A note on solid modeling: history, state of the art, future

doi:10.11996/JG.j.2095-302X.2022060987

Abstract

Abstract:

Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what geometric information a computer should store and how to store/manipulate them in order for the computer to aid the processes of design and manufacturing. This paper provides a brief review on the historical development of solid modeling, its fundamental research problems, as well as their challenges and state of the art. It then concludes with three prospective trends of solid modeling, especially the promising paradigm shift from “Computer-Aided Design” to “Computer-Automated Design”.

Key words: CAD, geometric modeling, solid modeling, parametric modeling, direct modeling, structure modeling; intelligent CAD

CLC Number:

TP 391

ZOU Qiang. A note on solid modeling: history, state of the art, future [J]. Journal of Graphics, 2022, 43(6): 987-1001.

References

[1] COONS S, MANN R W. Computer-aided design related to the engineering design process[R]. Cambridge: M.I.T. Electronic Systems Laboratory, 1960.

[2] SHAH J, MÄNTYLÄ M. Parametric and feature-based CAD/CAM: concepts, techniques, and applications[EB/OL]. [2022-05-19]. https://www.researchgate.net/publication/44371716_Parametric_ and_feature_based_CADCAM_concepts_techniques_and_ applications_Jami_J_shah_Martti_Mantyla.

[3] COONS S A. An outline of the requirements for a computer-aided design system[C]//Proceedings of the Spring Joint Computer Conference. New York: ACM Press, 1963: 299-304.

[4] ROSS D T. Computer-aided design: a statement of objectives[R]. Cambridge: Massachusetts Institute of Technology, 1960.

[5] REQUICHA A A G. GEOMETRIC MODELING : a First course 6-2, fundamental algorithms[R]. Los Angeles: Univevsity of Southern California, 1999: 1-28.

[6] REQUICHA A A G. Representations for rigid solids: theory, methods, and systems[J]. ACM Computing Surveys, 1980, 12(4): 437-464.

[7] STAFF N A O E, COMPTON W D, ENGINEERING N A O. Design and Analysis of Integrated Manufacturing Systems[M]. Washington DC: National Academies Press, 1988: 167-199.

[8] SUTHERLAND I E. Sketchpad a man-machine graphical communication system[J]. SIMULATION, 1964, 2(5): R-3.

[9] REQUICHA A A G, VOELCKER H B. Solid modeling: current status and research directions[J]. IEEE Computer Graphics and Applications, 1983, 3(7): 25-37.

[10] BRAID I C. Geometric modelling[M]//Advances in computer graphics I. Berlin: Springer Berlin, 1986: 325-362.

[11] COHEN E, LYCHE T, RIESENFELD R F. MCAD: Key historical developments[J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(5-8): 224-228.

[12] VOELCKER H B, REQUICHA A A G. Geometric modeling of mechanical parts and processes[J]. Computer, 1977, 10(12): 48-57.

[13] BRAID I C. The synthesis of solids bounded by many faces[J]. Communications of the ACM, 1975, 18(4): 209-216.

[14] SHAPIRO V. Solid modeling[M]//Handbook of computer aided geometric design. Amsterdam: Elsevier, 2002: 473-518.

[15] REQUICHA A A G. Constructive solid geometry[EB/OL]. [2022-06-19]. https://www.zhangqiaokeyan.com/ntis-sciencerepoort-thesis/020711454048.html.

[16] STROUD I. Boundary Representation Modelling Techniques[M]. London: Springer London, 2006.

[17] CAMBA J D, CONTERO M, COMPANY P. Parametric CAD modeling: an analysis of strategies for design reusability[J]. Computer-Aided Design, 2016, 74: 18-31.

[18] SHAH J J. Designing with Parametric CAD: classification and comparison of construction techniques[M]//Geometric modelling. Boston: Springer US, 2001: 53-68.

[19] HOFFMANN C M, JOAN-ARINYO R. Parametric modeling[M]//Handbook of computer aided geometric design. Amsterdam: Elsevier, 2002: 519-541.

[20] ROLLER D. An approach to computer-aided parametric design[J]. Computer-Aided Design, 1991, 23(5): 385-391.

[21] SHAH J J, ROGERS M T. Functional requirements and conceptual design of the Feature-Based Modelling System[J]. Computer-Aided Engineering Journal, 1988, 5(1): 9.

[22] SHAH J J, ANDERSON D, KIM Y S, et al. A discourse on geometric feature recognition from CAD models[J]. Journal of Computing and Information Science in Engineering, 2001, 1(1): 41-51.

[23] CAMBA J D, CONTERO M. Assessing the impact of geometric design intent annotations on parametric model alteration activities[J]. Computers in Industry, 2015, 71: 35-45.

[24] CHEN X P, HOFFMANN C M. On editability of feature-based design[J]. Computer-Aided Design, 1995, 27(12): 905-914.

[25] ROSSIGNAC J R. Issues on feature-based editing and interrogation of solid models[J]. Computers & Graphics, 1990, 14(2): 149-172.

[26] MONEDERO J. Parametric design: a review and some experiences[J]. Automation in Construction, 2000, 9(4): 369-377.

[27] ANDREWS P T J, SHAHIN T M M, SIVALOGANATHAN S. Design reuse in a CAD environment—four case studies[J]. Computers & Industrial Engineering, 1999, 37(1-2): 105-109.

[28] BETTIG B, BAPAT V, BHARADWAJ B. Limitations of parametric operators for supporting systematic design[C]// 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. New York: ASME, 2008: 131-142.

[29] BROWN P. CAD: do computers aid the design process after all?[J]. Intersect: The Stanford Journal of Science, Technology and Society, 2009, 2(1): 52-66.

[30] ZOU Q, FENG H Y. Push-pull direct modeling of solid CAD models[J]. Advances in Engineering Software, 2019, 127: 59-69.

[31] REQUICHA A A G. Mathematical models of rigid solid objects[EB/OL]. [2022-06-01]. https://www. zhangqiaokeyan. covn/ntis-science-report_other_thesis/020711446637.html.

[32] REQUICHA A A G. Representation of rigid solid objects[M]//Lecture notes in computer science. Berlin: Springer, 2006: 1-78.

[33] REQUICHA A A G, VOELCKER H B. Solid modeling: a historical summary and contemporary assessment[J]. IEEE Computer Graphics and Applications, 1982, 2(2): 9-24.

[34] MANTYLA M. A note on the modeling space of Euler operators[J]. Computer Vision, Graphics, and Image Processing, 1984, 26(1): 45-60.

[35] BAER A, EASTMAN C, HENRION M. Geometric modelling: a survey[J]. Computer-Aided Design, 1979, 11(5): 253-272.

[36] BOTSCH M, KOBBELT L, PAULY M, et al. Polygon Mesh Processing[M]. Wellesley: A K Peters, 2010: 1-250.

[37] JACOBSON A, KAVAN L, SORKINE-HORNUNG O. Robust inside-outside segmentation using generalized winding numbers[J]. ACM Transactions on Graphics, 2013, 32(4): 33.

[38] BRIDSON R, FEDKIW R, ANDERSON J. Robust treatment of collisions, contact and friction for cloth animation[C]// SIGGRAPH '05: ACM SIGGRAPH 2005 Courses. New York: ACM Press, 2005: 2-es.

[39] REQUICHA A A G, VOELCKER H B. Boolean operations in solid modeling: boundary evaluation and merging algorithms[J]. Proceedings of the IEEE, 1985, 73(1): 30-44.

[40] ROSSIGNAC J R, REQUICHA A A G. Offsetting operations in solid modelling[J]. Computer Aided Geometric Design, 1986, 3(2): 129-148.

[41] SHAPIRO V, VOSSLER D L. What is a parametric family of solids?[C]//The 3rd ACM Symposium on Solid Modeling and Applications. New York: ACM Press, 1995: 43-54.

[42] BODEIN Y, ROSE B, CAILLAUD E. Explicit reference 第 6 期邹强：浅谈实体建模：历史、现状与未来 999 modeling methodology in parametric CAD system[J]. Computers in Industry, 2014, 65(1): 136-147.

[43] BETTIG B, HOFFMANN C M. Geometric constraint solving in parametric computer-aided design[J]. Journal of Computing and Information Science in Engineering, 2011, 11(2): 1.

[44] BRAID I. Non-local blending of boundary models[J]. Computer-Aided Design, 1997, 29(2): 89-100.

[45] GRAYER A R. Alternative approaches in geometric modelling[J]. Computer-Aided Design, 1980, 12(4): 189-192.

[46] Michelucci D. An Introduction to the Robustness Issue[EB/OL]. [2022-05-21]. https://ufrsciencestech.u-bourgo gne.fr/master/mil-tc5/tmp/PAPERS/cadcam-swiss.pdf.

[47] HOFFMANN C M. Robustness in geometric computations[J]. Journal of Computing and Information Science in Engineering, 2001, 1(2): 143-155.

[48] ROSSIGNAC J R. Through the cracks of the solid modeling milestone[M]//From object modelling to advanced visual communication. Heidelberg: Springer, 1994: 1-75.

[49] HU C Y, PATRIKALAKIS N M, YE X Z. Robust interval solid modelling Part I: representations[J]. Computer-Aided Design, 1996, 28(10): 807-817.

[50] ZOU Q, FENG H Y. Push-pull direct modeling of solid CAD models[J]. Advances in Engineering Software, 2019, 127: 59-69.

[51] SHEN G L, SAKKALIS T, PATRIKALAKIS N. Analysis of boundary representation model rectification[C]//The 6th ACM Symposium on Solid Modeling and Applications. New York: ACM Press, 2001: 149-158.

[52] BERBERICH E, EIGENWILLIG A, HEMMER M, et al. Exacus: efficient and exact algorithms for curves and surfaces[M]//Algorithms - ESA 2005. Berlin: Springer, 2005: 155-166.

[53] KEYSER J, CULVER T, FOSKEY M, et al. ESOLID—a system for exact boundary evaluation[J]. Computer-Aided Design, 2004, 36(2): 175-193.

[54] BENOUAMER M, MICHELUCCI D, PÉROCHE B. Error-free boundary evaluation using lazy rational arithmetic: a detailed implementation[M]. New York: ACM Press, 1993: 115-26.

[55] TRETTNER P, NEHRING-WIRXEL J, KOBBELT L. EMBER: exact mesh booleans via efficient & robust local arrangements[J]. ACM Transactions on Graphics, 2022, 41(4): 39.

[56] WANG C C L, MANOCHA D. Efficient boundary extraction of BSP solids based on clipping operations[J]. IEEE Transactions on Visualization and Computer Graphics, 2013, 19(1): 16-29.

[57] BERNSTEIN G, FUSSELL D. Fast, exact, linear booleans[J]. Computer Graphics Forum, 2009, 28(5): 1269-1278.

[58] JACKSON D J. Boundary representation modelling with local tolerances[C]//The 3rd ACM Symposium on Solid Modeling and Applications. New York: ACM Press, 1995: 247-254.

[59] STROUD I, NAGY H. Solid modeling and CAD systems : how to survive a CAD system[EB/OL]. [2022-06-10]. https://www. researchgate.net/publication/267018694_solid_modelling_and_ CAD_systems_How_to_survive_a_CAD_system.

[60] QI J C, SHAPIRO V. ε-Topological formulation of tolerant solid modeling[J]. Computer-Aided Design, 2006, 38(4): 367-377.

[61] ROSSIGNAC J R. Constraints in constructive solid geometry[C]//1986 Workshop on Interactive 3D graphics. New York: ACM Press, 1987: 93-110.

[62] MUN D, HAN S, KIM J, et al. A set of standard modeling commands for the history-based parametric approach[J]. Computer-Aided Design, 2003, 35(13): 1171-1179.

[63] HOFFMANN C M, JOAN-ARINYO R. On user-defined features[J]. Computer-Aided Design, 1998, 30(5): 321-332.

[64] BETTIG B, SHAH J. Derivation of a standard set of geometric constraints for parametric modeling and data exchange[J]. Computer-Aided Design, 2001, 33(1): 17-33.

[65] BIDARRA R, BRONSVOORT W F. Semantic feature modelling[J]. Computer-Aided Design, 2000, 32(3): 201-225.

[66] LI L, ZHENG Y F, YANG M L, et al. A survey of feature modeling methods: historical evolution and new development[J]. Robotics and Computer-Integrated Manufacturing, 2020, 61: 101851.

[67] HOFFMANN C M. On the semantics of generative geometry representations[C]//1993 Design Technical Conferences. New York: ASME, 2021: 411-419.

[68] MARCHEIX D, PIERRA G. A survey of the persistent Naming problem[C]//The 7th ACM Symposium on Solid Modeling and Applications. New York: ACM Press, 2002: 13-22.

[69] FARJANA S H, HAN S. Mechanisms of persistent identification of topological entities in CAD systems: a review[J]. Alexandria Engineering Journal, 2018, 57(4): 2837-2849.

[70] CAPOYLEAS V, CHEN X P, M HOFFMANN C. Generic Naming in generative, constraint-based design[J]. ComputerAided Design, 1996, 28(1): 17-26.

[71] WANG Y, NNAJI B O. Geometry-based semantic ID for persistent and interoperable reference in feature-based parametric modeling[J]. Computer-Aided Design, 2005, 37(10): 1081-1093.

[72] BABA-ALI M, MARCHEIX D, SKAPIN X. A method to improve matching process by shape characteristics in parametric systems[J]. Computer-Aided Design and Applications, 2009, 6(3): 341-350.

[73] KRIPAC J. A mechanism for persistently Naming topological entities in history-based parametric solid models[J]. Computer-Aided Design, 1997, 29(2): 113-122.

[74] AGBODAN D, MARCHEIX D, PIERRA G, et al. A topological entity matching technique for geometric parametric models[C]//2003 Shape Modeling International. New York: IEEE Press, 2003: 235-244.

[75] WU J J, ZHANG T B, ZHANG X F, et al. A face based mechanism for Naming, recording and retrieving topological entities[J]. Computer-Aided Design, 2001, 33(10): 687-698.

[76] MUN D W, HAN S H. Identification of topological entities and Naming mapping for parametric CAD model exchanges[J]. International Journal of CAD/CAM, 2005, 5(1): 69-81.

[77] CHEON S U, MUN D, HAN S, et al. Name matching method using topology merging and splitting history for exchange of feature-based CAD models[J]. Journal of Mechanical Science and Technology, 2012, 26(10): 3201-3212.

[78] FARJANA S H, HAN S, MUN D. Implementation of persistent identification of topological entities based on macro-parametrics approach[J]. Journal of Computational Design and Engineering, 2016, 3(2): 161-177.

[79] RAGHOTHAMA S, SHAPIRO V. Boundary representation deformation in parametric solid modeling[J]. ACM Transactions on Graphics, 1998, 17(4): 259-286.

[80] RAGHOTHAMA S, SHAPIRO V. Topological framework for part families[J]. Journal of Computing and Information Science in Engineering, 2002, 2(4): 246-255.

[81] RAGHOTHAMA S, SHAPIRO V. Necessary conditions for 1000 综述 2022 年 boundary representation variance[C]//The 13th Annual Symposium on Computational Geometry. New York: ACM Press, 1997: 77-86.

[82] MARTIN K, WANG W P. Geometric modeling and processing 2000. Theory and applications[M]. New York: IEEE Press, 2002: 1-4.

[83] BIDARRA R, NYIRENDA P J, BRONSVOORT W F. A feature-based solution to the persistent Naming problem[J]. Computer-Aided Design and Applications, 2005, 2(1-4): 517-526.

[84] VAN DER MEIDEN H A, BRONSVOORT W F. Tracking topological changes in parametric models[J]. Computer Aided Geometric Design, 2010, 27(3): 281-293.

[85] HOFFMANN C M, KIM K J. Towards valid parametric CAD models[J]. Computer-Aided Design, 2001, 33(1): 81-90.

[86] TANG Z H, ZOU Q, GAO S M. Towards computing complete parameter ranges in parametric modeling[EB/OL]. [2022-05-19]. https://arxiv.org/abs/2206.08698.

[87] HOFFMAN C M, LOMONOSOV A, SITHARAM M. Decomposition plans for geometric constraint problems, part II: new algorithms[J]. Journal of Symbolic Computation, 2001, 31(4): 409-427.

[88] ZOU Q, TANG Z H, FENG H Y, et al. A review on geometric constraint solving[EB/OL]. [2022-04-21]. https://arxiv.org/ abs/2202.13795.

[89] DUFOURD J F, MATHIS P, SCHRECK P. Geometric construction by assembling solved subfigures[J]. Artificial Intelligence, 1998, 99(1): 73-119.

[90] JOAN-ARINYO R, SOTO A. A correct rule-based geometric constraint solver[J]. Computers & Graphics, 1997, 21(5): 599-609.

[91] OWEN J C. Algebraic solution for geometry from dimensional constraints[C]//The 1st ACM Symposium on Solid Modeling Foundations and CAD/CAM Applications. New York: ACM Press, 1991: 397-407.

[92] BOUMA W, FUDOS I, HOFFMANN C, et al. Geometric constraint solver[J]. Computer-Aided Design, 1995, 27(6): 487-501.

[93] FUDOS I, HOFFMANN C M. A graph-constructive approach to solving systems of geometric constraints[J]. ACM Transactions on Graphics, 1997, 16(2): 179-216.

[94] GAO X S, HOFFMANN C M, YANG W Q. Solving spatial basic geometric constraint configurations with locus intersection[C]//The 7th ACM Symposium on Solid Modeling and Applications. New York: ACM Press, 2002: 95-104.

[95] BARDORD L A. A graphical, language-based editor for generic solid models represented by constraints[M]. Ithaca: Cornell University, 1987.

[96] SERRANO D. Constraint management in conceptual design[EB/OL]. [2022-06-29]. https://www.researchgate.net/ publication/243764572_Constraints_in_conceptual_design.

[97] AIT-AOUDIA S, JEGOU R, MICHELUCCI D. Reduction of constraint systems[EB/OL]. [2022-05-17]. https://arxiv.org/ abs/1405.6131.

[98] LATHAM R S, MIDDLEDITCH A E. Connectivity analysis: a tool for processing geometric constraints[J]. Computer-Aided Design, 1996, 28(11): 917-928.

[99] HOFFMANN C M, LOMONOSOV A, SITHARAM M. Finding solvable subsets of constraint graphs[M]//Principles and practice of constraint programming-CP97. Berlin: Springer, 1997: 463-477.

[100] HIDALGO M, JOAN-ARINYO R. H-graphs: a new representation for tree decompositions of graphs[J]. Computer-Aided Design, 2015, 67-68: 38-47.

[101] GAO X S, LIN Q, ZHANG G F. A C-tree decomposition algorithm for 2D and 3D geometric constraint solving[J]. Computer-Aided Design, 2006, 38(1): 1-13.

[102] XIA H J, WANG B X, CHEN L P, et al. 3D geometric constraint solving using the method of kinematic analysis[J]. The International Journal of Advanced Manufacturing Technology, 2008, 35(7): 711-722.

[103] MICHELUCCI D, FOUFOU S. Geometric constraint solving: the witness configuration method[J]. Computer-Aided Design, 2006, 38(4): 284-299.

[104] KUBICKI A, MICHELUCCI D, FOUFOU S. Witness computation for solving geometric constraint systems[C]//2014 Science and Information Conference. New York: IEEE Press, 2014: 759-770.

[105] THIERRY S E B, SCHRECK P, MICHELUCCI D, et al. Extensions of the witness method to characterize under-, overand well-constrained geometric constraint systems[J]. Computer-Aided Design, 2011, 43(10): 1234-1249.

[106] FOUFOU S, MICHELUCCI D. Interrogating witnesses for geometric constraint solving[J]. Information and Computation, 2012, 216: 24-38.

[107] MOINET M, MANDIL G, SERRE P. Defining tools to address over-constrained geometric problems in computer aided design[J]. Computer-Aided Design, 2014, 48: 42-52.

[108] HU H, KLEINER M, PERNOT J P. Over-constraints detection and resolution in geometric equation systems[J]. ComputerAided Design, 2017, 90: 84-94.

[109] ZOU Q, FENG H Y. On limitations of the witness configuration method for geometric constraint solving in CAD modeling[EB/OL]. [2022-05-15]. https://arxiv.org/abs/1904. 00526.

[110] HALLER K, LEE-ST JOHN A, SITHARAM M, et al. Body-and-cad geometric constraint systems[J]. Computational Geometry, 2012, 45(8): 385-405.

[111] HU H, KLEINER M, PERNOT J P, et al. Correction to: geometric over-constraints detection: a survey[J]. Archives of Computational Methods in Engineering, 2021, 28(7): 5037.

[112] JERMANN C, HOSOBE H. A constraint hierarchies approach to geometric constraints on sketches[C]//2008 ACM Symposium on Applied Computing. New York: ACM Press, 2008: 1843-1844.

[113] BORNING A, FREEMAN-BENSON B, WILSON M. Constraint hierarchies[J]. LISP and Symbolic Computation, 1992, 5(3): 223-270.

[114] JOAN-ARINYO R, SOTO-RIERA A, VILA-MARTA S, et al. Transforming an under-constrained geometric constraint problem into a well-constrained one[C]//The 8th ACM Symposium on Solid Modeling and Applications. New York: ACM Press, 2003: 33-44.

[115] HOFFMANN C M, SITHARAM M, YUAN B. Making constraint solvers more usable: overconstraint problem[J]. Computer-Aided Design, 2004, 36(4): 377-399.

[116] ZHANG G F, GAO X S. Well-constrained completion and decomposition for under-constrained geometric constraint problems[J]. International Journal of Computational Geometry & Applications, 2006, 16(5/6): 461-478.

[117] MURUGAPPAN S, SELLAMANI S, RAMANI K. Towards beautification of freehand sketches using suggestions[C]//The 6th Eurographics Symposium on Sketch-Based Interfaces and Modeling. New York: ACM Press, 2009: 69-76.

[118] MILLS B I, LANGBEIN F C, MARSHALL A D, et al. 第 6 期邹强：浅谈实体建模：历史、现状与未来 1001 Estimate of frequencies of geometric regularities for use in reverse engineering of simple mechanical components[EB/OL]. [2022-06-15]. https://www.researchgate.net/publication/20001 8274_Estimate_of_Frequencies_of_Geometric_Regularities_fo r_use_in_Reverse_Engineering_of_Simple_Mechanical_Comp onents?channel=doi&linkld=0912f50b8c3cbzea23000000&sho wFulltes=true.

[119] ZOU H L, LEE Y T. Constraint-based beautification and dimensioning of 3D polyhedral models reconstructed from 2D sketches[J]. Computer-Aided Design, 2007, 39(11): 1025-1036.

[120] LANGBEIN F C, MARSHALL A D, MARTIN R R. Choosing consistent constraints for beautification of reverse engineered geometric models[J]. Computer-Aided Design, 2004, 36(3): 261-278.

[121] ZOU Q, FENG H Y. A decision-support method for information inconsistency resolution in direct modeling of CAD models[J]. Advanced Engineering Informatics, 2020, 44: 101087.

[122] STROUD I, XIROUCHAKIS P C. CAGD—computer-aided gravestone design[J]. Advances in Engineering Software, 2006, 37(5): 277-286.

[123] FAHLBUSCH K-P, ROSER TD. HP PE/SolidDesigner: dynamic modeling for three-dimensional computer-aided design[J]. Hewlett-Packard Journal, 1995, 46: 6-13.

[124] ZOU Q, FENG H Y. A robust direct modeling method for quadric B-rep models based on geometry–topology inconsistency tracking[J]. Engineering With Computers, 2022, 38(4): 3815-3830.

[125] WOO Y, LEE S H. Volumetric modification of solid CAD models independent of design features[J]. Advances in Engineering Software, 2006, 37(12): 826-835.

[126] KIM BC, Mun DW. Stepwise volume decomposition for the modification of B-rep models[J]. The International Journal of Advanced Manufacturing Technology, 2014, 75: 1393-403.

[127] FU J, CHEN X, GAO S M. Automatic synchronization of a feature model with direct editing based on cellular model[J]. Computer-Aided Design and Applications, 2017, 14(5): 680-692.

[128] QIN X L, TANG Z H, GAO S M. Automatic update of feature model after direct modeling operation[J]. Computer-Aided Design and Applications, 2020, 18(1): 170-185.

[129] ZOU Q. Parametric/direct CAD integration[EB/OL]. [2022- 05-17]. https://arxiv.org/abs/2203.02252.

[130] DING J H, ZOU Q, QU S, et al. STL-free design and manufacturing paradigm for high-precision powder bed fusion[J]. CIRP Annals, 2021, 70(1): 167-170.

[131] MASSARWI F, MACHCHHAR J, ANTOLIN P, et al. Hierarchical, random and bifurcation tiling with heterogeneity in micro-structures construction via functional composition[J]. Computer-Aided Design, 2018, 102: 148-159.

[132] GUPTA A, ALLEN G, ROSSIGNAC J. QUADOR: QUADric-of-revolution beams for lattices[J]. Computer-Aided Design, 2018, 102: 160-170.

[133] CHOUGRANI L, PERNOT J P, VÉRON P, et al. Lattice structure lightweight triangulation for additive manufacturing[J]. Computer-Aided Design, 2017, 90: 95-104.

[134] DONG G Y, TANG Y L, ZHAO Y F. A survey of modeling of lattice structures fabricated by additive manufacturing[J]. Journal of Mechanical Design, 2017, 139(10): 100906.

[135] SHAPIRO V, TSUKANOV I, GRISHIN A. Geometric issues in computer aided design/computer aided engineering integration[J]. Journal of Computing and Information Science in Engineering, 2011, 11(2): 1.

[136] WU J, SIGMUND O, GROEN J P. Topology optimization of multi-scale structures: a review[J]. Structural and Multidisciplinary Optimization, 2021, 63(3): 1455-1480.

[137] DING J H, ZOU Q, QU S, et al. STL-free design and manufacturing paradigm for high-precision powder bed fusion[J]. CIRP Annals, 2021, 70(1): 167-170.

[138] LIU S J, LIU T, ZOU Q, et al. Memory-efficient modeling and slicing of large-scale adaptive lattice structures[J]. Journal of Computing and Information Science in Engineering, 2021: 1-16.

[139] GUPTA A, ALLEN G, ROSSIGNAC J. QUADOR: QUADricof-revolution beams for lattices[J]. Computer-Aided Design, 2018, 102: 160-170.

[140] MASSARWI F, MACHCHHAR J, ANTOLIN P, et al. Hierarchical, random and bifurcation tiling with heterogeneity in micro-structures construction via functional composition[J]. Computer-Aided Design, 2018, 102: 148-159.

[141] LIU S J, LIU T, ZOU Q, et al. Memory-efficient modeling and slicing of large-scale adaptive lattice structures[J]. Journal of Computing and Information Science in Engineering, 2021: 1-16.

[142] LI C J, PAN H, BOUSSEAU A, et al. Free2CAD: parsing freehand drawings into CAD commands[J]. ACM Transactions on Graphics, 2022, 41(4): 93.

[143] LI C J, PAN H, BOUSSEAU A, et al. Sketch2CAD: sequential CAD modeling by sketching in context[J]. ACM Transactions on Graphics, 2020, 39(6): 164.

[144] SEFF A, ZHOU W D, RICHARDSON N, et al. Vitruvion: a generative model of parametric CAD sketches[EB/OL]. [2022-05-30]. https://arxiv.org/abs/2109.14124.

[145] GANIN Y, BARTUNOV S, LI Y N, et al. Computer-aided design as language[M]//Advances in neural information processing systems 2021. Cambridge: MIT Press, 2021: 5885-5897.

[146] UY M A, CHANG Y, SUNG M, et al. Point2Cyl: reverse engineering 3D objects from point clouds to extrusion cylinders[C]//2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition. New York: IEEE Press, 2022: 11840-11850.

[147] GUO H X, LIU S L, PAN H, et al. ComplexGen: CAD reconstruction by B-rep chain complex generation[EB/OL]. [2022-05-18]. https://arxiv.org/abs/2205.1457.

[148] WU R D, XIAO C, ZHENG C X. DeepCAD: a deep generative network for computer-aided design models[C]//2021 IEEE/CVF International Conference on Computer Vision. New York: IEEE Press, 2022: 6752-6762.

[149] XU X H, PENG W Z, CHENG C Y, et al. Inferring CAD modeling sequences using zone graphs[C]//2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition. New York: IEEE Press, 2021: 6058-6066.

[150] LAMBOURNE J G, WILLIS K D D, JAYARAMAN P K, et al. BRepNet: a topological message passing system for solid models[C]//2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition. New York: IEEE Press, 2021: 12768-12777.

[151] LI M, GAO S M, WANG C C L. Real-time collaborative design with heterogeneous CAD systems based on neutral modeling commands[J]. Journal of Computing and Information Science in Engineering, 2007, 7(2): 113-125.

[152] EASTMAN C M, WEILER K J. Geometric modeling using the Euler operators[R]. Pittsburgh: Carnegie Mellon University; 1979