Linear rotation-invariant coordinates for meshes
Linear rotation-invariant coordinates for meshes
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DOI：
10.1145/1186822.1073217
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发表时间：
2005-07
期刊：
影响因子：
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通讯作者：
Y. Lipman;O. Sorkine-Hornung;D. Levin;D. Cohen-Or
中科院分区：
文献类型：
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作者：
Y. Lipman;O. Sorkine-Hornung;D. Levin;D. Cohen-Or
我们基于网格上定义的离散形式引入了一个刚体运动不变的网格表示。来自该表示的网格几何形状的重建需要求解由离散形式产生的两个稀疏线性系统：第一个系统定义了网格上的局部帧之间的关系，第二个系统通过本地框架编码了人物的位置。重建的几何形状是独特的，直到网格的刚性转换。我们通过将用户定义的约束放在本地框架和顶点位置上来定义表面编辑操作。这些约束纳入了两个线性重建系统中，它们的解决方案产生了变形的表面几何形状，该几何形状在最小二乘中保留了局部差异性能。用我们表示表达的形状的线性组合实现了正确处理旋转的线性形状插值。我们通过各种详细的编辑操作员并塑造了新表示的有效性。
We introduce a rigid motion invariant mesh representation based on discrete forms defined on the mesh. The reconstruction of mesh geometry from this representation requires solving two sparse linear systems that arise from the discrete forms: the first system defines the relationship between local frames on the mesh, and the second encodes the position of the vertices via the local frames. The reconstructed geometry is unique up to a rigid transformation of the mesh. We define surface editing operations by placing user-defined constraints on the local frames and the vertex positions. These constraints are incorporated in the two linear reconstruction systems, and their solution produces a deformed surface geometry that preserves the local differential properties in the least-squares sense. Linear combination of shapes expressed with our representation enables linear shape interpolation that correctly handles rotations. We demonstrate the effectiveness of the new representation with various detail-preserving editing operators and shape morphing.