本文提出一种直接在点采样曲面上计算曲面的高斯曲率、平均曲率及主曲率等局部微分性质的方法。

An approach is proposed to estimate several differential properties, including Gaussian curvature, mean curvature and main curvature on point-sampled surfaces in presence of noise.

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并利用主曲率计算公式证明了W-超曲面的一个存在性定理。

Using the principal curvature formula, we prove an existence theorem of Weingarten hypersurface.

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由于给定主曲率函数的嵌入旋转曲面存在性已得到较好证明，故使得曲面的设计成为可能。

Since the existence of embedded rotation surface with given principal curvature function is well proofed, the design and modeling of the surface becomes possible.

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由于给定主曲率函数的嵌入旋转曲面存在性已得到较好证明，故使得曲面的设计成为可能。

Since the existence of embedded rotation surface with given principal curvature function is well proofed, the design and modeling of the surface becomes possible.

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