在處理某些問題時，我們需要收集一些幾何物件座標的樣本資料並嘗試在電腦上還原出原本的幾何物件。若幾何物件是彎曲的，有時，我們不一定能適當的還原出我們原本想研究的物件。如何辨別幾何圖形並在電腦上還原物件是本篇論文探討的主要目的。透過高斯絕妙定理，高斯曲率是一種幾何的不變量，換言之，幾何物件在剛體運動下，其高斯曲率不變。
本篇論文我們嘗試透過幾何物件座標的樣本資料估計幾何物體的高斯曲率，主要方法有二，第一為不足角法，第二為高斯映射的球面影像法。

Dealing with some problems, we need to collect some sample data of the coordinates of geometric objects and use the data to restore the objects on the computer When the objects are curved, it cannot be restored well. The main purpose of this study is to distinguish and restore geometric objects on computers. Through Gauss theorem, Gaussian curvature is an invariant, it is invariant under rigid motion.
In this thesis, we try to estimate Gaussian curvature through the some sample data of the coordinate of geometric objects. There are two main method discussed in this thesis: angular defect and spherical image.

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Institute of Computational Math. and Sci. and Eng. Computing, Academy of Mathematic and System Science, China Academy of Science, Beijing, 100080 China.
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