Solution space navigation for geometric constraint systems

Solving Geometric Constraint Systems

Finding the con gurations of a set of rigid bodies that satisfy a set of geometric constraints is a problem traditionally solved by reformulating the geometry and constraints as algebraic equations which are solved symbolically or numerically. But many such problems can be solved by reasoning symbolically about the geometric bodies themselves using a new technique called degrees of freedom anal...

Geometric Constraint Problems and Solution Instances

Geometric constraint solving is a growing field devoted to solve geometric problems defined by relationships, called constraints, established between the geometric elements. In this work we show that what characterizes a geometric constraint problem is the set of geometric elements on which the problem is defined. If the problem is wellconstrained, a given solution instance to the geometric con...

Interactive manipulation of a solution for a geometric constraint system

In CAD systems, symbolic geometric solvers allow to provide, for a constrained sketch drawn by the designer, a general construction program, that describes how and in which order the objects have to be built. Then this program is numerically interpreted to produce the required figure. If multiple solutions are generated, these kind of solvers generally allow to scan the entire space of the solu...

Sketch-based pruning of a solution space within a formal geometric constraint solver

Re-parameterization reduces irreducible geometric constraint systems

You recklessly told your boss that solving a non-linear system of size n (n unknowns and n equations) requires a time proportional to n, as you were not very attentive during algorithmic complexity lectures. So now, you have only one night to solve a problem of big size (e.g., 1000 equations/unknowns), otherwise you will be fired in the next morning. The system is well-constrained and structura...