高珊珊, 张彩明, 周元峰, 伯彭波. 壳空间剖分的隐式曲面三角化[J]. 计算机研究与发展, 2012, 49(2): 432-442.
 引用本文: 高珊珊, 张彩明, 周元峰, 伯彭波. 壳空间剖分的隐式曲面三角化[J]. 计算机研究与发展, 2012, 49(2): 432-442.
Gao Shanshan, Zhang Caiming, Zhou Yuanfeng, Bo Pengbo. Triangulation of Implicit Surfaces via Shell-Space Partition[J]. Journal of Computer Research and Development, 2012, 49(2): 432-442.
 Citation: Gao Shanshan, Zhang Caiming, Zhou Yuanfeng, Bo Pengbo. Triangulation of Implicit Surfaces via Shell-Space Partition[J]. Journal of Computer Research and Development, 2012, 49(2): 432-442.

## Triangulation of Implicit Surfaces via Shell-Space Partition

• 摘要: 提出了一种曲率自适应的壳空间剖分隐式曲面三角形化新方法.新方法首先采用粒子系统对隐式曲面进行采样,通过高斯曲率约束粒子的生成,使生成的网格模型在曲率大的区域具有较多的小三角形,在曲率小的区域具有较少的大三角形,从而使网格模型更好地逼近隐式曲面.新方法在每个采样粒子处沿曲面法线正负方向延伸适当距离得到两个附加点,对所有附加点进行四面体化形成对隐式曲面逼近的壳空间四面体网格,在每个壳空间四面体中抽取三角形,所有抽取的三角形拼合得到隐式曲面的三角网格表示.与以往方法相比,新的三角网格化方法更具有鲁棒性,可一次性获得高质量的三角形网格.最后给出了对常用隐式曲面进行三角化的实例比较,显示了新方法的有效性.

Abstract: A novel and robust method is presented for implicit surface triangulation problem. Particle system is used for sampling an implicit surface whose fission and death are guided by Gaussian curvature. This strategy leads to curvature adaptive samplings, so there are more small triangles in the high curvature region of constructed mesh. Triangular mesh can approximate the implicit surface better. More sample points are obtained by extending a proper distance along each normal vector. These new sample points are used as a sampling on surface of the shell space. Delaunay tetrahedron of these sample points fills in the shell space. Finally, triangles around zero set form a triangulation of the implicit surface. Compared with the existing methods, our method is more robust, and can achieve high quality model without post processing. Experiments are also conducted to demonstrate the efficiency of this new method.

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