Abstract
The geometric constructions problem is often studied from a combinatorial point of view: a pair data structure + algorithm is proposed, and then one tries to determine the variety of geometric problems which can be solved. Conversely, we present here a different approach starting with the definition of a simple class of geometric construction problems and resulting in an algorithm and data structures. We show that our algorithm is correct, complete with respect to the class of simply constrained polygons, and has a linear complexity. The presented framework is very simple, but in spite of its simplicity, this algorithm can solve non-trivial problems.
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S. Ait-Aoudia, R. Jegou and D. Michelucci: Reduction of constraint systems. In: Proceedings of the Compugraphics Conference. Compugraphics Alvor, Portugal (1993) 83–92.
B. Aldefeld, H. Malberg, H. Richter and K. Voss: Rule-based variational geometry in computer-Aided Design. In: D.T. Pham (ed):Artificial Intelligence in Design. Springer-Verlag (1992) 27–46.
B. Brüderlin: Automatizing geometric proofs and constructions. In: Proceeding s of Computational Geometry’ 88. Lecture Notes in Computer Science, Vol. 333. Springer-Verlag (1988) 232–252.
J.-F. Dufourd, P. Mathis, and P. Schreck: Formal resolution of geometric constraint systems by assembling. In:Proceedings of the ACM-Siggraph Solid Modelling Conference, Atlanta. ACM Press (1997) 271–284.
C. Essert-Villard, P. Schreck, and J.-F. Dufourd: Sketch-based pruning of a solution space within a formal geometric constraint solver. In: Journal of Artificial Intelligence, Num. 124. Elsevier (2000) 139–159.
I. Fudos and C. M. Hoffmann: Correctness proof of a geometric constraint solver. In: International Journal of Computational Geometry and Applications Num. 6. World Scientific Publishing Company(1996) 405–420.
C. M. Hoffmann, A. Lomonosov, M. Sitharam: Decomposition Plans for Geometric Constraint Systems, Part I: Performance Measures for CAD. In: Journal of Symbolic Computation Num. 31. Academic Press(2001) 367–408.
G.A. Kramer: A geometric constraint engine. In: Artificial Intelligence Num. 58. Elsevier(1992) 327–360.
H. Lamure and D. Michelucci: Solving constraints by homotopy. In: Proceedings of the ACM-Siggraph Solid Modelling Conference. ACM Press(1995) 134–145.
J. Owen: Algebraic solution for geometry from dimensional constraints. In: Proceedings of the 1st ACM Symposium of Solid Modelling and CAD/CAM Applications. ACM Press(1991) 134–145.
G. Sunde: Specification of shape by dimensions and other geometric constraints. In: Proceedings of the Eurographics Workshop on Intelligent CAD systems. Noordwisjkerout (1987).
I.E. Sutherland. Sketchpad: A man-machine graphical communication system. In: Proceedings of the IFIP Spring Joint Computer Conference.Detroit, Michigan (1963) 329–36.
A. Verroust, F. Schoneck and D. Roller: Rule-oriented method for parameterized computer-aided design. In: Computer-Aided Design Vol. 10 Num. 24. Elsevier (1992) 329–36.
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© 2002 Springer-Verlag Berlin Heidelberg
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Schramm, É., Schreck, P. (2002). A Case Study in Geometric Constructions. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46080-2_21
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DOI: https://doi.org/10.1007/3-540-46080-2_21
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