相邻的三角域和矩形域上有理Bézier曲面的GC^1连续条件

A Practical Mathematical Method for Ensuring Smooth Connection of Triangular Bézier Surface Patch to Rectangular One

给出了相邻的三角域和矩形域上Bezier曲面的GC^1连续条件,并得到了相邻的三角域和矩形域上有理Bezier曲面的GC^1连续条件.

In CAGD (Computer Aided Geometric Design) of Airplanes, Ships, and Automobiles, the smooth connection between triangular surface patch to rectangular one has always been an important but difficult problem. Farin gave a sufficient condition for smooth connection between triangular Bezier surface patch to rectangular one [1] and it has found application in CAD/ CAM [2]. In his derivation, Farin made use of cross derivatives in boundary, which however are unknown and hard to determine. In this paper, a new straight forward method is proposed. All the numerical constants needed in the authors' sufficient condition are determined mathematically from known conditions. Thus the new method is easy to use in engineering applications. As regards rational Bezier surface, now available methods for smooth connection are, in the authors' opinion, very inconvenient to use in engineering application. In this paper, the authors convert the problem of smooth connection between triangular and rectangular rational Bezier surfaces to that between non-rational ones, thus simplifying greatly the smooth connection between rational Bezier surfaces. Furthermore the authors give the GC^1 continuous condition for connecting smoothly triangular Bezier surface patch to rectangular one. Such a continuous condition is not only simple but also possesses clear geometric meaning; it is convenient for application in CAD / CAM.