用保正则网格逼近$R^3$中的曲面
Approximating Surfaces in $R^3$ by Meshes with Guaranteed Regularity
摘要：
我们研究了在$R^3$中用高质量的网格逼近曲面$F$的问题，该网格是一个分段平坦的三角形曲面，其三角形尽可能地接近等边。MidNormal算法生成的三角形网格的角度保证在间隔$[49.1^o, 81.8^o]$内。当网格尺寸为$e\rightarrow 0$时，网格通过与$F$同向的曲面逐点收敛到$F$。梯度正态算法给出$F$的分段$C^1$近似，其中间隔$[35.2^o, 101.5^o]$中的角度为$e\rightarrow 0$。之前获得的角度范围在区间$[30^o, 120^o]$内。
英文摘要：
We study the problem of approximating a surface $F$ in $R^3$ by a high quality mesh, a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The MidNormal algorithm generates a triangular mesh that is guaranteed to have angles in the interval $[49.1^o, 81.8^o]$. As the mesh size $e\rightarrow 0$, the mesh converges pointwise to $F$ through surfaces that are isotopic to $F$. The GradNormal algorithm gives a piecewise-$C^1$ approximation of $F$, with angles in the interval $[35.2^o, 101.5^o]$ as $e\rightarrow 0$. Previously achieved angle bounds were in the interval $[30^o, 120^o]$.
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