The intersection problems of parametric curve and surfaces by means of matrix based implicit representations

Ba Thang Luu (1, 2)

1 GALAAD - Geometry, algebra, algorithms
2 Hanoi National University of Education - Department of Mathematics and Informatics

In this paper, we introduce and study a new implicit representation of parametric curves and parametric surfaces . We show how these representations which we will call the matrix implied, establish a bridge between geometry and linear algebra, thus opening the possibility of a more robust digital processing. The contribution of this approach is discussed and illustrated on important issues of geometric modeling and Computer Aided Geometric Design (CAGD) : The curve/curve, urve/surface and surface/surface intersection problems, the point-on-curve and inversion problems, the computation of singularities points.

Domaines: Géométrie algébrique [math.AG]

Ba Thang Luu. The intersection problems of parametric curve and surfaces by means of matrix based implicit representations. 2013. ⟨hal-00809325v2⟩