One hundred years after the introduction of the Bernstein polynomial basis, we survey the
historical development and current state of theory, algorithms, and applications associated …

We review the treatment of trimmed geometries in the context of design, data exchange, and
computational simulation. Such models are omnipresent in current engineering modeling …

We present a new approach to building a solver for a set of geometric constraints
represented by multivariate rational functions. The constraints are formulated using …

This paper presents a new algorithm for solving a system of polynomials, in a domain of Rn.
It can be seen as an improvement of the Interval Projected Polyhedron algorithm proposed …

The medial axis transform (MAT) is a representation of an object which has been shown to
be useful in design, interrogation, animation, finite element mesh generation, performance …

The goal of this book is to teach the art of finding the root of a single algebraic equation or a
pair of such equations. We shall quote theorems and theory as necessary, but this is not …

A pipe (or tubular) surface is the envelope of a one-parameter family of spheres with
constant radii r and centers C (t). In this paper we investigate necessary and sufficient …

We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin
discretizations to build mass and stiffness matrices. Using the homotopy continuation …

The cut locus C, of a closed set A in the Euclidean space E is defined as the closure of the
set containing all points p which have at least two shortest paths to A. We present a theorem …

We present an accurate and efficient algorithm for continuous collision detection between
two moving ellipsoids. We start with a highly optimized implementation of interference …