LEAST DISTORTED PUMP MAPPING ONTO SURFACE PATCHES

When rendering a point on a textured surface, the parameters of the su rface are normally used to index the texture table in order to determi ne the texture of the point being rendered. This approach, however, fr equently leads to an undesirable texture distortion. This is because t hat as the surface is normally divided in equiparametric surface patch es for rendering, the curve lengths and areas of these patches are ine vitably not equal. A great deal of research effort has recently been e xpended in the ordinary colour texture mapping which has made minimiza tion of this texture distortion possible. In bump mapping, however, th e methods derived for ordinary texture mapping can not be trivially ap plied. 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 textur e distortion in bump mapping for a free form surface patch. This is do ne by two steps: establishing a mapping between the parameter space an d texture space using techniques of surface development: and texturing by reparameterizing the bump mapping function using the mapping estab lished at the first step. The proposed method can reduce the texture d istortion 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. (C) 1998 Elsevier Science Ltd. All rights reserved.