臺灣博碩士論文加值系統

本論文在探討幾何於計算機上的應用, 主要分兩大部分. 第一部份探討如何在計算機中計算幾何模型之幾何不變量. 並對於傳統的權重比例分配方法給予數學上的解釋及提出一種優於傳統權重的新權重. 第二部分探討幾何模型方割之方法, 提出一由幾何不變量所控制的新切割方法.

In this thesis, we present the \omega -weight normal vector and curvature forms on triangluar meshes. And show the result of two different kinds of weight, area-weight and centroid-weight. Then, we also describe subdivision methods, these methods are depend on their neighbors and normal vectors. Moreover, these subdivision methods have an important property: they can keep the normal vectors at the original triangular mesh and these subdivision methods are affine invariant.

1. Introduction
2. Preliminaries
3. Normal Vectors & Curvatures
4. Centroid subdivision methods
5. Future works

Chen, X.and Schmitt, F. Intrinsic surface properties from triangluation.
Do Carmo, M. Differential geometry of curves and surfaces.
Taubin, G. Estimating the tensor of curvature of a surface from a polyedral approximation.