DETAILED ACTION
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Claims 1, 6, 8, 10, 15, and 17 are presented for examination based on the amended claims in the application filed on February 25, 2026. Claims 2-5, 7, 9, 11-14, and 16 have been cancelled by the applicant.
Claims 1, 6, 8, 10, 15, and 17 are rejected under 35 U.S.C. § 101 because the claimed invention is directed to judicial exception, an abstract idea, and it has not been integrated into practical application. The claims further do not recite significantly more than the judicial exception.
Claims 1, 6, 8, 10, 15, and 17 are rejected under 35 U.S.C. § 102(a)(1) as being anticipated by Yang, Xunnian. “Efficient circular arc interpolation based on active tolerance control.” Computer-Aided Design 34, no. 13 (2002): 1037-1046.
This action is made 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 Amendment
The amendment filed February 25, 2026 has been entered. Claims 1, 6, 8, 10, 15, and 17 remain pending in the application. Applicant’s amendments to the Specification, Drawings, and Claims have overcome each and every objection, 112(b) rejections, and 112(a) rejections previously set forth in the Non-Final Office Action mailed November 25, 2025. The claim interpretation of the 112(f) limitation found in claim 9 is moot due the cancellation of the claim.
Information Disclosure Statement
The information disclosure statement (IDS) submitted on February 23, 2026 is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statements are being considered by the examiner.
Claim Objections
Claims 1, 6, 8, 10, 15, and 17 are objected to because of the following informality: Claim 1 recites the acronym “CNC” which is not spelled out. The first time the acronyms appear in the claim set, the acronyms should be spelled out. All claims dependent on an objected base claim are objected based on their dependency.
Appropriate correction is required.
Claims 1, 6, 8, 10, 15, and 17 are objected to because of the following informality: recitations of elements with previous recitations. For example, claim 1, “a computer processor” in Pg. 1 Ln. 8 and “a computer processor” in Pg. 2 Ln. 11, is improper because there has been a previous recitation of “a computer processor” in Pg. 1 Ln. 3. For the purpose of examination, “a computer processor” will be interpreted as “[[a]] the computer processor”. Similarly, the following are objected under similar rationale:
In claim 6, “an area surrounded by the two boundary lines” in Ln. 5 should be “[[an]] the area surrounded by the two boundary lines.
In claim 8, “a generation order of the fitting arcs” in Ln. 5 should be “[[a]] the generation order of fitting arcs”.
All claims dependent on an objected base claim are objected based on their dependency.
Appropriate correction is required.
Claims 10, 15, and 17 are objected to because of the following informality: Claim 10, which cites “when the program is executed” in Ln. 3, is improper because there has been no previous recitation of “the program”. For the purpose of examination, “when the program is executed” will be interpreted as “when the computer program is executed”. Claims 15 and 17, having similar limitations as claim 10, are similarly objected.
Appropriate correction is required.
Applicant is advised that should claim 1 be found allowable, both claims 6 and 8 will be objected to under 37 CFR 1.75 as being a substantial duplicate thereof. When two claims in an application are duplicates or else are so close in content that they both cover the same thing, despite a slight difference in wording, it is proper after allowing one claim to object to the other as being a substantial duplicate of the allowed claim. See MPEP § 608.01(m).
Claim Rejections - 35 U.S.C. § 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 1, 6, 8, 10, 15, and 17 are rejected under 35 U.S.C. § 101 because the claimed invention is directed to judicial exception, an abstract idea, and it has not been integrated into practical application. The claims further do not recite significantly more than the judicial exception. Examiner has evaluated the claims under the framework provided in the 2019 Patent Eligibility Guidance published in the Federal Register 01/07/2019 and has provided such analysis below.
Step 1:
Claims 1, 6, and 8 are directed to a method and fall within the statutory category of a process, and claims 10, 15, and 17 are directed to a computing device and fall within the statutory category of a machine. Therefore, “Are the claims to a process, machine, manufacture or composition of matter?” Yes.
In order to evaluate the Step 2A inquiry “Is the claim directed to a law of nature, a natural phenomenon or an abstract idea?” we must determine, at Step 2A Prong 1, whether the claim recites a law of nature, a natural phenomenon or an abstract idea and further whether the claim recites additional elements that integrate the judicial exception into a practical application.
Step 2A Prong 1:
Claim 1: The limitations of:
“generating two boundary lines on both sides of an original curve, and determining an area surrounded by the two boundary lines as a fitting area, wherein a distance of each of the two boundary lines from the original curve is less than respective distance thresholds”,
“performing at least one sub-fitting operation on the original curve in the fitting area until an end condition of curve fitting is satisfied”,
“wherein for an i-th sub-fitting operation of the at least one sub-fitting operation, when i is equal to 1, an arc starting point is a starting point of the original curve, and when i is greater than 1, the arc starting point is an end point of a fitting arc corresponding to an i-1 th sub-fitting operation”,
“wherein the i-th sub-fitting operation comprises generating a first tangent arc in the fitting area that is tangent to the original curve and passes through the arc starting point, the first tangent are being an arc with a largest radius among arcs that have passed through the arc starting point and being tangent to the original curve”,
“determining, on the first tangent arc, a first tangent point that is closest to a regional boundary line of the fitting area”,
“selecting, on the first tangent arc, a test end point between the first tangent point and an end point of the first tangent arc”,
“generating a second tangent arc in the fitting area based on the test end point, the second tangent arc being an arc with a largest radius among arcs that are tangent to the first tangent arc at the test end point”,
“determining an arc end point corresponding to the i-th sub-fitting operation on the second tangent arc”,
“determining, as a fitting arc corresponding to the i-th sub-fitting operation, a curve between the arc starting point and the arc end point on the first tangent arc”,
“generating a fitting curve corresponding to the original curve by splicing, and according to a generation order, fitting arcs corresponding to the i-th sub-fitting operation”, and
“wherein the end condition of the curve fitting comprises a distance between a current arc end point and an original curve end point being less than a third distance threshold, the current arc end point is an end point of the fitting arc corresponding to a last sub-fitting operation in the at least one sub-fitting operation”, as drafted, is a process that, but for the recitation of generic computing components, under its broadest reasonable interpretation, covers performance of the limitation in the mind or with pen and paper. For example, the limitations can be performed as the following:
a person can mentally create or draw with pen and paper boundary curves a certain distance less than a specified threshold from an original curve to create an area around the original curve,
a person can mentally create or draw with pen and paper an arc that is tangent to the original curve by passing the tangent arc through the starting point of the original curve and increasing or decreasing the radius of the tangent arc to fit the original curve as a fitted arc inside the area of the boundary curves,
a person can mentally create or draw with pen and paper an arc that is tangent to the original curve by passing the tangent arc through the starting point of the original curve and increasing or decreasing the radius of the tangent arc to fit the original curve as a fitted arc for one portion of the original curve and for the next portion of the curve the starting point will be the ending point of the previous fitted arc,
a person can mentally create or draw with pen and paper an arc that is tangent to the original curve by passing the tangent arc through the starting point of the original curve and increasing the radius of the tangent arc to fit the original curve,
a person can mentally select or draw with pen and paper the point on the tangent arc after increasing the radius that is closest to the maximum tolerance in the defined area as the tangent point,
a person can mentally determine or draw with pen and paper the half way point of first tangent arc between the tangent point and the endpoint on the tangent arc,
a person can mentally create or draw with pen and paper another arc that is tangent to the first tangent arc by passing the second tangent arc through the half way point of first tangent arc to blend the change between the 2 arcs and increasing the radius of the second tangent arc to fit the original curve,
a person can mentally select or draw with pen and paper the point on the second tangent arc that will terminate the first tangent arc for the respective portion for the original curve, and
a person can mentally define or draw with pen and paper the arc represented by the starting point and ending point on the first tangent arc as the fitted arc.
a person can mentally create or draw with pen and paper these fitted arcs for all portions across the entire length of the original and combine together each fitted arc potion to create a fitted curve to the original curve for the entire curve length, and
a person can mentally create or draw with pen and paper an arc that is tangent to the original curve by passing the tangent arc through the starting point of the original curve and increasing the radius of the tangent arc to fit the original curve as a fitted arc and continuing for every portion of the curve until the last point of a tangent curve is within a certain threshold of the last point on the original curve.
Furthermore, the specification describes that a person can perform these steps (see Pg. 1 Ln. 11-12, “In related technical fields, technicians usually manually fit first-order continuous curves”).
If a claim limitation, under its broadest reasonable interpretation, covers performance of the limitation in the mind or with pen and paper but for the recitation of generic computer components, then it falls within the “Mental Processes” grouping of abstract ideas. Accordingly, the claim recites an abstract idea under Prong I step 2A.
Furthermore, regarding claim 1: The limitations of “performing at least one sub-fitting operation on the original curve in the fitting area until the end condition of the curve fitting is satisfied”, and “generating a fitting curve corresponding to the original curve by splicing, and according to a generation order, fitting arcs corresponding to the i-th sub-fitting operation”, as drafted, is an operation that, but for the recitation of generic computing components, under its broadest reasonable interpretation, covers performance of the limitation of mathematical evaluations. For example, calculating fitted arc to be fitted to a portion of an original curve can be accomplished using simple geometry and mathematically combining the end point of a tangent arc of first portion of the original curve with the starting point of a tangent arc of another portion of the original curve until the entire length of the original curve has been fitted to create a continuous fitted curve and is within a certain threshold (see Pg. 1 Ln. 8-11, “In the CNC machining process, it is usually necessary to fit the first-order continuous curve with arcs and straight lines to facilitate processing; however, as the first-order continuous curve in engineering usually needs to be composed of multiple splines, it is relatively complex, difficult to express and fit with mathematical formulas”, e.g., done using mathematical formulas, and splicing curves also known as spline curves is a known mathematical concept that combines portions of curves together using vertices locations and mathematical blending techniques which can be found in the NPL document1.)
If a claim limitation, under its broadest reasonable interpretation, covers performance of the limitation of mathematic operation but for the recitation of generic computer components, then it falls within the “Mathematical Operation” grouping of abstract ideas. Accordingly, the claim recites an abstract idea under Prong I step 2A.
Therefore, yes, claim 1 recites judicial exceptions. The claim has been identified to recite judicial exceptions, Step 2A Prong 2 will evaluate whether the claim is directed to the judicial exception.
1DeRose, Anthony David. Geometric continuity: a parametrization independent measure of continuity for computer aided geometric design (curves, surfaces, splines). University of California, Berkeley, 1985.
Step 2A Prong 2:
Claim 1: The judicial exception is not integrated into a practical application. In particular, the claim recite the following additional elements: “A computer-implemented curve fitting method based on a drawing tool for CNC machining” and “by using a computer processor” which is merely a recitation of generic computing components and functions being used as a tool to implement the judicial exception (see MPEP § 2106.05(f)) with the broadest reasonable interpretation, which does not integrate a judicial exception into elements.
Therefore, “Do the claims recite additional elements that integrate the judicial exception into a practical application?” No, these additional elements do not integrate the abstract idea into a practical application and they do not impose any meaningful limits on practicing the abstract idea. The claim is directed to an abstract idea.
After having evaluated the inquires set forth in Steps 2A Prong 1 and 2, it has been concluded that claim 1 not only recites a judicial exception but that the claim is directed to the judicial exception as the judicial exception has not been integrated into practical application.
Step 2B:
Claim 1: The claim does not include additional elements, alone or in combination, that are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional elements amount to no more than generic computing components which do not amount to significantly more than the abstract idea.
Therefore, “Do the claims recite additional elements that amount to significantly more than the judicial exception?” No, these additional elements, alone or in combination, do not amount to significantly more than the judicial exception. Having concluded the analysis within the provided framework, claim 1 does not recite patent eligible subject matter under 35 U.S.C. § 101.
Regarding claim 6, it recites an additional limitation of “wherein, the determining the fitting area based on the original curve includes: generating two boundary lines whose distance from the original curve is less than a corresponding distance threshold on both sides of the original curve; determining an area surrounded by the two boundary lines as the fitting area”, as drafted, is a process that, but for the recitation of generic computing components, under its broadest reasonable interpretation, covers performance of the limitation in the mind or with pen and paper. For example, a person can mentally create or draw with pen and paper boundary curves a certain distance less than a specified threshold from an original curve to create an area around the original curve.
If a claim limitation, under its broadest reasonable interpretation, covers performance of the limitation in the mind or with pen and paper but for the recitation of generic computer components, then it falls within the “Mental Processes” grouping of abstract ideas. Accordingly, the claim recites an abstract idea under Prong I step 2A.
Regarding claim 8, it recites an additional limitation of “wherein, the at least one sub-fitting operation comprising at least two sub-fitting operations, based on the fitting arc corresponding to each sub-fitting operation in the at least one sub-fitting operation, generating the fitting curve corresponding to the original curve, includes: according to the generation order of the fitting arcs corresponding to the sub-fitting operations, splicing the fitting arcs corresponding to the sub-fitting operations to obtain the fitting curve corresponding to the original curve”, as drafted, is a process that, but for the recitation of generic computing components, under its broadest reasonable interpretation, covers performance of the limitation in the mind or with pen and paper. For example, a person can mentally create or draw with pen and paper these fitted arcs for all portions across the entire length of the original and combine together each fitted arc potion to create a fitted curve to the original curve for the entire curve length (the specification describes that a person can perform these steps (see Pg. 1 Ln. 11-12, “In related technical fields, technicians usually manually fit first-order continuous curves”).
If a claim limitation, under its broadest reasonable interpretation, covers performance of the limitation in the mind or with pen and paper but for the recitation of generic computer components, then it falls within the “Mental Processes” grouping of abstract ideas. Accordingly, the claim recites an abstract idea under Prong I step 2A.
Furthermore, regarding claim 8, it recites an additional limitation of “wherein, the at least one sub-fitting operation comprising at least two sub-fitting operations, based on the fitting arc corresponding to each sub-fitting operation in the at least one sub-fitting operation, generating a fitting curve corresponding to the original curve, includes: according to the generation order of the fitting arcs corresponding to the sub-fitting operations, splicing the fitting arcs corresponding to the sub-fitting operations to obtain the fitting curve corresponding to the original curve”, as drafted, is an operation that, but for the recitation of generic computing components, under its broadest reasonable interpretation, covers performance of the limitation of mathematical evaluations. For example, calculating fitted arc to be fitted to a portion of an original curve can be accomplished using simple geometry and mathematically combining the end point of a tangent arc of first portion of the original curve with the starting point of a tangent arc of another portion of the original curve until the entire length of the original curve has been fitted to create a continuous fitted curve and is within a certain threshold (see Pg. 1 Ln. 8-11, “In the CNC machining process, it is usually necessary to fit the first-order continuous curve with arcs and straight lines to facilitate processing; however, as the first-order continuous curve in engineering usually needs to be composed of multiple splines, it is relatively complex, difficult to express and fit with mathematical formulas”, e.g. can and is done using mathematical formulas, and splicing curves also known as spline curves is a known mathematical concept that combines portions of curves together using vertices locations and mathematical blending techniques which can be found in the NPL document1 as referenced above.)
If a claim limitation, under its broadest reasonable interpretation, covers performance of the limitation of mathematic operation but for the recitation of generic computer components, then it falls within the “Mathematical Operation” grouping of abstract ideas. Accordingly, the claim recites an abstract idea under Prong I step 2A.
Regarding claims 10, 15, and 17, they recite additional element recitations of “A computer device, comprising a memory, a processor, and a computer program stored on the memory and running on the processor, characterized in that the processor implements the method when the program is executed” which is a recitation of generic computing components and functions being used as a tool to implement the judicial exception (see MPEP § 2106.05(f)) Further, these claims do not recite any further additional elements and for the same reasons as above with regard to integration into practical application and whether additional elements amount to significantly more, these claims also fail both Step 2A prong 2, thus the claims are directed to the judicial exception as they have not been integrated into practical application, and fail Step 2B as not amounting to significantly more. Therefore, claims 10, 15, and 17 do not recite patent eligible subject matter under 35 U.S.C. § 101.
Therefore, having concluded the analysis within the provided framework, claims 1, 6, 8, 10, 15, and 17 do not recite patent eligible subject matter and are rejected under 35 U.S.C. § 101 because the claimed invention is directed to judicial exception, an abstract idea, that has not been integrated into a practical application. The claims further do not recite significantly more than the judicial exception. Claims 6, 8, 10, 15, and 17 are also rejected for incorporating the deficiency of their dependent claim 1.
Claim Rejections - 35 U.S.C. § 102
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 the appropriate paragraphs of 35 U.S.C. § 102 that form the basis for the rejections under this section made in this Office action:
A person shall be entitled to a patent unless –
(a)(1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention.
Claims 1, 6, 8, 10, 15, and 17 are rejected under 35 U.S.C. § 102(a)(1) as being anticipated by Yang, Xunnian. “Efficient circular arc interpolation based on active tolerance control.” Computer-Aided Design 34, no. 13 (2002): 1037-1046.
As per claim 1, Yang teaches “A computer-implemented curve fitting method based on a drawing tool for CNC machining”. (Pg. 1037 Abstract, “In this paper, we present an efficient sub-optimal algorithm for fitting smooth planar parametric curves by G1 arc splines” [a curve fitting method]. “The offset of an arc spline is another arc spline, and it often used as the description of tool path of CNC machinery” [based on a drawing tool for CNC machining]. Pg. 1037 Sect. 1, “computing smooth circular arc splines interpolating parametric curves with as few as possible segments has great significance for wide applications such as geometric modeling, CAD/CAM and robot path planning” [A computer-implemented curve fitting method based on a drawing tool for CNC machining]. Further see Sect. 1 and the Abstract. The examiner has interpreted that having algorithm for fitting curves by arc splines for CAD model used for the tool path of CNC machinery as a computer-implemented curve fitting method based on a drawing tool for CNC machining.)
Yang teaches “by using a computer processor, generating two boundary lines on both sides of an original curve, and determining an area surrounded by the two boundary lines as a fitting area, wherein a distance of each of the two boundary lines from the original curve is less than respective distance thresholds”. (Pg, 1037 Abstract, “By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end.” Pg. 1037 Sect. 1, “we compute the optimal interpolation biarc curve within the prescribed tolerance” [obtaining fitted curve within tolerance, e.g., determining an area a distance less than respective distance thresholds]. Pg. 1042 Sect. 4, “The active tolerance ϵi+1 at point Pn satisfies the inequality 0 ≤ ϵi+1 ≤ τ. If point Pn lies at the convex side of arc Ob, then we have ϵi+1 ≤ τ. Any point that lies at the convex side of arc Ob and is within ϵi+1 distance to the arc is also within the permitted tolerance to the original curve (see Fig. 6). If point Pn lies at the concave side of original curve, then the whole segment of arc Ob lies at the concave side of original curve. At this time, we have ϵi+1 = τ , an outer offset arc segment which is τ distance away to arc Ob is also within the permitted tolerance region of original curve. For these reasons the expansion magnitude can be well controlled by the active tolerances during the successive approximation steps” [e.g., generating two boundary lines on both sides of an original curve, and determining an area surrounded by the two boundary lines as a fitting area, wherein a distance of each of the two boundary lines from the original curve is less than respective distance thresholds]. Pg. 1043 Sect. 5, “The algorithm is implemented on a SGI octane workstation with MIPS RlO000 and 128 MB memory. We have applied our algorithm on a number of parametric curves and obtain satisfying approximating results. For all the examples we have experimented, we obtain interpolation arc splines in real time” [by using a computer processor]. Further see the Abstract and Sect. 1 and 4-5. The examiner has interpreted that computing a fitting arc spline by interpolating local biarc curves within tolerances on both the concave and convex side of the original curve in real time on a SGI octane workstation with MIPS R10000 as by using a computer processor, generating two boundary lines on both sides of an original curve, and determining an area surrounded by the two boundary lines as a fitting area, wherein a distance of each of the two boundary lines from the original curve is less than respective distance thresholds.)
Yang teaches “by using a computer processor, performing at least one sub-fitting operation on the original curve in the fitting area until an end condition of curve fitting is satisfied”. (Pg. 1038 Sect. 1, “the purpose of this paper is to interpolate an original parametric curve with low number of circular arcs. In fact, when we interpolate a part of the curve with an optimal biarc curve, the second segment of the biarc associated with some successive arcs can always be approximated by another new biarc curve within the tolerance. Then, we just choose the first segment of the optimal fitting biarc curve as the interpolation circular arc to the original parametric curve, except at the end of the curve where we choose both of the two segments” [fitting to the original curve with tolerance using segments successive of biarcs, e.g. performing at least one sub-fitting operation on the original curve in the fitting area until the end condition of the curve fitting is satisfied]. Pg. 1043 Sect. 5, “The algorithm is implemented on a SGI octane workstation with MIPS RlO000 and 128 MB memory. We have applied our algorithm on a number of parametric curves and obtain satisfying approximating results. For all the examples we have experimented, we obtain interpolation arc splines in real time” [by using a computer processor]. Further see the Abstract and Sect. 1 and 3. The examiner has interpreted that interpolating the original parametric curve by forming biarc curves with tolerance of successive biarcs to determine optimal fitting biarcs that interpolate two end points and end tangents in real time on a SGI octane workstation with MIPS R10000 as by using a computer processor, performing at least one sub-fitting operation on the original curve in the fitting area until an end condition of curve fitting is satisfied.)
Yang teaches “wherein for an i-th sub-fitting operation of the at least one sub-fitting operation, when i is equal to 1, an arc starting point is a starting point of the original curve, and when i is greater than 1, the arc starting point is an end point of a fitting arc corresponding to an i-1 th sub-fitting operation”. (Pg. 1039 Sect. 3, “A biarc curve consists of two smoothly connected arc segments that interpolate two end points and the end tangents” [wherein for an i-th sub-fitting operation of the at least one sub-fitting operation, when i is equal to 1, an arc starting point is a starting point of the original curve, and when i is greater than 1, the arc starting point is an end point of a fitting arc corresponding to an i-1 th sub-fitting operation]. Pg. 1037 Abstract, “the fitting arc spline has the same end points and end tangents with the original curve” [an arc starting point is a starting point of the original curve]. Further Pg. 1040 Sect. 4, “there are a family of biarc curves interpolating the same end points and end tangents of the spiral” [wherein for an i-th sub-fitting operation of the at least one sub-fitting operation, when i is equal to 1, an arc starting point is a starting point of the original curve, and when i is greater than 1, the arc starting point is an end point of a fitting arc corresponding to an i-1 th sub-fitting operation] and Pg. 1038 Sect. 1, “we just choose the first segment of the optimal fitting biarc curve as the interpolation circular arc to the original parametric curve, except at the end of the curve where we choose both of the two segments”. Further see Sect. 1 and 3-4. The examiner has interpreted that interpolating both end points using a biarc curve that is smoothly connected arc segments to generate the fitting arc which has the same end points as the original curve as wherein for an i-th sub-fitting operation of the at least one sub-fitting operation, when i is equal to 1, an arc starting point is a starting point of the original curve, and when i is greater than 1, the arc starting point is an end point of a fitting arc corresponding to an i-1 th sub-fitting operation.)
Yang teaches “wherein the i-th sub-fitting operation comprises generating a first tangent arc in the fitting area that is tangent to the original curve and passes through the arc starting point, the first tangent arc being an arc with a largest radius among arcs that have passed through the arc starting point and being tangent to the original curve, determining, on the first tangent arc, a first tangent point that is closest to a regional boundary line of the fitting area”. (Pg. 1039 Sect. 3, “A biarc curve consists of two smoothly connected arc segments that interpolate two end points and the end tangents” [wherein the i-th sub-fitting operation comprises generating a first tangent arc in the fitting area that is tangent to the original curve and passes through the arc starting point]. Pg. 1039-1040 Sect. 3, “For each step, we first sample a new point with a fixed step and check the distance from the interpolation biarc curve to the parametric curve. If the maximum distance is within the prescribed accuracy, we accept the interpolation biarc curve” [the first tangent arc being an arc with a largest radius among arcs that have passed through the arc starting point and being tangent to the original curve and determining, on the first tangent arc, a first tangent point that is closest to a regional boundary line of the fitting area]. Further see Sect. 3. The examiner has interpreted that constructing a biarc curve containing arc segment of an end point and tangent that has a sampled point whose maximum distance to the parametric curve is within the prescribed accuracy as wherein the i-th sub-fitting operation comprises generating a first tangent arc in the fitting area that is tangent to the original curve and passes through the arc starting point, the first tangent arc being an arc with a largest radius among arcs that have passed through the arc starting point and being tangent to the original curve, determining, on the first tangent arc, a first tangent point that is closest to a regional boundary line of the fitting area.)
Yang teaches “selecting, on the first tangent arc, a test end point between the first tangent point and an end point of the first tangent arc, and generating a second tangent arc in the fitting area based on the test end point, the second tangent arc being an arc with a largest radius among arcs that are tangent to the first tangent arc at the test end point”. (Pg. 1039 Sect. 3, “A biarc curve consists of two smoothly connected arc segments that interpolate two end points and the end tangents” [biarc is two arcs, e.g., generating a second tangent arc in the fitting area based on the test end point]. Pg. 1039 Sect. 3, “We can assume that O1 and O2 be the centers of two arc segments with radii r1 and r2 , respectively. Let PC be the joint point of the two arcs and U is the unit tangent vector at the joint point” [having different radii and connecting the arc segments at a joint point, e.g., based on the test end point and at the test end point, and selecting, on the first tangent arc, a test end point between the first tangent point and an end point of the first tangent arc,]. Further Fig. 1 shows the construction of a biarc curve where PA is the starting point and PC is the point at which the 2 arc segments are joined being after point PA on the first segment and would be before the ending of the arc. Pg. 1039-1040 Sect. 3, “For each step, we first sample a new point with a fixed step and check the distance from the interpolation biarc curve to the parametric curve. If the maximum distance is within the prescribed accuracy, we accept the interpolation biarc curve” [the second tangent arc being an arc with a largest radius among arcs that are tangent to the first tangent arc at the test end point]. Further see Sect. 3. Further see Sect. 3. The examiner has interpreted that constructing a biarc curve containing arc segment contain 2 smoothly connected arc segments having different arc radii that are connected through a joint point and tangent where a sampled point whose maximum distance to the parametric curve is within the prescribed accuracy as selecting, on the first tangent arc, a test end point between the first tangent point and an end point of the first tangent arc, and generating a second tangent arc in the fitting area based on the test end point, the second tangent arc being an arc with a largest radius among arcs that are tangent to the first tangent arc at the test end point.)
Yang teaches “determining an arc end point corresponding to the i-th sub-fitting operation on the second tangent arc, and determining, as a fitting arc corresponding to the i-th sub-fitting operation, a curve between the arc starting point and the arc end point on the first tangent arc”. (Pg. 1039 Sect. 3, “A biarc curve consists of two smoothly connected arc segments that interpolate two end points and the end tangents”. Pg. 1039 Sect. 3, “We can assume that O1 and O2 be the centers of two arc segments with radii r1 and r2 , respectively. Let PC be the joint point of the two arcs and U is the unit tangent vector at the joint point” [having different radii and connecting the arc segments at a joint point, e.g., determining an arc end point corresponding to the i-th sub-fitting operation on the second tangent arc]. Pg. 1039 Sect. 3, “When we construct a biarc curve interpolating a pair of sampled points and tangents on a parametric curve, we can estimate the fitting” [determining, as a fitting arc corresponding to the i-th sub-fitting operation]. Pg. 1040 Sect. 4, “we obtain the optimal biarc curve by expanding the first segment and shrinking the last segment of the corresponding arc span within the given tolerance… we leave the first segment of the biarc as an interpolation circular arc to the parametric curve” [effectively moving the joint point for creating of the fitting arc, e.g. determining, as a fitting arc corresponding to the i-th sub-fitting operation, a curve between the arc starting point and the arc end point on the first tangent arc]. Further see Sect. 3 and 4. The examiner has interpreted that connecting the arc segments having different arc radii that are connected through a joint point from one end point that is used to interpolate the sampled points and tangents by expanding and leaving the first segment as the interpolation circular arc to the curve as determining an arc end point corresponding to the i-th sub-fitting operation on the second tangent arc, and determining, as a fitting arc corresponding to the i-th sub-fitting operation, a curve between the arc starting point and the arc end point on the first tangent arc.)
Yang teaches “by using a computer processor, generating a fitting curve corresponding to the original curve by splicing, and according to a generation order, fitting arcs corresponding to the i-th sub-fitting operation”. (Pg. 1039 Sect. 3, “A biarc curve consists of two smoothly connected arc segments that interpolate two end points and the end tangents”. Pg. 1037 Abstract, “the fitting arc spline has the same end points and end tangents with the original curve”. Further see Pg. 1040, Sect. 4, “we leave the first segment of the biarc as an interpolation circular arc to the parametric curve and check a new triarc spiral that is consisted of the second segment of the biarc curve associated with another two successive arcs from the original fitting arc spline. If there exist inflection points in the triarc span or the triarc span is not a spiral, we leave the first segment as one interpolation arc, and check another triarc span with a new arc segment added. One advantage of the method is that it can keep the shape of the final interpolation arc spline compatible with the original curve well”. Pg. 1040 Sect. 4, “there are a family of biarc curves interpolating the same end points and end tangents of the spiral” and Pg. 1038 Sect. 1, “we just choose the first segment of the optimal fitting biarc curve as the interpolation circular arc to the original parametric curve, except at the end of the curve where we choose both of the two segments”. [generating a fitting curve corresponding to the original curve by splicing, and according to a generation order, fitting arcs corresponding to the i-th sub-fitting operation]. Pg. 1043 Sect. 5, “The algorithm is implemented on a SGI octane workstation with MIPS RlO000 and 128 MB memory. We have applied our algorithm on a number of parametric curves and obtain satisfying approximating results. For all the examples we have experimented, we obtain interpolation arc splines in real time” [by using a computer processor]. Further see Sect. 1 and 3-5. The examiner has interpreted that interpolating both end points using a biarc curve that is smoothly connected arc segments to generate the fitting arc which has the same end points as the original curve and choosing segments until the end of the curve as the optimal fitting biarc curve in real time on a SGI octane workstation with MIPS R10000 as by using a computer processor, generating a fitting curve corresponding to the original curve by splicing, and according to a generation order, fitting arcs corresponding to the i-th sub-fitting operation.)
As per claim 6, Yang teaches “wherein, the determining the fitting area based on the original curve includes: generating two boundary lines whose distance from the original curve is less than a corresponding distance threshold on both sides of the original curve; determining an area surrounded by the two boundary lines as the fitting area.” (Pg, 1037 Abstract, “By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end.” Pg. 1037 Sect. 1, “we compute the optimal interpolation biarc curve within the prescribed tolerance” [obtaining fitted curve within tolerance, e.g., the determining the fitting area based on the original curve]. Pg. 1042 Sect. 4, “The active tolerance ϵi+1 at point Pn satisfies the inequality 0 ≤ ϵi+1 ≤ τ. If point Pn lies at the convex side of arc Ob, then we have ϵi+1 ≤ τ. Any point that lies at the convex side of arc Ob and is within ϵi+1 distance to the arc is also within the permitted tolerance to the original curve (see Fig. 6). If point Pn lies at the concave side of original curve, then the whole segment of arc Ob lies at the concave side of original curve. At this time, we have ϵi+1 = τ , an outer offset arc segment which is τ distance away to arc Ob is also within the permitted tolerance region of original curve. For these reasons the expansion magnitude can be well controlled by the active tolerances during the successive approximation steps” [e.g., generating two boundary lines whose distance from the original curve is less than a corresponding distance threshold on both sides of the original curve; determining an area surrounded by the two boundary lines as the fitting area]. Further see Sect. 1. The examiner has interpreted that computing a fitting arc spline by interpolating local biarc curves within tolerances on both the concave and convex side of the original curve as wherein, the determining the fitting area based on the original curve includes: generating two boundary lines whose distance from the original curve is less than a corresponding distance threshold on both sides of the original curve; determining an area surrounded by the two boundary lines as the fitting area.)
As per claim 8, Yang teaches “wherein, the at least one sub-fitting operation comprising at least two sub-fitting operations, based on the fitting arc corresponding to each sub-fitting operation in the at least one sub-fitting operation, generating the fitting curve corresponding to the original curve, includes: according to a generation order of the fitting arcs corresponding to the sub-fitting operations, splicing the fitting arcs corresponding to the sub-fitting operations to obtain the fitting curve corresponding to the original curve.” (Pg. 1039 Sect. 3, “A biarc curve consists of two smoothly connected arc segments that interpolate two end points and the end tangents” [wherein: the at least one sub-fitting operation includes at least two sub-fitting operations]. Pg. 1037 Abstract, “the fitting arc spline has the same end points and end tangents with the original curve”. Pg. 1040 Sect. 4, “there are a family of biarc curves interpolating the same end points and end tangents of the spiral” and Pg. 1038 Sect. 1, “we just choose the first segment of the optimal fitting biarc curve as the interpolation circular arc to the original parametric curve, except at the end of the curve where we choose both of the two segments” [based on the fitting arc corresponding to each sub-fitting operation in the at least one sub-fitting operation, generating the fitting curve corresponding to the original curve, includes: according to a generation order of the fitting arcs corresponding to the sub-fitting operations, splicing the fitting arcs corresponding to the sub-fitting operations to obtain the fitting curve corresponding to the original curve]. Further see Sect. 1 and 3-4. The examiner has interpreted that interpolating both end points using a biarc curve that is smoothly connected arc segments to generate the fitting arc which has the same end points as the original curve and choosing segments until the end of the curve as the optimal fitting biarc curve as wherein, the at least one sub-fitting operation comprising at least two sub-fitting operations, based on the fitting arc corresponding to each sub-fitting operation in the at least one sub-fitting operation, generating the fitting curve corresponding to the original curve, includes: according to a generation order of the fitting arcs corresponding to the sub-fitting operations, splicing the fitting arcs corresponding to the sub-fitting operations to obtain the fitting curve corresponding to the original curve.)
Re Claim 10, it is a system claim, having similar limitations of claim 1. Thus, claim 10 is also rejected under the similar rationale as cited in the rejection of claim 1.
Furthermore, regarding claim 10, Yang teaches “A computer device, comprising a memory, a processor, and a computer program stored on the memory and running on the processor, characterized in that the processor implements the steps of the method according to claim 1 when the program is executed.” (Pg. 1043 Sect. 5, “The algorithm is implemented on a SGI octane workstation with MIPS RlO000 and 128 MB memory. We have applied our algorithm on a number of parametric curves and obtain satisfying approximating results. For all the examples we have experimented, we obtain interpolation arc splines in real time” [A computer device, comprising a memory, a processor, and a computer program stored on the memory and running on the processor, characterized in that the processor implements the steps of the method according to claim 1 when the program is executed]. Further see Sect. 5. The examiner has interpreted that implementing the algorithm on a number of parametric curves to obtain interpolation arc splines in real time on a SGI octane workstation with MIPS RlO000 and 128 MB memory as a computer device, comprising a memory, a processor, and a computer program stored on the memory and running on the processor, characterized in that the processor implements the steps of the method according to claim 1 when the program is executed.)
Re Claim 15, it is a system claim, having similar limitations of claims 6 and 10. Thus, claim 15 is also rejected under the similar rationale as cited in the rejection of claim 6 and 10.
Re Claim 17, it is a system claim, having similar limitations of claims 8 and 10. Thus, claim 17 is also rejected under the similar rationale as cited in the rejection of claim 8 and 10.
Response to Arguments
Applicant's arguments filed on February 25, 2026 have been fully considered but they are not persuasive.
Applicant argues that amended claim 1 features are patent eligible under 35 U.S.C. § 101 because the claims do not recite mental processes as they are not performed through manual analysis and require the use of a computer. (See Applicant’s response, Pg. 11-12).
MPEP § 2106.04(a)(2)(III)(A) recites “claims do recite a mental process when they contain limitations that can practically be performed in the human mind, including for example, observations, evaluations, judgments, and opinions”, “claims can recite a mental process even if they are claimed as being performed on a computer”, and “in evaluating whether a claim that requires a computer recites a mental process, examiners should carefully consider the broadest reasonable interpretation of the claim in light of the specification. For instance, examiners should review the specification to determine if the claimed invention is described as a concept that is performed in the human mind and applicant is merely claiming that concept performed 1) on a generic computer, or 2) in a computer environment, or 3) is merely using a computer as a tool to perform the concept. In these situations, the claim is considered to recite a mental process” (emphasis added).
The examiner has provided the rational for the claim limitations that are being directed to a mental process in the rejection above. The claims are directed to identifying a boundary area containing a curve and points on curves, drawing tangents lines to create arc segments, and combining the arc segments to curve fit the original curve, e.g. curve fitting, which is a mental process, since all of these steps can be done using pen and paper. Furthermore, the specification describes that a person, i.e., a technician, can perform these steps for curve fitting (see Pg. 1 Ln. 11-12, “In related technical fields, technicians usually manually fit first-order continuous curves”).
The examiner has properly identified that the claim recites a mental concept as provided in the rejection above is proper under the framework provided in the 2019 Patent Eligibility Guidance and MPEP § 2106.04(a)(2)(III)(C). The claim is directed to judicial exception, an abstract idea.
Applicant argues that the amended claims are patent eligible under 35 U.S.C. § 101 because the claims do not recite mathematical relations, formulas, or calculations (See Applicant’s response, Pg. 11-12).
MPEP 2106.04(a)(2)(I)(C) recites that a “claim that recites a mathematical calculation, when the claim is given its broadest reasonable interpretation in light of the specification, will be considered as falling within the ‘mathematical concepts’ grouping. A mathematical calculation is a mathematical operation (such as multiplication) or an act of calculating using mathematical methods to determine a variable or number” (emphasis added).
The examiner has provided the rational for the claim limitations that are being directed to a mathematical concept in the rejection above. For example, the claim 1 limitations of “performing at least one sub-fitting operation on the original curve in the fitting area until the end condition of the curve fitting is satisfied”, and “generating a fitting curve corresponding to the original curve by splicing, and according to a generation order, fitting arcs corresponding to the i-th sub-fitting operation” involves calculating fitted arc to be fitted to a portion of an original curve simple geometry and mathematically combining the end point of a tangent arc of first portion of the original curve with the starting point of a tangent arc of another portion of the original curve until the entire length of the original curve has been fitted to create a continuous fitted curve and is within a certain threshold. This is accomplish using known mathematical concept that combines portions of curves together using vertices locations and mathematical blending techniques. The specification also describes the curve fitting process as math (see Pg. 1 Ln. 8-11, “In the CNC machining process, it is usually necessary to fit the first-order continuous curve with arcs and straight lines to facilitate processing; however, as the first-order continuous curve in engineering usually needs to be composed of multiple splines, it is relatively complex, difficult to express and fit with mathematical formulas”, e.g., done using mathematical formulas, and splicing curves also known as spline curves is a known mathematical concept, e.g., combining curves together).
As such, this limitation would fall under a mathematical concept in step 2A Prong 1 of analysis above. The examiner has properly identified that the claim recites a mathematical concept as provided in the rejection above under the framework provided in the 2019 Patent Eligibility Guidance and MPEP 2106.04(a)(2)(I)(C). The claim is directed to judicial exception, an abstract idea.
Applicant argues that the amended claim 1 features are patent eligible under 35 U.S.C. § 101 because the claim is integrated into a practical application as claim features recite improvement to the functioning of the computer itself and provide other meaningful limitations beyond generally linking the use of the judicial exception to a particular technological environment (See Applicant’s response, Pg. 12-14).
MPEP § 2106.05(I) recites “An inventive concept "cannot be furnished by the unpatentable law of nature (or natural phenomenon or abstract idea) itself." Genetic Techs. Ltd. v. Merial LLC, 818 F.3d 1369, 1376, 118 USPQ2d 1541, 1546 (Fed. Cir. 2016).” 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")”; MPEP § 2106.05(a) recites “It is important to note, the judicial exception alone cannot provide the improvement. The improvement can be provided by one or more additional elements.”; MPEP § 2106.04(d)(II) recites “examiners evaluate integration into a practical application by: (1) identifying whether there are any additional elements recited in the claim beyond the judicial exception(s); and (2) evaluating those additional elements individually and in combination to determine whether they integrate the exception into a practical application”; MPEP § 2106.04(a)(2)(III)(A) recites “claims can recite a mental process even if they are claimed as being performed on a computer”, and “in evaluating whether a claim that requires a computer recites a mental process, examiners should carefully consider the broadest reasonable interpretation of the claim in light of the specification. For instance, examiners should review the specification to determine if the claimed invention is described as a concept that is performed in the human mind and applicant is merely claiming that concept performed 1) on a generic computer, or 2) in a computer environment, or 3) is merely using a computer as a tool to perform the concept. In these situations, the claim is considered to recite a mental process.”; and MPEP § 2106.05(a) also recites “Examples that the courts have indicated may not be sufficient to show an improvement in computer-functionality: Mere automation of manual processes, such as using a generic computer to process an application for financing a purchase, Credit Acceptance Corp. v. Westlake Services, 859 F.3d 1044, 1055, 123 USPQ2d 1100, 1108-09 (Fed. Cir. 2017) or speeding up a loan-application process by enabling borrowers to avoid physically going to or calling each lender and filling out a loan application, LendingTree, LLC v. Zillow, Inc., 656 Fed. App'x 991, 996-97 (Fed. Cir. 2016) (non-precedential)” (emphasis added).
The examiner has provided the rational for the independent claim limitations that are being directed to a mental process and mathematical concepts in the rejection above. The additional elements are recitations of “A computer-implemented curve fitting method based on a drawing tool for CNC machining” and “by using a computer processor” which are merely using the generic computer components and functions being used as a tool to perform the abstract idea. Furthermore, the applicant is merely claiming that the mental process be performed on a computer and arguing that the process is performed automatically, neither of which are an improvement to computer-functionality. Therefore, there are no additional element limitations in the independent claims which can integrate the abstract idea into a practical application by improvement to the functioning of the computer itself and provide other meaningful limitations beyond generally linking the use of the judicial exception to a particular technological environment as listed in MPEP § 2106.04(d)(I). Furthermore, the examiner has also provided the rational for the dependent claim limitations that are being directed to a mental process or a mathematical concept in the rejection above. With the exception of the additional element limitations in the dependent claims which are merely using the generic computer components and functions being used as a tool to perform the abstract idea, there are no additional limitations in the dependent claims which can integrate the abstract idea into a practical application by improvements to the technology or through the use of meaningful limitations.
Therefore, the examiner has properly identified that the claims recite mental processes, mathematical concepts, and limitations that merely use the computer as a tool to perform the abstract idea.
Applicant argues that reference does not teach each and every limitation in the amend claim 1 because cited reference fails to teach “generating two boundary lines on both sides of an original curve, and determining an area surrounded by the two boundary lines as a fitting area” (See Applicant’s response, Pg. 15).
MPEP § 2143.03 recites “All words in a claim must be considered in judging the patentability of that claim against the prior art” and “Examiners must consider all claim limitations when determining patentability of an invention over the prior art.”
As mapped in the rejection above in claim 1, Yang discloses “generating two boundary lines on both sides of an original curve, and determining an area surrounded by the two boundary lines as a fitting area, wherein a distance of each of the two boundary lines from the original curve is less than respective distance thresholds” as computing a fitting arc spline by interpolating local biarc curves within tolerances on both the concave and convex side of the original curve. Yang bounds the original curve by computing biarc curves that are placed both concave and convex sides of the original curve within a selected tolerance. The claim does not require different thresholds as the applicant argues. Thus, the claimed limitation is taught.
Therefore, all of the limitations of the amended claims 1 are disclosed in Yang. Therefore, applicant’s arguments are not persuasive and the rejection of claim 1 as anticipated by Yang is maintained.
Applicant argues that reference does not teach each and every limitation in the amend claim 1 because cited reference fails to teach “generating a first tangent arc in the fitting area that is tangent to the original curve and passes through the arc starting point, the first tangent are being an arc with a largest radius among arcs that have passed through the arc starting point and being tangent to the original curve, determining, on the first tangent arc, a first tangent point that is closest to a regional boundary line of the fitting area” (See Applicant’s response, Pg. 15-16).
MPEP § 2143.03 recites “All words in a claim must be considered in judging the patentability of that claim against the prior art” and “Examiners must consider all claim limitations when determining patentability of an invention over the prior art.”
As mapped in the rejection above in claim 1, Yang discloses “generating a first tangent arc in the fitting area that is tangent to the original curve and passes through the arc starting point, the first tangent arc being an arc with a largest radius among arcs that have passed through the arc starting point and being tangent to the original curve, determining, on the first tangent arc, a first tangent point that is closest to a regional boundary line of the fitting area” as constructing a biarc curve containing arc segment of an end point and tangent that has a sampled point whose maximum distance to the parametric curve is within the prescribed accuracy. After bounding the original curve by biarcs on the concave and convex sides within a selected tolerance, Yang starts by creating an arc segment having an end point of the original curve, that is tangent to the original curve and passes through the arc starting point. This arc segment also has a sampled point that is the largest distance within the prescribed accuracy, e.g., a first tangent point that is closest to a regional boundary line of the fitting area and a largest radius among arcs. Thus, the claimed limitation is taught.
Therefore, all of the limitations of the amended claims 1 are disclosed in Yang. Therefore, applicant’s arguments are not persuasive and the rejection of claim 1 as anticipated by Yang is maintained.
Applicant argues that reference does not teach each and every limitation in the amend claim 1 because cited reference fails to teach “selecting, on the first tangent arc, a test end point between the first tangent point and an end point of the first tangent arc, and generating a second tangent arc in the fitting area based on the test end point, the second tangent arc being an arc with a largest radius among arcs that are tangent to the first tangent arc at the test end point” (See Applicant’s response, Pg. 16-17).
MPEP § 2143.03 recites “All words in a claim must be considered in judging the patentability of that claim against the prior art” and “Examiners must consider all claim limitations when determining patentability of an invention over the prior art.”
As mapped in the rejection above in claim 1, Yang discloses “selecting, on the first tangent arc, a test end point between the first tangent point and an end point of the first tangent arc, and generating a second tangent arc in the fitting area based on the test end point, the second tangent arc being an arc with a largest radius among arcs that are tangent to the first tangent arc at the test end point” as constructing a biarc curve containing arc segment contain 2 smoothly connected arc segments having different arc radii that are connected through a joint point and tangent where a sampled point whose maximum distance to the parametric curve is within the prescribed accuracy. Yang creates a second arc segment similarly to the first arc segment, whose maximum distance to the parametric curve is within the prescribed accuracy, e.g., the second tangent arc being an arc with a largest radius. The second arc segment is connected to the first arc segment at a joint point. In reference to Fig. 1, PC is selected as the joint point of 2 arc segments are joined being after point PA on the first segment being the normal point to the original curve, and prior to point PB. Thus, a test end point between the first tangent point and an end point of the first tangent arc and the second tangent arc is generated based on the test point, and the claimed limitation is taught.
Therefore, all of the limitations of the amended claims 1 are disclosed in Yang. Therefore, applicant’s arguments are not persuasive and the rejection of claim 1 as anticipated by Yang is maintained.
Applicant argues that reference does not teach each and every limitation in the amend claim 1 because cited reference fails to teach “determining, as a fitting arc corresponding to the i-th sub-fitting operation, a curve between the arc starting point and the arc end point on the first tangent arc” (See Applicant’s response, Pg. 17).
MPEP § 2143.03 recites “All words in a claim must be considered in judging the patentability of that claim against the prior art” and “Examiners must consider all claim limitations when determining patentability of an invention over the prior art.”
As mapped in the rejection above in claim 1, Yang discloses “determining, as a fitting arc corresponding to the i-th sub-fitting operation, a curve between the arc starting point and the arc end point on the first tangent arc” as connecting the arc segments having different arc radii that are connected through a joint point from one end point that is used to interpolate the sampled points and tangents by expanding and leaving the first segment as the interpolation circular arc to the curve. After the segments are joined, the first segment is expanded. This moves effectively moves the joint point between the two segments. After which, only the expanded first segment is left, e.g., dropping off the second segment. The expanded first segment is used as the interpolation circular arc to the curve, e.g., the fitting arc between the start point and new end point on the first arc. Thus, the claimed limitation is taught.
Therefore, all of the limitations of the amended claims 1 are disclosed in Yang. Therefore, applicant’s arguments are not persuasive and the rejection of claim 1 as anticipated by Yang is maintained.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
Yang, Xunnian. "Curve fitting and fairing using conic splines." Computer-Aided Design 36, no. 5 (2004): 461-472 teaches of curving fitting conic splines by moving joints of connected curves to smooth curvature extrema at convex and concave inflection points.
Lee, Taik-Min, Eung-ki Lee, and Min-yang Yang. "Precise bi-arc curve fitting algorithm for machining an aspheric surface." The International Journal of Advanced Manufacturing Technology 31, no. 11 (2007): 1191-1197 teaches of minimizing error in the interpolating of CNC cutting tool path by curve fitting by obtaining tangent vectors of a curve.
Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). 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.
Examiner’s Note: The examiner has cited particular columns and line numbers in the reference that applied to the claims above for the convenience of the applicant. Although the specified citations are representative of the art and are applied to specific limitations within the individual claim, other passages and figures may apply as well. It is respectfully requested from the applicant, to fully consider the references in their entirety as potentially teaching all or part of the claimed invention, as well as the context of the passage as taught by the prior art or disclosed by the examiner. In the case of amending the claimed invention, the applicant is respectfully requested to indicate the portion(s) of the specification which dictate(s) the structure relied on for the proper interpretation and also to verify and ascertain the metes and bound of the claimed invention.
Any inquiry concerning this communication or earlier communications from the examiner should be directed to Simeon P Drapeau whose telephone number is (571)-272-1173. The examiner can normally be reached Monday - Friday, 8 a.m. - 5 p.m. ET.
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If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Ryan Pitaro can be reached on (571) 272-4071. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300.
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/SIMEON P DRAPEAU/Examiner, Art Unit 2188
/RYAN F PITARO/Supervisory Patent Examiner, Art Unit 2188
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