Curvature-dependent parameterization of curves and surfaces (Q1181948)

The rendering of curves and surfaces is one of the main problems in computer-aided design. An efficient way of drawing parametric curves and surfaces is to approximate the curve or the surface by a sequence of straight-line segments or a mesh of polygons. In such an approximation many small line segments or polygons are needed in regions of high curvature and fewer and larger ones are needed in regions of low curvature. The main result given in this paper is the translation of this intuitive criterion into a formal one. Special parameterizations, called angle parameterizations, are defined such that good approximations can be found by uniformly subdividing the parameter space. These parameterizations are easily computed numerically and the algorithm for surfaces is suitable for parallel processing.