Notice of Pre-AIA or AIA Status
Claims 1, 3-9, 11-17 and 19-24 are currently presented for Examination.
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 Amendment
The amendment filed on 01/26/2026 has been entered and considered by the examiner. By the amendment, claims 1, 3, 9, 11, 17 and 19-24 are amended. Following Applicants arguments and amendments made on, the 112 and 103 rejection of the claims is withdrawn. Regarding the 103 rejection, independent claims include previously objected dependent claim which was objected for allowable subject matter. The 101 rejection is still maintained. See office action for detail.
Applicant 101 arguments
As should be clear from both the claims and the Specification, the steps as recited in the claims which define the processes involved in constructing U-Spline meshes are highly complex and simply cannot, as a practical matter, be performed within the human mind. Accordingly, as in SiRF Tech., the claims are directed toward "inventions that 'could not, as a practical matter, be performed entirely in a human's mind."' The Office also asserted that limitations recited "mathematical algorithms and therefore fall "under the mathematical concepts of abstract ideas."' The Applicants respectfully disagree.
Examiner response
Examiner respectfully disagrees. Applicant argues the claimed process is too complex to be performed mentally. Complexity does not remove the claim from the mental process category. However, the mathematical operations remain abstract even if complex or impractical for mental performance. The claims may simply be using a general-purpose computer to automate a mathematical process, which is not patent-eligible. The claims recite the use of standard, well-understood computational components (e.g., processors, memory, CAD software) to perform the math. The claim recites constructing a mesh, assigning coordinate systems, assigning basis functions and constructing constraints, which constitute mathematical modeling operations. Therefore, the claim recites a mathematical concept and/or mental process under step 2A prong 1.
Applicant arguments
As recently pointed out in In re Dejjardins (and the associated Dec. 5, 2025, Subject Matter Eligibility, an "improvement in the functioning of a computer, or an improvement to other technology or a technical field" is to be considered patent-eligible subject matter and not an "abstract idea"" Further, ... mere recitation of a judicial exception does not mean that the claim is "directed to" that judicial exception under Step 2A Prong Two. 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." The Applicants submit that the claims are not "directed to" any of the mathematical concepts recited in the claims but, in contrast, the claims, when taken as a whole, do indeed recite "an improvement to a technology or a technical field" and should therefore comprise patent-eligible subject matter. In ExParteDejardins, the court decided that "the claims as a whole integrated what would otherwise be a judicial exception instead into a practical application ... and therefore the claims were deemed to be outside any specific, enumerated judicial exception."12. As noted in the Specification, (abstract, para [0005-0007]) Accordingly, the Specification clearly describes the improvements to finite element analysis (FEA), computer aided design (CAD), and computer aided engineering (CAE) (i.e., a technology and a technical field) and the claims (read in conjunction with the explicit details of the Specification) provide for the construction of U-Spline meshes and their use in the technical fields of FEA, CAD, and CAE. Accordingly, the claims do indeed recite the "steps of the invention that provide the improvement described in the Specification" and should therefore be considered to comprise patent-eligible subject matter under 35 U.S.C. § 101. Accordingly, the Applicants submit that the claims, when considered as a whole, provide the steps involved in creating U-Spline meshes which are useful in the technical fields of FEA, CAD, and CAE, and provide an improvement to those technical fields as are described within the Specification. Accordingly, the Applicants submit that each of independent claims 1, 9, and 17 do indeed recite patent-eligible subject matter under 35 U.S.C. § 101 and the rejections should therefore be withdrawn.
Examiner response
Examiner respectfully disagrees. Applicant argues that the claimed U-spline construction improves CAD and CAE modeling and therefore is integrated into a practical application citing DeJjardins. The specification does describe advantages of U-splines for CAD/CAE and finite-element analysis. However, under MPEP 2106.04(d)(1) if the specification sets forth an improvement in technology, the claim must be evaluated to ensure that the claim itself reflects the disclosed improvement. That is, the claim includes the components or steps of the invention that provide the improvement described in the specification. The present claim recites constructing a mesh, assigning coordinate systems, assigning basis functions and constructing continuity constraints, which constitute mathematical modeling operations for constructing a spline representation. Therefore, the claim recites a mathematical concept and/or mental process under step 2A prong 1. The claim further recites storing the mesh and employing it within CAD or CAE processes. These limitations constitute insignificant extra solution activity 2106.05(g) and field of use limitation see MPEP 2106.05(h). Claim does not require any particular simulation, geometry evaluation, or improved computer modeling operation over the mesh. Accordingly, the claim as a whole does not recite an improvement to computer modeling technology and does not integrate the abstract idea into a practical application.
Unlike the Desjardins decision focused on improvements in machine learning models that specifically improved the functioning of a computer, such as reducing system complexity or optimizing data storage, the present claim merely constructs the U-spline mesh and generally states that it is used on CAD/CAE. The claim must demonstrate that U-splines specifically improve the functionality of the CAD/CAE computer system (e.g., reduced CPU cycles, faster rendering times), not just produce a better theoretical CAD model. The instant claimed process merely improves the accuracy of the shape representation (a "better" model), thus it still considered an abstract idea applied to a specific field. Simply stating that U-splines improve the "design and engineering" process is a "field of use" limitation that does not save an abstract idea. The claims must do more than simply use a formula to obtain a numerical or graphical output. Simply stating that U-splines improve the "design and engineering" process is a "field of use" limitation that does not save an abstract idea. The claims must do more than simply use a formula to obtain a numerical or graphical output.
Also, all the case law claims cited by applicant is very different than the instant claims, since the instant claim of constructing U-spline meshes is merely using computer technology to automate a mathematical modeling process. The computer is acting as a tool to execute a geometric algorithm, not improving how the computer itself. The focus is on the outputted model, not the underlying computer functionality.
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.
5. Claims 1, 3-9, 11-17 and 19-24 are rejected under 35 U.S.C. 101 because the claimed invention is directed to non-statutory subject matter. These claims are directed to an abstract idea without significantly more.
(Step 1) Is the claims to a process, machine, manufacture, or composition of matter?
Claim 1 and 3-8 recites “system… comprising non-transitory computer readable storage media”., which falls into the one of the statutory categories, i.e., manufacture or machine.
Claims: 9 and 11-16 are directed method or process, which falls on the one of the statutory category.
Claim 17 and 19-24 recites “a computer program product… comprising non-transitory computer readable data storage”, which falls into the one of the statutory categories, i.e., manufacture or machine.
(Step 2A) (Prong 1) Is the claim directed to a law of nature, a natural phenomenon, or an abstract idea? (Judicially recognized exceptions)?
Claim 1, 9 and 17 recites:
construct a mesh which comprises a plurality of cells; (Under the broadest reasonable interpretation, this limitation covers mental process including an evaluation or judgment that could be performed in the human mind or with the aid of pencil and paper therefore falls within the “Mental Process” grouping of abstract ideas. A mesh itself is an abstraction, a mathematical representation of a complex shape or domain, divided into simpler components called cells.)
assign a coordinate system to each cell in the mesh, wherein each coordinate system is barycentric or formed from tensor products of barycentric coordinate systems; (Under the broadest reasonable interpretation, this limitation covers mental process including an evaluation or judgment that could be performed in the human mind or with the aid of pencil and paper therefore falls within the “Mental Process” grouping of abstract ideas. Also, this limitation are abstract mathematical constructs that define a point's location within a simplex (like a triangle or tetrahedron) by referencing the vertices of that simplex. So, it falls under the mental process or mathematical concepts of abstract ideas)
assign a parametric length to each edge of each cell in the mesh, wherein the parametric lengths satisfy the conditions for seamless similarity maps; (While the process of defining these lengths and applying them to a mesh certainly involves abstract ideas about shape and geometry, the core process is one of applying mathematical rules and calculations. The process involves computations based on mathematical algorithms and concepts, such as those related to conformal mapping. So, it falls under the mathematical concepts of abstract ideas)
assign a basis to each cell in the mesh, wherein each basis of each cell is a Bernstein or Bernstein-like basis; (The Bernstein basis itself is a well-defined mathematical concept, with specific properties, formulas, and applications, particularly in approximating functions and representing curves and surfaces.
So, it falls under the mathematical concepts of abstract ideas)
assign a minimum desired continuity to each interface between adjacent cells in the mesh;( In the context of meshes in specification, it refers to how smoothly the solution of a numerical simulation transitions across element boundaries. So, it falls under the mathematical concepts of abstract ideas)
construct a system of continuity constraints, termed the global system of constraints, from each interface in the mesh, wherein the global system of constraints is derived from a coordinate system, parametric lengths, and basis for each cell and the continuity associated with each interface; While the process of setting up and visualizing these constraints might involve a mental process of abstract ideas, the core principles and techniques used to construct the global system are based on rigorous mathematical definitions and procedures. So, it falls under the mathematical concepts of abstract ideas)
construct a refined U-spline mesh by partitioning the global system of constraints associated with the U-spline mesh into cell systems of constraints wherein: a cell system of constraints associated with cells of maximum dimension is empty; and a cell system of constraints for each cell of lower dimension is formed recursively from the cell systems of constraints of adjacent cells of higher dimension until an interface dimension is reached. (The construction of the mesh relies on understanding and manipulating abstract concepts related to partitioning constraints and recursive formation of systems. This involves mental processing of these abstract ideas to implement the mesh refinement process. U-splines are a mathematical approach to constructing spline bases used in CAD and CAE for representing smooth objects. The method described involves mathematically defined concepts like "global system of constraints," "cell systems of constraints," and "recursion" to refine the mesh based on continuity requirements. So, it falls under the combination of mental process and mathematical concepts of the abstract ideas.)
Step 2A, Prong 2: Does the claim recite additional elements that integrate the judicial exception
In accordance with Step 2A, Prong 2, the judicial exception is not integrated into a practical application. In particular, claim 1, 9 and 17 recites the additional elements of store the U-spline mesh in durable data storage is recited at a high level of generality (i.e., as a general means of storing data), and falls under the insignificant extra solution activity. (See MPEP 2106.05(g)) The additional elements of employ the refined U-spline mesh within further CAD or CAE processes for design, refinement, display and/or further analysis in claim 1, 9 and 17 amount to nothing more than a field of use limitation. (MPEP 2106.05(h)) The limitation merely restricts the use of the data (U-spline mesh) to a particular technological environment (CAD/CAE). This is a "token acquiescence to limiting the reach of the claim," as described in Flook, rather than an improvement to the CAD process itself. It describes the "field of use" (CAE analysis) rather than a "technical solution to a technical problem". The additional elements of one or more computer processors; and non-transitory computer readable storage media having stored therein computer-executable instructions which, when executed by the one or more computer processors in claim 1 and a computer program product for constructing a U-spline mesh in computer aided design (CAD) or computer aided engineering (CAE), the system comprising: non-transitory computer readable data storage having stored therein computer-executable instructions which, when executed by one or more computer processors within a computing system in claim 17 are amounts to no more than mere instructions to apply the exception using generic computer components. (MPEP 2106.05(f); Thus, a system or method for constructing a U-spline mesh in computer aided design (CAD) or computer aided engineering (CAE) as discussed on MPEP 2106.05(h). Therefore, claims 1, 9 and 17 are directed to an abstract idea.
Step 2B: Does the claim recite additional elements that amount to significantly more than the judicial exception?
The claims do not include additional elements that are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to the integration of the abstract idea into a practical application, the additional elements of store the U-spline mesh in durable data storage is recited at a high level of generality (i.e., as a general means of storing data), and falls under the insignificant extra solution activity and is well-understood, routine or conventional. ((See MPEP 2106.05(d)(II) (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; The additional elements of employ the refined U-spline mesh within further CAD or CAE processes for design, refinement, display and/or further analysis in claim 1, 9 and 17 amount to nothing more than a field of use limitation. (MPEP 2106.05(h)) The limitation merely restricts the use of the data (U-spline mesh) to a particular technological environment (CAD/CAE). This is a "token acquiescence to limiting the reach of the claim," as described in Flook, rather than an improvement to the CAD process itself. It describes the "field of use" (CAE analysis) rather than a "technical solution to a technical problem". The additional elements of one or more computer processors; and non-transitory computer readable storage media having stored therein computer-executable instructions which, when executed by the one or more computer processors in claim 1 and a computer program product for constructing a U-spline mesh in computer aided design (CAD) or computer aided engineering (CAE), the system comprising: non-transitory computer readable data storage having stored therein computer-executable instructions which, when executed by one or more computer processors within a computing system in claim 17 are amounts to no more than mere instructions to apply the exception using generic computer components. The statement that the method is performed by computer does not satisfy the test of “inventive concept.” See Alice Corp. Pty. Ltd. v. CLS Bank Int’l, 573 U.S. 208, 134 S. Ct. 2347, 2360 (2014). (MPEP 2106.05(f); Claim therefore, when taken as a whole, still does not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception. Thus, a method for controlling a coordinate measuring machine is no more than generally linking to the field of use as discussed on MPEP 2106.05(h). Therefore, claims 1, 9 and 17 are directed to abstract idea.
Claim 3, 11 and 19 further recites wherein a second refined U-spline mesh is constructed by constructing a set of vertex basis vectors for each vertex in the mesh by computing basis vectors for a nullspace of the cell system of constraints associated with each cell in the mesh, wherein: a basis vector for the nullspace has nonnegative coefficients when expressed in Bernstein form; a basis vector for the nullspace has a minimal number of nonzero coefficients in the Bernstein form; every nonzero coefficient in a basis vector for the nullspace is within one index unit of at least one other nonzero coefficient when other nonzero coefficients are required; a basis vector for the nullspace is computed from associated interfaces first; and
a basis vector for the nullspace for lower-dimensional cells is computed by analyzing a set of basis vectors associated with the nullspaces of adjacent cells of dimension one greater. It involves a specific algorithm and a set of mathematical conditions to construct a refined U-spline mesh and its corresponding basis functions. So, it falls under the mathematical concepts of abstract ideas. The claim does not include any additional element; thus, it does not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception.
Claim 4, 12 and 20 further recites wherein a third refined U-spline mesh is constructed by constructing a special set of basis vectors, termed the boundary set, for each set of vertex basis vectors in the mesh by:
determining a set of basis vectors associated with cell systems of constraints adjacent to the vertex, wherein nonzero coefficient indices in the basis vectors appear in at least one basis vector in the set of vertex basis vectors; determining appropriate charts for each cell adjacent to a vertex; forming equivalence classes of cell basis vectors adjacent to a vertex, wherein the equivalence class is determined through an appropriate projection; finding a basis vector from each equivalence class, wherein the nearest projected index point of the basis vector is furthest from the vertex in all appropriate charts; and forming a set containing the most distant basis vectors from each equivalence class. This process relies heavily on mathematical concepts such as basis vectors, projections, and geometric relationships between cells and vertices in a mesh. It involves understanding and applying principles from linear algebra (basis vectors) and geometry (charts, projections). So, it falls under the mathematical concepts of abstract ideas. The claim does not include any additional element; thus, it does not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception.
Claim 5, 13 and 21 further recites wherein a fourth refined U-spline mesh is constructed by constructing nonzero coefficients of a single basis vector for a nullspace of the global system of constraints from the vertex basis vectors by: Step 1: forming a set, termed the basis index set, wherein each index in the basis index set is contained in at least one vertex basis vector and the associated Bernstein coefficient is nonzero;
Step 2: given one vertex basis vector, using the boundary set to determine the vertex basis vectors of all adjacent vertices whose boundary sets are aligned and adding these to the basis index set; Step 3: repeating Steps 1-2 until no adjacent vertices contain vertex basis vectors with aligned boundaries that are not in the basis index set; Step 4: taking the basis index set produced in Steps 1-3 and computing values for all Bernstein coefficients associated with the indices in the basis index set, wherein the values are determined from the global system of constraints while also enforcing positivity of all nonzero Bernstein coefficients. The process is a blend of applying mathematical concepts (nullspaces, Bernstein coefficients, constraints) within a structured, computational algorithm for generating the U-spline mesh. So, it falls under the mathematical concepts of abstract ideas. The claim does not include any additional element; thus, it does not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception.
Claim 6, 14 and 22 further recites wherein Steps 14 are applied repeatedly until all unique basis vectors for the nullspace of the global system of constraints have been generated to form a U-spline basis. The process is a blend of applying mathematical concepts (nullspaces, Bernstein coefficients, constraints) within a structured, computational algorithm for generating the U-spline mesh. So, it falls under the mathematical concepts of abstract ideas. The claim does not include any additional element; thus, it does not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception.
Claim 7, 15 and 23 further recites wherein individual basis vectors are scaled so that the sum over all basis vectors in Bernstein form produces a vector with every entry equal to 1. This is a mathematical concept where a set of functions (like Bernstein basis polynomials) sum to 1 over a given domain. So, it falls under the mathematical concepts of abstract ideas. The claim does not include any additional element; thus, it does not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception. The claim does not include any additional element; thus, it does not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception.
Claim 8, 16 and 24 further recites wherein the U-spline mesh, basis of each cell, and minimum desired continuity of each interface between adjacent cells are modified such that v-separation, p-separation, and v-grading are satisfied. It involves the modifications described in the query involve applying and manipulating mathematical concepts related to splines and meshes to achieve desired outcomes or properties. So, it falls under the mathematical concepts of abstract ideas. The claim does not include any additional element; thus, it does not integrate the judicial exception into a practical application nor amount to significantly more than the judicial exception.
Conclusion
6. Claims 1, 3-9, 11-17 and 19-24 are rejected.
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure:
US 20190303531 A1 Urick et al.
Discussing a mechanism for reconstructing trimmed surfaces whose underlying spline surfaces intersect in model space, so that the reconstructed version of each original trimmed surface is geometrically close to the original trimmed surface, and so that the boundary of each respective reconstructed version includes a model space trim curve that approximates the geometric intersection of the underlying spline surfaces.
Toshniwal, Deepesh, Hendrik Speleers, and Thomas JR Hughes. "Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations." Computer Methods in Applied Mechanics and Engineering 327 (2017): 411-458.
Discussing a novel framework for geometric modeling and isogeometric analysis on unstructured quadrilateral meshes.
7. THIS ACTION IS MADE FINAL. Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a).
A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action.
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/PURSOTTAM GIRI/Examiner, Art Unit 2186
/RENEE D CHAVEZ/Supervisory Patent Examiner, Art Unit 2186