Publication 1996 Issue No. 1 - March Abstract - A Road Map To Solid Modeling
 This Article Share Bibliographic References Add to: Digg Furl Spurl Blink Simpy Google Del.icio.us Y!MyWeb Search Similar Articles Articles by Christoph M. Hoffmann Articles by Jaroslaw R. Rossignac
A Road Map To Solid Modeling
March 1996 (vol. 2 no. 1)
pp. 3-10
 ASCII Text x Christoph M. Hoffmann, Jaroslaw R. Rossignac, "A Road Map To Solid Modeling," IEEE Transactions on Visualization and Computer Graphics, vol. 2, no. 1, pp. 3-10, March, 1996.
 BibTex x @article{ 10.1109/2945.489381,author = {Christoph M. Hoffmann and Jaroslaw R. Rossignac},title = {A Road Map To Solid Modeling},journal ={IEEE Transactions on Visualization and Computer Graphics},volume = {2},number = {1},issn = {1077-2626},year = {1996},pages = {3-10},doi = {http://doi.ieeecomputersociety.org/10.1109/2945.489381},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Visualization and Computer GraphicsTI - A Road Map To Solid ModelingIS - 1SN - 1077-2626SP3EP10EPD - 3-10A1 - Christoph M. Hoffmann, A1 - Jaroslaw R. Rossignac, PY - 1996KW - Solid modelingKW - solid representationsKW - conversion between solid representationsKW - feature-based designKW - constraint-based design.VL - 2JA - IEEE Transactions on Visualization and Computer GraphicsER -

Abstract—The objective of solid modeling is to represent, manipulate, and reason about, the three-dimensional shape of solid physical objects, by computer. Such representations should be unambiguous.

Solid modeling is an application-oriented field that began in earnest in the early 1970s. [46]. Major application areas include design, manufacturing, computer vision, graphics, and virtual reality. Technically, the field draws on diverse sources including numerical analysis, symbolic algebraic computation, approximation theory, applied mathematics, point set topology, algebraic geometry, computational geometry, and data bases. Monographs and major surveys of solid modeling include [13], [19], [27], [37], [44], [45], [46].

In this road map article, we begin with some mathematical foundations of the field. We review next the major representation schemata of solids. Then, major layers of abstraction in a typical solid modeling system are characterized: The lowest level of abstraction comprises a substratum of basic service algorithms. At an intermediate level of abstraction there are algorithms for larger, more conceptual operations. Finally, a yet higher level of abstraction presents to the user a functional view that is typically targeted towards solid design. Here, we will look at some applications and at user interaction concepts.

The classical design paradigms of Solid Modeling concentrated on obtaining one specific final shape. Those paradigms are becoming supplanted by feature-based, constraint-based design paradigms that are oriented more toward the design process and define classes of shape instances. These new paradigms venture into territory that has yet to be explored systematically. Concurrent with this paradigm shift, there is also a shift in the system architecture towards modularized confederations of plug-compatible functional components. We explore these trends lightly in the last section.

[1] D. Blackmore and M. Leu,"A Differential Equations Approach to Swept Volume," Proc. Rensselaer Second Int'l Conf. on Computer-Integrated Manufacturing, pp. 143-149,Troy, N.Y., 1990.
[2] M. Bloor and M. Wilson,"Generating Blending Surfaces with Partial Differential Equations," Computer Aided Design, vol. 21, pp. 165-171, 1989.
[3] W. Bouma,I. Fudos,C. Hoffmann,J. Cai, and R. Paige,"A Geometric Constraint Solver," Computer Aided Design, 1995, to appear.
[4] A. Bowyer,J.H. Davenport,D.A. Lavender,P.S. Milne, and A.F. Wallis,"A Geometric Algebra System," D. Kapur, ed., Integration of Symbolic and Numeric Methods. MIT Press, 1991.
[5] I. Braid,"Nonlocal Blending of Boundary Models," Computer-Aided Design, 1996, to appear.
[6] P. Brunet and I. Navazo,"Solid Representation and Operation Using Extended Octrees," ACM Trans. Graphics, vol. 9, pp. 170-197, 1990.
[7] B. Buchberger,"Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory," N.K. Bose, ed., Multidimensional Systems Theory, pp. 184-232. D. Reidel Publishing Co., 1985.
[8] B. Buchberger,G. Collins, and B. Kutzler,"Algebraic Methods for Geometric Reasoning," Ann. Reviews in Computer Science, vol. 3, no. 85, p. 120, 1988.
[9] V. Capoyleas,X. Chen, and C.M. Hoffmann,"Generic Naming in Generative, Constraint-based Design," to appear in Computer Aided Design.
[10] X. Chen and C. Hoffmann,"Editing Feature Based Design," to appear in Computer Aided Design.
[11] X. Chen and C. Hoffmann,"Towards Feature Attachment," Computer Aided Design, 1995.
[12] C. Chiang,C. Hoffmann, and R. Lynch,"How to compute offsets without self-intersection," Proc SPIE Conf. Curves and Surfaces in Computer Vision and Graphics, vol. 1610, pp. 76-87. Int'l Society for Optical Engineering, 1991.
[13] H. Chiyokura,Solid Modeling with Designbase. Addison-Wesley, 1988.
[14] C.-S. Chou,Mechanical Theorem Proving. D. Reidel Publishing, 1987.
[15] M. Daehlen,T. Lyche, and L. Schumaker,Math. Methods for Curves and Surfaces. Vanderbilt University Press, 1995.
[16] G.E. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide.New York: Academic Press, 1988.
[17] M. Forsyth,"Shelling and Offsetting Bodies," Proc. Third Symp. on Solid Modeling. ACM Press, 1995.
[18] S. Fortune,"Polyhedral Modeling with Multiprecision Integer Arithmetic," Proc. Third Symp. on Solid Modeling. ACM Press, 1995.
[19] C.M. Hoffmann, Geometric and Solid Modeling, Morgan Kaufmann, San Mateo, Calif., 1989.
[20] C. Hoffmann,"Algebraic and Numerical Techniques for Offsets and Blends," S.M.M. Gasca, and W. Dahmen, eds., Computations of Curves and Surfaces, pp. 499-528. Kluwer Academic, 1990.
[21] C. Hoffmann,"Computer Vision, Descriptive Geometry, and Classical Mechanics, B. Falcidieno, and I. Herman, eds., Computer Graphics and Math., Eurographics Series, pp. 229-244, Springer Verlag, 1992.
[22] C. Hoffmann,"On the Semantics of Generative Geometry Representations," Proc. 19th ASME Design Automation Conf., vol. 2, pp. 411-420, 1993.
[23] C. Hoffmann,"On the Separability Problem of Real Functions and its Significance in Solid Modeling," Computational Algebra, pp. 191-204, Marcel Dekker, 1993. Lecture Notes in Pure and Applied Math., pp. 151.
[24] C. Hoffmann,"Geometric Approaches to Mesh Generation," I. Babuska, J. Flaherty, W. Henshaw, J. Hopcroft, J. Oliger, and T. Tezduyar, eds., Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations. Springer Verlag, 1995.
[25] C. Hoffmann and J. Hopcroft,"The Potential Method for Blending Surfaces and Corners, G. Farin, ed., Geometric Modeling, pp. 347-365. SIAM, 1987.
[26] C. Hoffmann and R. Juan,"Erep, An Editable, High-level Representation for Geometric Design and Analysis," P. Wilson, M. Wozny, and M. Pratt, eds., Geometric Modeling for Product Realization, pp. 129-164. NorthHolland, 1992.
[27] C. Hoffmann and G. $Van\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over e} \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over c} ek$,"Fundamental Techniques for Geometric and Solid Modeling," C.T. Leondes, ed., Advances in Control and Dynamics, vol. 48, pp. 101-165. Academic Press, 1991.
[28] C. Hoffmann and P. Vermeer,"Geometric Constraint Solving in R2and R3," D.Z. Du and F. Hwang, eds., Computing in Euclidean Geometry. World Scientific Publishing, second edition, 1994.
[29] M. Hohmeyer,"Surface Intersection," PhD thesis, Univ. of California, Berkeley, 1992.
[30] M. Hosaka,Modeling of Curves and Surfaces in CAD/CAM,New York, Springer Verlag, 1992.
[31] J. Hoschek and D. Lasser,Computer Aided Geometric Design, A.K. Peters, 1993.
[32] G. Kramer,Solving Geometric Constraint Systems, MIT Press, 1992.
[33] J. Kripac,"Topological ID System-A Mechanism for Persistently Naming Topological Entities in History-based Parametric Solid Models," PhD thesis, Czech Technical Univ., Prague, 1993.
[34] J. Kripac,"A Mechanism for Persistently Naming Topological Entities in History-based Parametric Solid Models," Proc. Third Symp. on Solid Modeling. ACM Press, 1995.
[35] J.-C. Latombe and R. Wilson,"Assembly Sequencing with Toleranced Parts," Proc. Third Symp. on Solid Modeling. ACM Press, 1995.
[37] M. Mantyla, An Introduction to Solid Modeling.Rockville, Md., Computer Science Press, 1988.
[38] B. Naylor,"Binary Space Partitioning Trees As an Alternative Representation of Polytopes," Computer Aided Design, vol. 22, 1990.
[39] B. Naylor and L. Rogers,"Constructing Binary Space Partitioning Trees From Piecewise Bézier curves," Graphics Interface '95, 1995.
[40] A. Pasko and V. Savchenko,"Function Representation for Sweeping By a Moving Solid," IEEE Trans. Visualization and Computer Graphics, 1996.
[41] J. Peters,"Joining Smooth Patches Around a Vertex to Form a ckSurface," Computer Aided Geometric Design, vol. 9, pp. 387-411, 1992.
[42] A. Rappoport,A. Sheffer, and M. Bercovier,"Volume-preserving Free-form Solids," IEEE Trans. Visualization and Computer Graphics, 1996.
[43] A. Requicha,"Mathematical Models of Rigid Solids," Tech. Report PAP Tech. Memo 28, Univ. of Rochester, 1977.
[44] A.A.G. Requicha,“Representations for rigid solids: Theory, methods, and systems,” ACM Computing Surveys, vol. 12, no. 4, pp. 437-464, 1980.
[45] A. Requicha,"Solid Modeling-a 1988 Update," B. Ravani, ed., CAD Based Programming for Sensory Robots, pp. 3-22,New York: Springer Verlag, 1988.
[46] A. Requicha and J. Rossignac,"Solid Modeling and Beyond," Tech. Report RC 17676, IBM, Yorktown Heights, 1992.
[47] J. Rossignac,"Issues in Feature-based Editing and Interrogation of Solid Models," Computers and Graphics, vol. 14, pp. 149-172, 1990.
[48] J. Rossignac and M. O'Conner,"SGC: a Dimension-independent Model for Pointsets with Internal Structure," M. Wozny, J. Turner, and K. Preiss, eds., Geometric Modeling for Product Engineering, pp. 145-180. NorthHolland, 1989.
[49] J. Rossignac and A. Requicha,"Constructive Nonregularized Geometry," Computer-Aided Design, vol. 23, pp. 21-32, 1991.
[50] H. Samet, Applications of Spatial Data Structures. Addison-Wesley, 1990.
[51] H. Samet, The Design and Analysis of Spatial Data Structures. Addison-Wesley, 1990.
[52] E. Sprangle and Y. Patt, Facilitating Superscalar Processing via a Combined Static/Dynamic Register Renaming Scheme,'' Proc. 27th Ann. ACM/IEEE Int'l Symp. Microarchitecture, pp. 143-147, 1994.
[53] V. Shapiro,"Representations of Semialgebraic Sets in Finite Algebras Generated by Space Decompositions," PhD thesis, Cornell University, Sibley School of Mechanical Engineering, 1991.
[54] V. Shapiro and D. Vossler,"Separation for Boundary to CSG Conversion, ACM Trans. Graphics, vol. 12, pp. 35-55, 1993.
[55] V. Shapiro and D. Vossler,"What Is a Parametric Family of Solids?," Proc. Third ACM Symp. on Solid Modeling, 1995.
[56] D. Sheehy,C. Armstrong, and D. Robinson,"Computing the Medial Surface of a Solid From a Domain Delaunay Triangulation," IEEE Trans. Visualization and Computer Graphics, 1996.
[57] E.C. Sherbrooke, N.M. Patrikalakis, and E. Brisson, “An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids,” IEEE Trans. Visualization and Computer Graphics, vol. 2, no. 1, pp. 44-61, Mar. 1996.
[58] V. Srinivasan and L. Nackman,"Voronoi Diagram of Multiply Connected Polygonal Domains," IBM J. Research and Development, vol. 31, pp. 373-381, 1987.
[59] K. Sugihara and M. Iri,"A Solid Modeling System Free From Topological Inconsistency," J. Information Processing, vol. 12, pp. 380-393, 1989.
[60] J. Thompson,Z. Warsi, and W. Mastin,Numerical Grid Generation. NorthHolland, 1985.
[61] P.J. Vermeer, “Medial Axis Transform to Boundary Representation Conversion,” PhD Thesis, Purdue Univ., 1994.
[62] K. Weiler,"Topological Structures for Geometric Modeling," PhD thesis, Rensselaer Polytechnic Inst., 1986.
[63] P. Wilson and M. Pratt,"A Taxonomy of Features for Solid Modeling," J.E.J. Wozny, and H.W. McLaughlin, eds., Geometric Modeling for CAD Applications, pp. 125-136. NorthHolland, 1988.

Index Terms:
Solid modeling, solid representations, conversion between solid representations, feature-based design, constraint-based design.
Citation:
Christoph M. Hoffmann, Jaroslaw R. Rossignac, "A Road Map To Solid Modeling," IEEE Transactions on Visualization and Computer Graphics, vol. 2, no. 1, pp. 3-10, March 1996, doi:10.1109/2945.489381