Notes on A Road Map To Solid Modeling

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本文回顾了1996年发表的固态建模领域文献，总结了该领域的研究方向和技术进展。涉及的主要主题包括代数半空间、扫掠体积、计算机辅助几何设计、表面交集等，并介绍了多位学者的相关工作。

Notes on A Road Map To Solid Modeling

用了很长时间读 A Road Map To Solid Modeling，概述了solid modeling的方向。此文发表于1996年---12年前。

Monographs and major surveys of solid modeling include

H. Chiyokura, Solid Modeling with Designable.Addison-Wesley, 1988
C. Hoffmann, Geometric and Solid Modeling.Morgan Kaufmann, 1989
C. Hoffmann and G. VanPZek, "Fundamental Techniques for Geometric and Solid Modehg," C.T. Leondes, ed.,Advances in Control and Dynamics, vol. 48, pp. 101-165. Academic Press, 1991.
M. Mantyla, An Introduction to Solid Modeling.Computer sdence Press, 1988
Requicha, "Representations For Rigid Solids: Theory, Methods, and Systems," ACM Computing Sumeys, vol. 12, pp.437-464, 1980
Recluicha, "Solid Modeling-a 1988 Update," B. Ravani, ed., CAD Based hogrammingjbr Senso6 Robots, pp: 3-22, New York: SpringerVerlarr. 1988
Revquicha and J. Rossignac, "Solid Modeling and Beyond," Tech. Report RC 17676, IBM, Yorktown Heights, 1992

Algebraic halfspace is defined as the point set H = ((x, y, z) I p(x, y, z) I 0 ), where p(x, y, z) is a polynomial in x, y, and z with real coefficients.

A semialgebraic set is any point set obtained as the result of a finite number of set operations (union, intersection, difference) applied to algebraic half spaces.

R-sets Bounded, homogeneously three-dimensional, semialgebraic sets were proposed in the 1970s as mathematical models for solids by Requicha (Mathematical Models of Rigid Solids), who called such sets r-sets.

Sweep

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.
C. Hoffmann and G. VanPZek, "Fundamental Techniques for Geometric and Solid Modeling," C.T. Leondes, ed., Advances in Control and Dynamics, vol. 48, pp. 101-165. Academic Press, 1991.
Pasko and V. Savchenko, "Function Representation for Sweeping By a Moving Solid," IEEE Tram. Visualization and Computer Graphics, 1996.

CAGD

M. Daehlen, T. Lyche, and L. Schumaker, Math. Methods for Curves and Surfaces. Vanderbilt University Press, 1995.
G. Farin, Curves and Surfaces for Computer-Aided Geometric Design. Academic Press, 1988
M. Hosaka, Modeling of Curves and Surfaces in CAD/CAM, New York, Springer Verlag, 1992
J. Hoschek and D. Lasser, Computer Aided Geometric Design, A.K. Peters, 1993.

Surface Intersection

M. Hohmeyer, "Surface Intersection," PhD thesis, Univ. of California, Berkeley, 1992.

Offsetting

M. Forsyth, "Shelling and Offsetting Bodies," Proc. Third Symp. On Solid Modeling. ACM Press, 1995.

Blending

M. Bloor and M. Wilson, "Generating Blending Surfaces with Partial Differential Equations," Computer Aided Design, vol. 21, pp. 165-171, 1989.
C. Hoffmann, "Algebraic and Numerical Techniques for Offsets and Blends," S.M.M. Gasca, and W. Dahmen, eds., Computations of Curves and Surfaces, p. 499-528. Kluwer Academic, 1990.
C. Hoffmann and J. Hopcroft, "The Potential Method for Blending Surfaces and Corners, “G. Farin, ed., Geometric Modeling, pp. 347-365. SIAM, 1987.
J. Peters, "Joining Smooth Patches Around a Vertex to Form a c^k Surface," Computer Aided Geometric Design, vol. 9, pp. 387411,1992
Braid, "Non local Blending of Boundary Models," Computer-Aided Design, 1996, to appear.

Deformations

Rappoport, A. Sheffer, and M. Bercovier, "Volume preserving Free form Solids," IEEE Trans. Visualization and Computer Graphics, 1996.
M. Bloor and M. Wilson, "Generating Blending Surfaces with Partial Differential Equations," Computer Aided Design, vol. 21, pp. 165-171, 1989.

Feature-Based Design

J. Shah, D. Hsiao, and J. Leonard, "A Systematic Approach for Design manufacturing Feature Mapping," P. Wilson, M. Wozny, and M. Pratt, eds., Geometric Modeling for Product Realization, pp. 205-222, North Holland, 1992.
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. North Holland, 1988
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. North Holland, 1992
X. Chen and C. Hoffmann, "Editing Feature Based Design," to appear in Computer Aided Design
X. Chen and C. Hoffmann, "Towards Feature Attachment," Computer Aided Design, 1995
J. Rossignac, "Issues in Feature based Editing and Interrogation of Solid Models," Computers and Graphics, vol. 14, pp. 149-172,1990

Constraint Solving

C.-S. Chou, Mechanical Theorem Proving. D. Reidel Publishing, 1987
S. Fortune, "Polyhedral Modeling with Multiprecision Integer Arithmetic," Proc. Third Symp. on Solid Modeling. ACM Press, 1995.
G. Gamer, Solving Geometric Constraint Systems, MIT Press, 1992.
W. Leler, Constraint Programming Languages. Addison-Wesley, 1988
B. Buchberger, G. Collins, and B. Kutzler, "Algebraic Methods for Geometric Reasoning," Ann. Reviews in Computer Science, vol. 3, no. 85, p. 120,1988.
W. Bouma, I. Fudos, C. Hoffmann, J. Cai, and R. Paige, "A Geometric Constraint Solver," Computer Aided Design, 1995, to appear

Persistent naming problem

C. Hoffmann, "On the Semantics of Generative Geometry Representations," Proc. 19th ASME Design Automation Conf, vol. 2, up. 411-420, 1993
V. Shapiro and D. Vossler, "What Is a Parametric Family of Solids?" Proc. Third ACM Symp. on Solid Modeling, 1995.
V. Capoyleas, X.Chen, and C.M. Hoffmann, "Generic Naming in Generative, Constraint-based Design," to appear in Computer Aided Design.
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.
J. Kripac, "A Mechanism for Persistently Naming Topological Entities in History-based Parametric Solid Models," Proc. nird Synp. on Solid Modeling. ACM Press, 1995.

Christoph M. Hoffmann，这位先生是大牛，仿佛他研究的东西我都很有兴趣，所以几乎弄到了他的所有论文。其实很早就注意到他了，源自一本书(有电子版)Geometric and Solid Modeling: An Introduction，成书于1989年---19年前？谁说计算机技术日新月异，我可一点都没感觉到:)