# THE INTERSECTION PROBLEMS OF REAL PARAMETRIC CURVES AND SURFACES BY MEANS OF MATRIX BASED IMPLICIT REPRESENTATIONS: A NEW APPROACH

### Abstract

Evaluating the intersection of two real rational parameterized algebraic surfaces is an important problem in solid modeling. In [9, 10, 22], we have already developed an approach based on generalized matrix representations of parameterized curves and surfaces in order to represent the intersection points or curves as the generalized eigenvalues of a matrix or the zero set of a matrix determinant. These computations based on complicate techniques from linear algebra such as QR-Decomposition, ΔW-Decomposition to obtain square matrices that hold the necessary properties. In this paper, we propose an new method to obtain intersection represented matrices that are square without complicate computing