GENERATING B-SPLINE APPROXIMATIONS OF PDE SURFACES

This paper considers a technique for obtaining B-spline approximations of a surface produced by the PDE surface design method. The motivation of the work was to obtain an approximation to PDE surfaces in a form suitable for data exchange between the majority of CAD/CAM systems. The B-spline approximation achieves this. The PDE method is being developed as a new surface design tool for computer-aided design. A PDE surface is the solution to an elliptic partial differential equation (where differentiation is with respect to parametric coordinates subject to boundary conditions). The B-spline approximation is obtain by solving the boundary value problem using the finite element method, with the basis formed from B-spline functions. The required degree of continuity of the surface can be ensured by the appropriate choice of PDE and B-spline parameters. The resulting solution is in the form of a set of control vertices for the approximating B-spline surface. Modification of these vertices enables hybrid surfaces to be produced. A variety of PDE surfaces have been generated; the examples considered here are blending surfaces.