Rapid generation of C2 continuous blending surfaces

Abstract

Most surface-blending methods are able to blend surfaces with tangent continuity. However, curvature continuity has become increasingly important in geometric modelling and its applications, such as computer animation, computer-aided design and virtual reality. In this paper, we present a method which is able to achieve C2 continuity based on the use of partial differential equations (PDE). A sixth order partial differential equation with one vector-valued parameter is introduced to produce such blending surfaces. Since computational efficiency is crucial for interactive computer graphics applications, we have developed a unified closed form (analytical) method for the resolution of this sixth order PDE. Therefore blending surfaces of up to C2 smoothness can be generated in real time. © Springer-Verlag Berlin Heidelberg 2002.