`Tel: 571-272-7822
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`Paper 23
`Entered: January 13, 2015
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`UNITED STATES PATENT AND TRADEMARK OFFICE
`_______________
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`BEFORE THE PATENT TRIAL AND APPEAL BOARD
`_______________
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`INTEL CORPORATION,
`Petitioner,
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`v.
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`FUZZYSHARP TECHNOLOGIES, INC.,
`Patent Owner.
`_______________
`
`Case IPR2014-00001
`Patent 6,618,047 B1
`_______________
`
`
`Before JUSTIN T. ARBES, TREVOR M. JEFFERSON, and
`DAVID C. MCKONE, Administrative Patent Judges.
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`MCKONE, Administrative Patent Judge.
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`FINAL WRITTEN DECISION
`35 U.S.C. § 318(a) and 37 C.F.R. § 42.73
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`IPR2014-00001
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`I. INTRODUCTION
`A. Background
`Intel Corporation (“Petitioner”) filed a Petition (Paper 1, “Pet.”) to
`institute an inter partes review of claims 1, 8, 11–13, 46, 57, 64, 65, and 67
`of U.S. Patent No. 6,618,047 B1 (Ex. 1001, “the ’047 patent”). FuzzySharp
`Technologies, Inc. (“Patent Owner”) filed a Preliminary Response (Paper 6,
`“Prelim. Resp.”). Pursuant to 35 U.S.C. § 314, in our Decision to Institute
`(Paper 7, “Dec.”), we instituted this proceeding as to all of the challenged
`claims of the ’047 patent.
`During this trial, Patent Owner filed a Patent Owner Response
`(Paper 15, “PO Resp.”) and Petitioner filed a Reply to the Patent Owner
`Response (Paper 19, “Reply”). An oral hearing in this matter and IPR2014-
`00002 (argued together) was held on October 28, 2014 (Paper 22, “Tr.”).
`We have jurisdiction under 35 U.S.C. § 6(c). This decision is a final
`written decision under 35 U.S.C. § 318(a) as to the patentability of the
`challenged claims. Based on the record before us, Petitioner has
`demonstrated by a preponderance of the evidence that claims 1, 8, 11–13,
`46, 57, 64, 65, and 67 are unpatentable.
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`B. Related Proceedings
`According to Petitioner, Patent Owner has asserted the ’047 patent
`against Petitioner in Case No. 4:12-cv-04413-YGR (N.D. Cal.) (“Intel
`action”), which is currently on appeal to the U.S. Court of Appeals for the
`Federal Circuit. Pet. 2; Paper 18.
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`According to Patent Owner, the only matter pending that may be
`affected by a decision in this proceeding is FuzzySharp Technologies, Inc. v.
`Nvidia Corp., Case No. 12-cv-6375-JST (N.D. Cal.). Paper 5, at 2.
`Petitioner also filed a petition for inter partes review of U.S. Patent
`No. 6,172,679 B1 (“the ’679 patent”). See Intel Corp. v. FuzzySharp
`Technologies, Inc., Case IPR2014-00002 (PTAB). The ’047 patent is a
`continuation of the ’679 patent. See Ex. 1001, at [63]. The ’679 patent also
`is asserted by Patent Owner in the Intel action. See, e.g., Ex. 1009.
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`C. References Relied Upon
`Petitioner relies upon the following prior art references:
`David Salesin & Jorge Stolfi, The ZZ-Buffer: A Simple and Efficient
`Rendering Algorithm with Reliable Antialiasing (1989)
`(Ex. 1002, “Salesin”);
`JAMES D. FOLEY ET AL., COMPUTER GRAPHICS, PRINCIPLES AND
`PRACTICE 340–41, 521–22, 665, 799 (2d ed. 1990) (Ex. 1003,
`“Foley”).
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`D. Grounds of Unpatentability
`We instituted this proceeding based on the grounds of unpatentability
`set forth in the table below. Dec. 36–37.
`Reference(s)
`Basis
`Claim(s) Challenged
`Salesin
`§ 102(b)
`1, 8, 12, 13, 46, 57, 64, 65, and 67
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`Salesin and Foley
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`§ 103(a)
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`Patennt 6,618,0447 B1
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`E. The ’’047 Patennt
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`(“3-DD”) compuuter graphics visibilitty calculatiions. Ex. 11001, 1:13
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`be viewedd from mulltiple viewwpoints. Idd. at 4:14–
`image can
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`poinnt in a 3-D
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`24. This is illuustrated in Figures 2 aand 3, reprroduced beelow:
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`The ’0477 patent deescribes tecchniques fofor improviing three-ddimensionaal
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`arbitrary vieoint at an arons of a pots projectioFiguure 2 depict
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`ewpoint. IId. at 3:13..
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`Figuure 3 depictts the relattionship beetween projjection boxxes and a ffuzzy
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`projeection box. Id. at 3:114–15.
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`be
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`A groupp of viewpooints (e.g., the three VVPs of Figgure 3) can
`bounding
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`associated withh a coordinnate systemm and grouuped in a “vviewpoint b
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`box”” (e.g., BB of Figure 3), which the patent
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`as the smaallest right
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`quaddrangular pprism encloosing the vviewpoints.. Id. at 4:335–40. Th
`e point to
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`be obbserved caan be said tto be totally visible frfrom the boounding boox if it is
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`alwaays visible from everyy possible viewpointt in the bouunding boxx and
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`totallly invisible if it is hiddden from every suchh viewpoinnt. Id. at 44:46–50.
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`The group of vviewpoints may contaain only a ssingle viewwpoint; in tthat case,
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`the bbounding bbox degeneerates into the viewpooint. Id. att 4:58–63.
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`As showwn in Figurre 2, the pooint to be oobserved (PPO) can bee
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`repreesented byy the interseection of aa projectionn plane (PPP) and a veector (VV)
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`fromm the point to be obseerved (PO)
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`to a viewppoint (VP)
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`be diivided intoo rectangullar cells or elements ((fuzzy arraay FA). Idd. at 6:27–
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`wn in Figuure 3, to facilitate sammpling, thee projectionn plane cann
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`36. As shown in Figure 2, the point may be included in a visible patch (PT)
`that occludes an invisible point (IP). Id. at 5:18–20. Surfaces can be
`approximated by meshes of patches and also by hierarchies that represent
`meshes of patches at different levels of detail. Id. at 6:43–46. The smallest
`right quadrangular prism that encloses a patch and whose edges are parallel
`to the coordinate system is termed a “bounding volume” of the patch. Id. at
`6:54–57.
`The ’047 patent describes detecting patches that are invisible to all
`viewpoints in a bounding box. Id. at 8:42–10:21. Similarly, it describes
`detecting patches that are totally visible to all viewpoints in the bounding
`box. Id. at 10:22–11:16. Overlapping patches can be stored in a linked list
`called a projection patch list. Id. at 11:20–25. The ’047 patent describes
`calculating a list of the totally visible and totally invisible patches for a
`viewpoint group. Id. at 11:20–12:57. The patches identified as totally
`visible and totally invisible can be ignored in subsequent visibility
`computations. Id. at 12:57–67. For example, they need not be compared
`with other patches to determine their visibility. Id. at 12:62–64.
`Claims 11 and 67, reproduced below, are illustrative of the claimed
`subject matter:
`11. A method of reducing a step of visibility
`computations in 3-D computer graphics from a perspective of a
`viewpoint, the method comprising:
`computing, before said step and from said perspective,
`the visibility of at least one entity selected from 3-
`D surfaces and sub-elements of said 3-D surfaces,
`wherein said computing step comprises at least a
`comparison between a pair of depth-related
`numbers to determine which of the surfaces or the
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`sub-elements of the surfaces associated with said
`numbers is closer to said viewpoint and said 3-D
`surfaces are arranged in a hierarchy represented by
`patches in varying levels of details; and
`skipping, at said step, at least an occlusion relationship
`calculation for at least one entity that has been
`determined to be invisible in said computing step.
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`67. A method in 3-D computer graphics for processing
`the visibility of 3-D surfaces before a subsequent step of
`visibility computations, said method comprising:
`for each selected 3-D surface or sub-element of a 3-D
`surface, identifying grid cells on a projection plane
`which are under or related
`to a projection
`associated with the bounding volume of said
`selected 3-D
`surface or
`sub-element,
`said
`projection and said subsequent step of visibility
`computations are from the perspective of a same
`viewpoint;
`for each of said grid cells, accessing the corresponding z-
`buffer element; and
`computing the visibility of the part of the bounding
`volume that projects onto said each of said grid
`cells by comparing the depth-related data stored in
`said corresponding z-buffer element with the
`depth-related value associated with said part.
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`II. ANALYSIS
`A. Claim Construction
`The ’047 patent is expired. “[T]he Board’s review of the claims of an
`expired patent is similar to that of a district court’s review.” In re Rambus
`Inc., 694 F.3d 42, 46 (Fed. Cir. 2012) (internal citations omitted). Thus, we
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`construe the claims in accordance with their ordinary and customary
`meanings, as would be understood by a person of ordinary skill in the art, in
`the context of the specification. See generally Phillips v. AWH Corp., 415
`F.3d 1303 (Fed. Cir. 2005) (en banc).
`In the Petition, Petitioner asserted that the parties had stipulated to the
`constructions of several claim terms in the Intel action. Pet. 14–17. Patent
`Owner did not propose a construction for any claim term in the Preliminary
`Response. For several claim terms, we preliminarily determined that the
`purportedly stipulated constructions proposed by Petitioner represented the
`ordinary and customary meaning of those terms, as would be understood by
`a person of ordinary skill in the art, in the context of the specification.
`Dec. 9–11. For other claim terms, we determined the purportedly stipulated
`constructions proposed by Petitioner were too narrow. Id. at 11–13.
`Additionally, Petitioner proposed a construction for “determining
`which of said at least one of 3-D surfaces or their sub-elements is always
`invisible or always visible,” as recited in claims 1 and 8, that would require
`determining which of the at least one of 3-D surfaces is either always
`invisible or always visible. Pet. 12–14; Dec. 15. We declined to adopt this
`construction and preliminarily determined that the term requires determining
`which of the at least one of the 3-D surfaces or their sub-elements is always
`invisible or determining which of the at least one of the 3-D surfaces or their
`sub-elements is always visible. Dec. 16.
`In sum, we preliminarily construed the claim terms of the ’047 patent
`as follows:
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`Construction
`prior art types of rendering
`computations that determine which
`pixels or groups of pixels of 3-D
`surface(s) are visible, which include
`z-buffering and other visibility tests
`performed during rendering
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`decreasing the number of
`computational operations to perform
`visibility computations
`surfaces (i.e., the exterior) of 3-D
`objects that are part of a scene
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`dividing a projection plane into an
`imaginary lattice structure, where a
`“grid” is an “imaginary lattice
`structure”
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`identical rectangular grid cells
`representation(s) of a 3-D object’s
`surfaces upon an imaginary plane
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`the spatial position and orientation
`of a viewer
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`Claim Term
`“visibility related computations”
`(claims 1, 8, 64)
`“visibility computation(s)” (all
`challenged claims)
`“occlusion relationship calculation”
`(claims 11–13, 46)
`“reducing the visibility related
`computations” (claims 1, 8, 64)
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`“3-D surfaces” (all challenged
`claims)
`“surfaces” (all challenged claims)
`“sub-elements” (all challenged
`claims)
`“identifying grid cells” (claims 1, 8,
`64, 65, 67)
`“identifying, from said perspective,
`grid cells” (claim 57)
`“regular” grid cells (claim 57)
`“projection(s)” (all challenged claims
`except claim 11)
`“extent(s) of projection(s)/projection
`region(s)” (claims 64, 65)
`“projection plane” (claims 8, 12, 13,
`46, 57, 65, 67)
`“projections or extents” (claims 1, 8,
`56, 64)
`“viewpoint” (all challenged claims)
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`Claim Term
`“always invisible” (claims 1, 8)
`“always visible” (claims 1, 8)
`“invisible” (claims 11, 12, 57, 64)
`“visible” (claim 46)
`“z-buffer” (claims 57, 65, 67)
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`“bounding volume” (claims 12, 13,
`46, 57, 64, 67)
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`“identifying regions on . . . projection
`plane(s)” (claims 8, 12, 13, 46)
`“largest depths of said 3-D surfaces
`or their sub-elements” (claim 8)
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`“depth-related” (claims 11, 65, 67)
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`“projection based computations”
`(claim 1)
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`“determining which of said at least
`one of 3-D surfaces or their sub-
`elements is always invisible or
`always visible” (claims 1, 8)
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`Construction
`totally invisible/visible from a single
`viewpoint (if a single viewpoint) or
`totally invisible/visible from every
`viewpoint (if from a group of
`viewpoints)
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`a data structure in memory that is
`used to store depth data
`the smallest imaginary right
`quadrangular prism just enclosing
`the 3-D object’s surfaces and whose
`edges are parallel to the axes of the
`group coordinate system that
`approximates the 3-D object’s
`surfaces
`(does not require express
`construction)
`largest distances from a viewpoint to
`the 3-D surfaces or their sub-
`elements along the z-axis
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`related to the distance from a
`viewpoint to a 3-D surface along the
`z-axis
`computations that are based on
`representation(s) of a 3-D object’s
`surfaces upon an imaginary plane or
`planes
`determining which of the at least one
`of the 3-D surfaces or their sub-
`elements is always invisible or
`determining which of the at least one
`of the 3-D surfaces or their sub-
`elements is always visible
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`Petitioner and Patent Owner do not dispute these constructions. We
`see no reason to change these constructions based on the complete record
`developed during this trial and, thus, maintain them for purposes of this
`Decision. Neither Petitioner nor Patent Owner identifies any additional
`terms requiring construction. We also do not identify any other terms that
`require express construction for purposes of this Decision.
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`B. Asserted Grounds of Unpatentability
`1. Anticipation by Salesin
`a. Salesin
`Salesin describes an improved algorithm for rendering 3-D images.
`Ex. 1002, p. 1, cols. 1–2.1 According to this algorithm, a screen plane is
`divided into a two-dimensional array of rectangular cells (in “x” and “y”
`directions of a coordinate system), each of which covers a fixed-sized block
`of pixels. Id. at p. 2, col. 1. This array is represented in memory by a “ZZ-
`buffer,” which is a two-dimensional array. Id. Figure 1, reproduced below,
`illustrates an example:
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`1 Citations to Exhibit 1002 are in the form of page number of the article and
`column number on the page (p. x, col. y).
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`entry incluudes a
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`ZZ-buffer fer. Each Z illustratess a ZZ-buff
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`Figure 1
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`poinnter to a “tilelist,” or llinked list of tiles, annd each tilee describess an object
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`that may be vissible withinn the ZZ-bbuffer cell.
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`reprooduced bellow, illustrrates Salesiin’s tiles:
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`incluudes minimmum and mmaximum ddepths (Zmmin and Zmmax, respecctively, in aa
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`Figure 22 illustratess the repressentation oof a tile in aa tilelist. EEach tile
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`“z” ddirection oof the coorddinate systeem) spannned by the oobject in thhe tile
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`its obbject is opaque and ccovers the ccell entirelly. Id.
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`relattive to the sscreen planne. Id. Eaach tile alsoo has a fielld indicatinng whetherr
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`During a “scan conversion” phase, tiles can be added to the tilelists of
`the cells. Id. at p. 3, col. 1. During the tile adding procedure, a quick
`visibility test is performed on a new tile based on its depth and opacity
`information, and the tile is thrown away if it is obscured completely by other
`tiles already in the tilelist. Id. at p. 2, col. 2–p. 3, col. 1. Similarly, if the
`new tile completely obscures other tiles in the tilelist, those other tiles are
`discarded. Id. at p. 3, col. 1.
`Salesin describes a “rendering” phase, performed after the scan
`conversion phase, during which the visibility of objects is further calculated,
`and visible objects are shaded. Id. at p. 3, cols. 1–2. According to Salesin, if
`the first object in a tilelist is opaque and covers the entire cell, then no
`visibility tests are performed for that cell. Id. at p. 12, cols. 1–2.
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`b. Claims 1, 8, 12, 13, 46, 57, 64, and 65
`Petitioner introduced, in the Petition, evidence that claims 1, 8, 12, 13,
`46, 57, 64, and 65 are anticipated by Salesin. Pet. 23–35. Petitioner’s
`evidence included the declaration testimony of Dr. Seth Teller, a professor in
`the Electrical Engineering and Computer Science department of the
`Massachusetts Institute of Technology. See id. (citing Ex. 1013 (“Teller
`Decl.”) ¶¶ 56, 102, 109, 110, 114–116).2 Based on the evidence presented in
`the Petition, we preliminarily determined that Petitioner established a
`reasonable likelihood of prevailing in showing that claims 1, 8, 12, 13, 46,
`57, 64, and 65 are anticipated by Salesin. Dec. 17–29.
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`2 The Petition cites to Exhibit 1008. Petitioner, however, filed Exhibit 1013
`correcting Exhibit 1008. See Paper 9, at 2–3; Paper 11, at 1–2.
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`The PO Response is silent as to these claims and does not present any
`argument or evidence to show that they are patentable. Patent Owner also
`did not present any argument or evidence as to the patentability of these
`claims in its Preliminary Response. We have reviewed the Petition (at 23–
`27, 31–35) and evidence cited therein (including Teller Decl., Ex. 1013
`¶¶ 56, 102, 109, 110, 114–16), and are persuaded, by a preponderance of the
`evidence, that claims 1, 8, 12, 13, 46, 57, 64, and 65 are unpatentable based
`on anticipation by Salesin. Cf. Corning Inc. v. DSM IP Assets B.V., Case
`IPR2013-00046, slip op. at 4–5 (PTAB May 1, 2014) (Paper 81, Final
`Written Decision) (concluding that the challenged claims were unpatentable
`where the patent owner provided no additional substantive arguments in its
`patent owner response).
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`c. Claim 67
`Petitioner contends that Salesin anticipates claim 67. Pet. 35.
`Petitioner and Patent Owner dispute whether Salesin discloses the “bounding
`volume” recited in claim 67. We are persuaded that a preponderance of the
`evidence shows that Salesin does disclose the recited bounding volume, as
`well as the remaining limitations of claim 67.
`Independent claim 67 (emphases added) recites, inter alia:
`for each selected 3-D surface or sub-element of a 3-D surface,
`identifying grid cells on a projection plane which are
`under or related to a projection associated with the
`bounding volume of said selected 3-D surface or sub-
`element . . . [and]
`computing the visibility of the part of the bounding volume that
`projects onto said each of said grid cells by comparing
`the depth-related data stored in said corresponding z-
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`buffer element with the depth-related value associated
`with said part.
`Petitioner contends that Salesin meets these claim limitations because
`Salesin describes performing its pre-rendering scan conversion phase on
`what amounts to a bounding volume. Pet. 32–33.3 Per our construction in
`Section II.A above, a “bounding volume” for a 3-D object is the smallest
`imaginary right quadrangular prism just enclosing the 3-D object’s surfaces
`and whose edges are parallel to the axes of the group coordinate system that
`approximates the 3-D object’s surfaces.
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`As explained above, Salesin describes a ZZ-buffer that includes a
`two-dimensional array of rectangular cells (represented in x and y directions
`of a coordinate system), each of which contains a field pointing to a linked
`list of tiles that are defined, in part, with zmin and zmax fields (which
`delineate boundaries in a z direction of the coordinate system). Ex. 1002,
`p. 2, cols. 1–2. Petitioner contends that Salesin discloses a bounding volume
`consisting of a number of cells in the xy plane along with depth dimensions
`of the tiles for those cells. Specifically, Petitioner points to Salesin’s
`description of classifying polygons to be rendered, where Salesin explains
`that it “consider[s] a polygon small if its xy-bounding box does not span
`more than a few cells (say, 5 or 6) in each dimension.” Ex. 1002, p. 4,
`col. 1. According to Petitioner, the xy extent of the polygon’s bounding box,
`along with the zmin and zmax fields for the cells of the bounding box,
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`3 As explained in the Decision to Institute, at 23, claim 12 recites a bounding
`volume in the alternative and, thus, does not require a bounding volume.
`Petitioner, however, provides its analysis of bounding volumes in
`conjunction with claim 12 and incorporates its analysis of claim 12 for
`claim 67. Pet. 35.
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`constitutes a bounding volume. Pet. 32. Petitioner contends that Salesin
`describes performing its pre-rendering scan conversion phase on this 3-D
`volume bounded by zmin, zmax, and the xy extent of the cells of the
`polygon. Id. at 32–33. Petitioner supports its arguments with the testimony
`of Dr. Teller. Ex. 1013 ¶ 114.
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`Patent Owner responds that the cells of Salesin’s ZZ-buffer are
`described specifically as two-dimensional cells in a screen plane and, thus,
`cannot constitute three-dimensional volumes. PO Resp. 2. As explained
`above, however, Petitioner is not relying on the xy extent of a polygon in
`grid cells alone. Rather, as Petitioner points out, Salesin describes
`performing scan conversion on volumes that also include zmin and zmax
`dimensions. For example, Salesin explains that, during scan conversion,
`“we take each object, compute a rough [zmin, zmax] interval for every cell
`that may contain some part of the object, and store the resulting tiles into the
`ZZ-buffer.” Ex. 1002, p. 3, col. 1. Thus, we are not persuaded by Patent
`Owner’s argument.
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`Patent Owner also argues that, assuming Salesin shows 3-D volumes,
`Salesin’s cells are defined arbitrarily as having the same dimensions and,
`thus, do not constitute the smallest imaginary right quadrangular prism that
`encompasses an object. PO Resp. 2. Patent Owner, however, does not
`explain why a bounding volume must be evaluated at a level of granularity
`finer than Salesin’s grid cell. Indeed, claim 67 recites “identifying grid cells
`on a projection plane which are under or related to a projection associated
`with the bounding volume of said selected 3-D surface or sub-element”
`(emphasis added). This suggests that a bounding volume can be evaluated in
`terms of a number of grid cells. In any case, each of Salesin’s grid cells
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`“covers a fixed-size rectangular block of pixels (or possibly a single pixel)
`of the final image.” Ex. 1002, p. 2, col. 1. Thus, Salesin’s cells may be
`defined as finely as a single pixel.
`As to the z-direction, the zmin and zmax values “need not represent
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`the smallest such interval”; however, “the programmer might code a very
`precise scan-conversion procedure that computes the tightest z range
`possible for each tile,” depending on the programmer’s tolerance for
`inefficiency. Id. at p. 3, col. 2. We find that, in the case of a small xy
`bounding box, with cells at a pixel level of granularity, for example, and the
`tightest possible z range for each tile in the bounding box, a 3-D surface will
`be enclosed in the smallest imaginary right quadrangular prism whose edges
`are parallel to the axes of the group coordinate system.
`As to Salesin’s disclosure that computing the tightest z range possible
`for each tile “may also be inefficient since it means wasting a lot of
`computation on objects that may become obscured later on,” Ex. 1002, p. 3,
`col. 2, Patent Owner argued at the oral hearing that Salesin teaches away
`from a bounding volume. Tr. 31:23–32:15. Petitioner’s contention,
`however, is that Salesin anticipates claim 67, not that it renders claim 67
`obvious. “Although [an] alleged teaching away would be relevant to an
`obviousness analysis, ‘whether a reference “teaches away” from [an]
`invention is inapplicable to an anticipation analysis.’” ClearValue, Inc. v.
`Pearl River Polymers, Inc., 668 F.3d 1340, 1344 (Fed. Cir. 2012) (quoting
`Celeritas Techs., Ltd. v. Rockwell Int’l Corp., 150 F.3d 1354, 1361
`(Fed. Cir. 1998)). Thus, we are not persuaded by Patent Owner’s argument.
`
`Patent Owner further argues that Salesin does not describe evaluating
`a bounding volume as to visibility. PO Resp. 2. Rather, Patent Owner
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`contends, Salesin discloses evaluating the contents in a ZZ-buffer one cell at
`a time. Id. However, as explained above, during its scan conversion phase,
`Salesin “take[s] each object [and] compute[s] a rough [zmin, zmax] interval
`for every cell that may contain some part of the object.” Ex. 1002, p. 3,
`col. 1. Moreover, Salesin discloses that, “[i]n the scan conversion phase, we
`estimate the set of cells that each object covers, either totally or partially.”
`Id. at p. 3, col. 2. Thus, Salesin does not limit evaluating the contents of a
`ZZ-buffer to one cell at a time.
`Also, as Petitioner points out (Pet. 32–33), Salesin discloses “scan
`convert[ing] an enlarged three-dimensional bounding box of [an] object.”
`Id. at p. 8, col. 1. This is another example of evaluating a bounding volume
`as to visibility. At the oral hearing, Patent Owner argued that this
`description in Salesin was “completely unrelated” because, here, Salesin is
`“not taking about objects” and instead is “talking about shadows.” Tr. 35:3–
`16. We are not persuaded. Although Salesin’s discussion is in the context
`of producing penumbrae (soft shadow edges) when rendering objects, it
`nevertheless describes rendering objects, including computing the visibility
`of a part of a “three-dimensional bounding box of [an] object” onto grid
`cells. Ex. 1002, p. 8, cols. 1–2; Ex. 1013 ¶ 114. Thus, Petitioner has shown
`that Salesin discloses evaluating a bounding volume as to visibility.
`
`Patent Owner does not present any evidence or argument contesting
`Petitioner’s showing that Salesin discloses the remaining limitations of claim
`67. In any case, Salesin describes a two-phase process for generating 3-D
`images: scan conversion, during which a ZZ-buffer is created, and rendering,
`where visibility is determined. Ex. 1002, p. 3, cols. 1–2, p. 5, col. 1. Thus,
`Salesin discloses a “method in 3-D computer graphics for processing the
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`visibility of 3-D surfaces before a subsequent step of visibility
`computations,” as recited in claim 67.
`We also find that the cells of the two-dimensional array shown in
`Salesin’s Figure 1 are grid cells that are related to representations of objects
`stored in the cells’ tilelists upon an imaginary plane formed by the two-
`dimensional array. Ex. 1002, p. 2, cols. 1–2. Moreover, as construed in
`Section II.A, a “z-buffer” is “a data structure in memory that is used to store
`depth data.” Salesin’s ZZ-buffer is a data structure that represents cells
`based on a z-buffer. Ex. 1002, p. 2, col. 2. Specifically, Salesin discloses
`“perform[ing] a quick visibility test, based on the zmin, zmax, and opaque
`attributes of the new tile and of the ZZ-buffer entry.” Ex. 1002, p. 2, col. 2.
`Thus, Salesin discloses “for each of said grid cells, accessing the
`corresponding z-buffer element,” as recited in claim 67.
`In sum, we conclude that Petitioner has proved by a preponderance of
`the evidence that claim 67 is anticipated by Salesin.
`
`
`2. Obviousness of Claim 11 over Salesin and Foley
`Petitioner contends that Salesin teaches each limitation of claim 11
`except “said 3-D surfaces are arranged in a hierarchy represented by patches
`in varying levels of details.” Pet. 27–29. Petitioner argues that Foley
`teaches the missing limitation and that it would have been obvious to
`combine the teachings of Salesin and Foley. Id. at 29–31. The parties
`dispute whether a skilled artisan would have combined Salesin and Foley.
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`a. Salesin’s Teachings
`Salesin describes a two-phase process for generating 3-D images: scan
`conversion, during which a ZZ-buffer is created, and rendering, where
`visibility is determined. Ex. 1002, p. 3, cols. 1–2, p. 5, col. 1. The rendering
`phase relies on the depth and opacity information determined in the scan
`conversion phase. Id. at p. 5, col. 1. Thus, Salesin discloses a “method of
`reducing a step of visibility computations in 3-D computer graphics from a
`perspective of a viewpoint,” as recited in claim 11.
`Salesin teaches “computing, before said step and from said
`perspective, the visibility of at least one entity selected from 3-D surfaces
`and sub-elements of said 3-D surfaces, wherein said computing step
`comprises at least a comparison between a pair of depth-related numbers to
`determine which of the surfaces or the sub-elements of the surfaces
`associated with said numbers is closer to said viewpoint,” as recited in
`claim 11. In particular, Salesin teaches discarding tiles if their minimum
`depths (zmin fields), from the perspective of a viewpoint, are greater than the
`maximum depths (zmax fields) of other tiles in the cell. Ex. 1002, p. 2,
`col. 2–p. 3, col. 1. As detailed above, Salesin discloses that the visibility of
`at least one tile is computed during this scan conversion step, which occurs
`prior to a rendering step. Ex. 1002, p. 2, col. 2–p. 3, col. 1.
`Salesin also teaches “skipping, at said step, at least an occlusion
`relationship calculation for at least one entity that has been determined to be
`invisible in said computing step,” as recited in claim 11. For example,
`Salesin describes throwing away tiles that are obscured completely by other
`tiles. Ex. 1002, p. 2, col. 2–p. 3, col. 1. No visibility computations,
`including occlusion relationship calculations, are performed in Salesin’s
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`rendering phase on tiles discarded during the scan conversion phase. Id. at
`p. 3, cols. 1–2.
`Patent Owner does not introduce evidence or argument disputing
`Petitioner’s showing that Salesin teaches these aspects of claim 11.
`In a “Further Work” section, Salesin states that “[i]t seems it would be
`easy to extend the ZZ-buffer algorithm to directly handle objects that are
`defined recursively, such as fractal terrains or Bézier patches.” Ex. 1002,
`p. 14, col. 1 (internal citations omitted).
`
`
`b. Foley’s Teachings
`According to Dr. Teller, Foley is a standard textbook in the field of
`computer graphics that would have been familiar to a person of ordinary
`skill in the art. Ex. 1013 ¶ 111.
`In separate sections of the textbook, Foley describes “level-of-detail
`elision” in which “successively more detail appear[s] as the user
`dynamically zoom[s] in on” an object, Ex. 1003, at 3, and Bézier patches,
`id. at 5–6. According to Dr. Teller, Foley describes Bézier patches as
`“smooth three-dimensional surfaces that are defined through repeated
`subdivision and blending of a set of vertices of the patch being represented.”
`Ex. 1013 ¶ 111 (citing Ex. 1003, at 5–6).
`
`
`c. A Skilled Artisan Would Have Combined Salesin and
`Foley to Arrive at Claim 11
`Petitioner contends that the combination of Salesin and Foley teaches
`“said 3-D surfaces are arranged in a hierarchy represented by patches in
`varying levels of details,” as recited in claim 11. Specifically, Petitioner
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`argues that Salesin explicitly states that its technique could be extended to
`handle recursively defined surfaces such as Bézier patches, and that Foley
`describes the characteristics of Bézier patches as well as other recursively
`defined surfaces such as level-of-detail elision. Pet. 29–30. According to
`Petitioner, Foley describes Bézier patches as surfaces that are arranged in a
`hierarchy of patches in varying levels of detail. Id. at 29–30. Relying on
`Dr. Teller, Petitioner argues that the overlapping discussions of Bézier
`patches in Salesin and Foley, Foley’s status as a standard reference in the art,
`and the similarity of the problems addressed by Salesin and Foley w