Section: New Results

Orthogonal projection of points on Bézier curves and surfaces

Participant : Laurent Busé.

In this work, we introduce a new method for computing the orthogonal projections of a point onto a Bézier curve or surface. It is based on the concept of matrix representation we have introduced and developed in some previous works, which is here applied to the parameterizations of the normal planes or lines of a curve or surface, respectively. It consists in the computation of a matrix depending of the ambient space variables, which is done in a pre-processing step, and then the use of tools from numerical linear algebra for a fast and accurate solving of each instance of the problem.

This is an on going work done in the context of the SYRAM project which is funded by the MathAmSud programme. It is a collaboration with N. Botbol (University of Buenos Aires) and M. Chardin (University of Paris 6).