Tracking Method for Reparametrized Geometrical Constraint Systems

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.