Matrix-based implicit representations of rational algebraic curves and applications

Laurent Buse; Thang Luu Ba

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Matrix-based implicit representations of rational algebraic curves and applications

机译：有理代数曲线的基于矩阵的隐式表示及其应用

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Given a parameterization of an algebraic rational curve in a projective space of arbitrary dimension, we introduce and study a new implicit representation of this curve which consists in the locus where the rank of a single matrix drops. Then, we illustrate the advantages of this representation by addressing several important problems of Computer Aided Geometric Design: the point-on-curve and inversion problems, the computation of singularities and the calculation of the intersection between two rational curves.

机译：给定任意尺寸的投影空间中的代数有理曲线的参数，我们引入并研究该曲线的新的隐式表示，该表示包含在单个矩阵的秩下降的轨迹中。然后，我们通过解决计算机辅助几何设计的几个重要问题来说明这种表示的优点：曲线上的点和反演问题，奇点的计算以及两条有理曲线之间的交点的计算。

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来源
《Computer Aided Geometric Design》 |2010年第9期|p.681-699|共19页
作者
Laurent Buse; Thang Luu Ba;
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作者单位

INRIA, Galaad,2004 route des Lucioles. 06902 Sophia Antipolis,France;

INRIA, Galaad,2004 route des Lucioles. 06902 Sophia Antipolis,France,Laboraroire J.A. Dieudonne. Universite de Nice, Parc Valrose, 06108 Nice Cedex 02, France;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
algebraic curves; μ-basis; elimination; matrix-based representations; intersection problems; singularities of algebraic curves;

机译：代数曲线μ-基;消除基于矩阵的表示;交叉路口问题代数曲线的奇点;

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1. Implicit matrix representations of rational Bezier curves and surfaces [J] . Buse Laurent Computer-Aided Design . 2014,第Null期

机译：有理Bezier曲线和曲面的隐式矩阵表示
2. A basis for the implicit representation of planar rational cubic Bezier curves [J] . Oliver J.D. Barrowclough Computer Aided Geometric Design . 2014,第3a4期

机译：平面有理三次贝塞尔曲线隐式表示的基础
3. Clifford algebra, spin representation, and rational parameterization of curves and surfaces [J] . Hyeong In Choi, Doo Seok Lee, Hwan Pyo Moon Advances in computational mathematics . 2002,第1a2期

机译：Clifford代数，自旋表示以及曲线和曲面的合理参数化
4. The preserving GC~1 planar quadratic algebraic curve approximate implicitization for planar parametric curves [C] . Ding Youdong, Hua Xuanji, Chen Changsong, International conference for young computer scientists . 1999

机译：Planar参数曲线的保留GC〜1平面二次代数曲线近似隐式化
5. Representations of the symplectic reflection algebras and of the rational Cherednik algebras. [D] . Chmutova, Tatyana S. 2006

机译：辛反射代数和有理Cherednik代数的表示。
6. Equivariant algebraic vector bundles over representations of reductive groups: applications. [O] . M Masuda, L Moser-Jauslin, T Petrie 1991

机译：等化代数向量束在归约组表示上的应用。
7. Matrix-based Implicit Representations of Rational Algebraic Curves and Applications [O] . Busé Laurent, Luu Ba Thang 2010

机译：有理代数曲线的基于矩阵的隐式表示及其应用

Matrix-based implicit representations of rational algebraic curves and applications

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