论文标题
在球形barycentric坐标上
On spherical barycentric coordinates
论文作者
论文摘要
本文介绍了一个在球体上的概括性重点坐标的新颖结构，相对于给定球形多边形的顶点，该坐标包含在公共半球中。尽管在标准方法中，此类坐标是从其经典平面对应物（例如Wachspress或平均值）得出的，而是我们从原点的3D Barycentric坐标中得出它们，并表明它们具有一些有用的属性，例如Edge Linarearity和Lagrange属性。此外，我们表明两种方法的球形平均值坐标一致，而它们相应的球形wachspress坐标通常不同。
This paper describes a novel construction of generalized barycentric coordinates of points on a sphere with respect to the vertices of a given spherical polygon that is contained in a common hemisphere. While in the standard approach such coordinates are derived from their classical planar counterparts (e.g. Wachspress, or mean value), we instead derive them from 3D barycentric coordinates of the origin and show that they are endowed with some useful properties such as edge linearity and Lagrange property. In addition, we show that spherical mean value coordinates of both approaches coincide while their corresponding spherical wachspress coordinates are in general different.
