Adaptive reconstruction of free-form surfaces using Bernstein basis function networks

Abstract

Many computer graphics and computer-aided design (CAD) applications require mathematical models to be generated from measured coordinate data. The three-dimensional surface model of a complex object can be created by fitting the data with low-order parametric surface patches, and adjusting the control parameters such that the constituent patches meet seamlessly at their common boundaries. Most neural networks that are designed for function approximation produce a solution that is not easily transferable to CAD software. An adaptive technique to reconstruct a smooth surface from Bézier patches is presented in this paper. The approach utilizes a neural network that performs a weighted summation of Bernstein polynomial basis functions. The number of basis neurons is related to the degree of the Bernstein polynomials and is equivalent to the number of control parameters. Free-form surfaces are reconstructed by simultaneously updating networks that correspond to the separate patches. A smooth transition between adjacent Bézier surface patches is achieved by imposing positional and tangential continuity constraints on the weights during the adaptation process. The final weights of the various networks correspond to the control points of the stitched Bézier surface, and can therefore be used directly in many commercial CAD packages. This method has been used to create a closed surface by adaptively fitting two adjacent patches to synthetic range data and a complex open surface by fitting four patches to experimentally measured range data.