A Crystalline, Red Green Strategy for Meshing Highly Deformable Objects with Tetrahedra
A Crystalline, Red Green Strategy for Meshing Highly Deformable Objects with Tetrahedra
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DOI：
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发表时间：
2003
影响因子：
12.1
通讯作者：
Neil P. Molino;R. Bridson;J. Teran;Ronald Fedkiw
中科院分区：
文献类型：
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作者：
Neil P. Molino;R. Bridson;J. Teran;Ronald Fedkiw
出于弹性变形的拉格朗日模拟，我们提出了一种新的四面体网格生成算法，产生高质量的元素和网格，以及随后的大变形的条件。我们使用一个有符号的距离函数定义在笛卡尔网格，以表示对象的几何形状。在基于晶体学用均匀晶格平铺空间之后，我们使用有符号距离函数或其他用户定义的标准来指导红绿色网格细分算法，该算法产生具有适当细节级别的候选网格。然后，我们仔细选择最终的拓扑结构，使连接适合大变形，网格近似所需的形状。最后，我们使用质量和弹簧，有限元方法或优化方法来放松节点的位置来压缩网格以紧密拟合对象边界。生成的网格非常适合模拟，因为它是高度结构化的，在面对大变形时具有强大的拓扑连接性，并且如果在后续模拟中认为有必要，可以随时进行细化。
Motivated by Lagrangian simulation of elastic deformation, we propose a new tetrahedral mesh generation algorithm that produces both high quality elements and a mesh that is well conditioned for subsequent large deformations. We use a signed distance function defined on a Cartesian grid in order to represent the object geometry. After tiling space with a uniform lattice based on crystallography, we use the signed distance function or other user defined criteria to guide a red green mesh subdivision algorithm that results in a candidate mesh with the appropriate level of detail. Then, we carefully select the final topology so that the connectivity is suitable for large deformation and the mesh approximates the desired shape. Finally, we compress the mesh to tightly fit the object boundary using either masses and springs, the finite element method or an optimization approach to relax the positions of the nodes. The resulting mesh is well suited for simulation since it is highly structured, has robust topological connectivity in the face of large deformations, and is readily refined if deemed necessary during subsequent simulation.