DETAILED ACTION
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 May 18th, 2026 has been entered. Claims 1-21 are pending in the application. Applicant’s amendments to the Claims 1, 6-7, 13, and 17 have overcome the rejections of claims 1-20 previously set forth in the Final Office Action mailed February 17th 2026. A further search has been performed to address the material amended in the aforementioned claims. Newly found references Nakagami (US 20230126000 A1), Ubeito (US 8274513 B1) and Graziosi (US 20210174551 A1) were utilized for the amended claims.
Response to Arguments
The Examiner appreciates the Applicant’s thorough review of the previous Advisory Action. Applicant’s arguments with respect to claim 1-21 have been considered but are moot because the new ground of rejection does not rely on any reference applied in the prior rejection of record for any teaching or matter specifically challenged in the argument.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-21 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Regarding claim 1:
Claim 1 recites:
determining, by a computing device and based on a ray, a first point, in a three-dimensional (3D) space, that is within a TriSoup triangle;
determining a second point, in the 3D space, by displacing the first point by a vector that is parallel to the ray; and
determining at least one voxel by voxelizing the first point and the second point.
Step 1: This part of the eligibility analysis evaluates whether the claim falls within any statutory category. MPEP 2106.03.
The claim recites at least one step or act, including determining a voxel. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: This part of the eligibility analysis evaluates whether the claim recites a judicial exception. As explained in MPEP 2106.04(II), a claim “recites” a judicial exception when the judicial exception is “set forth” or “described” in the claim.
Limitation (a) recites “determining, by a computing device and based on a ray, a first point, in a three-dimensional (3D) space, that is within a TriSoup triangle”. Determining a point based on a ray in 3D space that is within a triangle can be practically performed in the human mind. Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited limitation, the use of such physical aid does not negate the mental nature of this limitation. Thus, limitation (a) falls into the “mental process” groupings of abstract ideas.
Limitation (b) recites “determining a second point, in the 3D space, by displacing the first point by a vector that is parallel to the ray”. This limitation amounts to adding the x, y, and z components of a vector to the coordinates of a first point in 3D space. This limitation therefore recites a mathematical calculation. In addition, this type of arithmetic calculation (vector addition) can be practically performed in the human mind. Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited calculation, the use of such physical aid does not negate the mental nature of this limitation. Thus, limitation (b) also falls into the “mental process” groupings of abstract ideas. Accordingly, limitation (b) recites a judicial exception (an abstract idea that falls within the mathematical concept and mental process groupings).
Limitation (c) recites “determining at least one voxel by voxelizing the first point and the second point”. The limitation amounts to calculating coordinates of the first and second points such that they align with a voxel grid. This limitation therefore recites a mathematical calculation.
Step 2A Prong Two: This part of the eligibility analysis evaluates whether the claim as a whole integrates the recited judicial exception into a practical application of the exception.
Limitations (a), (b), and (c) all are directed to an abstract idea as discussed above. The claim recites one additional element, namely the “computing device”. The computing device is recited at a high level of generality such that it amounts no more than mere instructions to apply the exception using a generic computer component. Accordingly, this additional element does not integrate the abstract idea into a practical application because it does not impose any meaningful limits on practicing the abstract idea. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: This part of the eligibility analysis evaluates whether the claim as a whole amounts to significantly more than the recited exception, i.e., whether any additional element, or combination of additional elements, adds an inventive concept to the claim. MPEP 2106.05.
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 2106.05. Because limitations (a), (b), and (c) are all directed to an abstract idea, the claim cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 1 is ineligible.
Regarding claim 2:
Claim 2 recites:
wherein a set of voxels, including the at least one voxel, represent a point cloud associated with content.
Step 1: The claim depends on claim 1, and adds a wherein clause specifying a set of voxels representing a point cloud associated with content. The wherein clause further limits the method taught by claim 1, namely, that the voxel that is determined is included in a set of voxels representing a point cloud. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Claim 2 recites “a set of voxels, including the at least one voxel, represent a point cloud associated with content”. Representing a set of voxels as a point cloud amounts to calculating the coordinates of a point for each voxel in the set of voxels. This limitation therefore recites an mathematical relationship, i.e., the voxels are mathematically represented by points. “A mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols.” MPEP 2106.04(a)(2)(A). Therefore, claim 2 recites an abstract idea.
Step 2A Prong Two: Claim 2 recites the abstract idea described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The limitations of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 2 is ineligible.
Regarding claim 3:
Claim 3 recites:
wherein the first point within the TriSoup triangle is on an edge of the TriSoup triangle.
Step 1: Claim 3 depends on claim 1, and adds a wherein clause specifying that a first point within a triangle is on the edge of the triangle. The wherein clause further limits the method taught by claim 1. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Claim 3 further limits limitation (a) in claim 1, by stating that the first point that is determined is on the edge of a TriSoup triangle. In the rejection of claim 1 under 101, it was discussed that limitation (a) fell under the “mental process” grouping of abstract ideas.
Determining a point based on a ray in 3D space that is on the edge of a triangle can be practically performed in the human mind. Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited limitation, the use of such physical aid does not negate the mental nature of this limitation. Thus, the limitation falls into the “mental process” groupings of abstract ideas. Claim 3 therefore recites an abstract idea.
Step 2A Prong Two: Claim 3 recites the abstract idea described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The limitations of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 3 is ineligible.
Regarding claim 4:
Claim 4 recites:
The method of claim 1, wherein the second point is outside of a plane of the TriSoup triangle.
Step 1: Claim 4 depends on claim 1, and adds a wherein clause specifying that a second point is outside of a plane of a triangle. The wherein clause further limits the method taught by claim 1. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Claim 4 further limits limitation (b) in claim 1, by stating that the first point that is determined is on the edge of a TriSoup triangle. In the rejection of claim 1 under 101, it was discussed that limitation (a) fell under the “mathematical concept” and “mental process” groupings of abstract ideas.
Determining a second point outside of a plane of a triangle amounts to determining a point that does not satisfy the plane equation of the plane of the triangle. Therefore, the limitation recites a mathematical relationship. Additionally, the process of determining a second point outside of a triangle can be practically performed in the human mind. Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited calculation, the use of such physical aid does not negate the mental nature of this limitation. Claim 4 therefore recites an abstract idea (mathematical concept and mental process).
Step 2A Prong Two: Claim 4 recites the abstract idea described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The limitations of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 4 is ineligible.
Regarding claim 5:
Claim 5 recites:
wherein the TriSoup triangle comprises three vertices, and
wherein at least two of the three vertices are along two TriSoup edges of a cuboid associated with a TriSoup node.
Step 1: Claim 5 depends on claim 1, and adds two wherein clauses. The wherein clauses further limit the method taught by claim 1. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) of claim 5 recites that a “TriSoup triangle comprises three vertices”. The idea that a triangle comprises three points is a mathematical relationship, and therefore the limitation recites an abstract idea.
Limitation (b) of claim 5 recites that “at least two of the three vertices are along two TriSoup edges of a cuboid associated with a TriSoup node”. Determining whether points of a triangle such that they lie on edges of a cube is a mathematical calculation. Therefore, the limitation recites an abstract idea. It follows that Claim 5 as a whole recites at least one abstract idea.
Step 2A Prong Two: Claim 5 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. Limitations (a) and (b) of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 5 is ineligible.
Regarding claim 6:
Claim 6 recites:
determining that the first point is at a point of intersection between the TriSoup triangle and the ray,
wherein the ray is extended parallel to a coordinate axis that is most perpendicular, among a plurality of coordinate axes in the 3D space, to the TriSoup triangle.
Step 1: Claim 6 depends on claim 1, and includes a determining step. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) of claim 6 recites “determining that the first point is at a point of intersection between the TriSoup triangle and the ray”. Determining that a ray intersects a triangle at a point is a mathematical operation often performed by computers during ray-tracing, whereas determining that a point is “at” a point of intersection amounts to checking if the coordinates for each point are equal. Therefore, limitation (a) recites an abstract idea (mathematical concept).
Limitation (b) of claim 6 recites that “the ray is extended parallel to a coordinate axis that is most perpendicular, among a plurality of coordinate axes in the 3D space, to the TriSoup triangle”. The claim describes a mathematical relationship (parallelism) between the ray and a coordinate axis that is “most perpendicular, among a plurality of coordinate axes in the 3D space, to the TriSoup triangle”. Accordingly, limitation (b) recites an abstract idea (mathematical concept).
Step 2A Prong Two: Claim 6 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. Limitations (a) and (b) of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 6 is ineligible.
Regarding claim 7:
Claim 7 recites:
wherein the TriSoup triangle comprises three vertices, and
wherein the determining the first point comprises: determining the first point using:
(b) a Moller-Trumbore algorithm with the three vertices of the TriSoup triangle, and
(c) the ray, wherein the ray is extended parallel to a coordinate axis in the 3D space.
Step 1: Claim 7 depends on claim 1, and includes a determining step. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) of claim 7 recites that a “TriSoup triangle comprises three vertices”. The idea that a triangle comprises three points is a mathematical relationship, and therefore the limitation recites an abstract idea.
Limitation (b) of claim 7 recites that a first point is determined by ”a Moller-Trumbore algorithm with the three vertices of the TriSoup triangle”. “Examples of mathematical calculations recited in a claim include: […] v. using an algorithm for determining the optimal number of visits by a business representative to a client, In re Maucorps, 609 F.2d 481, 482, 203 USPQ 812, 813 (CCPA 1979)” MPEP 2106.04(a)(2). Similar to the example, the limitation describes a calculation of coordinates of a 3D point by using an algorithm. Therefore, the Examiner submits that limitation (b) recites a mathematical calculation.
Limitation (c) of claim 7 recites that “the ray is extended parallel to a coordinate axis in the 3D space”. The claim describes a mathematical relationship (parallelism) between the ray and a coordinate axis. Accordingly, limitation (c) recites an abstract idea (mathematical concept).
Step 2A Prong Two: Claim 7 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. Limitations (a), (b), and (c) of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 7 is ineligible.
Regarding claim 8:
Claim 8 recites:
voxelizing the first point to determine a first voxel; and
voxelizing the second point to determine a second voxel, and
wherein the at least one voxel comprises at least one of the first voxel or the second voxel.
Step 1: Claim 8 depends on claim 1, and includes a voxelizing step. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) recites that a “voxelizing the first point to determine a first voxel”. Voxelizing a first point amounts to calculating coordinates such that the point aligns with a voxel grid. For example, the specification of the present application states: “The G-PCC reference software encoder may perform voxelization, for example, by quantizing positions of points in a point cloud” [0038]. Therefore, limitation (a) recites a mathematical calculation.
Limitation (b) is substantially similar, reciting “voxelizing the second point to determine a second voxel”. For the same reasons applied to limitation (a), limitation (b) recites an abstract idea (mathematical calculation).
Limitation (c) recites that “at least one voxel comprises at least one of the first voxel or the second voxel”. The limitation describes a geometrical relationship at a high level of generality where a voxel includes two “sub-voxels”. Therefore, the limitation recites an abstract idea (mathematical relationship).
Step 2A Prong Two: Claim 8 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. Limitations (a), (b), and (c) of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 8 is ineligible.
Regarding claim 9:
Claim 9 recites:
wherein a magnitude of the vector is determined based on a voxel size of the 3D space.
Step 1: Claim 9 depends on claim 1, and includes a determining step. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) of claim 9 recites that a first point is determined by ”a magnitude of the vector is determined based on a voxel size of the 3D space”. The claim describes a mathematical relationship between a vector magnitude and voxel size. Therefore, the limitation recites an abstract idea (mathematical relationship).
Step 2A Prong Two: Claim 9 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The limitations of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 9 is ineligible.
Regarding claim 10:
Claim 10 recites:
outputting, via a display device and based on the at least one voxel, an image.
Step 1: Claim 10 depends on claim 1, and includes an outputting step. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: The limitation recites a “outputting, via a display device and based on the at least one voxel, an image”. This limitation, as drafted, is a process that, under its broadest reasonable interpretation, covers outputting via a pencil and paper (display device) an image based on at least one voxel. Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited calculation, the use of such physical aid does not negate the mental nature of this limitation. Thus, the limitation falls into the “mental process” groupings of abstract ideas.
Step 2A Prong Two: “In Flook, the Court reasoned that “[t]he notion that post-solution activity, no matter how conventional or obvious in itself, can transform an unpatentable principle into a patentable process exalts form over substance. A competent draftsman could attach some form of post-solution activity to almost any mathematical formula”. 437 U.S. at 590; 198 USPQ at 197; Id. (holding that step of adjusting an alarm limit variable to a figure computed according to a mathematical formula was “post-solution activity”).” MPEP 2106.05(g). The outputting step is a post-solution activity that is recited at a high level of generality (i.e., as a general means of displaying the voxel), and amounts to mere data gathering and outputting, which is a form of insignificant extra-solution activity. “When determining whether an additional element is insignificant extra-solution activity, examiners may consider the following: […] Whether the limitation amounts to necessary data gathering and outputting, (i.e., all uses of the recited judicial exception require such data gathering or data output).” (MPEP 2106.05) (Step 2A: YES).
Step 2B: “Limitations that the courts have found not to be enough to qualify as “significantly more” when recited in a claim with a judicial exception include: […] ii. Simply appending well-understood, routine, conventional activities previously known to the industry, specified at a high level of generality, to the judicial exception, e.g., a claim to an abstract idea requiring no more than a generic computer to perform generic computer functions that are well-understood, routine and conventional activities previously known to the industry, as discussed in Alice Corp., 573 U.S. at 225, 110 USPQ2d at 1984”. Outputting an image is well-understood, routine, and conventional. Furthermore, outputting based on a voxel merely links the judicial exception to the outputting, and therefore the limitation cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 10 is ineligible.
Regarding claim 11:
Claim 11 recites:
wherein the image is associated with content, and
wherein the display device comprises at least one of: a cathode rate tube display, a liquid crystal display, a plasma display, a light emitting diode display, a 3D display, a holographic display, or a head-mounted display.
Step 1: Claim 11 depends on claim 1, and adds two wherein clauses. The wherein clauses further limits the method taught by claim 1. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: With respect to limitation (a), rendering an image based on one voxel was previously discussed to be simple enough for a human to perform the process within their mind. Determining an image with content is simple enough to be performed within the human mind. Therefore, limitation (a) recites a mental process.
With respect to limitation (b), rendering an image, with content and based on one voxel, was previously discussed to be simple enough for a human to perform the process within their mind (or at least, with the aid of pen and paper). Furthermore, while the claim recites computers that are not generic, such as a 3D display or a holographic display, the claim, at the broadest reasonable interpretation, merely requires a generic display such as an LED or LCD display. The specification of the present application further recites that “any other display device suitable for displaying point cloud sequence 108” [0043] may be used to display a point cloud to the user. Therefore, the Examiner submits that the claim recites that a computer is used as a tool to perform the mental process: “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”. MPEP 2105.04(a)(2)(III)(C). Therefore, limitation (b) recites a mental process.
Step 2A Prong Two: Limitation (a) is directed to an abstract idea as discussed above. The claim recites additional elements, namely, the various display devices in limitation (b). Previously, the Examiner stated that limitation (b) only requires the use of a generic display (such as an LED or LCD display) to output the image. In essence, the limitation links the outputting of the image to a particular technological environment. “The courts have also identified limitations that did not integrate a judicial exception into a practical application: […] Generally linking the use of a judicial exception to a particular technological environment or field of use, as discussed in MPEP § 2106.05(h)”. MPEP 2106.04(d)(I). Therefore, the Examiner submits that the claim as a whole does not integrate the judicial exception into a practical application.
Step 2B: Limitation (a) is directed to a judicial exception. In the Step 2A Prong Two analysis above, Examiner stated that limitation (b) only requires the use of a generic display (such as an LED or LCD display) to output the image. Therefore, the Examiner submits that the claim as a whole does not amount to significantly more than the judicial exception. It follows that the claim cannot provide an inventive concept, and that the claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 11 is ineligible.
Regarding claim 12:
Claim 12 recites:
wherein the determining the second point comprises adding the vector to the first point,
wherein the method further comprises:
(b) determining a third point, in the 3D space, by subtracting the vector from the first point, and
(c) wherein the voxelizing comprises voxelizing the first point, the second point, and the third point to determine the at least one voxel.
Step 1: Claim 12 depends on claim 1, and includes a determining step. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) of claim 12 recites that a second point is determined by ” wherein the determining the second point comprises adding the vector to the first point”. The limitation describes a mathematical calculation (adding a vector to a point). Therefore, limitation (a) recites an abstract idea (mathematical calculation).
Limitation (b) of claim 12 recites that a third point is determined by ”subtracting the vector from the first point”. The claim describes a mathematical calculation (subtracting a vector from a point). Therefore, limitation (b) recites an abstract idea (mathematical calculation).
Limitation (c) recites “voxelizing the first point, the second point, and the third point to determine the at least one voxel”. The limitation amounts to calculating coordinates of the first, second, and third points such that they align with a voxel grid. This limitation therefore recites an abstract idea (mathematical calculation).
Step 2A Prong Two: Claim 12 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The limitations of the claim merely introduce further abstract ideas to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 12 is ineligible.
Regarding claim 13:
Claim 13 recites:
determining, by a computing device, a first point, in a three-dimensional (3D) space, that is within a TriSoup triangle;
determining a second point in the 3D space, wherein the second point is:
(b) displaced from the first point by a distance value in a direction not aligned with a plane of the TriSoup triangle, and
(c) outside of the plane of the TriSoup triangle; and
(d) determining at least one voxel by voxelizing the first point and the second point.
Step 1: The claim recites at least one step or act, including determining a voxel. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) recites “determining, by a computing device, a first point, in a three-dimensional (3D) space, that is within a TriSoup triangle”. Determining a point in 3D space that is within a triangle can be practically performed in the human mind. Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited limitation, the use of such physical aid does not negate the mental nature of this limitation. Thus, limitation (a) falls into the “mental process” groupings of abstract ideas.
Limitation (b) discusses determining a second point “displaced from the first point by a distance value in a direction not aligned with a plane of the TriSoup triangle”. This limitation amounts to adding the x, y, and z components of a vector to the coordinates of a first point in 3D space. This limitation therefore recites a mathematical calculation. Accordingly, limitation (b) recites a judicial exception (an abstract idea that falls within the mathematical concept grouping).
Limitation (c) discusses determining a second point outside of a plane of a triangle. The limitation amounts to determining a point that does not satisfy the plane equation of the plane of the triangle. Therefore, the limitation recites a mathematical relationship. Additionally, the process of determining a second point outside of a triangle can be practically performed in the human mind. Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited calculation, the use of such physical aid does not negate the mental nature of this limitation. Claim 4 therefore recites an abstract idea (mathematical concept and mental process).
Limitation (d) recites “determining at least one voxel by voxelizing the first point and the second point”. The limitation amounts to calculating coordinates of the first and second points such that they align with a voxel grid. This limitation therefore recites a mathematical calculation.
Step 2A Prong Two: Limitations (a), (b), (c), and (d) all are directed to an abstract idea as discussed above. The claim recites one additional element, namely the “computing device”. The computing device is recited at a high level of generality such that it amounts no more than mere instructions to apply the exception using a generic computer component. Accordingly, this additional element does not integrate the abstract idea into a practical application because it does not impose any meaningful limits on practicing the abstract idea. Accordingly, the clam does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: 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 2106.05. Because limitations (a), (b), (c), and (d) are all directed to an abstract idea, the claim cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 13 is ineligible.
Regarding claim 14:
Claim 14 recites:
wherein a set of voxels, including the at least one voxel, represent a point cloud associated with content.
Step 1: The claim depends on claim 13, and adds a wherein clause specifying a set of voxels representing a point cloud associated with content. The wherein clause further limits the method taught by claim 1, namely, that the voxel that is determined is included in a set of voxels representing a point cloud. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Claim 14 recites “a set of voxels, including the at least one voxel, represent a point cloud associated with content”. Representing a set of voxels as a point cloud amounts to calculating the coordinates of a point for each voxel in the set of voxels. This limitation therefore recites an mathematical relationship, i.e., the voxels are mathematically represented by points. “A mathematical relationship is a relationship between variables or numbers. A mathematical relationship may be expressed in words or using mathematical symbols.” MPEP 2106.04(a)(2)(A). Therefore, claim 14 recites an abstract idea.
Step 2A Prong Two: Claim 14 recites the abstract idea described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The limitations of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 13, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 14 is ineligible.
Regarding claim 15:
Claim 15 recites:
wherein the first point, the second point, and a third point, in the 3D space, are voxelized to at most two voxels of a point cloud associated with content.
Step 1: The claim depends on claim 13, and adds a wherein clause, which further limits the claimed method steps. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: The claim discusses voxelizing a first, second, and third point to at most two voxels. Voxelizing points amounts to calculating coordinates such that the point aligns with a voxel grid. Indeed, the specification of the present application states: “The G-PCC reference software encoder may perform voxelization, for example, by quantizing positions of points in a point cloud” [0038]. Therefore, limitation (a) recites a mathematical calculation.
Step 2A Prong Two: Claim 15 recites the abstract idea described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The limitations of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 13, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 15 is ineligible.
Regarding claim 16:
Claim 16 recites:
wherein the at least one voxel comprises one of:
a single voxel that corresponds to both the first point and the second point; or
a first voxel and a second voxel, wherein the first voxel corresponds to the first point, and the second voxel corresponds to the second point, and wherein the first voxel is different from the second voxel.
Step 1: Claim 16 depends on claim 13, and includes a wherein clause, which further limits the method steps of claim 1. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) of claim 16 further limits the determining step in claim 13: “determining at least one voxel by voxelizing the first point and the second point” such that “a single voxel that corresponds to both the first point and the second point”. Note that the first point is simply a point in 3D space within a triangle (limitation (a) of claim 13 above) and the second point is “displaced from the first point by a distance value in a direction not aligned with a plane of the TriSoup triangle”. The limitation is simple enough that it can be performed in the human mind, and therefore, the Examiner submits that the limitation recites a mental process. Note that even if most humans would use a physical aid (e.g., pen and paper, a slide rule, or a calculator) to help them complete the recited limitation, the use of such physical aid does not negate the mental nature of this limitation. Thus, limitation (a) falls into the “mental process” groupings of abstract ideas.
Similarly, limitation (b) of claim 16 describes a relationship between two voxels and two points at a high level of generality, with a difference in that the points are within separate voxels. This limitation is also simple enough to be performed in the human mind with the aid of a tool or pen and paper. Thus, limitation (b) falls into the “mental process” groupings of abstract ideas.
Step 2A Prong Two: Claim 16 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. Limitations (a) and (b) of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 13, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 16 is ineligible.
Regarding claim 17:
Claim 17 recites:
determining, by a computing device, a first point on a TriSoup triangle, in a three- dimensional (3D) space, by performing rasterization on the TriSoup triangle;
determining a second point, in the 3D space, that is displaced from the first point by a vector that is perpendicular to the TriSoup triangle; and
determining at least one voxel, of a set of voxels representing a coded point cloud associated with content, by voxelizing at least one of the first point or the second point.
Step 1: The claim recites at least one step or act, including determining a voxel. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) recites “determining, by a computing device, a first point on a TriSoup triangle, in a three- dimensional (3D) space, by performing rasterization on the TriSoup triangle”. Rasterization is a mathematical calculation (i.e., determining the intersection of a ray with a triangle) to determine the coordinates of a 3D point performed by a generic “computing device”. The Examiner submits that Limitation (a) therefore recites an abstract idea.
Limitation (b) recites “determining a second point, in the 3D space, that is displaced from the first point by a vector that is perpendicular to the TriSoup triangle”. This limitation amounts to adding the x, y, and z components of a vector to the coordinates of a first point in 3D space. This limitation therefore recites a mathematical calculation. Accordingly, limitation (b) recites a judicial exception (an abstract idea that falls within the mathematical concept grouping).
Limitation (c) recites “determining at least one voxel, of a set of voxels representing a coded point cloud associated with content, by voxelizing at least one of the first point or the second point”. The limitation amounts to calculating coordinates of the first and second points such that they align with a voxel grid. This limitation therefore recites a mathematical calculation.
Step 2A Prong Two: The claim recites an additional element, namely the “computing device”. The computing device is recited at a high level of generality such that it amounts no more than mere instructions to apply the exception using a generic computer component. Accordingly, this additional element does not integrate the abstract idea into a practical application because it does not impose any meaningful limits on practicing the abstract idea. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: 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 2106.05. Because limitations (a), (b), and (c) are all directed to an abstract idea, the claim cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 17 is ineligible.
Regarding claim 18:
Claim 18 recites:
Claims 18-20 are eligible as they are dependent on claim 17.
wherein the determining the first point by performing rasterization comprises:
converting the TriSoup triangle into a two-dimensional (2D) triangle;
determining a 2D point that is within the 2D triangle; and
determining the first point by projecting the 2D point to the 3D space.
Step 1: The claim recites at least one step or act, including determining a 2D point. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) recites “converting the TriSoup triangle into a two-dimensional (2D) triangle”. Converting a triangle into a two-dimensional triangle amounts to projecting a triangle’s vertices to a two dimensional plane, which is a mathematical calculation. Therefore, limitation (a) recites an abstract idea (mathematical calculation).
Limitation (b) recites “determining a 2D point that is within the 2D triangle”. In essence, the limitation recites a mathematical calculation of coordinates that lie within the bounds of a triangle. Additionally, determining a 2D point within a 2D triangle is a process that can be performed in the human mind. Therefore, the limitation recites an abstract idea (mathematical calculation and mental process).
Limitation (c) recites “determining the first point by projecting the 2D point to the 3D space”. The limitation amounts to calculating coordinates of a two-dimensional point in three-dimensions. Therefore, the limitation recites an abstract idea (mathematical calculation).
Step 2A Prong Two: Claim 16 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. Limitations (a), (b), and (c) of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 16, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 18 is ineligible.
Regarding claim 19:
Claim 19 recites:
wherein the determining the second point comprises adding the vector to the first point, and
wherein the method further comprises:
(b) determining a third point, in the 3D space, by subtracting the vector from the first point.
Step 1: Claim 19 depends on claim 16, and includes a determining step. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) of claim 19 recites that a second point is determined by ” wherein the determining the second point comprises adding the vector to the first point”. The limitation describes a mathematical calculation (adding a vector to a point). Therefore, limitation (a) recites an abstract idea (mathematical calculation).
Limitation (b) of claim 19 recites that a third point is determined by ”subtracting the vector from the first point”. The claim describes a mathematical calculation (subtracting a vector from a point). Therefore, limitation (b) recites an abstract idea (mathematical calculation).
Step 2A Prong Two: Claim 19 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The limitations of the claim merely introduce further abstract ideas to the abstract ideas recited in Claim 16, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 19 is ineligible.
Regarding claim 20:
Claim 20 recites:
wherein the determining the first point comprises:
determining the first point based on one of a digital differential analyzer (DDA) algorithm or a Bresenham algorithm.
Step 1: The claim depends on claim 16, and adds a wherein clause specifying a set of voxels representing a point cloud associated with content. The wherein clause further limits the method taught by claim 16, namely, that the voxel that is determined is included in a set of voxels representing a point cloud. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Claim 20 recites that a first point is determined “based on one of a digital differential analyzer (DDA) algorithm or a Bresenham algorithm.” “Examples of mathematical calculations recited in a claim include: […] v. using an algorithm for determining the optimal number of visits by a business representative to a client, In re Maucorps, 609 F.2d 481, 482, 203 USPQ 812, 813 (CCPA 1979)” MPEP 2106.04(a)(2). Similar to the example, the limitation describes a calculation of coordinates of a 3D point by using a selection of algorithms. Therefore, the Examiner submits that limitation (b) recites a mathematical calculation.
Step 2A Prong Two: Claim 20 recites the abstract idea described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The limitations of the claim merely introduce another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept (Step 2B: NO).
Therefore, claim 20 is ineligible.
Regarding claim 21:
Claim 21 recites:
wherein the vector is not parallel to the TriSoup triangle.
Step 1: Claim 21 depends on claim 1, and includes a determining step. Thus, the claim is to a process, which is one of the statutory categories of invention (Step 1: YES).
Step 2A Prong One: Limitation (a) of claim 21 recites that a “the vector is not parallel to the TriSoup triangle”. In other words, the claim describes a geometrical relationship between the vector and TriSoup triangle (i.e., not being parallel). Therefore, the claim recites an abstract idea (mathematical relationship).
Step 2A Prong Two: Claim 21 recites the abstract ideas described above and contains no additional elements. Accordingly, the claim does not integrate the recited judicial exception into a practical application and the claim is therefore directed to the judicial exception (Step 2A: YES).
Step 2B: RecogniCorp, LLC v. Nintendo Co., 855 F.3d 1322, 1327, 122 USPQ2d 1377 (Fed. Cir. 2017) (“Adding one abstract idea (math) to another abstract idea (encoding and decoding) does not render the claim non-abstract”). MPEP 2106.05. The claim merely introduces another abstract idea to the abstract ideas recited in Claim 1, and therefore cannot provide an inventive concept. The claim does not include additional elements that are sufficient to amount to significantly more than the judicial exception (Step 2B: NO).
Therefore, claim 21 is ineligible.
Claim Rejections - 35 USC § 103
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 1, 2, 3, 4, 6, 8, 9, 10, 13, 14, and 21 are rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1; see attachment for paragraph numbers).
Regarding claim 1:
Nakagami teaches:
A method comprising:
determining, by a computing device and based on a ray, a first point, in a three-dimensional (3D) space, that is within a TriSoup triangle (Nakagami: In a case where the vectors Vi intersect the triangular surface 22, the coordinate values of intersection points 24 between the vectors Vi and the triangular surface 22 are calculated, [0065]);
determining at least one voxel by voxelizing one or more points (Nakagami: for each of the voxels, whether or not points are contained in the voxel is indicated. This causes the position of each point to be quantized in units of voxels [0049]; see Note 1A).
Nakagami fails to explicitly teach:
determining a second point, in the 3D space, by displacing the first point by a vector that is parallel to the ray; and
determining at least one voxel by voxelizing the first point and the second point.
Ubieto teaches:
determining a second point, in the 3D space, by displacing the first point by a vector that is parallel to the ray (Ubieto: If the intersection is a segment, a thickened version of the segment may be drawn into the slice using a quad (e.g. see FIG. 3C). This quad may include two endpoints of the original segment and two additional points offset from these endpoints, […] the offset direction is the projection of a normal vector of the triangle onto the slice (28); see Note 1B); and
determining at least one voxel by voxelizing the first point and the second point (Ubieto: voxelization refers to any technique of converting objects (e.g. geometric objects) from their geometric representation into a voxel or plurality of voxels that approximate the object (11); Ubieto: a polygon mesh refers to any collection of vertices and/or polygons (e.g. triangles, quadrilaterals, etc.) that define a shape of an object. (12); see Note 1C)
Note 1A: In Nakagami, the rays are projected along the edge of the bounding box for a voxel: “Then, vectors Vi 603 are set each of which includes a start origin corresponding to a surface of the voxel 601 and is perpendicular to the surface” [0159] (emphasis added). That is, the vectors travel along the edge of the voxel relative to the intersection point. Similarly, Ubieto teaches that “the offset direction is the projection of a normal vector of the triangle onto the slice” (emphasis added). It follows that the offset direction in Ubieto also travels along the slice relative to the intersection point.
Therefore, the Examiner submits that it would be obvious to one of ordinary skill in the art to determine second points by displacing the first point by a vector parallel to the original ray.
Note 1B: In Ubieto, specifically, Fig. 3D, it is shown that intersection points on a triangle with a slice (i.e., the first points, points I1 and I2) are displaced by an “offset distance w” (28) to determine second points, I’1 and I’2.
Note 1C: Ubieto is directed towards voxelization of primitives, as shown in paragraphs 11 and 12 above. It was previously shown that Nakagami teaches voxelization of points by quantizing each point to a voxel: “for each of the voxels, whether or not points are contained in the voxel is indicated. This causes the position of each point to be quantized in units of voxels” [0049]. Therefore, the Examiner submits that it would be obvious to voxelize the first and second points determined by Nakagami.
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Ubieto with Nakagami. Determining a second point, in the 3D space, by displacing the first point by a vector that is parallel to the ray, as in Ubieto, would benefit the Nakagami teachings by increasing the accuracy of fluid simulations by establishing a thickness for triangles, preventing thin regions or holes during voxelization: “For fluid simulation purposes, both solid and boundary voxelizations are typically needed to determine whether a cell in the simulation domain is inside or outside an obstacle and what velocity the obstacle has at its boundary.” (paragraph (4)).
Regarding claim 2:
Nakagami in view of Ubieto teaches:
The method of claim 1 (as shown above), wherein a set of voxels, including the at least one voxel, represent a point cloud associated with content (Ubieto: voxelization refers to any technique of converting objects (e.g. geometric objects) from their geometric representation into a voxel or plurality of voxels that approximate the object, (11)).
Regarding claim 3:
Nakagami in view of Ubeito teaches:
The method of claim 1 (as shown above), wherein the first point within the TriSoup triangle is on an edge of the TriSoup triangle (Ubieto: Fig. 3D; see Note 3A).
Note 3A: Figure 3D of Ubieto showcases that the intersection points (I1 and I2) are on the edge of a triangle.
Regarding claim 4:
Nakagami in view of Ubieto teaches:
The method of claim 1 (as shown above), wherein the second point is outside of a plane of the TriSoup triangle (Ubieto: Fig. 3D; see Note 4A).
Note 4A: Figure 3D of Ubieto showcases that the offset points (I’1 and I’2) are offset from the plane of the triangle.
Regarding claim 6:
Nakagami in view of Ubeito teaches:
The method of claim 1 (as shown above), wherein the determining the first point comprises:
determining that the first point is at a point of intersection between the TriSoup triangle and a ray (Nakagami: intersection determination is performed between the decoded surface 22 of the mesh (that is, a triangular mesh) and the set vectors Vi (arrow 23) [0065]), wherein the ray is extended parallel to a coordinate axis that is most perpendicular, among a plurality of coordinate axes in the 3D space (Nakagami: as the directions of the vectors Vi, two directions corresponding to positive and negative directions can be set for each of an x-direction, a y-direction, and a z-direction that are perpendicular to one another (directions parallel to the respective sides of the bounding box). [0066]), to the TriSoup triangle.
Regarding claim 8:
Nakagami in view of Ubieto teaches:
The method of claim 1 (as shown above), wherein the determining the at least one voxel comprises:
voxelizing the first point to determine a first voxel (Nakagami: a three-dimensional region containing a point cloud is split into small three-dimensional regions referred to as voxels […] This causes the position of each point to be quantized in units of voxels. Consequently, by converting point cloud data into such data regarding voxels (also referred to as voxel data), an increase in the amount of information can be suppressed (typically the amount of information can be reduced), [0049]; see Note 8A); and
voxelizing the second point to determine a second voxel (see Note 8A), and
wherein the at least one voxel comprises at least one of the first voxel or the second voxel (Nakagami: as illustrated in FIG. 13, it is assumed that an Octree is applied to layers with lower resolutions (LoD=0 to 2); see Note 8B).
Note 8A: Nakagami teaches that each point in a point cloud may be quantized into voxels in [0049]. When combined with the teachings of Ubieto, which determines second points for the purposes of determining a thickness, it would be obvious to voxelize the both first and second points. Because the voxels are voxelized based on their position (“the position of each point to be quantized in units of voxels”), and the second points have positions that differ from the first, it would be obvious to one of ordinary skill in the art to voxelize the second points into a second voxel different from the first.
Note 8B: Nakagami teaches “The Octree corresponds to a tree structure into which the voxel data is formed” [0050], and that “as illustrated in FIG. 13, it is assumed that an Octree is applied to layers with lower resolutions” [0157]. That is, a voxel at LOD level 0 contains 8 voxels that are shown at LOD level 1, for example. Therefore, the Examiner submits that Nakagami teaches “wherein the at least one voxel comprises at least one of the first voxel or the second voxel”.
Regarding claim 9:
Nakagami in view of Ubieto teaches:
The method of claim 1 (as shown above), wherein a magnitude of the vector is determined based on a voxel size of the 3D space (Ubieto: the offset distance w is equal to the diagonal length of one texel in a slice of a 3D texture, (28); see Note 9A).
Note 9A: Because the offset distance in Ubieto is based on the texel size of the 3D texture and because Nakagami teaches “vectors Vi that have the same direction and length as those of the sides of a bounding box including data to be coded are generated at an interval k*d” [0064], the Examiner submits that it would be obvious for one of ordinary skill in the art to combine the teachings of Ubieto with Nakagami such that the magnitude of the offset vector is determined based on a voxel size of the 3D space.
Regarding claim 10:
Nakagami in view of Ubieto teaches:
The method of claim 1 (as shown above), wherein the method further comprises:
outputting, via a display device (Nakagami: The output section 912 includes, for example, a display, a speaker, an output terminal, and the like [0206]) and based on the at least one voxel, an image (Nakagami: information associated with coded data (image) may be transmitted on a transmission channel [0218]; Nakagami: The voxels are three-dimensional regions for quantization of position information regarding an object to be coded. [0048]; see Note 10A).
Note 10A: Nakagami teaches that “The bitstream generating section 515 generates a bitstream including the coded data of the position information fed from the Geometry coding section 512 and the coded data of the attribute information fed from the Attribute coding section 514, and outputs the bitstream to the outside of the coding apparatus 500.” In other words, a bitstream of coded data is output from the system. In [0218], Nakagami teaches that the coded data is analogous to an image, and teaches in [0048] that the voxels quantize position information to be coded. Therefore, the Examiner submits that Nakagami teaches outputting via a display device, an image based on at least one voxel.
Regarding claim 13:
Nakagami teaches:
A method comprising:
determining, by a computing device and based on a ray, a first point, in a three-dimensional (3D) space, that is within a TriSoup triangle (Nakagami: In a case where the vectors Vi intersect the triangular surface 22, the coordinate values of intersection points 24 between the vectors Vi and the triangular surface 22 are calculated, [0065]);
determining at least one voxel by voxelizing one or more points (Nakagami: for each of the voxels, whether or not points are contained in the voxel is indicated. This causes the position of each point to be quantized in units of voxels [0049]; see Note 1A).
Nakagami fails to explicitly teach:
determining a second point in the 3D space, wherein the second point is:
displaced from the first point by a distance value in a direction not aligned with a plane of the TriSoup triangle, and
outside of the plane of the TriSoup triangle; and
determining at least one voxel by voxelizing the first point and the second point.
Ubeito teaches:
determining a second point in the 3D space (Ubieto: If the intersection is a segment, a thickened version of the segment may be drawn into the slice using a quad (e.g. see FIG. 3C). This quad may include two endpoints of the original segment and two additional points offset from these endpoints, […] the offset direction is the projection of a normal vector of the triangle onto the slice (28); see Note 1B), wherein the second point is:
displaced from the first point by a distance value (Ubeito: the offset distance w is equal to the diagonal length of one texel in a slice of a 3D texture, paragraph (28)) in a direction not aligned with a plane of the TriSoup triangle (Ubeito: the offset direction is the projection of a normal vector of the triangle onto the slice; paragraph (28)), and
outside of the plane of the TriSoup triangle (Ubieto: Fig. 3D; see Note 4A); and
determining at least one voxel by voxelizing the first point and the second point (Ubieto: voxelization refers to any technique of converting objects (e.g. geometric objects) from their geometric representation into a voxel or plurality of voxels that approximate the object (11); Ubieto: a polygon mesh refers to any collection of vertices and/or polygons (e.g. triangles, quadrilaterals, etc.) that define a shape of an object. (12); see Note 1C)
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Ubieto with Nakagami. Determining a second point, in the 3D space, by displacing the first point by a vector that is parallel to the ray, as in Ubieto, would benefit the Nakagami teachings by increasing the accuracy of fluid simulations by establishing a thickness for triangles, preventing thin regions or holes during voxelization: “For fluid simulation purposes, both solid and boundary voxelizations are typically needed to determine whether a cell in the simulation domain is inside or outside an obstacle and what velocity the obstacle has at its boundary.” (paragraph (4)).
Regarding claim 21:
Nakagami in view of Ubieto teaches:
The method of claim 1 (as shown above), wherein the vector is not parallel to the TriSoup triangle (Ubieto: the offset direction is the projection of a normal vector of the triangle onto the slice (paragraph (28); see Note 21A).
Note 21A: Ubieto teaches that the offset direction is based on the normal vector of the triangle (see Figure 3D, where the normal is the vector marked by N), and therefore will not be parallel to the triangle itself.
Claim 5 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1) and Dricot (NPL: Adaptive Multi-level Triangle Soup for Geometry-based Point Cloud Coding).
Regarding claim 5:
Nakagami in view of Ubieto teaches:
The method of claim 1 (as shown above), wherein the TriSoup triangle comprises three vertices (Ubieto: Fig. 3D; see Note 5A), and
Note 5A: Figure 3D of Ubieto showcases that the triangle has three vertices.
Nakagami in view of Ubieto fails to explicitly teach:
wherein at least two of the three vertices are along two TriSoup edges of a cuboid associated with a TriSoup node.
Dricot teaches:
wherein at least two of the three vertices are along two TriSoup edges of a cuboid associated with a TriSoup node (Dricot: Figure 2, Pg. 2; see Note 5A).
Note 5A: In Figure 2 of Dricot, all three vertices of the triangle soup triangles are shown to be along the edges of a cuboid. Dricot further teaches that the cuboid is an “octant in the target level of an octree” (Pg. 2, Section B. Triangle soup (trisoup), par. 1). In Figure 1, the octants are showcased in a node graph, where some nodes are colored to indicate the presence of vertices. Therefore, it is reasonable to refer to this octant as a ‘TriSoup node’. This is consistent with the definition of Trisoup node in the specification of the present application, which states: “An occupied leaf node of an occupancy tree that corresponds to a cuboid with a volume greater than one voxel may be referred to as a TriSoup node” [0077].
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Dricot with Nakagami in view of Ubieto. Having at least two of the three vertices are along two TriSoup edges of a cuboid associated with a TriSoup node, as in Dricot, would benefit the Nakagami in view of Ubieto teachings by increasing the accuracy of fluid simulations by establishing a thickness for triangles, preventing thin regions or holes during voxelization: “For fluid simulation purposes, both solid and boundary voxelizations are typically needed to determine whether a cell in the simulation domain is inside or outside an obstacle and what velocity the obstacle has at its boundary.” (paragraph (4)).
Claim 7 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1) and Wikipedia (NPL: Möller–Trumbore intersection algorithm).
Regarding claim 7:
Nakagami in view of Ubieto teaches:
The method of claim 1 (as shown above),
wherein the TriSoup triangle comprises three vertices (Ubieto: Fig. 3D; see Note 5A above), and
wherein the determining the first point comprises: determining the first point using:
the ray, wherein the ray is extended parallel to a coordinate axis in the 3D space (Nakagami: as the directions of the vectors Vi, two directions corresponding to positive and negative directions can be set for each of an x-direction, a y-direction, and a z-direction that are perpendicular to one another (directions parallel to the respective sides of the bounding box). [0066]).
Nakagami in view of Ubieto fails to teach:
wherein the determining the first point comprises: determining the first point using:
a Moller-Trumbore algorithm with the three vertices of the TriSoup triangle, and
Wikipedia teaches:
wherein the determining the first point comprises: determining the first point using:
a Moller-Trumbore algorithm with the three vertices of the TriSoup triangle, and (Wikipedia: “The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle.”, Pg. 1)
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Wikipedia with Nakagami in view of Ubieto. Utilizing the Moller-Trumbore algorithm, as in Wikipedia, would benefit the Nakagami in view of Ubieto teachings by quickly locating intersection points of a ray with a triangle
Claim 11 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1) and Vosoughi (US 20210067805 A1).
Regarding claim 11:
Nakagami in view of Ubieto teaches:
The method of claim 10 (as shown above), wherein the image is associated with content, and
Nakagami in view of Ubieto fails to teach:
wherein the display device comprises at least one of: a cathode rate tube display, a liquid crystal display, a plasma display, a light emitting diode display, a 3D display, a holographic display, or a head-mounted display.
Vosoughi teaches:
wherein the display device comprises at least one of: a cathode rate tube display, a liquid crystal display, a plasma display, a light emitting diode display, a 3D display, a holographic display, or ahead-mounted display (Vosoughi: visual output devices (such as screens 1410 to include CRT screens, LCD screens, plasma screens, OLED screens, [0118]).
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Vosoughi with Nakagami in view of Ubieto. Utilizing multiple types of displays, as in Vosoughi, would benefit the Nakagami in view of Ubieto teachings by enabling the system to output image data to many conventional displays.
Claim 12 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1) and Burgess (US 20230081791 A1).
Regarding claim 12:
Nakagami in view of Ubieto teaches:
The method of claim 1 (as shown above), wherein the determining the second point comprises adding the vector to the first point (Ubieto: two additional end points (I'.sub.1 and I'.sub.2) offset from the endpoints of the triangle, paragraph (28); see Note 12A),
wherein the voxelizing comprises voxelizing one or more points to determine the at least one voxel (Nakagami: a three-dimensional region containing a point cloud is split into small three-dimensional regions referred to as voxels […] This causes the position of each point to be quantized in units of voxels [0049]; see Note 12B).
Note 12A: Figure 3D of Ubeito showcases that the second points I’1 and I’2 are “offset from the endpoints of the triangle,” wherein “the offset distance w is equal to the diagonal length of one texel in a slice of a 3D texture, and the offset direction is the projection of a normal vector of the triangle onto the slice” (paragraph (28)). The Examiner submits that offsetting a point by a vector is analogous to adding that vector to the point.
Note 12B: Nakagami teaches that each point will be voxelized in [0049], and the Examiner discussed that it would be obvious to voxelize the first and second points in Note 1C. The Examiner submits that it would be obvious to further voxelize the third points generated by subtracting the direction vector from the intersection points, when the teachings of Burgess (discussed below) are combined with Nakagami in view of Ubeito.
Nakagami in view of Ubieto fails to teach:
wherein the method further comprises:
determining a third point, in the 3D space, by subtracting the vector from the first point, and
Burgess teaches:
wherein the determining the second point comprises adding the vector to the first point (Burgess: Referring again to FIGS. 17A-17C, 18, one can see two additional planar triangles anchored to the base triangle vertex direction vectors […] The maximum triangle is further displaced from the base triangle than the micro-mesh surface, [0263]);
wherein the method further comprises:
determining a third point, in the 3D space, by subtracting the vector from the first point (Burgess: and the minimum triangle is less displaced from the base triangle than the micro-mesh surface [0263]), and
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Burgess with Nakagami in view of Ubeito. Having the second point be determined based on adding the vector to the first point and determining a third point based on subtracting the vector from the first point, as in Burgess, would benefit the Nakagami in view of Ubeito teachings by enabling intersection testing within a range of the intersection point.
Regarding claim 14:
Nakagami in view of Ubeito teaches:
The method of claim 13 (as shown above), wherein a set of voxels, including the at least one voxel, represent a point cloud associated with content (Ubieto: voxelization refers to any technique of converting objects (e.g. geometric objects) from their geometric representation into a voxel or plurality of voxels that approximate the object, (11)).
Claim 15 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1) and Hur 2021 (US 20210104090 A1; hereinafter Hur 2021).
Regarding claim 15:
Nakagami in view of Ubeito teaches:
The method of claim 13 (as shown above), wherein the image is associated with content (Nakagami: information associated with coded data (image) may be transmitted on a transmission channel [0218]), and wherein the first point, the second point, and a third point, in the 3D space, are voxelized to at most two voxels of a point cloud associated with content (see Note 1C and Note 15A).
Note 15A: Figure 3D of Ubeito showcases four points. In Note 1C, the Examiner stated that it would be obvious to voxelize the first (I1 and I2) and second (I’1 and I’2) points. Because Nakagami teaches that each point in a point cloud can be assigned to a voxel “for each of the voxels, whether or not points are contained in the voxel is indicated. This causes the position of each point to be quantized in units of voxels” [0049], the Examiner submits that it would be obvious to also voxelize a third point in the 3D space.
Nakagami in view of Ubeito fails to teach:
wherein the first point, the second point, and a third point, in the 3D space, are voxelized to at most two voxels of a point cloud associated with content.
Hur 2021 teaches:
wherein the first point, the second point, and a third point, in the 3D space (Hur 2021: The quantizer 40001 may match groups of points in the 3D space with voxels [0106]), are voxelized (Hur 2021: The quantizer 40001 according to the embodiments performs voxelization based on the quantized positions to reconstruct quantized points [0106]) to at most two voxels of a point (Hur 2021: In an embodiment, in the case where quantization is performed before voxelization is performed, a plurality of points may belong to one voxel. [0106], emphasis added, see Note 15B) cloud associated with content (Hur 2021: points of point cloud content (or 3D point cloud video) according to the embodiments may be included in one or more voxels [0082]).
Note 15B: Hur 2021 teaches: “In an embodiment, in the case where quantization is performed before voxelization is performed, a plurality of points may belong to one voxel.” [0260]. That is, Hur 2021 teaches an embodiment where two or more points belong to one voxel. When there is a first, second, and third point, the points may be voxelized to at most two voxels, because in the embodiment taught by Hur 2021, at least one voxel must contain a plurality, or two out of the three points. Therefore, it would be obvious to one of ordinary skill in the art to voxelize the three points to at most two voxels.
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Hur 2021 with Nakagami in view of Ubeito. Limiting the amount of voxels to assign points to two, as in Hur 2021, would benefit the Nakagami in view of Ubeito teachings by preventing processing of duplicate data points, which could otherwise cause unnecessary slowdown.
Claim 16 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1) and Hur (US 20240064332 A1; hereinafter Hur 2024).
Regarding claim 16:
Nakagami in view of Ubeito teaches:
The method of claim 13 (as shown above), wherein the at least one voxel comprises one of:
Nakagami in view of Ubeito fails to explicitly teach:
a single voxel that corresponds to both the first point and the second point; or
a first voxel and a second voxel, wherein the first voxel corresponds to the first point, and the second voxel corresponds to the second point, and wherein the first voxel is different from the second voxel.
Hur 2024 teaches:
a single voxel if that corresponds to both the first point and the second point (Hur 2024: According to embodiments, one voxel may include one or more points [0082]); or
a first voxel and a second voxel, wherein the first voxel corresponds to the first point, and the second voxel corresponds to the second point, and wherein the first voxel is different from the second voxel (Hur 2024: According to embodiments, one voxel may include only one point. [0082]; see Note 16A).
Note 16A: Hur 2024 teaches that: “As in the case of a pixel, which is the minimum unit containing 2D image/video information, points of point cloud content (or 3D point cloud video) according to the embodiments may be included in one or more voxels.” [0082]. Hur 2024 also teaches an embodiment where each voxel contains only one point. Because Hur 2024 teaches that there may be multiple voxels in [0082], one of ordinary skill in the understand would understand that Hur teaches that there will be at least a first and second voxel, each with corresponding points, that are different.
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Hur 2024 with Nakagami in view of Ubeito. Having a one of the first point and the second point if the first point and the second point are the same; and both the first point and the second point if the first point and the second point are different, as in Hur 2024, would benefit the Nakagami in view of Ubeito teachings by preventing processing of duplicate data points, which could otherwise cause unnecessary slowdown.
Claim 17 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1) and Graziosi (US 20210174551 A1).
Regarding claim 17:
Nakagami teaches:
A method comprising:
determining, by a computing device, a first point on a TriSoup triangle, in a three- dimensional (3D) space (Nakagami: In a case where the vectors Vi intersect the triangular surface 22, the coordinate values of intersection points 24 between the vectors Vi and the triangular surface 22 are calculated, [0065]);
determining at least one voxel by voxelizing one or more points (Nakagami: for each of the voxels, whether or not points are contained in the voxel is indicated. This causes the position of each point to be quantized in units of voxels [0049]; see Note 1A).
Nakagami fails to teach:
determining, by a computing device, a first point on a TriSoup triangle, in a three- dimensional (3D) space, by performing rasterization on the TriSoup triangle;
determining a second point, in the 3D space, that is displaced from the first point by a vector that is perpendicular to the TriSoup triangle; and
determining at least one voxel, of a set of voxels representing a coded point cloud associated with content, by voxelizing at least one of the first point or the second point.
Ubeito teaches:
determining a second point, in the 3D space, by displacing the first point by a vector that is vector that is perpendicular to the TriSoup triangle (Ubieto: If the intersection is a segment, a thickened version of the segment may be drawn into the slice using a quad (e.g. see FIG. 3C). This quad may include two endpoints of the original segment and two additional points offset from these endpoints, […] the offset direction is the projection of a normal vector of the triangle onto the slice (28); see Note 1B); and
determining at least one voxel, of a set of voxels representing a coded point cloud associated with content, by voxelizing at least one of the first point or the second point (Ubieto: voxelization refers to any technique of converting objects (e.g. geometric objects) from their geometric representation into a voxel or plurality of voxels that approximate the object (11); Ubieto: a polygon mesh refers to any collection of vertices and/or polygons (e.g. triangles, quadrilaterals, etc.) that define a shape of an object. (12); see Note 1C)
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Ubieto with Nakagami. Determining a second point, in the 3D space, by displacing the first point by a vector that is parallel to the ray, as in Ubieto, would benefit the Nakagami teachings by increasing the accuracy of fluid simulations by establishing a thickness for triangles, preventing thin regions or holes during voxelization: “For fluid simulation purposes, both solid and boundary voxelizations are typically needed to determine whether a cell in the simulation domain is inside or outside an obstacle and what velocity the obstacle has at its boundary.” (paragraph (4)).
Nakagami in view of Ubeito still fails to teach:
determining, by a computing device, a first point on a TriSoup triangle, in a three- dimensional (3D) space, by performing rasterization on the TriSoup triangle;
Graziosi teaches:
determining, by a computing device (Graziosi: computing device 1100 [0057]), a first point on a TriSoup triangle (Graziosi: implementing patch generation which segments the mesh into patches including a rasterized mesh surface and vertices location [0105]; emphasis added), in a three-dimensional (3D) space (Graziosi: Connectivity information describes how the points are connected in 3D [0034]; see Note 17A), by performing rasterization on the TriSoup triangle (Graziosi: The triangle is rasterized to generate the points for the point cloud representation. [0038]);
Note 17A: Because Graziosi teaches that the connectivity information defines how the points are connected in 3D, the points must necessarily be points in 3D space.
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Graziosi with Nakagami in view of Ubeito. Determining an intersection point by rasterization, as in Graziosi, would benefit the Nakagami in view of Ubeito by enabling the use of standard rasterization techniques to determine 3D points.
Claim 18 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1), Graziosi (US 20210174551 A1), and Dunn (NPL: 3D Math Primer for Graphics and Game Development: Chapter 9: Geometric Primitives) and Gao (US 20250252610 A1).
Regarding claim 18:
Nakagami in view of Ubeito and Graziosi teaches:
The method of claim 17 (as shown above), wherein the determining the first point by performing rasterization comprises:
Nakagami in view of Ubeito and Graziosi fails to teach:
converting the TriSoup triangle into a two-dimensional (2D) triangle;
determining a 2D point that is within the 2D triangle; and
determining the first point by projecting a 2D point to the 3D space.
Dunn teaches:
converting the TriSoup triangle into a two-dimensional (2D) triangle (Dunn: One trick that works is to turn the 3D problem into a 2D problem simply by discarding one of x, y, or z. This has the effect of projecting the triangle onto one of the three cardinal planes, Pg. 18, par. 3);
determining a 2D point that is within the 2D triangle (Dunn: We start in 2D with Figure 9.20, which shows the three vertices v1, v2, and v3, and the point p, Pg. 17, Section 9.6.4: Calculating Barycentric Coordinates; see Note 18A); and
Note 18A: Figure 9.20 of Dunn showcases that point P is within the 2D triangle.
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Dunn with Nakagami in view of Ubeito and Graziosi. Converting the TriSoup triangle into a two-dimensional (2D) triangle and determining a 2D point within the 2D triangle, as in Dunn, would enhance the teachings of Nakagami in view of Ubeito and Graziosi, because “Computing barycentric coordinates for an arbitrary point in 3D is more complicated than in 2D.” (Dunn, Pg. 17, par. 5)
Nakagami in view of Ubeito, Graziosi, and Dunn fails to explicitly teach:
determining the first point by projecting a 2D point to the 3D space.
Gao teaches:
determining the first point by projecting a 2D point to the 3D space (Gao: Any point P of the 3D space can be uniquely represented by its barycentric coordinates relative to any non-degenerated 3D triangle ABC [0101]; This intersection point P belongs to the triangle if and only if 0≤u, v, w, [0107]; see Note 18B).
Note 18B: Barycentric coordinates are known in the art to define points on the plane of the triangle relative to the edges of the triangle (Indeed, Dunn, discussed above, teaches: “Even though we certainly use triangles in 3D, the surface of a triangle lies in a plane and is inherently a 2D object. Moving around on the surface of a triangle that is arbitrarily oriented in 3D is somewhat awkward. It would be nice to have a coordinate space that is related to the surface of the triangle and is independent of the 3D space in which the triangle “lives.” Barycentric space is just such a coordinate space,” Pg. 15, Section 9.5.3: Barycentric space). Therefore, the Examiner interprets the barycentric coordinates to define points in a 2D space. Furthermore, as Gao teaches that points in 3D space can be represented by barycentric coordinates, the Examiner submits that it would be obvious to project from the 2D barycentric coordinates to receive a 3D point.
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Gao with Nakagami in view of Ubeito, Graziosi, and Dunn. Determining the first point by projecting a 2D point to the 3D space, as in Gao, would enhance the teachings of Nakagami in view of Ubeito, Graziosi and Dunn, by ensuring that the intersection point is within the 2D plane of the triangle.
Claim 19 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1), Graziosi (US 20210174551 A1), and Burgess (US 20230081791 A1).
Regarding claim 19:
Nakagami in view of Ubeito and Graziosi teaches:
The method of claim 17 (as shown above), wherein the determining the second point comprises adding the vector to the first point (Ubieto: two additional end points (I'.sub.1 and I'.sub.2) offset from the endpoints of the triangle, paragraph (28); see Note 12A),
Nakagami in view of Ubieto and Graziosi fails to teach:
wherein the method further comprises:
determining a third point, in the 3D space, by subtracting the vector from the first point, and
Burgess teaches:
wherein the determining the second point comprises adding the vector to the first point (Burgess: Referring again to FIGS. 17A-17C, 18, one can see two additional planar triangles anchored to the base triangle vertex direction vectors […] The maximum triangle is further displaced from the base triangle than the micro-mesh surface, [0263]);
wherein the method further comprises:
determining a third point, in the 3D space, by subtracting the vector from the first point (Burgess: and the minimum triangle is less displaced from the base triangle than the micro-mesh surface [0263]), and
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Burgess with Nakagami in view of Ubeito and Graziosi. Having the second point be determined based on adding the vector to the first point and determining a third point based on subtracting the vector from the first point, as in Burgess, would benefit the Nakagami in view of Ubeito and Graziosi teachings by enabling intersection testing within a range of the intersection point.
Claim 20 is rejected under 35 U.S.C. 103 as being unpatentable over Nakagami (US 20230126000 A1) In view of Ubieto (US 8274513 B1), Graziosi (US 20210174551 A1), and Panigrahi: (NPL: Difference Between DDA and Bresenham Line Drawing algorithm).
Regarding claim 20:
Nakagami in view of Ubeito and Graziosi teaches:
The method of claim 17 (as shown above), wherein the determining the first point comprises:
Nakagami in view of Ubeito and Graziosi fails to teach:
determining the first point based on one of a digital differential analyzer (DDA) algorithm or a Bresenham algorithm.
Panigrahi teaches:
determining the first point based on one of a digital differential analyzer (DDA) algorithm or a Bresenham algorithm (see Note 20A).
Note 20A: Nakagami teaches that vectors may be generated to intersect a triangular plane: “Assuming that “P” denotes the coordinates of an intersection point, “origin” denotes the coordinates of ray, “ray” denotes a direction vector, and “t” denotes a scalar value, an intersection point passing through ray is represented as follows by using a linear expression. P=origin+ray*t” [0071]. Panigrahi teaches: “Within the realm of computer graphics, the DDA and Bresenham's method serve very similar functions. Each of them can be used to create line segments as well as a variety of other things.” Therefore, it would be obvious to one of ordinary skill in the art to utilize the DDA algorithm or Bresenham’s algorithm to generate the vectors taught by Nakagami.
Before the effective filing date of the claimed invention, it would have been obvious to a person having ordinary skill in the art to combine the teachings of Panigrahi with Nakagami in view of Ubeito and Graziosi. Utilizing DDA or Bresenham’s algorithm to generate vectors, as in Panigrahi, would benefit the Nakagami in view of Ubeito and Graziosi teachings by further optimizing vector generation. See also the figure below from Panigrahi, Pg. 4:
PNG
media_image1.png
628
756
media_image1.png
Greyscale
Table from Panigrahi, Pg. 4, illustrating a few differences between the DDA and Bresenham algorithms.
Conclusion
Any inquiry concerning this communication or earlier communications from the examiner should be directed to VINCENT ALEXANDER PROVIDENCE whose telephone number is (571)270-5765. The examiner can normally be reached Monday-Thursday 8:30-5:00.
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/VINCENT ALEXANDER PROVIDENCE/Examiner, Art Unit 2617 /KING Y POON/Supervisory Patent Examiner, Art Unit 2617
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