Prosecution Insights
Last updated: July 17, 2026
Application No. 18/945,110

Point Cloud Encoding Method, and Decoding Method Using Rotation Matrices, Encoder, and Decoder

Final Rejection §103§112
Filed
Nov 12, 2024
Priority
Jul 12, 2018 — CN 201810766911.3 +2 more
Examiner
SULLIVAN, TYLER
Art Unit
2487
Tech Center
2400 — Computer Networks
Assignee
Huawei Technologies Co., Ltd.
OA Round
2 (Final)
67%
Grant Probability
Favorable
3-4
OA Rounds
1y 2m
Est. Remaining
98%
With Interview

Examiner Intelligence

Grants 67% — above average
67%
Career Allowance Rate
259 granted / 388 resolved
+8.8% vs TC avg
Strong +31% interview lift
Without
With
+31.0%
Interview Lift
resolved cases with interview
Typical timeline
2y 10m
Avg Prosecution
36 currently pending
Career history
425
Total Applications
across all art units

Statute-Specific Performance

§101
1.3%
-38.7% vs TC avg
§103
87.5%
+47.5% vs TC avg
§102
1.2%
-38.8% vs TC avg
§112
8.7%
-31.3% vs TC avg
Black line = Tech Center average estimate • Based on career data from 388 resolved cases

Office Action

§103 §112
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 . Priority Receipt is acknowledged of certified copies of papers required by 37 CFR 1.55 (Chinese Application CN2018107669113 filed on July 12th, 2018). Response to Arguments Applicant amended claims 2, 4 – 7, 9, and 11 – 20 beyond formalities and 112 Rejections. The pending claims are 1 – 20 [Page 15 lines 1 – 7]. Applicant requests to hold Examiner’s ODP Rejection in abeyance [Page 15 lines 8 – 17]. The Rejection is thus maintained and may be amended in view of the amended claims. Applicant amends the Specification and Drawings to address Examiner’s Drawing Objections [Page 15 line 18 – Page 16 line 2]. The Examiner reconsiders the Drawings Objections in view of the amendments made. Applicant amends the claims to address Examiner’s Claim Objections [Page 16 lines 3 – 20]. The Examiner reconsiders the Claim Objections in view of the amended claims. Applicant's arguments filed March 30th, 2026 [Page 16 line 21 – Page19 line 5] have been fully considered but they are not persuasive. Applicant’s arguments do not present any derivation on how to arrive at the claimed matrices but merely a critique on the Examiner’s very reasonable derivation based on known techniques including as an additional courtesy prior art citations [Page 16 line 21 – Page 19 line 5]. However, even if the other ordering of matrices is performed, the result is not the claimed matrices, thus without any showing the claimed matrices cannot be reasonably derived as a mathematical error may have occurred in the Applicant’s derivation. Thus, the argument is unpersuasive in view of no real argument made as just a general critique and assertion of validity of the claimed which the Examiner rebutted properly [MPEP 2163 III and MPEP2163.04]. While the Applicant’s points may possibly be understood, the Examiner respectfully disagrees thus maintains the Rejection. Applicant amends the claims to address Examiner’s 112(b) Rejection [Page 19 lines 6 – 20]. The Examiner reconsiders the Rejections in view of the amended claims. Applicant's arguments filed March 30th, 2026 [Page 19 line 21 – Page 22 line 23] have been fully considered but they are not persuasive. First, the Applicant recites the references against the claims [Page 19 line 21 – Page 20 line 5] and makes general remarks regarding an Obvious Rejection [Page 20 lines 5 – 9]. Second, the Applicant broadly alleges the references as not rendering obvious features of claim 1 and recites claim 1 [Page 20 lines 9 – 27] with reiteration of features claimed and broad allegations of features not taught [Page 20 line 28 – Page 23 line 6]. Third, the Applicant provides their interpretation of Kato Paragraphs 90 – 95 as not teaching the claimed coordinate transform and then broadly mentions Tsai as teaching such coordinate transform [Page 21 lines 7 – 18]. Tsai in at least Figures 3 – 4 (subfigures included) render obvious the 3D to 3D patch projection and then in Paragraphs 56 – 61 (and associated Tables and Figures) renders obvious the claimed coordinate transform (form original to frame coordinates) with and index syntax element to signal the matrix transformation to use (see Table 2 at least) and encoding information in at least Figures 10 – 12 and associated description. Kato was also relied on to render obvious encoding syntax elements (e.g. Kato Paragraphs 11 and 362). Applicant's arguments fail to comply with 37 CFR 1.111(b) because they amount to a general allegation that the claims define a patentable invention without specifically pointing out how the language of the claims patentably distinguishes them from the references. Fourth, the Applicant contends there is no motivation to combine the references effectively arguing hindsight was used [Page 21 line 18 – Page 22 line 5]. In response to applicant's argument that the examiner's conclusion of obviousness is based upon improper hindsight reasoning, it must be recognized that any judgment on obviousness is in a sense necessarily a reconstruction based upon hindsight reasoning. But so long as it takes into account only knowledge which was within the level of ordinary skill at the time the claimed invention was made, and does not include knowledge gleaned only from the applicant's disclosure, such a reconstruction is proper. See In re McLaughlin, 443 F.2d 1392, 170 USPQ 209 (CCPA 1971). Fifth, the Applicant contends Joyce and Texas are not analogous art [Page 22 lines 6 – 23]. However, in view of MPEP 2141.01(a) [“The Federal Circuit reads KSR as "direct[ing] us to construe the scope of analogous art broadly" because "familiar items may have obvious uses beyond their primary purposes, and a person of ordinary skill often will be able to fit the teachings of multiple patents together like pieces of a puzzle." Wyers v. Master Lock Co., 616 F.3d 1231, 1238, 95 USPQ2d 1525, 1530 (Fed. Cir. 2010) (quoting KSR, 550 U.S. at 402, 127 S. Ct. at 1727)”], the Examiner observe the Joyce and Texas references satisfy the requirements of “reasonable pertinent” as matrix mathematics and manipulations to affect coordinate transformations are at the crux of the problem considered by the Applicant. Thus, the argument is unpersuasive. In response to applicant's argument that Joyce and Texas is nonanalogous art, it has been held that a prior art reference must either be in the field of the inventor’s endeavor or, if not, then be reasonably pertinent to the particular problem with which the inventor was concerned, in order to be relied upon as a basis for rejection of the claimed invention. See In re Oetiker, 977 F.2d 1443, 24 USPQ2d 1443 (Fed. Cir. 1992). In this case, the requirements of “reasonable pertinent” as matrix mathematics and manipulations to affect coordinate transformations are at the crux of the problem considered by the Applicant. While the Applicant’s points may possibly be understood, the Examiner respectfully disagrees thus maintains the Rejection. Applicant’s arguments with respect to claim(s) 2, 4 – 7, 9, 11 – 15 and 17 – 20 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. The Examiner notes the Applicant on Page 21 lines 6 – 7 states Kato teaches optimal patch placement Due to the scope change in the claims, the Examiner notes new grounds of Rejection may be made in view of the amended claims in the sole interest to expedite prosecution. Information Disclosure Statement The information disclosure statement (IDS) submitted on November 12th, 2024 was filed before the mailing date of the First Action on the Merits (mailed January 8th, 2026). The submission is in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the Examiner. The information disclosure statement filed November 12th, 2024 fails to comply with 37 CFR 1.98(a)(2), which requires a legible copy of each cited foreign patent document; each non-patent literature publication or that portion which caused it to be listed; and all other information or that portion which caused it to be listed. It has been placed in the application file, but the information referred to therein has not been considered. Due to the excessively lengthy Information Disclosure Statement submitted by applicant, the examiner has given only a cursory review of the listed references. In accordance with MPEP 609.04(a), applicant is encouraged to provide a concise explanation of why the information is being submitted and how it is understood to be relevant. Concise explanations (especially those which point out the relevant pages and lines) are helpful to the Office, particularly where documents are lengthy and complex and applicant is aware of a section that is highly relevant to patentability or where a large number of documents are submitted and applicant is aware that one or more are highly relevant to patentability. Applicant is required to comply with this statement for any non-English language documents. See 37 CFR § 1.56 Duty to Disclose Information Material to Patentability. Specification The lengthy specification has not been checked to the extent necessary to determine the presence of all possible minor errors. Applicant’s cooperation is requested in correcting any errors of which applicant may become aware in the specification. Double Patenting The nonstatutory double patenting rejection is based on a judicially created doctrine grounded in public policy (a policy reflected in the statute) so as to prevent the unjustified or improper timewise extension of the “right to exclude” granted by a patent and to prevent possible harassment by multiple assignees. A nonstatutory double patenting rejection is appropriate where the conflicting claims are not identical, but at least one examined application claim is not patentably distinct from the reference claim(s) because the examined application claim is either anticipated by, or would have been obvious over, the reference claim(s). See, e.g., In re Berg, 140 F.3d 1428, 46 USPQ2d 1226 (Fed. Cir. 1998); In re Goodman, 11 F.3d 1046, 29 USPQ2d 2010 (Fed. Cir. 1993); In re Longi, 759 F.2d 887, 225 USPQ 645 (Fed. Cir. 1985); In re Van Ornum, 686 F.2d 937, 214 USPQ 761 (CCPA 1982); In re Vogel, 422 F.2d 438, 164 USPQ 619 (CCPA 1970); In re Thorington, 418 F.2d 528, 163 USPQ 644 (CCPA 1969). A timely filed terminal disclaimer in compliance with 37 CFR 1.321(c) or 1.321(d) may be used to overcome an actual or provisional rejection based on nonstatutory double patenting provided the reference application or patent either is shown to be commonly owned with the examined application, or claims an invention made as a result of activities undertaken within the scope of a joint research agreement. See MPEP § 717.02 for applications subject to examination under the first inventor to file provisions of the AIA as explained in MPEP § 2159. See MPEP § 2146 et seq. for applications not subject to examination under the first inventor to file provisions of the AIA . A terminal disclaimer must be signed in compliance with 37 CFR 1.321(b). The filing of a terminal disclaimer by itself is not a complete reply to a nonstatutory double patenting (NSDP) rejection. A complete reply requires that the terminal disclaimer be accompanied by a reply requesting reconsideration of the prior Office action. Even where the NSDP rejection is provisional the reply must be complete. See MPEP § 804, subsection I.B.1. For a reply to a non-final Office action, see 37 CFR 1.111(a). For a reply to final Office action, see 37 CFR 1.113(c). A request for reconsideration while not provided for in 37 CFR 1.113(c) may be filed after final for consideration. See MPEP §§ 706.07(e) and 714.13. The USPTO Internet website contains terminal disclaimer forms which may be used. Please visit www.uspto.gov/patent/patents-forms. The actual filing date of the application in which the form is filed determines what form (e.g., PTO/SB/25, PTO/SB/26, PTO/AIA /25, or PTO/AIA /26) should be used. A web-based eTerminal Disclaimer may be filled out completely online using web-screens. An eTerminal Disclaimer that meets all requirements is auto-processed and approved immediately upon submission. For more information about eTerminal Disclaimers, refer to www.uspto.gov/patents/apply/applying-online/eterminal-disclaimer. Claims 1 – 8, 10 – 14, and 16 – 19 are rejected on the ground of nonstatutory double patenting as being unpatentable over claims 1 – 2, 5 – 6, 8, 10 – 11, 13 – 14 of U.S. Patent No. 12,165,366. Although the claims at issue are not identical, they are not patentably distinct from each other because: Note: The Examiner refers to the numbering of the August 19th, 2024 claim set before the claims were renumbered Regarding claim 16, the encoding program / apparatus is within the scope of Patented claim 1 (encoding apparatus and similarly Patented claim 11 is the program) in at least the “project a current patch…”; “transforming first coordinates …”; “encoding a syntax …” limitations where the “generating one of more syntax elements …” (using Patented claim 11 gerunds) renders obvious at least the transformation matrix from the claimed options in the pending claims to one of ordinary skill in the art. Regarding claim 17, see Patented claim 5 or 13 which is the same / similar limitation and thus are obvious variants to one of ordinary skill in the art. Regarding claim 18, see Patented claim 2 which is the same / similar limitation and thus are obvious variants to one of ordinary skill in the art. Regarding claim 19, see Patented claim 2 in which the transform / rotation matrix is based on the rotation angle and thus within the scope of the claim as readily recognized by one of ordinary skill in the art. Regarding claim 1, see claim 16 which the program / apparatus implements the step of claim 1 and thus for similar reasons within the scope of at least Patented claims 1 or 11. Regarding claim 2, see claim 17 which the program / apparatus implements the step of claim 2 and thus for similar reasons within the scope of at least Patented claims 5 or 13. Regarding claim 3, see claim 18 which the program / apparatus implements the step of claim 3 and thus for similar reasons within the scope of at least Patented claim 2. Regarding claimed 4 – 7, see Patented claims 5 or 13 as the matrices given are for the respective angles theta for 0, 90, 180, and 270 degrees as would be readily recognized by one of ordinary skill in the art. Regarding claim 8, see claim 19 which the program / apparatus implements the step of claim 8 and thus for similar reasons within the scope of at least Patented claim 2. Regarding claim 10, the decoding method is within the scope of Patented claim 6 or 14 (decoding program / apparatus) in at least the “parsing a bitstream…” (obvious variant of the pending “obtaining a bitstream …” limitation); “reconstructing a point cloud …” and “transforming second coordinates …” limitation (as rendering obvious the pending “reconstructing the point cloud …” limitation to one of ordinary skill in the art); “and the first “wherein the first coordinates …” limitation renders obvious at least the transformation matrix from the claimed options in the pending claims to one of ordinary skill in the art. Regarding claim 11, see claims 2 or 17 for the same / similar limitation thus rendered obvious as being within the scope of Patented claim 10 (and similarly Patented claims 5 or 13). Regarding claim 12, see claims 3 or 18 for the same / similar limitation thus rendered obvious as being within the scope of Patented claim 8 (and similarly Patented claim 2). Regarding claims 13 - 14, see claims 4 – 7 for the same / similar limitations (see the angles being evaluated as claim 13 is either claims 4 or 5 and claim 14 is either claim 6 or 7) thus rendered obvious as being within the scope of Patented claim 8 (and similarly Patented claim 2). It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to understand the obvious variants performed in the Patented claims to the pending claims including the differences in matrices recited as the patented matrices were initially claimed as those in the pending claims and amended in view of the 112(a) Rejections made and thus one of ordinary skill in the art would understand the patented matrices as the correct version of the matrices in the pending claims (see 112(a) Rejections made). Additionally one of ordinary skill in the art would recognize the pending claims as being within the scope of the patented claims. Claim Rejections - 35 USC § 112 The following is a quotation of the first paragraph of 35 U.S.C. 112(a): (a) IN GENERAL.—The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor or joint inventor of carrying out the invention. The following is a quotation of the first paragraph of pre-AIA 35 U.S.C. 112: The specification shall contain a written description of the invention, and of the manner and process of making and using it, in such full, clear, concise, and exact terms as to enable any person skilled in the art to which it pertains, or with which it is most nearly connected, to make and use the same, and shall set forth the best mode contemplated by the inventor of carrying out his invention. Claims 2, 4 – 7, 9, 11, 13 – 15, 17, and 20 are rejected under 35 U.S.C. 112(a) or 35 U.S.C. 112 (pre-AIA ), first paragraph, as failing to comply with the written description requirement. The claim(s) contains subject matter which was not described in the specification in such a way as to reasonably convey to one skilled in the relevant art that the inventor or a joint inventor, or for applications subject to pre-AIA 35 U.S.C. 112, the inventor(s), at the time the application was filed, had possession of the claimed invention. Regarding claims 2, 4 – 7, and 9, the matrices claimed are incorrect in view of how one of ordinary skill in the art would understand rotation and reflection matrices. Specification Paragraphs 379 – 409 present without derivation a transformation matrix to perform the rotation claimed (In fact in view of Specification Paragraph 387, the incorrect inverse matrix is given and the product of the given rotation matrix and its inverse does not yield the Identity matrix as expected to one of ordinary skill in the art). In view of Figures 7, 10, and 14 one of ordinary skill in the art would notice a reflection occurs and then a rotation occurs. However, one of ordinary skill in the art would understand the result of the rotation differently as those described in the Specification and claimed. In view of the prior art cited against claim 9 (Joyce and Texas citations), Joyce presents reflection about the horizontal axis (x-axis in the paper – see Example 4) as 1 0 0 - 1 and to rotate about a point by an angle as using the matrix cos ⁡ θ - sin ⁡ θ sin ⁡ θ cos ⁡ θ for a counterclockwise rotation or in the case of a clockwise rotation the matrix cos ⁡ θ sin ⁡ θ - sin ⁡ θ cos ⁡ θ (derived from Joyce in view of the Texas paper – see Page 3 multiplying matrices to combine transforms / rotations where one is obvious in view of the other due to negative angle trigonometry identities). Thus applying the transforms of reflecting and then performing the rotation would yield in a clockwise rotation: 1 0 0 - 1 ∙ cos ⁡ θ - sin ⁡ θ sin ⁡ θ cos ⁡ θ = cos ⁡ θ - sin ⁡ θ - sin ⁡ θ - cos ⁡ θ or in a counter clockwise rotation: 1 0 0 - 1 ∙ cos ⁡ θ sin ⁡ θ - sin ⁡ θ cos ⁡ θ = cos ⁡ θ sin ⁡ θ sin ⁡ θ - cos ⁡ θ of which both results are not the same as those being claimed and the Specification lacks any direction in achieving such a result. As the discussion is directed towards claim 9, claims 2 and 4 – 7 similarly are Rejected as the matrices in claims 2 and 4 – 7 are simple substitutions of θ at 0, 90, 180, and 270 degrees. Additionally regarding claim 4, the matrix given is not an identity matrix as Joyce and Texas clearly teach thus claim 4 additionally incorrectly claims an identity matrix as would be readily recognized to one of ordinary skill in the art. One of ordinary skill in the art in understanding the state of the prior art (Factor C) and affording a high level to one of ordinary skill in the art (Factor D) would understand the lack of predictability in the results being claimed (Factor E) as there is no direction presented in the Specification by the Inventors or Applicants (Factor F) and the lack of working examples (Factor G including incorrectly claiming an identity matrix) as weighing negatively against the claims since the understanding of one of ordinary skill in the art would derive a different result as show above. Thus, Wands Factors C, D, E, F, and G weight negatively against the claimed matrices. Regarding claims 15 and 20, see claim 9 as the limitation are similar and thus the claims are similarly Rejected. Regarding claims 11 and 17, see claim 2 as the limitation are similar and thus the claims are similarly Rejected. Regarding claims 13 – 14, see claims 4 – 7 as the limitations are alternative options from claims 4 – 7 thus reciting similar limitations and thus the claims are similarly Rejected. The following is a quotation of 35 U.S.C. 112(b): (b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention. The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph: The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention. Claims 2, 9, and 15 – 20 are rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention. The term “optimal” in claims 2 and 17 is a relative term which renders the claim indefinite. The term “optimizing” is not defined by the claim, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention. The Specification in Paragraphs 286 – 287 discusses rotation angle selection, but provides no clear optimization criteria (as to the patch size after rotation or the RDO cost). The term “valid” in claims 9, 15, and 20 is a relative term which renders the claim indefinite. The term “valid” is not defined by the claim, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention. the term has Indefinite metes and bounds as an assertion by the Applicant rather than a result of a derivation that was explained to be understood to one of ordinary skill in the art thus the assertions of valid transformations has Indefinite metes and bounds. Regarding claim 16, the claimed “apparatus for encoding point cloud data” has indefinite metes and bounds regarding patentable weight to afford the limitation as intended use language or as invoking Functional Analysis. Regarding claims 17 – 20, the dependent claims do not cure the deficiency of independent claim 16 and thus are similarly Rejected. For purposes of Examiner, the preamble is not being afforded patentable weight. Regarding claim 17, the matrices appear struck in the amended claim and the phrase “coordinate system as wherein the transformation” claimed has Indefinite metes and bounds as claim 17 was not amended similarly to claim 2. For purposes of Examination, claim 17 will be rejected similarly to claim 2. Claim Rejections - 35 USC § 103 In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status. This application currently names joint inventors. In considering patentability of the claims the examiner presumes that the subject matter of the various claims was commonly owned as of the effective filing date of the claimed invention(s) absent any evidence to the contrary. Applicant is advised of the obligation under 37 CFR 1.56 to point out the inventor and effective filing dates of each claim that was not commonly owned as of the effective filing date of the later invention in order for the examiner to consider the applicability of 35 U.S.C. 102(b)(2)(C) for any potential 35 U.S.C. 102(a)(2) prior art against the later invention. 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. Claim(s) 1, 3, 8, 10, 16, and 18 – 19 are rejected under 35 U.S.C. 103 as being unpatentable over Kato, et al. (US PG PUB 2021/0176474 A1 referred to as “Kato” throughout) [Cited in Applicant’s November 12th, 2024 IDS], and further in view of Tsai, et al. (US PG PUB 2020/0013235 A1 in which citations will come from the US PG PUB instead of the enabling description in US Provisional Application 62/693,485) [Cited in Applicant’s November 12th, 2024 IDS]. Regarding claim 1, see claim 16 which is the apparatus / program performing the steps of the claimed method. Regarding claim 3, see claim 18 which is the apparatus / program performing the steps of the claimed method. Regarding claim 8, see claim 19 which is the apparatus / program performing the steps of the claimed method. Regarding claim 10, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai. The Examiner observes Kato at least in Figures 7 and 9, 15 – 16, and 19 as well as Paragraphs 7 – 10, 62 – 65, and 130 – 132 teach decoding encoded data and processing the bitstream created by the encoder rendering obvious the decoder as the inverse process of the encoder thus encoder citations may be included in the rejection of a decoder as the decoder is the faithful inverse of the encoder as readily recognized by one of ordinary skill in the art. The combination teaches obtaining a bitstream comprising a syntax element that determines a transformation matrix for a patch of a point cloud [See next limitation for combination with Tsai and Kato Figures 8 – 9, 16, and 19 (see at least reference characters 151 – 153, 216 and S406) as well as Paragraphs 119 – 123 (encoding inverse rotation parameter for decoder), 139, 152, 201 – 205, and 235 – 241 (using the inverse rotation matrix / having the angle to undo the rotation from the encoder)] or determines an inverse of the transformation matrix of a point cloud [Tsai Figure 9 (see at least reference characters 903, 906, and 908) as well as Paragraphs 55 – 66 (signaling transform matrices and index values used to the decoder to rotate / transform patches including Tables 1 and 2 and Paragraphs 60 – 66 (regular rotation or inverse rotation matrices as the transform matrix)]; and reconstructing the point cloud by transforming, based on the transformation matrix or the inverse of the transformation matrix, second coordinates (x2, y2) of a point of the patch [See next limitation for additional citations for combination with Tsai and Kato Figures 8 – 9 and 17 (see at least reference character 217) as well as Paragraphs 132 – 136 (reconstructing the point cloud by decoding the patches), 139 – 142 (decoding images for point cloud to display), and 203 – 206 (unpacking to decode images for point cloud reconstruction)] to first coordinates (x1, y1) of the point [Kato Figures 8 – 9, 16, and 19 (see at least reference characters 151 – 153, 216 and S406) as well as Paragraphs 119 – 123 (encoding inverse rotation parameter for decoder), 139, 152, 201 – 205, and 235 – 241 (using the inverse rotation matrix / having the angle to undo the rotation from the encoder); Tsai Figure 9 (see at least reference characters 903, 906, and 908) as well as Paragraphs 56 – 59 (adjusting coordinates of patches) and 60 – 66 (signaling transform matrices to the decoder to rotate / transform patches)], wherein the first coordinates (x1, y1) are in a first coordinate system [See next limitation for combination with Tsai regarding “coordinate system” and Kato Figures 8 – 9, 16, and 19 (see at least reference characters 151 – 153, 216 and S406) as well as Paragraphs 119 – 123 (encoding inverse rotation parameter for decoder), 139, 152, 201 – 205, and 235 – 241 (using the inverse rotation matrix / having the angle to undo the rotation from the encoder)], and wherein the second coordinates (x2, y2) are in a second coordinate system [Tsai Figure 9 (see at least reference characters 903, 906, and 908) as well as Paragraphs 56 – 59 (adjusting coordinates of patches) and 60 – 66 (signaling transform matrices to the decoder to rotate / transform patches including Table 2 and the “U” and “V” size variables for designation of the coordinate system to use (rotating one set of coordinates to another system as readily understood by one of ordinary skill in the art)]. See claim 1 for the motivation to combine Kato and Tsai as claim 1 is the encoder claim generating rotation / transformation of patches to be processed by the faithful inverse decoding claim and thus similar motivation exists. Regarding claim 16, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai. The combination teaches one or more processors [Kato Figure 22 (see at least reference characters 900 and 901) as well as Paragraphs 276 – 283 (CPU to execute programs on a memory)]; and a non-transitory storage medium storing instructions that [Kato Figure 22 (see at least reference characters 902 and 903) as well as Paragraphs 276 – 283 (programs stored on memories)], when executed by the one or more processors [Kato Figure 22 (see at least reference characters 900 and 901) as well as Paragraphs 276 – 283 (CPU to execute programs on a memory)], cause the apparatus [Kato Paragraphs 284 – 292 (computer / AV device)] to: project a patch from a three-dimensional space to a two-dimensional space [Tsai Figures 3 — 5 as well as Paragraphs 35 — 40 (projection techniques for patches from 3D data to 2D data (to combine with Kato Paragraphs 52 – 62 and 107 as well) with rotation data tested as part of the projection to determine — to combine with Paragraphs 51 – 61 which further teaches projection and generation of an occupancy map)]; transform, based on a transformation matrix or an inverse of the transformation matrix [Tsai Figures 4 – 8 (patch placement see at least reference characters 602, 603, and 610) and 10 – 11 (how many indices to select from to place a patch with reflect / rotation consideration) as well as Tables 1 and 2 (see the “Idx” in Table 2 at least) as well as Paragraphs 34 and 37 – 42 (tables to store index values relating to patch placement in an image which is compressed / encoded to form a bitstream see further Paragraphs 43 – 46 and Paragraph 38 with the same index for regular or inverted rotation (to combine with Kato see at least last citation in the “wherein” limitation)), 51 – 61 (the (u,v) and (x,y) coordinates used render obvious the claimed coordinates and the transformed coordinates and see at least Equation 1 and Tables 1 – 2 in which rotation matrices and shifts are applied render obvious the coordinates claimed of the patch being placed in an image where Paragraphs 62 – 67 teach compressing the index / multiplexing into the bitstream as well as signaling inverse / inversion parameters)], first coordinates (x1, y1) of a point of the patch in the two-dimensional space to second coordinates (x2, y2) of the point in the two-dimensional space, wherein the first coordinates (x1, y1) are in a first coordinate system, and wherein the second coordinates (x2, y2) are in a second coordinate system [Kato Figures 3 (see the search over rotation and invertible transform methods listed), 11 – 12 (searching of optimal patch placement with coordinate / position / placement considerations – to combine with Tsai’s coordinate teachings and transforms), 15 – 21 (see the search for rotation of patches and at least reference characters S306, S307, S311, S506, S507, S511, S531, and S533) as well as Paragraphs 81 – 82 (rotation angle to be determined – similar to Paragraphs 97 – 99), 119 – 123 (inversion and rotation parameters determined for patch placement), 160 – 169 (searching for transformation (rotation and inversion / flipping of the patch which as obvious transformations to apply as would be readily recognized by one of ordinary skill in the art)), 212 – 217 (method to determine flipping and rotating the patch – to combine with matrices of Tsai in the previous citation (in particular the equations used in Paragraphs 51 – 61), 254 – 257 (method to determine flipping and rotating the patch – to combine with matrices of Tsai), and 266 – 270 (searching for optimal patch placement of the patch in view of previous embodiment conducting the search)]; and encode a syntax element into a bitstream [Next limitation regarding the syntax element and additionally Kato Figures 3 and 7 (see at least reference characters 113 – 117 (compression / encoding information about the patches to multiplex into a bitstream) as well as Paragraph 48 and 53 – 57 (obvious to one of ordinary skill in the art to encode indices, rotations, and matrices as syntax elements), 120, 196 – 200 (multiplexing encoded data and parameters into a bitstream)], wherein the syntax element indicates the transformation matrix for the patch [In combination with next limitation Tsai Figures 4 – 8 (patch placement) and 10 – 11 (how many indices to select from to place a patch with reflect / rotation consideration) as well as Tables 1 and 2 (see the “Idx” in Table 2 at least) as well as Paragraphs 34 and 37 – 42 (tables to store index values relating to patch placement in an image which is compressed / encoded to form a bitstream see further Paragraphs 43 – 46 and Paragraph 38 with the same index for regular or inverted rotation), 51 – 61 (store / encode index of orientation of the rotation / transformation matrix applied to the current patch where Paragraphs 62 – 66 teach compressing the index / multiplexing into the bitstream as well as signaling inverse / inversion parameters)] or indicates the inverse of the transformation matrix [Kato Figures 17 – 20 (see at least reference characters S311, S406, S504) as well as Paragraphs 81 – 82 (inverting / inverse transforms / modifications to rotation matrices are considered), 99 (free selection of inverting matrix), 112 – 114 (matrix for packing patches), and 119 – 123 (control information / parameters signaling the use of inverse parameters), 160 – 162 (testing all inverse states to select one), 201 – 212 (decoding inverse parameters)]. The motivation to combine Tsai with Kato is to combine features in the same / related field of invention of encoding / decoding patches related to point clouds [Tsai Paragraphs 2 – 3] in order to improve packing of the patches in 2D images and occupancy maps for better compression [Tsai Paragraphs 6 – 8 where the Examiner also observes KSR Rationales (D) or (F) are also applicable]. This is the motivation to combine Kato and Tsai which will be used throughout the Rejection. Regarding claim 18, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai. The combination teaches wherein the transform matrix is a rotation matrix, and the rotation matrix corresponds to a rotation angle θ associated with the patch [Kato Figures 7 – 8 and 10 (see at least reference characters 151, 152, S127, S151, S152, and S153), 17, and 20 as well as Paragraphs 161 – 168 (searching through rotation angles to transform patch into the occupancy map), 211 – 215 (searching to optimize rotation angle), 252 – 257 (rotation angle searched to place patch in occupancy map); Tsai Figures 3 – 5 (exemplary rotation angles shown), 8, and 10 – 11 (flowcharts test angle for rotation) as well as Paragraphs 31 – 38 (angles tested), and 53 – 61 (see at least Tables 1 and 2 listing various rotation angles and corresponding transform matrices to use to perform the rotation and further the index is a function of the rotation angle)]. See claim 16 for the motivation to combine Kato and Tsai. Regarding claim 19, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai. The combination teaches wherein the rotation matrix determined based on the rotation angle θ [See next limitation for citations]; or is determined based on a functional relationship of the rotation angle θ [Kato Figures 7 – 8 and 10 (see at least reference characters 151, 152, S127, S151, S152, and S153), 17, and 20 as well as Paragraphs 161 – 168 (searching through rotation angles to transform patch into the occupancy map), 211 – 215 (searching to optimize rotation angle), 252 – 257 (rotation angle searched to place patch in occupancy map); Tsai Figures 3 – 5 (exemplary rotation angles shown), 8, and 10 – 11 (flowcharts test angle for rotation and determine corresponding matrices) as well as Paragraphs 31 – 38 (angles tested), and 53 – 61 (see at least Tables 1 and 2 listing various rotation angles and corresponding rotation matrices to perform the rotation and Equation 1 in Paragraph 56 applying the rotation matrix to the patch coordinates)]. See claim 16 for the motivation to combine Kato and Tsai. Claim(s) 2, 4 – 7, 9, 11 – 15, 17, and 20 are rejected under 35 U.S.C. 103 as being unpatentable over Kato, Tsai, and further in view of Joyce (“Some linear transformations on R2” Fall 2013 referred to as “Joyce” throughout and found at: https://www2.clarku.edu/faculty/djoyce/ma130/lintrans2.pdf) [Cited in Applicant’s November 12th, 2024 IDS], “Geometric Transformations” (NPL found at https://web.ma.utexas.edu/users/gilbert/M340L/LA05GeometricTrans.pdf and referred to as “Texas” throughout where the NPL is afforded a date of January 2013) [Cited in Applicant’s November 12th, 2024 IDS], and Mammou, et al. (US PG PUB 2020/0014953 A1 referred to as "Mammou" throughout in which citations will come from the US PG PUB in lieu of US Provisional Application 62/694,124 where the Application associated with the US PG PUB has been Patented (now US Patent 1,202,098) and thus presumed enabled). Regarding claim 11, the claim is the inverse of the encoding method performed in claim 2 reciting the same / similar features and thus is similarly Rejected. Regarding claim 12, the claim is the inverse of the encoding method performed in claim 3 reciting the same / similar features and thus is similarly Rejected. Regarding claim 13, the claim is the inverse of the encoding method performed in claims 4 or 5 reciting the same / similar features and thus is similarly Rejected. Regarding claim 14, the claim is the inverse of the encoding method performed in claims 6 or 7 reciting the same / similar features and thus is similarly Rejected. Regarding claim 15, the claim is the inverse of the encoding method performed in claim 9 reciting the same / similar features and thus is similarly Rejected. Regarding claim 17, see claim 2 which is the method performing the steps of the claimed apparatus. Regarding claim 20, see claim 9 which is the method performing the steps of the claimed apparatus. Regarding claim 2, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. Joyce teaches specific rotation and reflection matrices with serval examples to combine the matrices to elaborate on the teaches and understandings supporting Tsai. Texas teaches rotation and reflection matrices fundamentals and treatments on combining operations similar to Joyce with a different approach and more clear teaching of taking products to combine rotation and reflection transformation matrices. Mammou renders obvious additional optimization criteria to supplement the teachings of Kato and Tsai including minimizing patch sizes during packing frames for encoding / decoding. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai with the understanding of rotation and reflection matrices as taught by Joyce and Texas and with the optimization criteria as taught by Mammou. The combination teaches wherein the transformation matrix for transforming coordinates between the first coordinate system and the second coordinate system is represented as 1 0 0 - 1 , 0 - 1 1 0 , - 1 0 0 1 , or 0 1 - 1 0 , and wherein the transformation matrix represents a coordinate transformation comprising at least one of rotation or reflection operations for optimizing patch placement in point cloud encoding [See claim 1 and for the “coordinate system” citations and additionally Tsai Paragraphs 53 – 61 (see at least Table 2 where idx = 1, 3, 4, or 6 yields one of the claimed rotation / transformation matrices between coordinate systems) and in view of at least Joyce Examples 1, 3, 4, and 11 (reflection / rotation matrices) as well as Texas Pages 2 – 4 render obvious the evaluation of such a matrix (see the 112a Rejection for further analysis and incorporated into this limitation’s Rejection); Kato Figures 3, 8, 11 – 12 and at least Paragraphs 90 – 95 (as characterized by Applicant rendering obvious the “optimizing” feature claimed which is considered in combination with Mammou Figure 3 (subfigures included), 8, 10, and 12 (subfigures included) as well as Paragraphs 84 – 87 (minimization of non-used pixels / optimizing packing patches by minimizing patch area), 141 – 147 (minimization of patch size to minimize image size with techniques listed to achieve such minimization such as MFFD (Paragraph 146) and resolution (patch size limits in Paragraph 147)), 346 – 351 (rotating patches for placement in occupancy maps / forming meta data for patch placement to signal where other transformations are suggested in Paragraph 130)]. See claim 1 for the motivation to combine Kato and Tsai. The motivation to combine Joyce with Tsai and Kato is to combine features in the same / related field of invention to elaboration on the rotations taught by Kato and Tsai (see at least claims 39 and 40 for citations) in order to combine known techniques to yield predictable results [Joyce Page 1 where the Examiner observes KSR Rationales (A) or (C) or (G) are also applicable]. The motivation to combine Texas with Joyce, Tsai, and Kato is to combine features in the same / related field of invention to elaboration on the rotations taught by Kato and Tsai (see at least claims 39 and 40 for citations) in order to combine known techniques to yield predictable results [Texas Page 1 where the Examiner observes KSR Rationales (A) or (C) or (G) are also applicable]. The motivation to combine Mammou with Texas, Joyce, Tsai, and Kato is to combine features in the same / related field of invention of compression / decompression of point cloud data [Mammou Paragraphs 2 - 3] in order to improve encoding efficiency [Mammou Paragraph 199] and to further render obvious the routine optimizations as taught by Tsai (e.g. minimizing patch size) [Mammou Paragraphs 84 and 141 and additionally MPEP2144.05 Il where the teachings of Mammou render the claims "minimum bounding rectangle" a routine optimization to one of ordinary skill in the art where the Examiner observes at least KSR Rationale (D) is also applicable]. This is the motivation to combine Kato, Tsai, Joyce, Texas, and Mammou which will be used throughout the Rejection. Regarding claim 4, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. Joyce teaches specific rotation and reflection matrices with serval examples to combine the matrices to elaborate on the teaches and understandings supporting Tsai. Texas teaches rotation and reflection matrices fundamentals and treatments on combining operations similar to Joyce with a different approach and more clear teaching of taking products to combine rotation and reflection transformation matrices. Mammou renders obvious additional optimization criteria to supplement the teachings of Kato and Tsai including minimizing patch sizes during packing frames for encoding / decoding. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai with the understanding of rotation and reflection matrices as taught by Joyce and Texas and with the optimization criteria as taught by Mammou. The combination teaches the rotation matrix used for transforming patch coordinates in point cloud encoding is represented as 1 0 0 - 1 when the rotation angle θ is zero degrees, and wherein the rotation matrix corresponds to an identity transformation. [Tsai Paragraphs 53 – 61 (see at least Table 2 where idx = 6 yields the same rotation matrix) and in view of at least Joyce Examples 3 (result from the angle being 0 degrees), 4 – 6 (scaling of an identity matrix where a scaling factor of 1 would be obvious to one of ordinary skill in the art), and 11 as well as Texas Pages 2 – 4 render obvious the evaluation of such a matrix (see the 112a Rejection for further analysis and incorporated into this limitation’s Rejection)]. See claim 2 for the motivation to combine Kato, Tsai, Joyce, Texas, and Mammou. Regarding claim 5, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. Joyce teaches specific rotation and reflection matrices with serval examples to combine the matrices to elaborate on the teaches and understandings supporting Tsai. Texas teaches rotation and reflection matrices fundamentals and treatments on combining operations similar to Joyce with a different approach and more clear teaching of taking products to combine rotation and reflection transformation matrices. Mammou renders obvious additional optimization criteria to supplement the teachings of Kato and Tsai including minimizing patch sizes during packing frames for encoding / decoding. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai with the understanding of rotation and reflection matrices as taught by Joyce and Texas and with the optimization criteria as taught by Mammou. The combination teaches the rotation matrix is represented as 0 - 1 1 0 when the rotation angle θ is 90 degrees, and wherein the rotation matrix represents a coordinate transformation for rotating patch coordinates by 90 degrees in point cloud encoding [Tsai Paragraphs 53 – 61 (see at least Table 2 where idx = 1 yields the same rotation matrix) and in view of at least Joyce Figure 3 (90 degree rotation) and Examples 2 – 4, and 11 as well as Texas Pages 2 – 4 render obvious the evaluation of such a matrix (see the 112a Rejection for further analysis and incorporated into this limitation’s Rejection)]. See claim 2 for the motivation to combine Kato, Tsai, Joyce, Texas, and Mammou. Regarding claim 6, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. Joyce teaches specific rotation and reflection matrices with serval examples to combine the matrices to elaborate on the teaches and understandings supporting Tsai. Texas teaches rotation and reflection matrices fundamentals and treatments on combining operations similar to Joyce with a different approach and more clear teaching of taking products to combine rotation and reflection transformation matrices. Mammou renders obvious additional optimization criteria to supplement the teachings of Kato and Tsai including minimizing patch sizes during packing frames for encoding / decoding. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai with the understanding of rotation and reflection matrices as taught by Joyce and Texas and with the optimization criteria as taught by Mammou. The combination teaches the rotation matrix is represented as - 1 0 0 1 when the rotation angle θ is 180°, and wherein the rotation matrix represents a coordinate transformation for rotating patch coordinates by 180 degrees in point cloud encoding [Tsai Paragraphs 53 – 61 (see at least Table 2 where idx = 4 yields the same rotation matrix) and in view of at least Joyce Examples 3, 4, and 11 as well as Texas Pages 2 – 4 (see reflections over axes) which renders obvious the evaluation of such a matrix (see the 112a Rejection for further analysis and incorporated into this limitation’s Rejection)]. See claim 2 for the motivation to combine Kato, Tsai, Joyce, Texas, and Mammou. Regarding claim 7, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. Joyce teaches specific rotation and reflection matrices with serval examples to combine the matrices to elaborate on the teaches and understandings supporting Tsai. Texas teaches rotation and reflection matrices fundamentals and treatments on combining operations similar to Joyce with a different approach and more clear teaching of taking products to combine rotation and reflection transformation matrices. Mammou renders obvious additional optimization criteria to supplement the teachings of Kato and Tsai including minimizing patch sizes during packing frames for encoding / decoding. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai with the understanding of rotation and reflection matrices as taught by Joyce and Texas and with the optimization criteria as taught by Mammou. The combination teaches the rotation matrix used for transforming patch coordinates in point cloud encoding is represented as 0 1 - 1 0 when the rotation angle θ is 270° , and wherein the rotation matrix represents a coordinate transformation for rotating patch coordinates by 270 degrees [Tsai Paragraphs 53 – 61 (see at least Table 2 where idx = 3 yields the same rotation matrix) and in view of at least Joyce Examples 3, 4, and 11 as well as Texas Pages 2 – 4 render obvious the evaluation of such a matrix (see the 112a Rejection for further analysis and incorporated into this limitation’s Rejection)]. See claim 2 for the motivation to combine Kato, Tsai, Joyce, Texas, and Mammou. Regarding claim 9, Kato teaches searching for a rotation angle to place a patch and signaling the patches and rotation selected from an encoder to be decoded. While Kato addresses selection of transformations / rotations to use, Tsai teaches particular rotations to use and transforming coordinates and changing coordinate systems through reflections and rotations for encoding and later decoding patches. Joyce teaches specific rotation and reflection matrices with serval examples to combine the matrices to elaborate on the teaches and understandings supporting Tsai. Texas teaches rotation and reflection matrices fundamentals and treatments on combining operations similar to Joyce with a different approach and more clear teaching of taking products to combine rotation and reflection transformation matrices. Mammou renders obvious additional optimization criteria to supplement the teachings of Kato and Tsai including minimizing patch sizes during packing frames for encoding / decoding. It would have been obvious to one of ordinary skill art before the effective filing date of the claimed invention to modify the teachings of Kato’s rotation angle search to applying in packing / projecting patches into frames and form the occupancy maps with matrices and suggested computations as taught by Tsai with the understanding of rotation and reflection matrices as taught by Joyce and Texas and with the optimization criteria as taught by Mammou. The combination teaches the rotation matrix for transforming coordinates between the first coordinate system and the second coordinate system is represented as cos ⁡ θ - sin ⁡ θ sin ⁡ θ - cos ⁡ θ wherein the rotation matrix represents a valid orthogonal coordinate transformation for point cloud patch encoding that combines rotation and reflection operations [Tsai Paragraphs 53 – 61 (see at least Tables 1 and 2) where one of ordinary skill in the art understands Tsai’s matrices as being evaluated as a particular point and further in view of Joyce in Examples 3 and 11 teach a general rotation matrix and Texas in Pages 3 – 4 teach combining the rotation matrix with reflections rendering the claim obvious (see the 112a Rejection for further analysis and incorporated into this limitation’s Rejection); Mammou Figures 4 – 6 (subfigures included) as well as Paragraphs 346 – 348 (rotation parameters signaled and encoded for angles determined placing patches to be combined with Kato Paragraphs 240 – 260 at least coding the rotation parameter including the angle and renders obvious the “valid” transformations claimed to combine with Tsai)]. See claim 2 for the motivation to combine Kato, Tsai, Joyce, Texas, and Mammou. Conclusion The prior art made of record and not relied upon is considered pertinent to applicant's disclosure. Oh (US PG PUB 2021/0005006 A1 referred to as “Oh” throughout) teaches in Paragraphs 769 – 774 syntax elements (e.g. a patch orientation index) to encode specific syntax elements and further describes the encoding for syntax in Kato and Tsai. Reference considered that is NOT prior art: Oh (US PG PUB 2021/0209807 A1 referred to as “Oh 07” throughout) teaches the matrices and syntax for signaling rotations / reflections of patches. Applicant's amendment necessitated the new ground(s) of rejection presented in this Office action. Accordingly, THIS ACTION IS MADE FINAL. See MPEP § 706.07(a). Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a). A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any nonprovisional extension fee (37 CFR 1.17(a)) pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action. Any inquiry concerning this communication or earlier communications from the examiner should be directed to Tyler W Sullivan whose telephone number is (571)270-5684. The examiner can normally be reached IFP. Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice. If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, David Czekaj can be reached at (571)-272-7327. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300. Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000. /TYLER W. SULLIVAN/ Primary Examiner, Art Unit 2487
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Prosecution Timeline

Nov 12, 2024
Application Filed
Nov 27, 2024
Response after Non-Final Action
Jan 08, 2026
Non-Final Rejection mailed — §103, §112
Mar 30, 2026
Response Filed
Jun 05, 2026
Final Rejection mailed — §103, §112 (current)

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