Synthesis of Curved Surfaces Using the Parametric B-Spline Tensor Product

Abstract A general, computational geometry design procedure for the synthesis of curved surfaces is presented. The method applies the parametric B-spline (basis spline) tensor product to interpolate prescribed geometrical constraints, even when the set of constraints is sizable. Using the well-developed mathematical tool, B-spline functions, the method is very dependable, versatile, and numerically stable for the design of mechanical parts with complex shapes. Since a curved surface can be represented by a formula of B-spline tensor product, the approach enables the coordinates required for analysis or manufacturing to be easily generated. Typical examples for the synthesis of curved surfaces are given to illustrate the application of the approach.