Multi‐Scale Geometry Interpolation
Multi‐Scale Geometry Interpolation
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DOI：
10.1111/j.1467-8659.2009.01600.x
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发表时间：
2010-05
影响因子：
2.5
通讯作者：
T. Winkler;Jens Drieseberg;M. Alexa;K. Hormann
中科院分区：
文献类型：
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作者：
T. Winkler;Jens Drieseberg;M. Alexa;K. Hormann
在具有相同顶点边图的三角形网格之间插值顶点位置是许多几何建模系统的基本部分。线性顶点插值很稳健，但无法保留局部形状。最近的方法识别网格部分的局部仿射变换，对仿射变换的所需插值进行建模，然后优化顶点位置以符合所需的变换。然而，对于两个以上的输入配置来说，旋转部分的局部插值是很重要的，并且如果网格变形显着，则旋转部分的局部插值是不明确的。我们提出了一种顶点插值问题的解决方案，该解决方案从插值局部度量（边长）和平均曲率（二面角）开始，并使用应用于网格的连续较大部分的形状匹配来做出局部仿射变换的一致选择。局部插值可以应用于任意数量的输入顶点配置，并且由于生成合并顶点位置的分层方案，该方法速度很快并且可以应用于非常大的网格。
Interpolating vertex positions among triangle meshes with identical vertex‐edge graphs is a fundamental part of many geometric modelling systems. Linear vertex interpolation is robust but fails to preserve local shape. Most recent approaches identify local affine transformations for parts of the mesh, model desired interpolations of the affine transformations, and then optimize vertex positions to conform with the desired transformations. However, the local interpolation of the rotational part is non‐trivial for more than two input configurations and ambiguous if the meshes are deformed significantly. We propose a solution to the vertex interpolation problem that starts from interpolating the local metric (edge lengths) and mean curvature (dihedral angles) and makes consistent choices of local affine transformations using shape matching applied to successively larger parts of the mesh. The local interpolation can be applied to any number of input vertex configurations and due to the hierarchical scheme for generating consolidated vertex positions, the approach is fast and can be applied to very large meshes.