三維封閉曲面上的圖型切割線

Abstract

一個在三維空間的封閉曲面，使用三角網格將其離散化，搭配半邊結構的方式將其儲存在電腦中。本論文將對三種不同類型的封閉曲面(球，虧格數１，虧格數１接合虧格數１)進行探討，欲將該封閉曲面進行切割，使得其沿著圖形切割線能將曲面展開成不同型態的基本定義域(fundamental domain)，進而創建覆蓋空間(covering space)。在實作三維封閉曲面上的圖形切割線時，運用兩種不同的演算法分別在不同的的權重(weight)下，控制生成的圖形切割線。 不同的演算法分別在不同的權重下，分別得出了不同的圖形切割線，但是每一條圖形切割線的走勢並不完全依照當初設計權重的希望進行。

A closed surface in three-dimensional space, using the triangular meshes to discrete, with half edge structure will be stored in the computer. This work will have three different types of closed surface (ball, genus of one, genus of two) to discuss, For the closed surface to cut, cutting down the cut graph able to transform surfaces into different types of fundamental domain, and thus created covering space. Working cut graph on closed surface of the three-dimensional using two different algorithms with different weights to control generated cut graph. Different algorithms with different weights, get different cut graph, but cut graph does not completely in accordance with the original design weight hope.