This paper establishes some formulas on orientable closed surfaces in 3-dimensional space forms.

本文建立关于三维空间型中的可定向闭曲面的某些公式。

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The quadrilateral grid graph of closed surfaces was obtained through surface slicing, offset point picking up, ordering of point array, 1d interpolation, and data merging.

经过曲面切片、型值点提取、点列排序、一维插值、数据融合，得到闭曲面四边形网格图。

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Some properties of the "super plane" in space forms are investigated, which is helpful to construct the example showing the banding properties of the closed surfaces in space forms.

而且探讨了空间型中“超平面”的性质，这对构造体现空间型中闭曲面整体弯曲程度的例子是有帮助的。

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His conjecture, made in 1904, was that in this four-dimensional world, all closed three-dimensional surfaces that are simply connected could be transformed to look like a three-dimensional sphere.

ECONOMIST: Proof of the truth of the Poincar�� conjecture