參數曲面間的端點調合曲面計算

Abstract

調合曲面一直是電腦輔助幾何設計中重要的研究課題，最主要是由邊線調 合曲面與端點調合曲面組合而成。邊線調合曲面通常可以用一個曲面完全 得表示，而一個端點調合曲面則需由數個小曲面組合而成，因此曲面與曲 面之間的連續性關係著調合曲面的品質。本論文將針對端點調合曲面的計 算，提出一種可行作法，並實作測試。主要方法是使用setback的概念， 將端點調合曲面分割為數個小曲面，再利用基底曲面與邊線調合曲面上取 得一的資訊，建立每個小曲面並且將其維持在G1連續性上。而每個小曲面 最後將以NURBS表示 Blending surface is an important research topic in computer aided geometric design. Blending for an edge can be represented by a simple patch, while blendingfor a vertex requires several patches. Continuity between each patch emblematizesthe quality of vertex blending surface. In this thesis, we propose a methodthat subdivides vertex blending surface into several sub- patches by the conceptof setback split and derive the continuity information along intersectionsbetween sub-patches. These sub- patches are represented by NURBS surface.