报告题目: Subdividing barycentric coordinates
摘要: Barycentric coordinates are commonly used to represent a point inside a polygon as an affine combination of the polygon’s vertices and to interpolate data given at these vertices. While unique for triangles, various generalizations to arbitrary simple polygons exist, each satisfying a different set of properties. Some of these generalized barycentric coordinates do not have a closed form and can only be approximated by piecewise linear functions. In this paper we show that subdivision can be used to refine these piecewise linear functions without losing the key barycentric properties. For a wide range of subdivision schemes, this generates a sequence of piecewise linear coordinates which converges to non-negative and C1 continuous coordinates in the limit. The power of the described approach comes from the possibility of evaluating the C1 limit coordinates and their derivatives directly. We support our theoretical results with several examples, where we use Loop or Catmull–Clark subdivision to generate C1 coordinates, which inherit the favourable shape properties of harmonic coordinates or the small support of local barycentric coordinates.
时间：2016年12月11日上午11:00
地点：物理机电大楼661室
个人简介:
邓重阳, 湖南隆回人, 杭州电子科技大学教授, 浙江省高等学校中青年学科带头人。2008年在浙江大学获应用数学博士学位。2014.06-2014.11在瑞士提挈诺大学任访问教授. 曾多次赴香港城市大学, 日本横滨国立大学, 挪威奥斯陆大学学术访问。完成国家自然科学基金数学天元青年基金，青年基金各1项，现主持面上项目1项。在ACM Transactions on Graphics发表论文1篇，另在Computer Graphics Forum，Computer-Aided Design，Computer Aided Geometric Design等国际期刊发表论文近20篇。主要研究方向为细分曲线曲面，推广重心坐标，曲线曲面插值与逼近等。