation is claiming an affine transformation)
It would have been obvious to one of ordinary skill in the art before the effective filing date of the claimed invention to combine the teachings from Liepa, as modified above, on a system “A method, apparatus, and article of manufacture provide the ability to map a detail model to a destination while preserving the shape of the detail model” wherein this includes “A parameterization of the mesh representation is then generated” (Liepa, abstract) with the teachings from Fu on “an efficient and simple mesh parameterization method is presented in this paper” (Fu, abstract). The motivation to combine would have been that Fu’s technique was “efficient and simple”.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Datta, Ranadev, and C. Guedes Soares. "NURBS based scheme for automatic quadrilateral mesh generation for FE and BEM analysis." Marine Systems & Ocean Technology 7.1 (2012): 29-35. § 2.2, last two paragraphs, discussing how NURB surfaces are, by mathematical definition per equation 4, mapped to a “unit square” in R2 (two dimensional space), specifically note the “u” and “v” coordinates for this.
Dimitriou, V., A. Kanarachos, and D. Koulocheris. "An approach to unstructured finite element mesh generation using Coons mapping and smoothing techniques." WSEAS Transactions on Circuits and Systems 2 (2003): 473-478. § 2 discussing mapping to parametric (u, v) surfaces is mapping to “the unit square”, e.g. fig. 1, mathematically, and further describes in equations 2-3 a “Coons patch” calculation, wherein “Consequently, a line ui=const (rsp. vj=const) is mapped into a 3D Cartesian curve s(ui,v), (rsp. s(u,vj)) as it is presented in Fig. 1. This property is used for the production of finite element meshes.” Wherein it appears this is discussing the conventional generation of FEM meshes (§ 3 ¶¶ 1-2 and figures to contrast).
GOENKA, MOHIT. "Technique for Adaptive Mesh Generation." (2013). Mid-semester Interim B.Tech Report, Nov. 2013, INDIAN INSTITUTE OF TECHNOLOGY in Kharagpur, India. See § 5.2: “One of the most commonly used Adaptive meshing techniques is Mapped element approach. This approach requires an object be subdivided manually into simple regions, each of which consists of three or four sides… Given a four sided region, a mesh can be induced in it by mapping a mesh template of the unit square in the parametric space to the region”
Grimm, Cindy M. "Parameterization using manifolds." International Journal of Shape Modeling 10.01 (2004): 51-81. Abstract and § 1 including: “There are many surface representations, such as meshes and implicit surfaces, that lack a “built-in” parameterization, such as the one provided by spline surfaces. The primary use of a surface parameterization in graphics is as a texture map. A parametric surface equation is also useful for calculating differential geometry entities such as geodesics and principal curvature. These metrics can then be used for applications such as feature extraction, shape classification, and comparisons of 3D objects. Parameterization is essentially the problem of flattening a surface (or piece of a surface) to the plane without folding or creasing it. This creates a mapping from the surface to the plane. Current approaches with meshes have focused on finding “nice” mappings that distribute distortions in well-behaved ways…” then see pages 5-6 paragraph split between the pages: “Several papers describe surface construction techniques using manifolds 15,16,35,36,31. Grimm’s approach 16 begins with a mesh and builds a manifold with one chart per mesh element. The approach in Navau and Garcia’s first paper 36 builds a manifold for a planar mesh by mapping the boundary of the mesh to the unit square. Charts and embedding functions can then be built on the unit square. We adopt this approach for planar meshes”
Ho-Le, K. "Finite element mesh generation methods: a review and classification." Computer-aided design 20.1 (1988): 27-38. Section “Mapped element approach” on page 3: “The mesh template is a rectangular mesh in the unit square (or a triangular mesh in a unit triangle) in the parametric space. It is mapped onto a four-sided (or three-sided) region to induce a mesh in the region via a blending function 23. An arbitrary object has to be subdivided manually into three- or four-sided regions, which are in effect macro elements (see Figure 13). This approach is the mainstay of existing commercial mesh generators.”
Hua, Tienyong, and Ibrahim Zeid. "A free-form mesh generator for three-dimensional surfaces." International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Vol. 97690. American Society of Mechanical Engineers, 1993. Abstract, § 2 ¶¶ 1-2: “Parametric surface representation is realized by using a continuous, vector-valued function P(u, v) of two parameters, ii and n. In most cases, u and v intervals are [0,1 ]. That makes the parametric surface maps into a unit square in the parametric space. The free-form surface mesh generation concept is described as follows. An analytic or synthetic surface can always's be transformed into its parametric space which is a two-dimensional space of u and v.” and see § 3.4, including its subsection “B-spline Surface”, noting B-splines are in the “u, v” parametric space as part of their definition (by equation)
Laug, P., and H. Borouchaki. "Interpolating and meshing 3d surface grids." International Journal for Numerical Methods in Engineering 58.2 (2003): 209-225. Pages 210-211, then see § 3.
Lee, Michael, and Hanan Samet. "Navigating through triangle meshes implemented as linear quadtrees." ACM Transactions on Graphics (TOG) 19.2 (2000): 79-121. Page 81, including: “Triangular meshes are not restricted to purely two-dimensional data. They are also useful in the modeling of data that lies on the surface of a sphere, as is the case, for example, in applications that involve modeling the earth (e.g., De Floriani et al. [1996]). Traditional ways of representing such data invariably resort to projections onto the plane (e.g., Tobler and Chen [1986]) using one of many possible projections (e.g., Snyder [1987]). Clearly, there is no perfect projection. Ideally, we would like the projection to facilitate a decomposition into units of equal area. The difficulty here is that units of equal area in the projection do not necessarily correspond to units of equal area on the surface of the sphere. For example, it would be ideal if the projection made use of the common concepts of latitudes and longitudes, as in the case of the Mercator projection (e.g., Snyder [1987]). Unfortunately, this leads to great distortion around the poles, thereby precluding the use of equally-spaced lines of latitude.”
Mounoury, Valérie, and Olivier Stab. "Automatic quadrilateral and hexahedral finite element mesh generation: review of existing methods." Revue européenne des éléments finis 4.1 (1995): 75-102. § 4.2, fig. 15 and: “Blaker uses various primitives as triangles, circles, semi-circles. But the other decomposition algorithms provide quadrilateral primitives. Most of the primitive meshing methods are based on mathematical transformations that allow to map a mesh template of a unit square (or a unit cube in 3D) onto a region with the same topology.”, followed by pages 95-96 incl.: “Chinnaswamy ([CHI 91]) uses an inverse transfinite mapping. A super-element, superimposed on a regular mesh of the domain, is mapped by an inverse transfinite mapping on a unit square. The external elements are removed ; those which intersect the square boundary are deformed or cut. Afterwards, the mesh is mapped again on the region. Figure 16 shows an example.”
Nguyen, Thien, and Bert Jüttler. "Parameterization of contractible domains using sequences of harmonic maps." International conference on curves and surfaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. Abstract and § I including: “To achieve that, our method creates a mapping from the domain to the unit square or unit cube, see Figure 1. The mapping should be regular or injective”
Peiró, Joaquim, Spencer J. Sherwin, and Sergio Giordana. "Automatic reconstruction of a patient-specific high-order surface representation and its application to mesh generation for CFD calculations." Medical & biological engineering & computing 46.11 (2008): 1069-1083. § 5, including # 3.
Provatidis, Christopher G. "CAD-FEA integration using Coons interpolation." ideas. Vol. 20. 2002. Abstract, and § 6 ¶¶ 1-4, and page 38 for fig. 3
Provatidis, C. G. "A review on attempts towards CAD/CAE integration using macroelements." Computational Research 1.3 (2013): 61-84. Abstract, then see § 2.1, then § 2.2.5.1, also see § 2.2.26 and its subsections including § 2.2.7. Then, see §§ 2.3.1.1 -2.3.1.2, then see § 2.3.1 including fig. 2.3.1
Weiss, Kenneth, and Leila De Floriani. "Sparse terrain pyramids." Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems. 2008. § 3 and figure 1
Russel et al., US US 2003/0191554, fig. 5 and accompanying description, ¶¶ 120-132, including: “Projection is the inverse of texture mapping. Each node in the mesh of triangles has co-ordinates in the unit texture square given by its (x, y) coordinates relative to the XY extent of the mesh. The co-ordinates of any given point are transformed by an inverse of the texture transformation matrix to give a point in an output space of the TCG…”
Muller-Fischer et al., US 2007/0024620, figures 4 and accompanying description.
GIANNACOPOULOS et al., US 2015/0120261 ¶ 139: “Element merging in the FGaBP algorithm is demonstrated using a structured triangular mesh on a unit square domain. The Laplace equation is solved in the domain using zero Dirichlet on the boundary. The unit square is subdivided into equally spaced sub-squares where each square is further divided into two right triangles.”
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/David A Hopkins/Primary Examiner, Art Unit 2188