A unified approach to resultant matrices for Bernstein basis polynomials

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design Pub Date : 2008-10-01 DOI:10.1016/j.cagd.2007.09.004

Joab R. Winkler

引用次数: 9

Abstract

Resultant matrices can be used to compute the intersection points of curves that are defined by polynomials. They were originally developed for polynomials expressed in the power (monomial) basis, but the recent development of resultant matrices for Bernstein basis polynomials has increased their use in computer aided geometric design, for which the Bernstein basis is the standard polynomial basis. In this paper, the equations that relate the Sylvester, Bézout and companion resultant matrices for Bernstein basis polynomials are derived, thereby establishing their equivalence. It is shown that these equations are more complicated than their power basis equivalents.

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伯恩斯坦基多项式合成矩阵的统一方法

合成矩阵可以用来计算由多项式定义的曲线的交点。它们最初是为幂(单)基表示的多项式而开发的，但伯恩斯坦基多项式的合成矩阵的最近发展增加了它们在计算机辅助几何设计中的应用，伯恩斯坦基是标准的多项式基。本文导出了Bernstein基多项式的Sylvester、b zout及其伴合矩阵的关系式，从而建立了它们的等价性。结果表明，这些方程比等效的幂基方程更为复杂。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Aided Geometric Design 工程技术-计算机：软件工程

CiteScore

3.50

自引率

13.30%

发文量

审稿时长

60 days

期刊介绍： The journal Computer Aided Geometric Design is for researchers, scholars, and software developers dealing with mathematical and computational methods for the description of geometric objects as they arise in areas ranging from CAD/CAM to robotics and scientific visualization. The journal publishes original research papers, survey papers and with quick editorial decisions short communications of at most 3 pages. The primary objects of interest are curves, surfaces, and volumes such as splines (NURBS), meshes, subdivision surfaces as well as algorithms to generate, analyze, and manipulate them. This journal will report on new developments in CAGD and its applications, including but not restricted to the following: -Mathematical and Geometric Foundations- Curve, Surface, and Volume generation- CAGD applications in Numerical Analysis, Computational Geometry, Computer Graphics, or Computer Vision- Industrial, medical, and scientific applications. The aim is to collect and disseminate information on computer aided design in one journal. To provide the user community with methods and algorithms for representing curves and surfaces. To illustrate computer aided geometric design by means of interesting applications. To combine curve and surface methods with computer graphics. To explain scientific phenomena by means of computer graphics. To concentrate on the interaction between theory and application. To expose unsolved problems of the practice. To develop new methods in computer aided geometry.