Analytical C smooth blending surfaces

Two factors are important in the generation of blending surfaces for interactive graphical and CAD applications, computational speed and the degree of smoothness. Most surface-blending methods blend surfaces with tangent continuity. However, curvature continuity has recently become increasingly important in various applications. In this paper, we present a method that is able to achieve curvature continuity based on the use of partial differential equations (PDE). The blending surfaces are generated as the solution to a sixth-order PDE with one vector-valued parameter. To achieve interactive performance, we propose an effective analytical method for the resolution of this sixth-order PDE.