幾何模型之局部編修

Abstract

本篇論文主要是探討如何應用高次多項式來協助幾何模型的局部編修。我們使用高次多項式的理由是因為其具有良好的曲線造形及優異的操控性。首先，我們在編修曲面上拉出一條剖面參考曲線決定編修曲面的大致外觀，其次拉出另一條外形參考曲線決定前一條曲線在該方向的流線造形，最後再應用摻合函數以內插的方式建構出編修曲面。 局部曲線的編修，我們以高次多項式曲線來替代原有之參數曲線，在接點的部份均設計使其能滿足連續的要求，在曲面的編修方面，我們以同樣的方法，最後證明，一樣可以達到很好的連續效果，使幾何模型的編修造型更加完美。

The aim of this research study is to apply the polymial equation of a higher-degree to modify geometric modeling locally. The reson for using a higher-degree curve segment is for better shape modification and manipulation. First, we set a curve as reference curve of section to define the profile of modified patch, then set another curve as reference curve of shape to define the tangent vector of the first curve in its direction. Finally, we use the Hermitian functions to evaluate the data points between patch boundaries and reference curves by interpolation. To achieve local adjustment, we replace the original parametric cubic curve segment by a parametric curve segment of a higher degree. Naturally, the replacing curve segment must satisfy the original set of continuity conditions at the joint. By extending this concept of curve local adjustment to the parametric surface model, a versatile geometric modeling module can be accomplished with a reasonalble amount of effort.