Court Opinion

ID: 6113240
Source: CourtListenerOpinion
Date Created: 2022-01-27 17:01:06.841132+00
Date Added: 2024-06-11T08:59:50.657510
License: Public Domain

Case: 20-2257   Document: 31     Page: 1    Filed: 01/27/2022

   United States Court of Appeals
       for the Federal Circuit
                 ______________________

       NATURE SIMULATION SYSTEMS INC.,
                Plaintiff-Appellant

                            v.

                   AUTODESK, INC.,
                   Defendant-Appellee
                 ______________________

                       2020-2257
                 ______________________

    Appeal from the United States District Court for the
 Northern District of California in No. 3:19-cv-03192-SK,
 Magistrate Judge Sallie Kim.
                 ______________________

                Decided: January 27, 2022
                 ______________________

     MATTHEW MICHAEL WAWRZYN, Wawrzyn LLC, Chi-
 cago, IL, argued for plaintiff-appellant.

     BRIAN ROBERT MATSUI, Morrison & Foerster LLP,
 Washington, DC, argued for defendant-appellee. Also rep-
 resented by SETH W. LLOYD; RUDOLPH KIM, ROMAN A.
 SWOOPES, Palo Alto, CA.
                ______________________
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2           NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.

     Before NEWMAN, LOURIE, and DYK, Circuit Judges.
    Opinion for the court filed by Circuit Judge NEWMAN.
         Dissenting opinion filed by Circuit Judge DYK.
 NEWMAN, Circuit Judge.
     Nature Simulation Systems, Inc. (“NSS”) is the owner
 of United States Patents No. 10,120,961 (“the ’961 patent”)
 and No. 10,109,105 (“the ’105 patent”), both entitled
 “Method for Immediate Boolean Operations Using Geomet-
 ric Facets.” The patents relate to methods of packaging
 computer-aided data for three-dimensional objects. 1
     NSS brought suit for infringement against Autodesk,
 Inc. in the United States District Court for the Northern
 District of California. At issue are claims 1 and 8 of the
 ’961 patent and claim 1 of the ’105 patent. The district
 court held a claim construction (Markman) hearing, and
 ruled the claims invalid on the ground of claim indefinite-
 ness, 35 U.S.C. § 112(b). 2 That decision is the subject of
 this appeal.
     We conclude that the district court erred on the legal
 standard for claim indefiniteness, and that on the correct
 standard the claims are not indefinite. The decision of in-
 validity on this ground is reversed.

     1   The ’961 patent is a continuation-in-part of the ’105
 patent, and the specifications and claims do not materially
 differ with respect to the issues of this appeal; thus the par-
 ties and this court generally cite to the ’961 patent.
      2  Nature Simulation Systems Inc. v. Autodesk, Inc.,
 No. 19-CV-03192-SK, ECF. No. 61, (N.D. Cal. July 31,
 2020) (“Dist. Ct. Op.”); Final Judgment, 2020 WL 5525170
 (N.D. Cal. Aug. 11, 2020).
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.               3

                        BACKGROUND
     Standards of review
      Claim construction is a question of law, and receives de
 novo review on appeal. Markman v. Westview Instruments,
 Inc., 517 U.S. 370, 390–91 (1996); Teva Pharms. USA Inc.
 v. Sandoz, Inc., 574 U.S. 318, 325 (2015). Claim indefinite-
 ness is a legal conclusion, in implementation of 35 U.S.C.
 § 112. See Atmel Corp. v. Info. Storage Devices, Inc., 198
 F.3d 1374, 1378 (Fed. Cir. 1999) (“‘A determination of claim
 indefiniteness is a legal conclusion that is drawn from the
 court’s performance of its duty as the construer of patent
 claims.’ Indefiniteness, therefore, like claim construction,
 is a question of law that we review de novo.”) (quoting Per-
 sonalized Media Communications, LLC v. Int’l Trade
 Comm’n, 161 F.3d 696, 705 (Fed. Cir. 1998)).
     Claim indefiniteness is decided from the viewpoint of
 persons skilled in the field of the invention. Personalized
 Media, 161 F.3d at 705. The district court and the parties
 agreed that for the technology here at issue, such persons
 would have “at least a master’s degree in computer science
 or a related field, or a bachelor’s degree in computer science
 or a related field plus two years of relevant experience,
 with experience in computer graphics, computer-aided de-
 sign, solid modeling, or geometric modeling.” Dist. Ct. Op.
 at 7.
     United States patents are accompanied by a presump-
 tion of validity, 35 U.S.C. § 282, and invalidity must be es-
 tablished by clear and convincing evidence. Sonix Tech.
 Co. Ltd. v. Pubs. Int’l, Ltd., 844 F.3d 1370, 1377 (Fed. Cir.
 2017).
     The patented inventions
     The ’961 and ’105 patents are for a computer-imple-
 mented method for building three-dimensional objects em-
 ploying a computation method called “Boolean operation.”
 The patents introduce the invention as follows:
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4          NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.

     This invention provides an immediate Boolean op-
     eration method for building three (3) dimensional
     geometric models from primary geometric objects
     to Computer Aided Design, Computer Graphics,
     Solid Modeling systems, and Surface Modeling sys-
     tems, which are widely used in product design,
     manufacturing, and simulation. Mechanic indus-
     try, culture and sports, everywhere there are geo-
     metric shapes, may have CAD/CG applications.
 ’961 patent, col.1, ll.7–14. The patents are for data struc-
 tures and algorithms for the claimed method, which is de-
 scribed as a modification of a known Boolean operation
 published in 1981 for analyzing and representing three-di-
 mensional geometric shapes (“the Watson method”). The
 district court states: “NSS concedes that the general idea
 of performing Boolean operations in this area was well
 known before the patents in dispute, as the asserted pa-
 tents cite to prior art disclosing this concept.” Dist. Ct. Op.
 at 2. The court summarized the prior art:
     There are two methods from prior art that are cited
     in the asserted patents. The Delaunay method is a
     known method of triangulation (known as the “De-
     launay triangulation”), and the Watson method is
     a known algorithm for computing a Delaunay tri-
     angulation that is described in a paper written in
     1981 by D.F. Watson.
 Id. (citing ’961 patent col.6 ll.64–66; ’105 patent col.6 ll.42–
 44). The patents state that the “modified Watson method”
 described therein provides simplicity and flexibility com-
 pared with prior methods, and is easier to program and im-
 plement. ’961 patent, col.1, ll.17–62. Both sides presented
 technology tutorials to the district court; the NSS tutorial
 was presented by inventor Shangwen Cao, and the Auto-
 desk tutorial was presented by expert Dr. Daniel Aliaga.
     At the Markman hearing, Autodesk requested con-
 struction of eight terms in the claims, and supported this
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.              5

 request with the Declaration of Dr. Aliaga. NSS argued
 that the challenged terms do not require construction, are
 clearly set forth in the specification, and should receive
 their ordinary meaning in this field of technology.
     The district court based its decision on two of the chal-
 lenged terms, shown in boldface in clauses [2] and [3] of
 Claim 1:
     1. A method that performs immediate Boolean op-
     erations using geometric facets of geometric objects
     implemented in a computer system and operating
     with a computer, the method comprising:
         [1] mapping rendering facets to extended
         triangles that contain neighbors;
         [2] building intersection lines starting with
         and ending with searching for the first pair
         of triangles that hold a start point of an in-
         tersection line by detecting whether two
         minimum bounding boxes overlap and per-
         forming edge-triangle intersection calcula-
         tions for locating an intersection point,
         then searching neighboring triangles
         of the last triangle pair that holds the
         last intersection point to extend the in-
         tersection line until the first intersection
         point is identical to the last intersection
         point of the intersection line ensuring that
         the intersection line gets closed or until all
         triangles are traversed;
         [3] splitting each triangle through which
         an intersection line passes using modified
         Watson method, wherein the modified
         Watson method includes removing dupli-
         cate intersection points, identifying posi-
         tions of end intersection points, and
         splitting portion of each triangle including
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6          NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.

         an upper portion, a lower portion, and a
         middle portion;
         [4] checking each triangle whether it is ob-
         scure or visible for Boolean operations or
         for surface trimming;
         [5] regrouping facets in separate steps that
         includes copying triangles, deleting trian-
         gles, reversing the normal of each triangle
         of a geometric object, and merging reserved
         triangles to form one or more new extended
         triangle sets; and
         [6] mapping extended triangles to render-
         ing facets.
 ’961 patent, col.9, ll.17–48 (bracketed numbers and bold-
 face added).
     After the Markman hearing the district court ruled
 that these two claim terms are indefinite, rendering the
 claims invalid. The district court did not define the two
 terms; instead, the court held that a claim term is indefi-
 nite, as a matter of law, if there are any “unanswered ques-
 tions” about the term. The court referred to the conflict
 between the opinion of Autodesk’s expert, and the patent
 examiner’s resolution of indefiniteness, and stated:
     [T]he question is thus: if the PTO issues a patent
     after amendment to clarify an indefinite term, but
     an expert later opines that a POSITA would not un-
     derstand the term, how does the Court determine
     whether the term is indefinite? The only way to do
     so here is to look at each argument to see if Auto-
     desk raises any unanswered questions. Here, Au-
     todesk does.
 Dist. Ct. Op. at 8. The district court recited several “unan-
 swered questions,” and further stated that even if the ques-
 tions are answered in the specification, the definiteness
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.               7

 requirement is not met if the questions are not answered
 in the claims. Thus the court held the claims invalid under
 35 U.S.C. § 112.
     NSS states that the court applied incorrect legal stand-
 ards, and that on the correct law the claims are not indefi-
 nite.
                         DISCUSSION
     Patent claims must provide reasonable certainty in de-
 fining what is patented, in conformity with the require-
 ments of 35 U.S.C. § 112. We start with the statute:
     35 U.S.C. § 112
      Section 112 states the required content of the patent
 document. Section 112(a) provides that the specification
 must describe the invention in full, clear, concise, and exact
 terms, as to enable its practice by any person skilled in the
 field of the invention, and must include the best mode
 known to the inventor:
     § 112. Specification
     (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.
 Section 112(b) requires that the specification conclude with
 claims that state the subject matter that is patented:
     (b) Conclusion.-- The specification shall conclude
     with one or more claims particularly pointing out
     and distinctly claiming the subject matter which
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8          NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.

     the inventor or a joint inventor regards as the in-
     vention.
 The claims define the patent right, and perform the “no-
 tice” function of legal documents; thus precision and clarity
 are necessary. See Ariad Pharms., Inc. v. Eli Lilly & Co.,
 598 F.3d 1336 (Fed. Cir. 2010):
     [The claims’] principal function, therefore, is to pro-
     vide notice of the boundaries of the right to exclude
     and to define limits; it is not to describe the inven-
     tion, although their original language contributes
     to the description and in certain cases satisfies it.
     Claims define and circumscribe, the written de-
     scription discloses and teaches.
 Id. at 1347. See Nautilus, Inc. v. Biosig Instruments, Inc.,
 572 U.S. 898, 909 (2014) (“a patent must be precise enough
 to afford clear notice of what is claimed, thereby ‘ap-
 pris[ing] the public of what is still open to them.’” (quot-
 ing Markman, 517 U.S. at 373)).
     The claims are viewed and understood in the context of
 the specification and the prosecution history, as the Court
 summarized in Nautilus:
     Cognizant of the competing concerns, we read
     § 112, ¶ 2 to require that a patent’s claims, viewed
     in light of the specification and prosecution history,
     inform those skilled in the art about the scope of
     the invention with reasonable certainty. The defi-
     niteness requirement, so understood, mandates
     clarity, while recognizing that absolute precision is
     unattainable.
 572 U.S. at 910. When the meaning or scope of a patent
 claim is disputed by litigants, the judicial role is to construe
 the claim as a matter of law, on review of appropriate
 sources of relevant information. As summarized in Phillips
 v. AWH Corp., the court looks first to the intrinsic record of
 the patent document, including “the words of the claims
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 themselves, the remainder of the specification, the prose-
 cution history, and extrinsic evidence concerning relevant
 scientific principles, the meaning of technical terms, and
 the state of the art.” 415 F.3d 1303, 1314 (Fed. Cir. 2005)
 (en banc) (quoting Innova/Pure Water, Inc. v. Safari Water
 Filtration Sys., Inc., 381 F.3d 1111, 1116 (Fed. Cir. 2004)).
     Here, however, the district court did not construe the
 claims, did not apply the protocols of intrinsic and extrinsic
 evidence, and did not resolve the meaning and scope of the
 challenged claims. The district court applied an incorrect
 standard of “unanswered questions” and a flawed analysis
 of validity.
    The district court’s standard of “unanswered
 questions”
     The district court held the claims indefinite based on
 the “unanswered questions” that were suggested by Auto-
 desk’s expert. For the term “searching neighboring trian-
 gles of the last triangle pair that holds the last intersection
 point,” the court recited three unanswered questions:
     Aliaga points to several unanswered questions
     about this language: (1) whether the phrase re-
     quires searching repeatedly or iteratively or merely
     once; (2) what the “last triangle pair” or “last inter-
     section point” is; (3) how can one “extend an inter-
     section line” when in some cases it is not possible,
     as Aliaga demonstrates.
 Dist. Ct. Op. at 17–18 (citing Aliaga Decl. ¶ 26).
     For the term “modified Watson method,” the district
 court recited four unanswered questions provided by Auto-
 desk’s expert:
     The claim language leaves unanswered the follow-
     ing questions: (1) What is a neighboring point of in-
     tersection (referred to as PET in the patents)?; (2)
     What is the meaning of an ‘identical’ point of
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 10         NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.

      intersection?; (3) What is the meaning of removing
      a point of intersection?; (4) From what is the point
      of intersection being removed? NSS does not re-
      spond to these specific questions, which highlight
      the ambiguity of the claim language.
 Dist. Ct. Op. at 9.
     In response to NSS’s argument that these questions
 are answered in the specification, the court held that defi-
 niteness requires that the questions are answered in “the
 claim language, standing alone,” as stated in the Aliaga
 Declaration:
          ¶ 27. [T]he claim language, standing alone,
      does not specify which of those neighboring, inter-
      secting triangles should be used to identify addi-
      tional intersection points. Nor does the claim
      specify (where there are multiple potential inter-
      section points for a given pair of neighboring trian-
      gles) which of the multiple potential intersection
      points should be used to extend the intersection
      line. Thus, the claim language is indefinite.
 Aliaga Decl. ¶ 27. “Claim language, standing alone” is not
 the correct standard of law, and is contrary to uniform
 precedent. Patent claims are viewed and understood in
 light of the specification, the prosecution history, and other
 relevant evidence, as “would have allowed a skilled artisan
 to know the scope of the claimed invention with reasonable
 certainty.” Sonix Tech., 844 F.3d at 1376.
     The district court did not apply this standard protocol
 for analyzing claim definiteness, and did not construe the
 claims. Instead, the court held that the questions raised
 by Autodesk must be answered, and that the answers must
 be in the claims. NSS states that on the correct claim con-
 struction, the claims are not indefinite.
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.               11

     The specification
      The specification describes the invention in text, draw-
 ings, and flowcharts. NSS states on this appeal that even
 if the theory of “unanswered questions” were accepted, any
 relevant questions are answered in the specification. For
 example, with respect to the intersection points that were
 a focus of the criticism recited by the district court, NSS
 cites the description in the specification captioned “The
 First Intersection Point” and “Extending an Intersection
 Line.” ’961 patent, col.5, l.41–col.6, l.24. NSS also points
 to the Figure 4 flowchart for building intersection lines, to
 Figures 6A and 6B for showing intersection points, and
 Figures 9A–9D for examples of intersection lines.
     The specification describes, and the claim recites, that
 the intersection line is built from the intersection points
 around the objects being compared, “searching neighboring
 triangles of the last triangle pair that holds the last inter-
 section point to extend the intersection line until the first
 intersection point is identical to the last intersection point
 of the intersection line ensuring that the last line gets
 closed or until all triangles are traversed.” ’961 patent,
 col.9, ll.23–33.
     Figure 13 is a flowchart of “Delaunay mesh modified
 Watson method that created the sequence” shown in Fig-
 ure 12. Figures 12A–12H show the decomposition of a
 square into triangles, the placement of intersection points
 within those triangles, and the use of triangles containing
 intersection points to build polygons from which new trian-
 gles are generated, along with comparisons with the prior
 art Watson method. Figure 13 shows that where any tri-
 angle contains a valid intersection point, the claimed
 method “moves the triangle to the deleted Triangle Set,
 uses deleted Triangle Set to build a polygon,” and “uses the
 polygon to generate triangles.”
     The specification describes the Watson and Delaunay
 prior art, in text and drawings to show how they are used
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 12         NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.

 and modified in the subject invention. Dr. Aliaga acknowl-
 edged this prior art in his expert declaration, stating: “To
 be clear, I am familiar with the Delaunay method, which is
 a known method of triangulation that is mentioned in the
 patents. . . . And I am also aware of the ‘Watson’ algorithm
 for computing a Delaunay triangulation that is described
 in a 1981 paper by D.F. Watson cited in the patents.” Ali-
 aga Decl. ¶ 15.
      The claims are properly viewed in light of this
 knowledge, for this prior art constitutes “extrinsic evidence
 concerning relevant scientific principles [and] the meaning
 of technical terms.” Phillips, 415 F.3d at 1313 (quoting In-
 nova/Pure Water, 381 F.3d at 1116). The Court guided in
 Nautilus:
      One must bear in mind, moreover, that patents are
      “not addressed to lawyers, or even to the public
      generally,” but rather to those skilled in the rele-
      vant art. Carnegie Steel Co. v. Cambria Iron
      Co., 185 U.S. 403, 437 (1902) (also stating that
      “any description which is sufficient to apprise
      [steel manufacturers] in the language of the art of
      the definite feature of the invention, and to serve
      as a warning to others of what the patent claims as
      a monopoly, is sufficiently definite to sustain the
      patent”).
    572 U.S. at 909. The function of the claims is not to
 duplicate the specification.
      The district court declined to consider information in
 the specification that was not included in the claims. For
 example, in rejecting NSS’s argument that the modified
 Watson method is described in the specification, the dis-
 trict court stated:
      NSS points to column 7 of the specification and re-
      lies on step 5(a) of column 7 to show the modifica-
      tion of the Watson method. (’961 patent at 7:17–
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     23). This language adds an additional condition:
     “or last segment passes through the triangle.”
     Again, this language is not contained in the claim
     language and does not explain the challenged claim
     language.
 Dist. Ct. Op. at 10.
     The district court misperceived the function of patent
 claims; see In re Vamco Machine & Tool, Inc., 752 F.2d 1564
 (Fed. Cir. 1985):
     The function of claims is (a) to point out what the
     invention is in such a way as to distinguish it from
     what was previously known, i.e., from the prior art;
     and (b) to define the scope of protection afforded by
     the patent. In both of those aspects, claims are not
     technical descriptions of the disclosed inventions
     but are legal documents like the descriptions of
     lands by metes and bounds in a deed which define
     the area conveyed but do not describe the land.
 Id. at 1577 n.5 (emphases original). As noted in SRI Inter-
 national v. Matsushita Electric Corp. of Am., 775 F.2d
 1107, 1121 n.14 (Fed. Cir. 1985): “Specifications teach.
 Claims claim.”
     The prosecution history
     The prosecution history here is significant, for the pa-
 tent examiner had initially rejected the claims on the
 ground of indefiniteness, and the examiner required addi-
 tional definition in the claim clauses here at issue. For ex-
 ample, the examiner had initially rejected the claims for
 indefiniteness of the clause “extending intersection lines
 until they get closed by searching neighboring triangles;”
 the examiner wrote: “What is causing the closure of the in-
 tersection lines? The nexus between ‘extending the inter-
 section lines’ and ‘searching neighboring triangle pairs’ is
 also not clearly set forth.” Appl. No. 15/840,052, Official
 Action (Non-Final Rejection) of Feb. 6, 2018, at 3. The
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 14         NATURE SIMULATION SYSTEMS INC.      v. AUTODESK, INC.

 applicant, in consultation with the examiner, amended this
 term in claim clause [2], as shown in the prosecution rec-
 ord:
      [2] building intersection lines starting with and
      ending with searching for the first pair of triangles
      that hold a start point of an intersection line by de-
      tecting whether two minimum bounding boxes
      overlap and performing edge-triangle intersection
      calculations for locating an intersection point, ex
      tending the intersection lines until they get closed
      by searching neighboring triangles or all triangles
      are traversed; then searching neighboring trian-
      gles of the last triangle pair that holds the last in-
      tersection point to extend the intersection line until
      the first intersection point is identical to the last
      intersection point of the intersection line ensuring
      that the intersection line gets closed or until all tri-
      angles are traversed;
 Appl. No. 15/840,052, Amend. of Apr. 4, 2018, at 9 (mark-
 ings in original). With this amendment the examiner with-
 drew the indefiniteness rejection relating to the
 intersection lines.
     The applicant and the examiner also interacted to
 amend the term “modified Watson method.” An Exam-
 iner’s Amendment of August 28, 2018 amended claim
 clause [3] as follows:
      [3] splitting each triangle through which an inter-
      section line passes using modified Watson method,
      wherein the modified Watson method includes re-
      moving duplicate intersection points, identifying
      positions of end intersection points, and splitting
      portion of each triangle including an upper portion,
      a lower portion, and a middle portion;
 Appl. No. 15/840,052, Examiner’s Amend. in Notice of Al-
 lowance, Sept. 18, 2018, at 4–5 (markings in original).
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     With the agreed amendments, the examiner withdrew
 the rejections for indefiniteness and allowed the claims. Id.
     However, the district court rejected the examiner’s con-
 clusion as to indefiniteness, the court reciting the initial
 rejection and the amendment, and stating that this action
 did not answer “the questions posed by Aliaga”:
     The prosecution history does not show how or why
     the amendment answered the unanswered ques-
     tions. The prosecution history does not provide a
     clear reason for the amendment that clarifies the
     underling ambiguity. The PTO initially rejected
     Claim 1 as indefinite: “The nexus between ‘extend-
     ing the intersection lines’ and ‘searching neighbor-
     ing triangles’ is also not clearly set forth. The
     examiner is not able to ascertain the scope of the
     claimed invention,” (Dkt. 37-1 (Ex. A at page 4).)
     In response, NSS added the following language:
     “building intersection lines starting with and end-
     ing with . . . calculations for locating an intersection
     point, then searching neighboring triangles of the
     last triangle pair that holds the last intersection
     point to extend the intersection line until the first
     intersection point is identical to the last intersec-
     tion point of the intersection line ensuring that the
     intersection line gets closed or until all triangles
     are traversed.” (Id.) This added language does not
     answer the questions posed by Aliaga.
 Dist. Ct. Op. at 19 (ellipses and parentheticals in original).
     The district court gave no weight to the prosecution
 history showing the resolution of indefiniteness by adding
 the designated technologic limitations to the claims. The
 court did not discuss the Examiner’s Amendment, and held
 that since Dr. Aliaga’s questions were not answered, the
 claims are invalid.
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 16         NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.

     Actions by PTO examiners are entitled to appropriate
 deference as official agency actions, for the examiners are
 deemed to be experienced in the relevant technology as
 well as the statutory requirements for patentability:
      We presume that an examiner would not introduce
      an indefinite term into a claim when he/she chooses
      to amend the claim for the very purpose of putting
      the application in a condition for allowance.
 Tinnus Enters., LLC v. Telebrands Corp., 733 F. App’x
 1011, 1020 (Fed. Cir. 2018). See also PowerOasis, Inc. v. T-
 Mobile USA, Inc., 522 F.3d 1299, 1304 (Fed. Cir. 2008)
 (stating that PTO examiners are “assumed to have some
 expertise in interpreting the references and to be familiar
 from their work with the level of skill in the art and whose
 duty it is to issue only valid patents.” (quoting Am. Hoist &
 Derrick Co. v. Sonra & Sons, Inc., 725 F.2d 1350, 1359
 (Fed. Cir. 1984) (overruled on other grounds))).
     The Court recognized, in discussing claim definiteness,
 that:
      The standard we adopt accords with opinions of
      this Court stating that “the certainty which the law
      requires in patents is not greater than is reasona-
      ble, having regard to their subject-matter.” Miner-
      als Separation, Ltd. v. Hyde, 242 U.S. 261, 270
      (1916).
 Nautilus, 572 U.S. at 910.
     The subject matter herein is an improvement on the
 known Watson and Delaunay methods, and partakes of
 known usages for established technologies. Precedent
 teaches that when “the general approach was sufficiently
 well established in the art and referenced in the patent”
 this “render[ed] the claims not indefinite.” Presidio Com-
 ponents, Inc. v. Am. Tech. Ceramics Corp., 875 F.3d 1369,
 1377 (Fed. Cir. 2017). The situation here is analogous, for
 the 1981 Watson method and the Delaunay method were
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.             17

 known in the art. It is not disputed that the specification
 describes and enables practice of the claimed method, in-
 cluding the best mode. The claims, as amended during
 prosecution, were held by the examiner to distinguish the
 claimed method from the prior art and to define the scope
 of the patented subject matter. The district court made no
 contrary findings. Indefiniteness under 35 U.S.C. § 112
 was not established as a matter of law.
                        CONCLUSION
     The district court’s decision is reversed. We remand for
 further proceedings.
                REVERSED AND REMANDED
Case: 20-2257    Document: 31      Page: 18   Filed: 01/27/2022

    United States Court of Appeals
        for the Federal Circuit
                   ______________________

        NATURE SIMULATION SYSTEMS INC.,
                 Plaintiff-Appellant

                              v.

                     AUTODESK, INC.,
                     Defendant-Appellee
                   ______________________

                         2020-2257
                   ______________________

    Appeal from the United States District Court for the
 Northern District of California in No. 3:19-cv-03192-SK,
 Magistrate Judge Sallie Kim.
                 ______________________

 DYK, Circuit Judge, dissenting.
     Contrary to the majority, I think that the asserted
 claims are invalid because they are indefinite. The fact
 that a patent examiner introduced the indefinite language
 does not absolve the claims from the requirements of 35
 U.S.C. § 112. I respectfully dissent.
     The majority faults the district court for applying an
 incorrect “unanswered questions” standard, Maj. Op. 9, but
 this is not the district court’s decision. In a detailed and
 thorough analysis, the district court read the patent’s
 claims in light of the specification to determine if it would
 inform those skilled in the art about the scope of the inven-
 tion with reasonable certainty, which is exactly what is re-
 quired under Nautilus, Inc. v. Biosig Instruments, Inc., 572
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 2         NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.

 U.S. 898, 910 (2014). Regardless, the question of definite-
 ness is a legal question which we review de novo, and the
 majority's legal conclusion is, in my view, manifestly incor-
 rect.
     The field of art here, computer-aided design, is unusu-
 ally complex, involving methods of using computer systems
 to build geometric objects. The patents purport to improve
 on two established methods of computer-aided design: con-
 structive solid geometry, which combines simple objects us-
 ing Boolean operations (e.g., intersection, combination,
 exclusion) to build complex objects, and boundary repre-
 sentation, which represents three-dimensional objects by
 defining their surfaces as meshes of two-dimensional ob-
 jects.
     Claim 1 of U.S. Patent No. 10,120,961 (“the ’961 pa-
 tent”) claims:
     1. A method that performs immediate Boolean op-
     erations using geometric facets of geometric objects
     implemented in a computer system and operating
     with a computer, the method comprising:
         mapping rendering facets to extended tri-
         angles that contain neighbors;
         building intersection lines starting with
         and ending with searching for the first pair
         of triangles that hold a start point of an in-
         tersection line by detecting whether two
         minimum bounding boxes overlap and per-
         forming edge-triangle intersection calcula-
         tions for locating an intersection point,
         then searching neighboring triangles of the
         last triangle pair that holds the last inter-
         section point to extend the intersection line
         until the first intersection point is identical
         to the last intersection point of the intersec-
         tion line ensuring that the intersection line
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.               3

         gets closed or until all triangles are trav-
         ersed;
         splitting each triangle through which an
         intersection line passes using modified
         Watson method, wherein the modified
         Watson method includes removing dupli-
         cate intersection points, identifying posi-
         tions of end intersection points, and
         splitting portion of each triangle including
         an upper portion, a lower portion, and a
         middle portion . . . .
 ’961 patent, col. 9, ll. 17–40; see also U.S. Patent No.
 10,109,105, col. 8, l. 47–col. 9, l. 3. (emphasis added). The
 indefiniteness issue concerns the underscored language.
     There is no dispute that the term “modified Watson
 method” does not have, and did not have at the time the
 patents were issued, an ordinary and customary meaning
 to a person of ordinary skill in the art. The majority finds
 that Figures 12 and 13 of each patent define the “modified
 Watson method.” Maj. Op. 11–12 (“The specification de-
 scribes the Watson and Delaunay prior art, in text and
 drawings to show how they are used and modified in the
 subject invention.”). Figures 12A through 12H of the pa-
 tents at issue “show a Delaunay mesh sequence in which
 each intersection point is inserted into the mesh step by
 step,” while Figure 13 “is the flowchart of Delaunay mesh
 modified Watson method that created the sequence of [Fig-
 ures] 12A through 12H.” ’961 patent, col. 3, ll. 36–41.
      The problem with the majority’s definition is that it ig-
 nores the claim language. As the district court found, J.A.
 9–10, and Nature concedes, Nature Reply Br. 6, claim 1
 adds limitations not found in Figures 12A–H or 13: “remov-
 ing duplicate intersection points, identifying positions of
 end intersection points, and splitting portion of each trian-
 gle including an upper portion, a lower portion, and a mid-
 dle portion.” Thus, the majority’s definition of “modified
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 4         NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.

 Watson method” in claim 1 is inconsistent with the claim
 itself: the majority looks to figures 12 and 13 to find the
 “modified Watson method” but those figures do not include
 the additional limitations which are expressly required by
 the claim language. Even more significant, nothing in the
 patent specification defines what these additional limita-
 tions mean. The only expert evidence on these limitations
 in the record is by Autodesk’s expert, who testified without
 contradiction that these limitations are “not describe[d]” in
 the patent, “ambiguous” and “unclear,” and “inconsistent
 with” Figure 13 and the accompanying text. J.A. 54–56.
     The majority simply does not address this problem, in-
 stead relying on the fact that these limitations were sug-
 gested by the patent examiner. The majority holds that
 “[a]ctions by PTO examiners are entitled to appropriate
 deference” because examiners are “deemed to be experi-
 enced in the relevant technology as well as the statutory
 requirements for patentability.” Maj. Op. 16. But the test
 for definiteness is whether the claims “inform those skilled
 in the art about the scope of the invention with reasonable
 certainty,” Nautilus, 572 U.S. at 910, not whether the claim
 language was added by a patent examiner or was not in-
 definite to the examiner. There is no reasonable basis in
 the claims or specification for the majority’s decision. I re-
 spectfully dissent.