Court Opinion

ID: 8311502
Source: CourtListenerOpinion
Date Created: 2022-10-17 14:00:46.682626+00
Date Added: 2024-06-11T16:44:44.749440
License: Public Domain

Case: 20-2257   Document: 42     Page: 1   Filed: 10/17/2022

   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.
                 ______________________

           OPINION ISSUED: January 27, 2022
          OPINION MODIFIED: October 17, 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.

    ∗   This opinion has been modified and reissued fol-
 lowing a petition for rehearing filed by Appellee.
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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 performing
 computer-aided operations 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 were 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 Sys. Inc. v. Autodesk, Inc., No.
 19-CV-03192-SK, (N.D. Cal. July 31, 2020), ECF No. 61
 (“Dist. Ct. Order”).
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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 Commc’ns, 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. Or-
 der 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. v. Publ’ns 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. Or-
 der 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 flexibil-
 ity compared with prior methods, and is easier to program
 and implement. ’961 patent, col.1, ll.17–62. Both sides pre-
 sented technology tutorials to the district court; the NSS
 tutorial was presented by inventor Shangwen Cao, and the
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.               5

 Autodesk tutorial was presented by expert Dr. Daniel Ali-
 aga. 3
     At the Markman hearing, Autodesk requested con-
 struction of eight terms in the claims and supported this
 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

     3    The dissent criticizes by footnote our recital that
 the inventor presented a technical tutorial to the district
 court. Our statement is correct. Technical tutorials were
 provided by both sides. The NSS tutorial was provided by
 the inventor, Dr. Shangwen Cao, and presented at the tu-
 torial hearing by NSS counsel. See ECF No. 44 (slideshow
 captioned “Tutorial Presentation by the Inventor
 Shangwen Cao”). The Autodesk tutorial was provided by
 Autodesk’s expert, Dr. Daniel Aliaga, and presented at the
 tutorial hearing by Dr. Aliaga. See ECF No. 45; see also
 ECF No. 42 (Clerk’s Notice: “The Court requests that both
 sides file the slideshows presented at today’s tutorial on the
 docket.”).
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6         NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.

        intersection 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
        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).
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.               7

     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. Order at 8. The district court recited several “un-
 answered questions,” and further stated that even if the
 questions are answered in the specification, the definite-
 ness requirement is not met if the questions are not an-
 swered 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
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8          NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.

 terms, as to enable its practice by any person skilled in the
 field of the invention:
     § 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
     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
 ‘appris[ing] the public of what is still open to them.’”
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 NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.               9

 (second alteration in original) (quoting 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
 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
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 10         NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.

 Autodesk’s expert. For the term “searching neighboring
 triangles of the last triangle pair that holds the last inter-
 section point,” the court recited three unanswered ques-
 tions:
      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. Order at 17–18 (citing Aliaga Decl. ¶ 26, ECF No.
 36-1).
     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 in-
      tersection?; (3) What is the meaning of removing a
      point of intersection?; (4) From what is the point of
      intersection being removed? NSS does not respond
      to these specific questions, which highlight the am-
      biguity of the claim language.
 Dist. Ct. Order at 9. The district court acknowledged that
 “NSS points to the specification’s discussion of optional
 splitting of partitions,” but the court held that “[t]his argu-
 ment does not enable NSS to succeed in re-writing the lan-
 guage of the claim itself.” Id.
     In response to NSS’s argument that these questions
 are answered in the specification, the court held that defi-
 niteness requires that questions are answered in “the claim
 language, standing alone,” as stated in the Aliaga Declara-
 tion:
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 NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.               11

         ¶ 27. . . . the 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, ECF No. 36-1.
      “Claim language, standing alone” is not the correct
 standard of law and is contrary to uniform precedent. Pa-
 tent claims are viewed and understood in light of the spec-
 ification, the prosecution history, and other relevant
 evidence, as “would have allowed a skilled artisan to know
 the scope of the claimed invention with reasonable cer-
 tainty.” 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’s expert must be answered, and that the an-
 swers must be in the claims.
     NSS states that on the correct claim construction, the
 claims are not indefinite.
     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
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 12        NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.

 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 intersection 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 poly-
 gon to generate triangles.
     The specification describes the Watson and Delaunay
 prior art in text and drawings to show how they are used
 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
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.               13

 of technical terms.” Phillips, 415 F.3d at 1314 (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 (alteration in original).
      The function of the claims is not to duplicate the speci-
 fication. 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–
     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. Order at 10. However, the language that the court
 stated “is not contained in the claim language” is in the
 specification. Figure 13 is a flowchart describing the
 claimed modified Watson method, showing how to build an
 intersection line that references two triangles and use the
 intersection line to split triangles. ’961 patent, Sheet 5.
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 14         NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.

 The specification describes the steps of the modified Wat-
 son method, stating that an “edge-triangle intersection
 point(s) falls inside a triangle” and the system “stores the
 point data into an intersection line set.” ’961 patent, col.2,
 ll.18–21. Then “[t]o extend the current intersection line,
 this method traces neighboring triangles and calculates
 edge-triangle intersection points until the intersection line
 becomes closed.” ’961 patent, col.2, ll.22–24. “Each seg-
 ment of the intersection lines references two (2) triangles,
 each of the triangles has at least one sub-intersection line
 that contains one or more segments, which divide a trian-
 gle into three (3) or more smaller triangles.” ’961 patent,
 col.2, ll.26–30. Figures 12G–H demonstrate how multiple
 triangles (not a single polygon, as the district court states)
 are split when a non-duplicate point on the intersection
 line is identified. ’961 patent, Sheet 4.
     The district court misperceived the function of patent
 claims; see In re Vamco Mach. & 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 in original). As noted in SRI Int’l
 v. Matsushita Elec. Corp. of Am., 775 F.2d 1107, 1121 n.14
 (Fed. Cir. 1985): “Specifications teach. Claims claim.”
     Although the district court adopted the argument of
 Autodesk’s expert that there are “unanswered questions”
 about the claims, this was not the correct standard for eval-
 uating whether the claims met the standard for definite-
 ness. The claims set forth the metes and bounds of the
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 NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.               15

 invention; they are not intended to repeat the detailed op-
 eration of the method as described in the specification. See
 Liberty Ammunition, Inc. v. United States, 835 F.3d 1388,
 1396 (Fed. Cir. 2016) (finding the patent specification
 “saves the term [in the claim] from indefiniteness” by dis-
 closing additional information about the invention that
 clarifies meaning).
     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 the intersection
 lines until they get closed by searching neighboring trian-
 gles;” the examiner wrote: “What is causing the closure of
 the intersection lines? The nexus between ‘extending the
 intersection lines’ and ‘searching neighboring triangles’ is
 also not clearly set forth.” Appl. No. 15/840,052, Official Ac-
 tion (Non-Final Rejection) of Feb. 6, 2018, at 3. The appli-
 cant, 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
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 16         NATURE SIMULATION SYSTEMS INC.      v. AUTODESK, INC.

      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 Examiner’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).
     With the agreed amendments, the examiner withdrew
 the rejections for indefiniteness and allowed the claims. Id.
 The claims as amended during prosecution distinguish the
 claimed method from the prior art and define the scope of
 the patented subject matter. The district court made no
 contrary findings. However, the district court rejected the
 examiner’s conclusion as to indefiniteness, the court recit-
 ing the initial rejection and the amendment, and stating
 that this action did not answer “the questions posed by Ali-
 aga.” The district court stated:
      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
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 NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.               17

     ‘extending the intersection lines’ and ‘searching
     neighboring 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 lan-
     guage: “building intersection lines starting with
     and ending with . . . calculations for locating an in-
     tersection point, then searching neighboring trian-
     gles 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 intersection point of the intersection line en-
     suring that the intersection line gets closed or until
     all triangles are traversed.” (Id.) This added lan-
     guage does not answer the questions posed by Ali-
     aga.
 Dist. Ct. Order at 18–19 (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. The district court did not apply the
 Court’s guidance that “‘[e]xperts may be examined to ex-
 plain terms of art, and the state of the art . . . but they can-
 not be used to prove ‘the proper or legal construction of any
 instrument of writing.’” Teva Pharms., 574 U.S. at 332
 (quoting Winans v. N.Y. & Erie R.R. Co., 62 U.S. 88, 100–
 01 (1859)). The Court recognized, in discussing claim defi-
 niteness, 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.”
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 18        NATURE SIMULATION SYSTEMS INC.      v. AUTODESK, INC.

 Nautilus, 572 U.S. at 910 (quoting Mins. Separation, Ltd.
 v. Hyde, 242 U.S. 261, 270 (1916)).
     The subject matter herein is an improvement on the
 known Watson and Delaunay methods and partakes of
 known usages for these established technologies. Prece-
 dent teaches that when “the general approach was suffi-
 ciently well established in the art and referenced in the
 patent” this “render[ed] the claims not indefinite.” Presidio
 Components, Inc. v. Am. Tech. Ceramics Corp., 875 F.3d
 1369, 1377 (Fed. Cir. 2017); see Ethicon Endo-Surgery, Inc.
 v. Covidien, Inc., 796 F.3d 1312, 1322 (Fed. Cir. 2015); Phil-
 lips, 415 F.3d at 1316–19 (patent claims are construed in
 light of the specification, the prosecution history, and the
 knowledge of persons skilled in the field of the invention).
                         CONCLUSION
     Indefiniteness under 35 U.S.C. § 112 was not estab-
 lished as a matter of law. The district court’s decision is
 reversed. We remand for further proceedings.
                REVERSED AND REMANDED
                            COSTS
 Each party shall bear its costs.
Case: 20-2257   Document: 42       Page: 19   Filed: 10/17/2022

    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 major-
 ity faults the district court for applying an incorrect
 “[c]laim language, standing alone” standard for definite-
 ness. Maj. Op. 10–11. This language, quoted from Auto-
 desk’s expert declaration, appears nowhere in the district
 court’s opinion and forms no part of its decision. 1 In a

     1  The expert himself did not apply an incorrect
 standard. In searching for a meaning for the term “modi-
 fied Watson method,” the expert looked not just to the
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 2         NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.

 detailed and thorough analysis, the district court read the
 patent’s claims in light of the specification and prosecution
 history to determine if it would inform those skilled in the
 art about the scope of the invention with reasonable cer-
 tainty, which is exactly what is required under Nautilus,
 Inc. v. Biosig Instruments, Inc., 572 U.S. 898, 910 (2014).
 Regardless, the question of definiteness is a legal question
 which we review de novo, and the majority’s legal conclu-
 sion is, in my view, manifestly incorrect.
     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

 claim language itself, but also to the specification, includ-
 ing the very figures that the majority cites. See Aliaga
 Decl. ¶¶ 16–19, J.A. 54–58.
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 NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.              3

         intersection 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
         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 (emphasis added); see also U.S.
 Patent No. 10,109,105, col. 8, l. 47–col. 9, l. 3. The indefi-
 niteness issue concerns the underscored language, addi-
 tional limitations which were added during prosecution at
 the suggestion of the examiner.
     While the Watson method itself was well understood, 2
 there is no claim that the term “modified Watson method”
 has, or had at the time the patents were issued, an ordinary

     2   The Delaunay method is a known method of trian-
 gulation. The Watson method is a known algorithm for
 computing a Delaunay triangulation that was described in
 a paper written by D.F. Watson in 1981. J.A. 2; Aliaga
 Decl. ¶ 15, J.A. 53–54.
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 4         NATURE SIMULATION SYSTEMS INC.     v. AUTODESK, INC.

 and customary meaning to a person of ordinary skill in the
 art. The sole expert testimony on that subject, by Auto-
 desk’s expert, confirms that it did not. Aliaga Decl. ¶ 15,
 J.A. 53–54. 3 The majority says that “[t]he 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.” Maj. Op. 12.
     The majority first relies on figures in the specification:
 Figures 12 and 13. Maj. Op. 12–14. The problem is that
 nothing in these figures defines “modified Watson method”
 or the language “removing duplicate intersection points,
 identifying positions of end intersection points, and split-
 ting portion of each triangle including an upper portion, a
 lower portion, and a middle portion.”
      Figures 12A through 12H of the patents 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 [Figures] 12A through 12H.”
 ’961 patent, col. 3, ll. 36–41. These figures were submitted
 with the initial application and so predate the limitations
 added during prosecution. As the district court found, J.A.
 9–17, and Nature concedes, Reply Br. 6 (“Figures 12 and
 13 do not add all of the limitations of claim 1 because the
 examiner amended claim 1.”), claim 1 adds limitations not
 found in Figures 12A–H or 13: “removing duplicate

     3    The majority asserts that the inventor provided a
 technical tutorial to the district court. Maj. Op. 4–5. While
 it is true that the inventor prepared slides that were uti-
 lized by counsel, the district court confirmed that Nature
 presented no expert witnesses at the tutorial. Dist. Ct. Or-
 der 1, J.A. 1 (“[Nature] presented no expert witness testi-
 mony at the tutorial hearing.”); see also ECF No. 43, J.A.
 284. Nature does not rely on the tutorial for any purpose.
 The tutorial apparently was not recorded.
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.              5

 intersection points, identifying positions of end intersec-
 tion points, and splitting portion of each triangle including
 an upper portion, a lower portion, and a middle portion.”
 Thus, 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.
     Apart from the figures, the majority finds that “[t]he
 specification describes the steps of the modified Watson
 method” based on quotes from the portion of the specifica-
 tion reproduced below:
     The second step of a Boolean operation this inven-
     tion described is to search and build intersection
     lines between triangle sets. It starts with finding
     the first pair of intersecting triangles: this system
     builds an axis aligned minimum bounding box for
     each triangle and checks whether two bounding
     boxes overlap to decide if edge-triangle intersection
     needs to be calculated. Once the edge-triangle in-
     tersection point(s) falls inside a triangle, this sys-
     tem completes the searching task and stores the
     point data into an intersection line set.
     To extend the current intersection line, this
     method traces neighboring triangles and calculates
     edge-triangle intersection points until the intersec-
     tion line becomes closed.
     The third step of a Boolean operation this invention
     described is to split triangles. Each segment of the
     intersection lines references two (2) triangles, each
     of the triangles has at least one sub-intersection
     line that contains one or more segments, which di-
     vide a triangle into three (3) or more smaller trian-
     gles. After splitting the triangles, the original
     triangles are removed, and those smaller triangles
     are added to the BIOpTriangleSet.
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 6         NATURE SIMULATION SYSTEMS INC.      v. AUTODESK, INC.

 ’961 patent, col. 2, ll. 12–32; Maj. Op. 14. But this portion
 of the specification again deals with the claims before the
 amendments and does not mention “modified Watson
 method” or the language that was added during prosecu-
 tion, “removing 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.” See ’961 patent, col. 2, ll. 12–32.
 Instead, this portion of the specification describes “step[s]
 of a Boolean operation.” Id. The quoted part of the speci-
 fication largely corresponds to limitations other than “mod-
 ified Watson method” that are elsewhere described in the
 claims, i.e.,
     building intersection lines starting with and end-
     ing 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, 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 intersection point of the
     intersection line ensuring that the intersection line
     gets closed or until all triangles are traversed.
 ’961 patent, col. 9, ll. 23–33 (emphasis added).
     The only expert evidence on the meaning of the addi-
 tional limitations added during prosecution in the record is
 by Autodesk’s expert, who testified without contradiction
 that these limitations are “not describe[d]” in the patent,
 are “ambiguous” and “unclear,” and are “inconsistent with”
 Figure 13 and the accompanying text. Aliaga Decl. ¶¶ 16–
 17, J.A. 54–56. The majority faults the district court for
 “declin[ing] to consider information in the specification
 that was not included in the claims,” Maj. Op. 13, but it
 seems to me that the district court correctly determined
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 NATURE SIMULATION SYSTEMS INC.   v. AUTODESK, INC.               7

 that the cited portions of the specification simply “do[] not
 explain the challenged claim language.” Dist. Ct. Order 10,
 J.A. 10. 4
     The majority relies on the prosecution history as some-
 how providing clarity to the meaning of the claim language.
 The majority states that the prosecution history is “signif-
 icant,” Maj. Op. 15, and implies that the district court erred
 when it “gave no weight to the prosecution history showing
 the resolution of indefiniteness by adding the designated
 technologic limitations to the claims,” Maj. Op. 17. But the
 majority does not identify anything in the prosecution his-
 tory, whether statements by the applicant or by the exam-
 iner, that would illuminate the meaning of “modified
 Watson method” or the language “removing duplicate in-
 tersection points, identifying positions of end intersection
 points, and splitting portion of each triangle including an
 upper portion, a lower portion, and a middle portion.”

     4   The added claim language may also present a writ-
 ten description problem, though that issue is not before us.
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 8         NATURE SIMULATION SYSTEMS INC.    v. AUTODESK, INC.

     Lastly, the majority suggests that the claim language
 is not indefinite because it is “an improvement on the
 known Watson and Delaunay methods and partakes of
 known usages for these established technologies.” Maj. Op.
 18. It cites to Presidio Components, Inc. v. Am. Tech. Ce-
 ramics Corp., 875 F.3d 1369, 1377 (Fed. Cir. 2017), for the
 proposition that when “the general approach [is] suffi-
 ciently well established in the art and referenced in the pa-
 tent,” the claims are not indefinite. But in Presidio, there
 was expert testimony that the general approach of the
 methodology at issue was within the knowledge of someone
 skilled in the art. Id. at 1376–77. As noted, there is noth-
 ing in the record to suggest that someone skilled in the art
 would know the meaning of the added claim language, and
 the sole evidence on that point is to the contrary.
     I respectfully dissent.