中文摘要：

在二维重心坐标——复数重心坐标的基础上引入二维矩阵重心坐标的概念,并利用球面坐标将二维矩阵重心坐标推广到三维.三维矩阵重心坐标适用于三角控制网格、四边形控制网格甚至一般的混合控制网格.对所提出的重心坐标性质进行了研究,发现其满足大部分好的重心坐标所应具有的性质.最后对矩阵重心坐标在三维网格模型中的应用进行了细致的实验,分析了它的优缺点.

英文摘要：

Based on recently studied 2D barycentric coordinates,this paper extends it to complex barycentric coordinates as 2D matrix barycentric coordinates,and then generalizes the latter to 3D space.The new coordinates are well defined for triangular,quadrilateral and even arbitrary polygonal control meshes.We find that they satisfy most properties that good barycentric coordinates should possess.Finally,we also show their effectiveness in 3D mesh editing and analyze their pros and cons in this application.