應用曲面上之曲面原理建構幾何模型之壓力分佈

Abstract

本論文主要是研究幾何模型曲面上的函數曲面，一般處理的方法有二。一是修正薛普法，二是三角基本法，本論文主要是使用三角基本法。 一般而言，幾何曲面與函數曲面的不同點在於切線向量的求得方式，幾何曲面的切線向量可以由複合曲線求得，進而建立幾何曲面，函數曲面因點群分佈較不規則，無法用複合曲線來求得切線向量，只能用近似球面的方式計算，進而建立近似函數曲面。 文中的曲線使用赫米特曲線，幾何曲面則以四角綴面組成，近似函數曲面則以三角綴面組成。

The aim of this thesis is researched for surface on surface. There are two methods which can construct them. One is a modified Shepard's method and the other is a triangular-based method. The triangular-based method for constructing surface on surface is used in this thesis. Generally, the difference between geometric surface and functional surface are decided tangent vectors. Tangent vectors of geometric surface are decided by composite curves and constructed a geometric surface. The points on the functional surface are more irregular so they can not use composite curve to decide tangent vectors. They only used approximate sphere to decide tangent vectors and constructed an approximate surface. In this thesis, the Hermite curves are used and geometric surface constructed by rectangular patch. An approximate functional surface is constructed by triangular patch.