Globally smooth parameterizations with low distortion
Globally smooth parameterizations with low distortion
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DOI：
10.1145/1201775.882275
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发表时间：
2003-07
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影响因子：
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通讯作者：
A. Khodakovsky;Nathan Litke;P. Schröder
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文献类型：
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作者：
A. Khodakovsky;Nathan Litke;P. Schröder
在许多数字几何处理任务中，良好的参数化是至关重要的。通常，这种处理算法的行为与参数化的平稳性以及它所包含的失真程度有关。由于参数化将平面的有界区域映射到曲面，因此对于不同于圆盘的曲面，其参数化必须由多个片段组成。提出了一种新的任意拓扑面网格的参数化算法，该算法计算出了一个全局光滑的低失真的参数化算法。我们根据形状质量和度量失真等准则对面片布局进行优化，以此来指导基础复杂构造的网格简化方法。全局光滑性是通过在所有面片上同时松弛来实现的，在松弛过程中结合了适当的面片之间的过渡函数。我们通过对失真度量的数值评估和用这些参数生成的半正则网格的优异的率失真性能来展示我们的参数的质量。即使对于大网格，计算参数化所需的数值算法也是健壮的，并且运行在几分钟的量级上。
Good parameterizations are of central importance in many digital geometry processing tasks. Typically the behavior of such processing algorithms is related to the smoothness of the parameterization and how much distortion it contains. Since a parameterization maps a bounded region of the plane to the surface, a parameterization for a surface which is not homeomorphic to a disc must be made up of multiple pieces. We present a novel parameterization algorithm for arbitrary topology surface meshes which computes a globally smooth parameterization with low distortion. We optimize the patch layout subject to criteria such as shape quality and metric distortion, which are used to steer a mesh simplification approach for base complex construction. Global smoothness is achieved through simultaneous relaxation over all patches, with suitable transition functions between patches incorporated into the relaxation procedure. We demonstrate the quality of our parameterizations through numerical evaluation of distortion measures and the excellent rate distortion performance of semi-regular remeshes produced with these parameterizations. The numerical algorithms required to compute the parameterizations are robust and run on the order of minutes even for large meshes.