Green Coordinates
Green Coordinates
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DOI：
10.1145/1399504.1360677
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发表时间：
2008-08
期刊：
影响因子：
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通讯作者：
Y. Lipman;D. Levin;D. Cohen-Or
中科院分区：
文献类型：
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作者：
Y. Lipman;D. Levin;D. Cohen-Or
我们介绍了封闭多面体笼的绿色坐标。这些坐标由绿色的第三积分恒等式激发，并且尊重笼子的顶点位置和面方向。我们表明，绿色坐标导致空间变形的形状保持属性。特别地，在二维中，它们诱导共形映射，并自然地推广到三维中的拟共形映射。在这两种情况下，我们推导出封闭形式的坐标表达式，产生一个简单而快速的算法基于笼子的空间变形。我们比较的性能的绿色坐标与那些的平均值坐标和调和坐标，并表明，形状保持属性的优点是不以牺牲速度或简单性。我们还表明，新的坐标扩展映射在一个自然的分析方式的笼的外部，允许就业的部分笼。
We introduce Green Coordinates for closed polyhedral cages. The coordinates are motivated by Green's third integral identity and respect both the vertices position and faces orientation of the cage. We show that Green Coordinates lead to space deformations with a shape-preserving property. In particular, in 2D they induce conformal mappings, and extend naturally to quasi-conformal mappings in 3D. In both cases we derive closed-form expressions for the coordinates, yielding a simple and fast algorithm for cage-based space deformation. We compare the performance of Green Coordinates with those of Mean Value Coordinates and Harmonic Coordinates and show that the advantage of the shape-preserving property is not achieved at the expense of speed or simplicity. We also show that the new coordinates extend the mapping in a natural analytic manner to the exterior of the cage, allowing the employment of partial cages.