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

  • Luu Ba Thang
Keywords: Matrix-based implicit representations, real parametric curves and surfaces, intersection

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

Published
2020-02-04