Bezier曲线曲面的拼接

Bezier曲线曲面的拼接

摘要

曲线曲面的表示是计算机图形学的重要研究内容之1，Bézier曲线曲面又是计算机图形学中常用的曲线曲面，它采用分段和分片参数多项式的形式。Bézier曲线曲面之所以被广泛使用是因为它有许多特别适合计算机图形学和计算机辅助几何设计的特点。

本文依次详细论述了Bézier曲线的定义和性质、Bernstein基函数性质、介绍了双3次Bézier曲面、递推算法、构图法及其应用、Bézier曲线曲面的拼接。通过对Bézier曲线曲面的论述，阐述了Bézier曲线曲面的原理及其特性，研究Bézier曲线拼接的几何连续性及参数连续性,总结出G ,G 及C ,C 连续的几何意义。最后研究了Bézier曲面拼接的几何连续性。

关键词： C 连续;G 连续;Bernstein基函数;参数连续性;几何连续性

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