报告题目：An improved algorithm for checking the injectivity of 2D toric surface patches

报告人： 朱春钢 教授

报告时间：2021年4月2日（周五）14:00—15:00

报告地点：腾讯会议ID: 847 720 937

报告摘要: Injective parametrizations are widely used both in theory and in applications. The injectivity of parametric curve and surface means that there are no self-intersections. Toric surface patch is defined by a set of integer lattice points A and corresponding control points and weights, which includes rational tensor product and triangle Bézier patches as special cases. In 2011, Sottile and Zhu presented a geometric method to check the injectivity of 2D toric surface patches with arbitrary positive weights. In this talk, we present an improved algorithm of their method, based on directed area of triangles, Pick’s Theorem and Farey sequence. The complexity of the improved algorithm is reduced from O(n^3) to O(n^2), where n=#(A). Some examples are shown to illustrate the effectiveness of our algorithm. And the algorithm is also applied to check the injectivity of parametrization in isogeometric analysis. Furthermore, we generalize the algorithm to check the injectivity of 3D toric volumes with arbitrary positive weights. This work is joint with Yingying Yu and Ye Ji.

个人简介：朱春钢，大连理工大学数学科学学院教授，博士生导师，计算科学研究所所长，中国工业与应用数学学会(CSIAM)常务理事，辽宁省计算数学与数据智能重点实验室副主任. 主要从事计算几何与计算机辅助设计方向的研究工作，内容包括多元样条、分片代数曲线与分片代数簇、几何造型、等几何分析等。到目前为止，在国内外重要期刊发表论文多篇，出版教材2部，主持包括5项国家自然科学基金项目在内的多项科研项目，参加了包括2项国家自然科学基金重点项目在内的多个科研与教学项目建设。

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