The intersection problems of parametric curve and surfaces by means of matrix based implicit representations
نویسنده
چکیده
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, curve/surface and surface/surface intersection problems, the point-oncurve and inversion problems, the computation of singularities points. Keyword Geometric modeling, parametric curves and surfaces, intersection, pencils of matrix, singular points.
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