Solving Dynamic Geometric Constraints Involving Inequalities
This paper presents a specialized method for solving dynamic geometric constraints involving equalities and inequalities. The method works by decomposing the system of constraints into finitely many explicit solution representations in terms of parameters with radicals using triangular decomposition and real quantifier elimination. For any given values of the parameters, if they verify some set of computed relations, the values of the dependent variables may be easily computed by direct evaluation of the corresponding explicit expressions. The effectiveness of our method and its experimental implementation is illustrated by some examples of diagram generation.
KeywordsInequality Constraint Real Solution Geometric Constraint Geometric Object Radical Expression
Unable to display preview. Download preview PDF.
- 1.Brown, C.W., Hong, H.: QEPCAD — Quantifier elimination by partial cylindrical algebraic decomposition (2004), http://www.cs.usna.edu/~qepcad/B/QEPCAD.html
- 4.González-Vega, L.: A combinatorial algorithm solving some quantifier elimination problems. In: Caviness, B., Johnson, J. (eds.) Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 300–316. Springer, Wien (1996)Google Scholar
- 5.Hong, H.: Quantifier elimination for formulas constrained by quadratic equations via slope resultants. The Computer J. 36(5), 440–449 (1993)Google Scholar
- 6.Joan-Arinyo, R., Hoffmann, C.M.: A brief on constraint solving (2005), http://www.cs.purdue.edu/homes/cmh/distribution/papers/Constraints/ThailandFull.pdf
- 10.Wang, D.: Automated generation of diagrams with Maple and Java. In: Joswig, M., Takayama, N. (eds.) Algebra, Geometry, and Software Systems, pp. 277–287. Springer, Heidelberg (2003)Google Scholar