引用本文: 苗苗, 李亚娟, 邓重阳. 基于点多边形的混合坐标[J]. 计算机辅助设计与图形学学报. Blended CoordinatesBased on Point Polygons[J]. Journal of Computer-Aided Design & Computer Graphics.
 Citation: Blended CoordinatesBased on Point Polygons[J]. Journal of Computer-Aided Design & Computer Graphics. ## Blended CoordinatesBased on Point Polygons

• 摘要: 为了构造非负且光滑的广义重心坐标, 提出一种基于点多边形的混合坐标构建方法. 首先将原多边形三角剖分, 计算所有网格顶点的重心坐标, 并确定每个网格顶点的点多边形; 然后分别计算原多边形内点关于其所在三角形的点多边形的重心坐标与混合系数, 根据以上计算结果得到混合坐标; 最后使用迭代坐标或调和坐标计算网格顶点的重心坐标, 用均值坐标和迭代坐标计算原多边形内点关于点多边形的重心坐标. 数值实例与推导结果表明, 所提方法具有良好的光滑性, 且在任意多边形内部具有非负性.

Abstract: In order to construct nonnegative and smooth generalized barycentric coordinates, a blended coordinates construction method based on point polygons was proposed. Firstly, triangulated the original polygon, calculated the barycentric coordinates of all mesh vertices, and determined the point polygons of each mesh vertex; Furthermore, the barycentric coordinates and blended coefficients of the point inside the original polygon with respect to the point polygons of the triangle in which they were located were calculated respectively, then the blended coordinates were obtained according to the above calculation results. Finally, the barycentric coordinates of the mesh vertices were calculated using iterative coordinates or harmonic coordinates, and the barycentric coordinates of the points inside the original polygon with respect to the point polygons were calculated using mean value coordinates and iterative coordinates. Numerical examples and derivation results show that the proposed method has good smoothness and is nonnegative inside any polygon. / 下载:  全尺寸图片 幻灯片
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