Survey on the theory and applications of μ-bases for rational curves and surfaces
Survey on the theory and applications of μ-bases for rational curves and surfaces
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DOI：
10.1016/j.cam.2017.07.023
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发表时间：
2018-02
期刊：
影响因子：
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通讯作者：
Xiaohong Jia;Xiaoran Shi;Falai Chen
中科院分区：
文献类型：
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作者：
Xiaohong Jia;Xiaoran Shi;Falai Chen
μ基是有理曲线和曲面的一种新的表示形式，是它们的参数形式和隐式形式之间的桥梁。在几何上，μ基用移动的线或移动的平面表示，而它们的代数对应是有理曲线或有理曲面的参数方程的特殊合。μ基已被证明在解决几何建模中的许多重要问题，如快速隐式化、奇异计算、重参数化以及提供简单的点的反演公式等方面具有重要意义。综述了有理曲线曲面μ基理论及其应用的最新研究成果，并提出了有待进一步研究的问题。
Abstract μ-Bases are new representations for rational curves and surfaces which serve as a bridge between their parametric forms and implicit forms. Geometrically, μ-bases are represented by moving lines or moving planes, while their algebraic counterparts are special syzygies of the parametric equations of rational curves or surfaces. μ-bases have been proven to be significant in solving many important problems in geometric modeling, such as fast implicitization, singularity computation, reparametrization as well as providing easy inversion formulas for points. We review the state-of-the-art results in μ-bases theory and applications for rational curves and surfaces, and raise unsolved problems for future research.