Approximate Implicitization Using Linear Algebra

[摘要] We consider a family of algorithms for approximateimplicitization of rational parametric curves and surfaces. The main approximationtool in all of the approaches is the singular value decomposition, andthey are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD) systems. We unify the approaches under thenames of commonly known polynomial basis functions and consider varioustheoretical and practical aspects of the algorithms. We offer new methodsfor a least squares approach to approximate implicitization using orthogonalpolynomials, which tend to be faster and more numerically stable than someexisting algorithms. We propose several simple propositions relating the propertiesof the polynomial bases to their implicit approximation properties.

[学科分类] 应用数学