Bezier Patches with Local Shape Control Parameters

Abstract

In this paper, we introduce three types of shape control parmeters (tension, bias, and continuity) into the modelling of free-form surfaces composed of bicubic Bernstein-Bezier patches. This is an extension to surfaces of the three control parameters introduced in the local interpolatory spline curves by Kochanck and Bartels [12]. We first analyze the general conditions for guaranteeing the G' continuity of the surface at corners where three, four, or five patches meet. The analysis of the continuity constraints reveals the remaining degrees of freedom which can be exploited for the control of the surface shape. The shape control parameters arc then introduced. Experimental results are provided. They show the efficiency of these parameters for an easy and intuitive control of the surface shape.