Near-Optimal Parameterization of the Intersection of Quadrics: IV. An Efficient and Exact Implementation

Sylvain Lazard (1) , Luis Mariano Peñaranda (2) , Sylvain Petitjean (1)

1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
2 FCEIA - Facultad de Ciencias Exactas, Ingenieria y Agrimensura [Rosario]

We present the first complete, robust, and efficient C++ implementation for parameterizing the intersection of two implicit quadrics with integer coefficients of arbitrary size. It is based on the near-optimal algorithm presented in Parts I, II, and III [5, 6, 7] of this paper. Our implementation correctly identifies and parameterizes all the algebraic components of the intersection in all cases, returning parameterizations with rational functions whenever such parameterizations exist. In addition, the field of the coefficients of the parameterizations is either of minimal degree or involves one possibly unneeded square root. We also prove upper bounds on the size of the coefficients of the output parameterizations and compare these bounds to observed values. We give other experimental results and present some examples.

Mots clés: INTERSECTION OF SURFACES; QUADRICS; CURVE PARAMETERIZATION; IMPLEMENTATION

Domaines: Géométrie algorithmique [cs.CG]; Autre [cs.OH]

Sylvain Lazard, Luis Mariano Peñaranda, Sylvain Petitjean. Near-Optimal Parameterization of the Intersection of Quadrics: IV. An Efficient and Exact Implementation. [Research Report] RR-5670, INRIA. 2005, pp.30. ⟨inria-00070341⟩