Bezier曲線曲面的拼接
摘要
曲線曲面的表示是計算機圖形學的重要研究內容之1，Bézier曲線曲面又是計算機圖形學中常用的曲線曲面，它採用分段和分片參數多項式的形式。Bézier曲線曲面之所以被廣泛使用是因爲它有許多特別適合計算機圖形學和計算機輔助幾何設計的特點。
本文依次詳細論述了Bézier曲線的定義和性質、Bernstein基函數性質、介紹了雙3次Bézier曲面、遞推算法、構圖法及其應用、Bézier曲線曲面的拼接。透過對Bézier曲線曲面的論述，闡述了Bézier曲線曲面的`原理及其特性，研究Bézier曲線拼接的幾何連續性及參數連續性,總結出G ,G 及C ,C 連續的幾何意義。最後研究了Bézier曲面拼接的幾何連續性。
關鍵詞： C 連續;G 連續;Bernstein基函數;參數連續性;幾何連續性
Abstract
The curve curved surface expression is one of computer graphics important research contents, Bézier the curve curved surface also is in the computer graphics the commonly used curve curved surface, it uses the partition and the lamination parameter multinomial form. Bézier the curve curved surface the reason that by the widespread use is because it has many suits the computer graphics and the computer assistance geometry design characteristic specially.
This article in detail elaborated Bézier the curve definition and the nature, the Bernstein primary function nature in turn, introduced a pair of three Bézier curved surface, the recursion algorithm, the composition law and the application, Bézier curve curved surface splicing. Through to Bézier the curve curved surface elaboration, elaborated Bézier the curve curved surface principle and the characteristic, the research Bézier curve splicing geometry continuity and the parameter continuity,Summarizes G,G and C,C continual geometry significance. Finally has studied Bézier the curved surface splicing geometry continuity.
Key words： C continuity ; G continuity; Bernstein basic function ; parametric continuity ; geometric continuity