Tracking Method for Reparametrized Geometrical Constraint Systems

Rémi Imbach (1) , Pascal Mathis (2) , Pascal Schreck (2)

1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
2 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

In CAD, constraint solvers allow a user to describe a figure or an object with a set of constraints like distances, angles, tangencies, incidences and so on. Geometric solvers proceed in two stages. First, a symbolic construction plan is provided from the set of constraints. Then, the dimensions of constraints are used in a numerical stage to evaluate the construction plan. However, construction plans can not be easily provided for many problems in 3D. A classic idea consists in removing and adding some constraints in order to make the problem solvable by a geometric method. This leads to a numerical problem in which numerical values for the added constraints have to be computed in order to find the values of the added dimensions that validate the removed dimensions. Finding these values is usually done by sampling which is very time-consuming when there are more than 2 variables to sample. In this paper we address the numerical stage by adapting a path-tracking method. This allows to find several solutions and this method is efficient when the number of values is greater than 2.

Mots clés: Design automation; Vectors; Three dimensional displays; Complexity theory; Knowledge based systems; Equations; Orbits

Domaines: Géométrie algorithmique [cs.CG]; Ingénierie assistée par ordinateur

Rémi Imbach, Pascal Mathis, Pascal Schreck. Tracking Method for Reparametrized Geometrical Constraint Systems. SYNASC 2011 - 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, Sep 2011, Timisoara, Romania. pp.31-38, ⟨10.1109/SYNASC.2011.26⟩. ⟨hal-02077924⟩