Optimal Adaptive Polygonal Approximation of Parametric Surfaces

. We present a new method for adaptive polygonization of parametric surfaces. The method combines recursive simplicial subdivision of the domain and point sampling along curves on the surface. We avoid cracks in the polygonal mesh by determining the optimal sampling rate along the edges of a cell before subdividing it. The method is suitable for surfaces with low variations, such as bicubic patches, as well as for surfaces with high variations, such as height fields. 1 Introduction The polygonization of parametric surfaces is a classical problem in computer graphics and geometric modeling that has many practical applications. The problem is computing a piecewise linear approximation for a continuous surface described by parametric functions. A polygonal approximation is the simplest form of surface description and therefore is the representation of choice in the implementation of a large number of algorithms. Moreover, existing graphics hardware and libraries have special support for ..