Least distorted bump mapping onto surface patches

Abstract

When rendering a point on a textured surface, the parameters of the surface are normally used to index the texture table in order to determine the texture of the point being rendered. This approach, however, frequently leads to an undesirable texture distortion. This is because that as the surface is normally divided in equiparametric surface patches for rendering, the curve lengths and areas of these patches are inevitably not equal. A great deal of research effort has recently been expended in the ordinary colour texture mapping which has made minimization of this texture distortion possible. In bump mapping, however, the methods derived for ordinary texture mapping can not be trivially applied, as it is subject to more geometric constraints and complexity. Thus texture distortion, in bump mapping, is still an unsolved problem. This paper introduces a new approach which achieves the least texture distortion in bump mapping for a free form surface patch. This is done by two steps: establishing a mapping between the parameter space and texture space using techniques of surface development; and texturing by reparameterizing the bump mapping function using the mapping established at the first step. The proposed method can reduce the texture distortion of bump mapping as much as that of ordinary texture mapping achieved by the most effective least distorted texture mapping methods reported in the literature.