Numerical methods of generating random points with prescribed distributional properties on (non)rational bezier surfaces

Different numerical methods to produce nonrational and rational Bezier curves and surfaces are described. With the introduction of marginal and conditional density functions, a sequence of random numbers with a given density function in 2-D cases can be sampled by the inverse method. Consequently, the generation of random points on a (non)rational Bezier surface with a prescribed distributional density function denned on the parametric space or the real space can be transformed to 2-D random variable simulation according to the parametric form of a Bezier surface. By the establishment of a probability table, the efficiency of the algorithms developed is considerably increased. Numerical examples illustrate the computing results.