Bezier曲線(xiàn)曲面的拼接

Bezier曲線(xiàn)曲面的拼接

摘要

曲線(xiàn)曲面的表示是計(jì)算機(jī)圖形學(xué)的重要研究?jī)?nèi)容之1，Bézier曲線(xiàn)曲面又是計(jì)算機(jī)圖形學(xué)中常用的曲線(xiàn)曲面，它采用分段和分片參數(shù)多項(xiàng)式的形式。Bézier曲線(xiàn)曲面之所以被廣泛使用是因?yàn)樗�有許多特別適合計(jì)算機(jī)圖形學(xué)和計(jì)算機(jī)輔助幾何設(shè)計(jì)的特點(diǎn)。
本文依次詳細(xì)論述了Bézier曲線(xiàn)的定義和性質(zhì)、Bernstein基函數(shù)性質(zhì)、介紹了雙3次Bézier曲面、遞推算法、構(gòu)圖法及其應(yīng)用、Bézier曲線(xiàn)曲面的拼接。通過(guò)對(duì)Bézier曲線(xiàn)曲面的論述，闡述了Bézier曲線(xiàn)曲面的原理及其特性，研究Bézier曲線(xiàn)拼接的幾何連續(xù)性及參數(shù)連續(xù)性,總結(jié)出G ,G 及C ,C 連續(xù)的幾何意義。最后研究了Bézier曲面拼接的幾何連續(xù)性。
關(guān)鍵詞： C 連續(xù);G 連續(xù);Bernstein基函數(shù);參數(shù)連續(xù)性;幾何連續(xù)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

 

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