IP Library › Granted Patent US 12,353,191
Granted Patent B2
US 12,353,191 · App. 18/537,713 · Granted Jul 8, 2025

Conversion of mesh geometry to editable and watertight boundary representation in computer aided design

Inventors: Martin Cvetanov Marinov (Cambridge, GB); Peter Hugh Charrot (Cambridge, GB); Suguru Furuta (Cambridge, GB); Nandakumar Santhanam (Ithaca, NY); Justin Nicholas Hallet (North Warrandyte, AU); Stephen Alan Barley (Cambridge, GB); Jean Alison Flower (Uckfield, GB); Gordon Thomas Finnigan (Harvard, MA); Siavash Navadeh Meshkat (Carlsbad, CA); Iain Edward Henley (Great Chesterford, GB); Tristan Ward Barback (Cambridge, GB); Maciej Sapun (Stalowa Wola, PL); Marco Amagliani (Cambridge, GB); Pawel Wolski (Cracow, PL)
Assignee: Autodesk, Inc.
G05B19/4099B23Q3/16B29C64/393B33Y50/00B33Y50/02G06F30/10G05B2219/35134G05B2219/49007G06F2113/10G06F2119/18
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Quick Facts
Patent No.
US 12,353,191
App. No.
18/537,713
Granted
Jul 8, 2025
Kind
B2
Abstract

Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include, in at least one aspect, a fully automatic method of converting a generative design into an editable, watertight B-Rep by leveraging the generative solver input and representation to: (1) embed the exact input solid boundary surfaces where the design coincides with the input, (2) approximate everywhere else the design boundary with globally smooth, editable “organic” surfaces, and (3) join all surfaces to form a generative design output B-Rep.

Claims (89)

1. A method comprising:

obtaining a first three-dimensional model of an object, wherein the first three-dimensional model comprises a polygon mesh;

partitioning the polygon mesh into a first portion corresponding to one or more solids and a second portion not corresponding to the one or more solids, wherein the one or more solids are in a boundary representation format;

constructing one or more editable smooth surfaces for the second portion of the polygon mesh;

modifying one or more boundaries of the one or more editable smooth surfaces to contact the one or more solids at one or more gap-free contact curves that are homeomorphic with the one or more boundaries, thereby forming one or more modified smooth surfaces; and

combining the one or more modified smooth surfaces with the one or more solids to form a second three-dimensional model of the object, wherein the second three-dimensional model comprises the one or more modified smooth surfaces in watertight contact with one or more portions of the one or more solids in the boundary representation format at the one or more gap-free contact curves.

2. The method of claim 1 , wherein the obtaining comprises receiving the polygon mesh from a generative design process that used the one or more solids in the generative design process, and each of the one or more gap-free contact curves and each of the one or more modified smooth surfaces is editable using free-form modeling operations.

3. The method of claim 2 , wherein the generative design process employs a level set method, the polygon mesh is extracted from a level set representation of the object, the method comprises propagating incidence attributes from grid points in the level set representation to vertices of the polygon mesh, and the grid points comprise grid points that are on or inside the one or more solids and that participate in the polygon mesh extraction.

4. The method of claim 1 , wherein the partitioning comprises assigning polygons of the polygon mesh to the first portion in accordance with a polygon having at least one vertex that is contained by at least one of the one or more solids or is within a threshold distance of a surface of the at least one of the one or more solids, and the threshold distance is based on a discretization accuracy of the polygon mesh.

5. The method of claim 4 , wherein the assigning comprises initially assigning the polygon to the first portion responsive to the polygon having each of the polygon's vertices being contained by the at least one of the one or more solids or being within the threshold distance of the surface of the at least one of the one or more solids, and the partitioning comprises reassigning the polygon from the first portion to the second portion responsive to the polygon including a boundary vertex that (i) lies on a boundary between the first portion and the second portion and (ii) connects more than two boundary edges that lie on the boundary between the first portion and the second portion.

6. The method of claim 1 , comprising smoothing one or more piecewise-linear curves of a boundary between the first portion and the second portion.

7. The method of claim 6 , comprising remeshing polygons around the one or more piecewise-linear curves of the boundary between the first portion and the second portion, and wherein the smoothing comprises shifting boundary vertex positions towards their averages.

8. The method of claim 6 , comprising, before the smoothing:

adding regularity constraints on one or more boundary vertices with a flat interior surface angle; and

applying boundary curve tangent direction propagation along the one or more piecewise-linear curves of the boundary between the first portion and the second portion.

9. The method of claim 1 , wherein the constructing comprises fitting the one or more editable smooth surfaces to the second portion of the polygon mesh to form at least one globally smooth free-form surface that deviates from the polygon mesh no further than a specified approximation tolerance.

10. The method of claim 9 , wherein the constructing comprises computing an anisotropic adaptive size-field that specifies control mesh edge length sizes for the one or more editable smooth surfaces.

11. The method of claim 9 , wherein the constructing comprises computing cross, size and field-guided quad parameterization of the second portion of the polygon mesh.

12. The method of claim 1 , wherein the constructing comprises obtaining a quantized globally continuous map, and the one or more editable smooth surfaces comprise one or more Non-Uniform Rational Catmull-Clark Surfaces with T-junctions (T-NURCC) or T-Spline surfaces.

13. The method of claim 1 , wherein the modifying comprises:

pulling at least one boundary of the one or more editable smooth surfaces toward at least one of the one or more solids;

setting a safety tolerance value for the modifying based on an accuracy limitation; and

adjusting the safety tolerance value to ensure the one or more gap-free contact curves are homeomorphic with the one or more boundaries.

14. The method of claim 13 , wherein the one or more solids comprise two solids having a minimum distance between the two solids, and the method comprises expanding at least one of the two solids responsive to the minimum distance being smaller than the accuracy limitation.

15. The method of claim 13 , comprising adding at least one fairing energy term for at least one region of the at least one boundary responsive to a curvature of the at one region of the at least one boundary exceeding a threshold.

16. The method of claim 1 , wherein the combining comprises using cellular modelling techniques.

17. The method of claim 1 , comprising applying a blend to at least one contact curve of the one or more gap-free contact curves responsive to the at least one contact curve not providing at least tangent continuity with the one or more solids.

18. The method of claim 1 , wherein the obtaining comprises receiving the polygon mesh, and the partitioning comprises fitting one or more regular geometrical shapes to the polygon mesh to determine the one or more solids.

19. The method of claim 18 , wherein the object is a physical object, and the polygon mesh was produced by a scanner than scanned the physical object.

20. A non-transitory computer readable medium encoding instructions of a computer program operable to cause one or more data processing apparatus to perform operations comprising:

obtaining a first three-dimensional model of an object, wherein the first three-dimensional model comprises a polygon mesh;

partitioning the polygon mesh into a first portion corresponding to one or more solids and a second portion not corresponding to the one or more solids, wherein the one or more solids are in a boundary representation format;

constructing one or more editable smooth surfaces for the second portion of the polygon mesh;

modifying one or more boundaries of the one or more editable smooth surfaces to contact the one or more solids at one or more gap-free contact curves that are homeomorphic with the one or more boundaries, thereby forming one or more modified smooth surfaces; and

combining the one or more modified smooth surfaces with the one or more solids to form a second three-dimensional model of the object, wherein the second three-dimensional model comprises the one or more modified smooth surfaces in watertight contact with one or more portions of the one or more solids in the boundary representation format at the one or more gap-free contact curves.

21. The non-transitory computer readable medium of claim 20 , wherein the obtaining comprises receiving the polygon mesh from a generative design process that used the one or more solids in the generative design process, and each of the one or more gap-free contact curves and each of the one or more modified smooth surfaces is editable using free-form modeling operations.

22. The non-transitory computer readable medium of claim 21 , wherein the generative design process employs a level set method, the polygon mesh is extracted from a level set representation of the object, the operations comprises propagating incidence attributes from grid points in the level set representation to vertices of the polygon mesh, and the grid points comprise grid points that are on or inside the one or more solids and that participate in the polygon mesh extraction.

23. The non-transitory computer readable medium of claim 20 , wherein the partitioning comprises assigning polygons of the polygon mesh to the first portion in accordance with a polygon having at least one vertex that is contained by at least one of the one or more solids or is within a threshold distance of a surface of the at least one of the one or more solids, and the threshold distance is based on a discretization accuracy of the polygon mesh.

24. The non-transitory computer readable medium of claim 23 , wherein the assigning comprises initially assigning the polygon to the first portion responsive to the polygon having each of the polygon's vertices being contained by the at least one of the one or more solids or being within the threshold distance of the surface of the at least one of the one or more solids, and the partitioning comprises reassigning the polygon from the first portion to the second portion responsive to the polygon including a boundary vertex that (i) lies on a boundary between the first portion and the second portion and (ii) connects more than two boundary edges that lie on the boundary between the first portion and the second portion.

25. The non-transitory computer readable medium of claim 20 , wherein the operations comprise smoothing one or more piecewise-linear curves of a boundary between the first portion and the second portion.

26. The non-transitory computer readable medium of claim 25 , wherein the operations comprise remeshing polygons around the one or more piecewise-linear curves of the boundary between the first portion and the second portion, and wherein the smoothing comprises shifting boundary vertex positions towards their averages.

27. The non-transitory computer readable medium of claim 25 , wherein the operations comprise, before the smoothing:

adding regularity constraints on one or more boundary vertices with a flat interior surface angle; and

applying boundary curve tangent direction propagation along the one or more piecewise-linear curves of the boundary between the first portion and the second portion.

28. The non-transitory computer readable medium of claim 20 , wherein the constructing comprises fitting the one or more editable smooth surfaces to the second portion of the polygon mesh to form at least one globally smooth free-form surface that deviates from the polygon mesh no further than a specified approximation tolerance.

29. The non-transitory computer readable medium of claim 28 , wherein the constructing comprises computing an anisotropic adaptive size-field that specifies control mesh edge length sizes for the one or more editable smooth surfaces.

30. The non-transitory computer readable medium of claim 28 , wherein the constructing comprises computing cross, size and field-guided quad parameterization of the second portion of the polygon mesh.

31. The non-transitory computer readable medium of claim 20 , wherein the constructing comprises obtaining a quantized globally continuous map, and the one or more editable smooth surfaces comprise one or more Non-Uniform Rational Catmull-Clark Surfaces with T-junctions (T-NURCC) or T-Spline surfaces.

32. The non-transitory computer readable medium of claim 20 , wherein the modifying comprises:

pulling at least one boundary of the one or more editable smooth surfaces toward at least one of the one or more solids;

setting a safety tolerance value for the modifying based on an accuracy limitation; and

adjusting the safety tolerance value to ensure the one or more gap-free contact curves are homeomorphic with the one or more boundaries.

33. The non-transitory computer readable medium of claim 32 , wherein the one or more solids comprise two solids having a minimum distance between the two solids, and the operations comprise expanding at least one of the two solids responsive to the minimum distance being smaller than the accuracy limitation.

34. The non-transitory computer readable medium of claim 32 , wherein the operations comprise adding at least one fairing energy term for at least one region of the at least one boundary responsive to a curvature of the at one region of the at least one boundary exceeding a threshold.

35. The non-transitory computer readable medium of claim 20 , wherein the combining comprises using cellular modelling techniques.

36. The non-transitory computer readable medium of claim 20 , wherein the operations comprise applying a blend to at least one contact curve of the one or more gap-free contact curves responsive to the at least one contact curve not providing at least tangent continuity with the one or more solids.

37. The non-transitory computer readable medium of claim 20 , wherein the obtaining comprises receiving the polygon mesh, and the partitioning comprises fitting one or more regular geometrical shapes to the polygon mesh to determine the one or more solids.

38. The non-transitory computer readable medium of claim 37 , wherein the object is a physical object, and the polygon mesh was produced by a scanner than scanned the physical object.

39. A system comprising:

a non-transitory storage medium having instructions of a computer program stored thereon; and

one or more data processing apparatus configured to run the instructions of the computer program to

obtain a first three-dimensional model of an object, wherein the first three-dimensional model comprises a polygon mesh,

partition the polygon mesh into a first portion corresponding to one or more solids and a second portion not corresponding to the one or more solids, wherein the one or more solids are in a boundary representation format,

construct one or more editable smooth surfaces for the second portion of the polygon mesh,

modify one or more boundaries of the one or more editable smooth surfaces to contact the one or more solids at one or more gap-free contact curves that are homeomorphic with the one or more boundaries, thereby forming one or more modified smooth surfaces, and

combine the one or more modified smooth surfaces with the one or more solids to form a second three-dimensional model of the object, wherein the second three-dimensional model comprises the one or more modified smooth surfaces in watertight contact with one or more portions of the one or more solids in the boundary representation format at the one or more gap-free contact curves.

40. The system of claim 39 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to receive the polygon mesh from a generative design process that used the one or more solids in the generative design process, and each of the one or more gap-free contact curves and each of the one or more modified smooth surfaces is editable using free-form modeling operations.

41. The system of claim 40 , wherein the generative design process employs a level set method, the polygon mesh is extracted from a level set representation of the object, the one or more data processing apparatus are configured to run the instructions of the computer program to propagate incidence attributes from grid points in the level set representation to vertices of the polygon mesh, and the grid points comprise grid points that are on or inside the one or more solids and that participate in the polygon mesh extraction.

42. The system of claim 39 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to assign polygons of the polygon mesh to the first portion in accordance with a polygon having at least one vertex that is contained by at least one of the one or more solids or is within a threshold distance of a surface of the at least one of the one or more solids, and the threshold distance is based on a discretization accuracy of the polygon mesh.

43. The system of claim 42 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to initially assign the polygon to the first portion responsive to the polygon having each of the polygon's vertices being contained by the at least one of the one or more solids or being within the threshold distance of the surface of the at least one of the one or more solids, and the one or more data processing apparatus are configured to run the instructions of the computer program to reassign the polygon from the first portion to the second portion responsive to the polygon including a boundary vertex that (i) lies on a boundary between the first portion and the second portion and (ii) connects more than two boundary edges that lie on the boundary between the first portion and the second portion.

44. The system of claim 39 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to smooth one or more piecewise-linear curves of a boundary between the first portion and the second portion.

45. The system of claim 44 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to remesh polygons around the one or more piecewise-linear curves of the boundary between the first portion and the second portion, and the one or more data processing apparatus are configured to run the instructions of the computer program to shift boundary vertex positions towards their averages.

46. The system of claim 44 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to, before the one or more piecewise-linear curves are smoothed:

add regularity constraints on one or more boundary vertices with a flat interior surface angle; and

apply boundary curve tangent direction propagation along the one or more piecewise-linear curves of the boundary between the first portion and the second portion.

47. The system of claim 39 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to fit the one or more editable smooth surfaces to the second portion of the polygon mesh to form at least one globally smooth free-form surface that deviates from the polygon mesh no further than a specified approximation tolerance.

48. The system of claim 47 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to compute an anisotropic adaptive size-field that specifies control mesh edge length sizes for the one or more editable smooth surfaces.

49. The system of claim 47 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to compute cross, size and field-guided quad parameterization of the second portion of the polygon mesh.

50. The system of claim 39 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to obtain a quantized globally continuous map, and the one or more editable smooth surfaces comprise one or more Non-Uniform Rational Catmull-Clark Surfaces with T-junctions (T-NURCC) or T-Spline surfaces.

51. The system of claim 39 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to:

pull at least one boundary of the one or more editable smooth surfaces toward at least one of the one or more solids;

set a safety tolerance value for the modifying based on an accuracy limitation; and

adjust the safety tolerance value to ensure the one or more gap-free contact curves are homeomorphic with the one or more boundaries.

52. The system of claim 51 , wherein the one or more solids comprise two solids having a minimum distance between the two solids, and the one or more data processing apparatus are configured to run the instructions of the computer program to expand at least one of the two solids responsive to the minimum distance being smaller than the accuracy limitation.

53. The system of claim 51 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to add at least one fairing energy term for at least one region of the at least one boundary responsive to a curvature of the at one region of the at least one boundary exceeding a threshold.

54. The system of claim 39 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to use cellular modelling techniques to combine the one or more modified smooth surfaces with the one or more solids.

55. The system of claim 39 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to apply a blend to at least one contact curve of the one or more gap-free contact curves responsive to the at least one contact curve not providing at least tangent continuity with the one or more solids.

56. The system of claim 39 , wherein the one or more data processing apparatus are configured to run the instructions of the computer program to receive the polygon mesh, and the one or more data processing apparatus are configured to run the instructions of the computer program to fit one or more regular geometrical shapes to the polygon mesh to determine the one or more solids.

57. The system of claim 56 , wherein the object is a physical object, and the polygon mesh was produced by a scanner than scanned the physical object.

Assignments (1)
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Jan 4, 2024
From: MARINOV, MARTIN CVETANOV; CHARROT, PETER HUGH; FURUTA, SUGURU; SANTHANAM, NANDAKUMAR; HALLET, JUSTIN NICHOLAS; BARLEY, STEPHEN ALAN; FLOWER, JEAN ALISON; FINNIGAN, GORDON THOMAS; MESHKAT, SIAVASH NAVADEH; HENLEY, IAIN EDWARD; BARBACK, TRISTAN WARD; SAPUN, MACIEJ; AMAGLIANI, MARCO; WOLSKI, PAWEL
To: AUTODESK, INC.
Reel/Frame 066025/0313 →
Continuity (4)
Continuation 17229320 · Apr 13, 2021
Continuation PCTUS2019034221 · May 28, 2019
Provisional Application 62758053 · Nov 9, 2018
Related Publication 20240168460A1 · May 23, 2024
References Cited (100)
US 8970590B1 · Brennan et al. · 2015 [cited by applicant]
US 9697326B1 · Bowman et al. · 2017 [cited by applicant]
US 9902114B2 · Musuvathy · 2018 [cited by applicant]
US 10339226B2 · Schmitter · 2019 [cited by examiner]
US 10467807B1 · Strater · 2019 [cited by examiner]
US 10599809B2 · Urick et al. · 2020 [cited by applicant]
US 10810795B2 · Sederberg · 2020 [cited by examiner]
US 10974446B2 · Nosenzo et al. · 2021 [cited by applicant]
US 11016470B2 · Marinov · 2021 [cited by examiner]
US 11886165B2 · Marinov et al. · 2024 [cited by applicant]
US 20030191554A1 · Russell et al. · 2003 [cited by applicant]
US 20110087350A1 · Fogel et al. · 2011 [cited by applicant]
US 20120029882A1 · Bommes et al. · 2012 [cited by applicant]
US 20130300735A1 · Schmidt · 2013 [cited by applicant]
US 20160133049A1 · Hill et al. · 2016 [cited by applicant]
US 20160224693A1 · Maisonneuve · 2016 [cited by applicant]
US 20170037518A1 · Oxford et al. · 2017 [cited by applicant]
US 20170357736A1 · Schmitter et al. · 2017 [cited by applicant]
US 20180120478A1 · Imhof · 2018 [cited by applicant]
US 20190303532A1 · Urick et al. · 2019 [cited by applicant]
US 20200150624A1 · Marinov et al. · 2020 [cited by applicant]
US 20200151953A1 · Strater et al. · 2020 [cited by applicant]
US 20210232120A1 · Marinov et al. · 2021 [cited by applicant]
US 20210263499A1 · Marinov et al. · 2021 [cited by applicant]
CN 103617603 · 2014 [cited by applicant]
CN 106204748 · 2016 [cited by applicant]
WO WO2017142953 · 2017 [cited by applicant]
Notice of Allowance in Chinese Appln. No. 201980073804.5, dated Mar. 13, 2024, 8 pages (with English translation). [cited by applicant]
Alliez et al., “3D Fast Intersection and Distance Computation”, CGAL User and Reference Manual 3, 2016. [cited by applicant]
Alliez et al., “Anisotropic polygonal remeshing”, ACM SIGGRAPH 2003 Papers, 2003, pp. 485-493. [cited by applicant]
Authorized officer Katarzyna Nesciobello, International Search Report and Written Opinion in PCT/US2019/034221, mailed Sep. 23, 2019, 17 pages. [cited by applicant]
Authorized officer Katarzyna Nesciobello, International Search Report and Written Opinion in PCT/US2019/060589, mailed Mar. 31, 2020, 16 pages. [cited by applicant]
Autodesk Dreamcatcher. Project Dreamcatcher | Autodesk Research. https://autodeskresearch.com/projects/dreamcatcher. [cited by applicant]
Autodesk PowerShape. PowerShape | Manufacturing CAD Software for Complex Parts | Autodesk. https://www.autodesk.com/products/powershape/overview#. [cited by applicant]
Bajaj et al., “Reconstructing Surfaces and Functions on Surfaces from Unorganized Three-Dimensional Data”, Algorithmica (New York), Sep. 1997, 19(1):243-261. [cited by applicant]
Benko et al., “Algorithms for reverse engineering boundary representation models”, Comput. Des., Sep. 2001, 33(11): 839-851. [cited by applicant]
Biermann et al., “Approximate Boolean Operations on Free-form Solids”, in: Proc. of SIGGRAPH 01, 2001, pp. 185-194. URL https://mrl.nyu.edu/publications/booleans/booleans2001.pdf. [cited by applicant]
Biermann et al., “Sharp Features on Multiresolution Subdivision Surfaces”, Graphical Models 64 (2) (2002) 61-77. doi:10.1006/gmod.2002.0570. URL http://linkinghub.elsevier.com/retrieve/pii/S1524070302905709. [cited by applicant]
Bommes et al., “Integer-grid Maps for Reliable Quad Meshing”, ACM Transactions on Graphics 32 (4) (2013) 1. doi:10.1145/2461912.2462014. URL http://dl.acm.org/citation.cfm?doid=2461912.2462014. [cited by applicant]
Bommes et al., “Mixed-integer Quadrangulation”, ACM Transactions on Graphics 28 (3) (2009) 1. doi:10.1145/1531326.1531383. URL http://portal.acm.org/citation.cfm?doid=1531326.1531383. [cited by applicant]
Brackett et al., “Topology optimization for additive manufacturing”, Proceedings of the Solid Freeform Fabrication Symposium, 2011, pp. 348-362. [cited by applicant]
Campen et al., “Aligned Parameterization”, Computer Graphics Forum 33 (8) (2014) 69-81. [cited by applicant]
Campen et al., “Quantized Global Parametrization”, ACM Transactions on Graphics 34 (6) (2015) 1-12. doi:10.1145/2816795.2818140. URL http://dl.acm.org/citation.cfm?doid=2816795.2818140. [cited by applicant]
Cohen-Steiner et al., “Restricted delaunay triangulations and normal cycle”, Proceedings of the 19th Annual Symposium on Computational Geometry, 2003, 312-321. [cited by applicant]
Cohen-Steiner et al., “Variational shape approximation”, Proc. of ACM SIGGRAPH 04, 2004, 23(3):905-914. [cited by applicant]
Coons, “Surfaces for Computer-aided Design of Space Forms”, Technical Report (1967). URL https://dl.acm.org/citation.cfm?id=889976. [cited by applicant]
Eck et al., “Automatic Reconstruction of B-spline Surfaces of Arbitrary Topological Type”, in: Proceedings of the 23rd annual conference on Computer graphics and interactive techniques—SIGGRAPH '96, 1996, pp. 325-334. d… [cited by applicant]
Garland et al., “Hierarchical Face Clustering on Polygonal Surfaces”, 2001 ACM Symposium on Interactive 3D Graphics, 2001, pp. 49-58. [cited by applicant]
Gregory et al., “A C1 Triangular Interpolation Patch for Computer-aided Geometric Design”, Computer Graphics and Image Processing 13(1) (1980) 80-87. doi:10.1016/0146-664X(80)90117-3. URL https://www.sciencedirect.com/s… [cited by applicant]
Hachenberger et al., “{3D} Boolean Operations on Nef Polyhedra” {CGAL} User and Reference Manual. CGAL Editorial Board. [cited by applicant]
Hoppe et al., “Piecewise smooth surface reconstruction”, Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques—SIGGRAPH, 1994, pp. 295-302. [cited by applicant]
Hoppe et al., “Surface reconstruction from unorganized points”, ACM SIGGRAPH Computer Graphics, 1992, 26(2):71-78. [cited by applicant]
Jackson, “Boundary Representation Modelling with Local Tolerances,” Dec. 1995, SMA '95: Proceedings of the third ACM symposium on Solid modeling and applications, pp. 247-254, source: https://doi.org/10.1145/218013.2180… [cited by applicant]
Joshi et al., A. Yurova, “CAD-integrated Topology Optimization”, (Dec. 31, 2016), XP055621476, retrieved from the Internet: URL:https://www5.in.tum.de/pub/bgceproject2016report.pdf), 77 pages. [cited by applicant]
Ju et al., “Dual Contouring of Hermite Data”, Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques, 2002, pp. 339-346. [cited by applicant]
Knoppel et al., “Globally Optimal Direction Fields”, ACM Transactions on Graphics, 2013, 32(4):1-10. [cited by applicant]
Kobbelt et al., “Feature Sensitive Surface Extraction from Volume Data”, Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, 2001, pp. 57-66. [cited by applicant]
Krishnamurthy et al., “Fitting smooth surfaces to dense polygon meshes” Proceedings of the 23rd annual conference on Computer graphics and interactive techniques—SIGGRAPH '96, ACM Press, 313-324. [cited by applicant]
Kruth et al., “Reverse engineering modelling of free-form surfaces from point clouds subject to boundary conditions”, J. Mater. Process. Technol., Apr. 1998, 76(1-3):120-127. [cited by applicant]
Lai et al., “Blending of mesh objects to parametric surface”, Comput. Graph, Feb. 2015, 46( C ): 283-293. [cited by applicant]
Levin, “Combined Subdivision Schemes for the Design of Surfaces Satisfying Boundary Conditions”, preprint submitted to Elsevier Preprint (Nov. 23, 1998). URL http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.16.4… [cited by applicant]
Levin, “Interpolating Nets of Curves by Smooth Subdivision Surfaces”, Proceedings of the 26th annual conference on Computer graphics and interactive techniques—SIGGRAPH '99 (1999) 57-64 doi:10.1145/311535.311541. URL ht… [cited by applicant]
Li et al., “Automatic and Interactive Mesh to T-spline Conversion”, in: Proceedings of the Fourth Eurographics Symposium on Geometry Processing, 2006, pp. 191-200. doi:10.1145/1281957.1281982. URL http://dl.acm.org/cita… [cited by applicant]
Limitstate3d.com [online], “Limitstate:Form”, published on or before Apr. 12, 2021, retrieved on May 5, 2021, retrieved from URL<http://limitstate3d.com/.>, 4 pages. [cited by applicant]
Litke et al., “Fitting Subdivision Surfaces”, in: IEEE Visualization 2001, 2001, pp. 319-324. URL http://www.multires.caltech.edu/pubs/fitting.pdf. [cited by applicant]
Litke et al., “Trimming for Subdivision Surfaces”, Computer-Aided Geometric Design 18 (5) (2001) 463-481. URL http://www.multires.caltech.edu/pubs/trimming.pdf. [cited by applicant]
Ma et al., “A direct approach for subdivision surface fitting from a dense triangle mesh”, Comput. Des., May 2004, 36(6):525-536. [cited by applicant]
Mangan et al., “Partitioning 3D surfaces meshes using watershed segmentation”, IEEE Trans. Vis. Comput. Graph., 1999, 5(4):308-321. [cited by applicant]
Marinov et al., “Generative Design Conversion to Editable and Watertight Boundary Representation,” Computer-Aided Design, May 2019, 115:194-205. [cited by applicant]
Marinov et al., “Automatic generation of structure preserving multiresolution models”, Comput. Graph. Forum, 2005, 24(3):479-489. [cited by applicant]
Marinov et al., “Optimization Methods for Scattered Data Approximation with Subdivision Surfaces”, Graphical Models, 2005, 67(5):452-473. [cited by applicant]
Marinov et al., “Optimization techniques for approximation with subdivision surfaces”, ACM Symposium on Solid Modeling and Applications, 2004, p. 10. [cited by applicant]
Marinov et al., “Boundary Conforming Mesh to T-NURCC Surface Conversion,” Computers & Graphics, May 2019, 82:95-105. [cited by applicant]
Mscsoftware.com [online], “MSC Nastran: Multidisciplinary Structural Analysis”, published on or before Apr. 12, 2021, retrieved on May 5, 2021, retrieved from URL<http://www.mscsoftware.com/product/msc-nastran>, 5 pages. [cited by applicant]
Myles et al., “Robust field-aligned global parametrization”, ACM Transactions on Graphics, 2014, 33(4):1-14. [cited by applicant]
Peterson, “Arc Length Parameterization of Spline Curves”, Journal of Computer-Aided Design 14 (2) (2006) 1-11. [cited by applicant]
plm.automation.siemens.com [online], “Convergent Modeling”, published on or before Apr. 12, 2021, retrieved on May 5, 2021, retrieved from URL<https://www.plm.automation.siemens.com/global/en/our-story/glossary/converge… [cited by applicant]
plm.automation.siemens.com [online], “Parasolid”, published on or before Apr. 12, 2021, retrieved on May 5, 2021, retrieved from URL<https://www.plm.automation.siemens.com/global/en/products/plm-components/parasolid.htm… [cited by applicant]
plm.automation.siemens.com [online], “PLM Components”, published on or before Apr. 12, 2021, retrieved on May 5, 2021, retrieved from URL<https://www.https://www.plm.automation.siemens.com/global/en/products/plm-compone… [cited by applicant]
PTC.com [online], “Innovate Faster with Generative Design and AI”, published on or before Apr. 12, 2021, retrieved on May 5, 2021, retrieved from URL<https://www.frustum.com/product>, 12 pages. [cited by applicant]
Ray et al., “Periodic Global Parameterization”, ACM Transactions on Graphics, 2006, 25(4):1460-1485. [cited by applicant]
Rouhani et al., “Implicit B-Spline Surface Reconstruction”, IEEE Trans. Image Process., Jan. 2015, 24(1):22-32. [cited by applicant]
Sabin, “Transfinite Surface Interpolation”, in: Proceedings of the 6th IMA Conference on the Mathematics of Surfaces, Clarendon Press, New York, NY, USA, 1996, pp. 517-534. [cited by applicant]
Scott et al., “Local refinement of analysis-suitable T splines”, Computer Methods in Applied Mechanics and Engineering 213-216 (2012) 206 222. [cited by applicant]
Sederberg et al., “T-spline simplification and local refinement”, in: ACM SIGGRAPH 2004 Papers on—SIGGRAPH '04, 2004, p. 276. doi:10.1145/1186562.1015715. URL http://portal.acm.org/citation.cfm?doid=1186562.1015715. [cited by applicant]
Sederberg et al., “T-splines and T-NURCCs”, in: ACM Transactions on Graphics, vol. 22, 2003, p. 477. doi:10.1145/882262.882295. URL http://portal.acm.org/citation.cfm?doid=882262.882295. [cited by applicant]
Sederberg et al., “Watertight Trimmed NURBS”, in: ACM SIGGRAPH 2008 papers on—SIGGRAPH '08, vol. 27, ACM Press, New York, New York, USA, 2008, p. 1. doi:10.1145/1399504.1360678. URL http://portal.acm.org/citation.cfm?do… [cited by applicant]
Sharpe et al., “Numerical method for extracting an arc length parameterization from parametric curves”, Computer-Aided Design 14 (2) (1982) 79-81. [cited by applicant]
Shen et al., “Converting a CAD Model into a Non-uniform Subdivision Surface”, Computer Aided Geometric Design 48 (2016) 17-35. doi:10.1016/j.cagd.2016.07.003. URL https://linkinghub.elsevier.com/retrieve/pii/S0167839616… [cited by applicant]
Siemens.com [online], “PLM Components: 3D Software Development Toolkits for CAD, CAM, CAE and Robotics”, published on or before Apr. 12, 2021, retrieved on Apr. 14, 2021, retrieved from URL<https://www.plm.automation.si… [cited by applicant]
Sigmund and Maute, “Topology Optimization Approaches—a Comparative Review,” Struct. Multidisc. Optim. (2013) 48:1031-1055. [cited by applicant]
Taubin, “A Signal Processing Approach to Fair Surface Design”, Proceedings of ACM SIGGRAPH, 1995, 351-358. [cited by applicant]
Unknown Author, “Topology Optimization R18.0 Feature and Usage Highlights Additive Manufacturing Application”, (Mar. 12, 2017), XP055621368, retrieved from the Internet: URL:https://www.fluidcodes.com/archives/products/… [cited by applicant]
Van Dijk et al., “Level-set Methods for Structural Topology Optimization: a Review,” Struct. Multidisc. Optim. (2013) 48:437-472. [cited by applicant]
Wang et al., “Adaptive T-spline Surface Approximation of Triangular Meshes”, in: 2007 6th International Conference on Information, Communications and Signal Processing, ICICS, IEEE, 2007, pp. 1-5. doi:10.1109/ICICS.2007… [cited by applicant]
Wu et al., “Structure recovery via Hybrid Variational Surface Approximation”, Comput. Graph. Forum, Sep. 2005, 24(3):277-284. [cited by applicant]
Wu et al., “Variational reconstruction using subdivision surfaces with continuous sharpness control”, Comput. Vis. Media, Sep. 2017, 3(3):217-228. [cited by applicant]
Yan et al., “Quadric Surface Extraction by Variational Shape Approximation”, Springer, Berlin, Heidelberg, 2006, pp. 73-86. [cited by applicant]
Yan et al., “Variational mesh segmentation via quadric surface fitting”, Comput. Design., Nov. 2012, 44(11):1072-1082. [cited by applicant]
Zhang et al., “A wave based anisotropic quadrangulation method”, ACM SIGGRAPH 2010, pp. 1-8. [cited by applicant]