Solving geometric constraint systems. I. A global propagation approach

CAD Computer Aided Design

Volumn 30, Issue 1, 1998, Pages 47-54

  Gao, Xiao Shan ^a   Chou, Shang Ching ^b  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

^b Wichita State University   (United States)

Author keywords

Geometric constraint system solving; Global propagation; Intelligent CAD

Indexed keywords

ALGORITHMS; COMPUTER SOFTWARE; CONSTRAINT THEORY; DRAWING (GRAPHICS); GEOMETRY; INTELLIGENT BUILDINGS;

INTELLIGENT CAD;

COMPUTER AIDED DESIGN;

EID: 0031703314     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4485(97)00052-3     Document Type: Article

References (25)

1. F. Arbab & B. Wang, Reasoning About Geometric Constraints, Intelligent CAD II, H. Yoshikawa and T. Holden (eds), North-Holland, 93-107, 1990.
2. B. Brudelin, Constructing Three-Dimensional Geometric Objects Defined by Constraints, in Workshop on Interactive 3D Graphics. p. 111-129, ACM, 1986.
3. 3, in Computing in Euclidean Geometry, eds D.Z. Du and F. Huang, p. 266-298. World Scientific, 1995.
4. G. Kramer, Solving Geometric Constraint Systems, MIT Press. 1992.
5. J. Owen, Algebraic Solution for Geometry from Dimensional Constraints, in ACM symp. Found of Solid Modeling, ACM press. p. 397-407, Austin TX, 1991.
6. G. Sunde, Specification of Shape by Dimensions and Other Geometric Constraints, in Geometric Modeling for CAD Applications. M.J. Wozny, et al., eds, 199-213, North Holland, 1988.
7. R.C. Veltkamp, Geometric Constraint Management with Quanta, Intelligent Computer Aided Design, D.C. Brown et al., eds. 409-426, North-Holland, 1992.
8. A. Borning, The Programming Language Aspect of ThingLab, ACN Tras. on Programming Language and Systems, Vol. 3, No. 4, 353-387. 1981.
9. A. Heydon & G. Nelson, The Juno-2 Constraint-Based Drawing Editor, SRC Research Report 13Ia, 1994.
10. I. Sutherland, Sketchpad, A Man-Machine Graphical Communication System, in Proc. of the Spring Joint Comp. Conference. North-Holland, 329-345, 1963.
11. G.L. Steele & G.L. Sussman. CONSTRAINTS - A Language for Expressing Almost-Hierarchical Descriptions. Artificial Intelligence. p. 1-39, Vol. 14, 1980.
12. W. Leler, Constraint Programming Languages, Addison Wesley, 1988.
13. S.C. Chou, X.S. Gao, & S.Z. Zhang, A Fixpoint Approach To Automated Geometry Theorem Proving, WSUCS-95-2, CS Dept, Wichita State University, 1995.
14. S.C. Chou, Mechanical Geometry Theorem Proving, D. Reidel Publishing Company, Dordrecht, Netherlands, 1988.
15. S.C. Chou, X.S. Gao, & J.Z. Zhang, Machine Proofs in Geometry, World Scientific, 1994.
16. Todd, P., A k-tree Generalization that Characterizes Consistency of Dimensioned Engineering Drawings. SIAM J. of Disc. Math., 1989, 2, 255-261.
17. A. Verroust, F. Schonek, and D. Roller, Rule-oriented method for parameterized computer-aided design. Geometric Aided Design, 24(3), p. 531-540, October, 1992.
18. Lin, V.C., Gossard, D.C. and Light, R.A., Variational Geometry In Computer-Aided Design. Computer Graphics, 1981, 15(3), 171-177.
19. Kondo, K., Algebraic method for manipulation of dimensional relationships in geometric models. Geometric Aided Design, 1992, 24(3), 141-147.
20. Wu Wen-tsun, Basic Principles of Mechanical Theorem Proving in Geometries, Springer-Verlag, 1993.
21. S.C. Chou & X.S. Gao, Mechanical Formula Derivation in Elementary Geometries, Proc. ISSAC-90, ACM, New York. 1990, p. 265-270.
22. Zhang, J.Z., Yang, L. and Yang, X.C., The realization of Elementary Configurations in Euclidean Space. Science in China (series A), 1994, 37(1), 15-26.
23. S.C. Chou, X.S. Gao, & J.Z. Zhang, A Collection of 130 Geometric Constraint Problems and Their Solutions, WSUCS-96-2, CS Dept, Wichita State University, 1996.
24. I. Fudos and C. Hoffmann, Correctness Proof of a Geometric Constraint Solver, Int. J of Comp Geometry and Applic, vol. 6, Dec. 1996, p. 405-420.
25. X.S. Gao & S.C. Chou, Solving Geometric Constraint Problems, II. A Symbolic Approach and Decision of Rc-constructibility. WSUCS-96-3, CS Dept, Wichita State University, 1996.