Abstract
A new generation of CAD systems has become available in which geometric constraints can be defined to determine properties of mechanical parts. The new design concept, often called constraint-based design or design by features [9, 17], offers users the capability of easily defining and modifying a design, but introduces the problem of solving complicated, not always well defined, constraint problems [3].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
B. Aldefeld. Variation of geometries based on a geometric-reasoning method. Computer Aided Design, 20(3):117–126, April 1988.
E. L. Allgower and K. Georg. Continuation and path following. Acta Numerica, pages 1–64, 1993.
B. Bruderlin and D. Roller (eds). Geometric Constraint Solving and Applications. Springer Verlag, 1998.
Paula L. Beaty, Patrick A. Fitzhorn, and Gary J. Herron. Extensions in variational geometry that generate and modify object edges composed of rational Bézier curves. Computer Aided Design, 26(2):98–107, 1994.
W. Bouma, I. Fudos, C. M. Hoffmann, J. Cai, and R. Paige. A Geometric Constraint Solver. Computer Aided Design, 27(6):487–501, June 1995. Also available through http://www.cs.purdue.edu/people/fudos/people/fudos.
B. Bruderlin. Using geometric rewrite rules for solving geometric problems symbolically. Theoretical Computer Science, 116:291–303, 1993.
Beat Bruderlin. Constructing Three-Dimensional Geometric Objects Defined by Constraints. In Workshop on Interactive 3D Graphics, pages 111–129. ACM, October 23–24 1986.
B. Buchberger. Grobner Bases: An Algorithmic Method in Polynomial Ideal Theory. In N. K. Bose, editor, Multidimensional Systems Theory, pages 184–232. D. Reidel Publishing Company, 1985.
X. Chen and C. M. Hoffmann. On Editability of Feature Based Design. Computer Aided Design, 27:905–914, 1995.
W. Chyz. Constraint management for csg. Masters’ thesis, MIT, June 1985.
D-Cubed Ltd, 68 Castle Street, Cambridge, CB3 OAJ, England. The Dimensional Constraint Manager, June 1994. Version 2.7.
W. Fitzerland. Using Axial Dimensions to Determine the Proportions of Line Drawings in Computer Graphics. Computer Aided Design, 13(6), November 1981.
I. Fudos and C. M. Hoffmann. Correctness Proof of a Geometric Constraint solver. International Journal of Computational Geometry & Applications, 1995. Also available through http://www.cs.purdue.edu/people/fudos/people/fudos.
I. Fudos and C. M. Hoffmann. A Graph-constructive Method to Solving systems of Geometric Constraints. ACM Transactions on Graphics, 16(2):179–216, 1997.
Ioannis Fudos. Editable Representations for 2D Geometric Design. Masters’ thesis, Dept of Computer Sciences, Purdue University, December 1993. Available through http://www.cs.purduc.edu/people/fudos/people/fudos.
Ioannis Fudos. Constraint Solving for Computer Aided Design. PhD thesis, Department of Computer Sciences, Purdue University, August 1995.
C. M. Hoffmann and R. Joan. On User-Defined Features. Computer Aided Design, 30:321–332, 1998.
C. M. Hoffmann, A. Lomonosov, and M. Sitharam. Finding Solvable Subsets of Constraint Graphs. In G. Smolka, editor, LNCS 1330, pages 463–477. Springer Verlag, 1997.
H. Imai. On combinatorial structures of line drawings of polyhedra. Discrete and applied Mathematics, 10:79, 1985.
R. Juan-Arinyo and Antoni Soto. A rule-constructive geometric constraint solver. Technical Report LSI-95-25-R, Universitat Politecnica de Catalunya, 1995.
H. Lamure and D. Michelucci. Solving geometric constraints by homotopy. In Proc. Third Symposium on solid Modeling and Applications, pages 263–269, Salt Lake City, 1995. ACM.
Robert Light and David Gossard. Modification of geometric models through variational geometry. Computer Aided Design, 14(4):209–214, July 1982.
A. Morgan. Solving polynomial systems using continuation for engineering and scientific problems. Prentice-Hall, Inc., 1987.
G. Nelson. Juno, a costraint-based graphics system. In SIGGRAPH, pages 235–243, San Francisco, July 22-26 1985. ACM.
J. C. Owen. Algebraic Solution for Geometry from Dimensional Constraints. In ACM Symp. Found. of Solid Modeling, Austin, TX, pages 397–407. ACM, 1991.
A. Requicha. Dimensionining and tolerancing. Technical report, Production Automation Project, University of Rochester, May 1977. PADL TM-19.
D. Serrano and D. Gossard. Combining mathematical models and geometric models in CAE systems. In Proc. ASME Computers in Eng. Conf., pages 277–284, Chicago, July 1986. ASME.
Wolfang Sohrt. Interaction with Constraints in three-dimensional Modeling. Masters’ thesis, Dept of Computer Science, The University of Utah, March 1991.
K. Sugihara. Detection of Structural Inconsistencies in Systems of Equations with Degrees of Freedom and its Applications. Discrete Applied Mathematics, 10:297–312, 1985.
Geir Sunde. Specification of shape by dimensions and other geometric constraints. In M. J. Wozny, H. W. McLaughlin, and J. L. Encarnacao, editors, Geometric modeling for CAD applications, pages 199–213. North Holland, IFIP, 1988.
I. Sutherland. Sketchpad, a man-machine graphical communication system. In Proc. of the spring Joint Comp. Conference, pages 329–345. IFIPS, 1963.
Hirimasa Suzuki, Hidetoshi Ando, and Fumihiko Kimura. Variation of geometries based on a geometric-reasoning method. Comput. & Graphics, 14(2):211–224, 1990.
Philip Todd. A k-tree generalization that characterizes consistency of dimensioned engineering drawings. SIAM J. DISC. MATH., 2(2):255–261, 1989.
A. Verroust, F. Schonek, and D. Roller. Rule-oriented method for parameterized computer-aided design. Computer Aided Design, 24(3):531–540, October 1992.
Wu Wen-Tsun. Basic Principles of Mechanical Theorem Proving in Elementary Geometries. Journal of Automated Reasoning, 2:221–252, 1986.
Yasushi Yamaguchi and Fumihiko Kimura. A constraint modeling system for variational geometry. In M. J. Wozny, J. U. Turner, and K. Preiss, editors, Geometric Modeling for Product Engineering, pages 221–233. Elsevier Science Publishers B.V. (North Holland), 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Fudos, I. (1999). An Interactive Geometric Constraint Solver. In: Tzafestas, S.G. (eds) Advances in Intelligent Systems. International Series on Microprocessor-Based and Intelligent Systems Engineering, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4840-5_2
Download citation
DOI: https://doi.org/10.1007/978-94-011-4840-5_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0393-6
Online ISBN: 978-94-011-4840-5
eBook Packages: Springer Book Archive