Significant progress has been accomplished during the past decades about geometric
constraint solving, in particular thanks to its applications in industrial fields like CAD and …

This paper presents a comprehensive review of geometric constraint solving in parametric
computer-aided design (CAD), with the major focus on its advances in the last 15 years …

The classical notion of rigidity (that a formation of agents in R 2 or R 3 is rigidly-constrained
by interagent distances up to rigid-body transformations of space) is inherently dependent …

We define the notion of affine rigidity of a hypergraph and prove a variety of fundamental
results for this notion. First, we show that affine rigidity can be determined by the rank of a …

This paper describes new ways to tackle several important problems encountered in
geometric constraint solving, in the context of CAD, and which are linked to the handling of …

The geometric constructions obtained with only straightedge and compass are famous and
play a special role in the development of geometry. On the one hand, the constructibility of …

For more than a decade, the trend in geometric constraint systems solving has been to use a
geometric decomposition/recombination approach. These methods are generally grounded …

The simplest geometric constraints are incidences between points and lines in the projective
plane. This problem is universal, in the sense that all algebraic systems reduce to such …

This paper deals with the resolution of geometric constraint systems encountered in CAD-
CAM. The main results are that the witness method can be used to detect that a constraint …

In this work, the notions of formation and rigidity (first developed for formation control in
Euclidean spaces) are recast in a general framework of principal fiber bundles and a control …