论文标题
网眼近似$ r^3 $的近似表面具有保证的规律性
Approximating Surfaces in $R^3$ by Meshes with Guaranteed Regularity
论文作者
论文摘要
我们研究了一个高质量网状的$ r^3 $中表面$ f $的问题，高质量的网格是一种分段式三角形的表面，其三角形尽可能接近等边。 Midnormal算法会生成一个三角形网状，保证在间隔$ [49.1^o，81.8^o] $中具有角度。作为网格尺寸$ e \ rightarrow 0 $，网格通过同位素到$ f $的表面将$ f $转化为$ f $。 Gradnortoral算法给出了$ f $的分段 - $ c^1 $近似值，在间隔$ [35.2^o，101.5^o] $的角度为$ e \ rightarrow 0 $。以前达到的角度界限是在间隔$ [30^o，120^o] $中。
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 $[30^o, 120^o]$.
