Iterative Smoothing of Curves and Surfaces

Abstract

Algorithms for drawing smooth curves and surfaces are well-known but may be too expensive in CPU time to use for certain high speed interactive graphics applications. This paper looks at some new geometrically-based smoothing algorithms that arrive at the final smooth curve or surface after the application of an infinite number of iterations of the algorithm using subdivision refinement. When CPU time is scarce low iteration counts can be used to provide an acceptable level of approximation of smoothness and when CPU time is more plentiful higher levels of iteration can be applied for greater visual smoothing accuracy. Three new algorithms are presented and analysed. Convergence is proved geometrically for each and their timings are reported. Mixing iterations provides new opportunities for achieving various different effects in curve and surface smoothing.