Texture Mapping Functions and Surface Flattening.

摘要

Surface flattening stands for spreading a curved surface onto a plane with minimal distortion. Applications of surface flattening include cartography, ship building, shoe manufacturing, among many others. The paper considers in particular the use of surface flattening in texture mapping for computer graphics. The texture mapping functions presented in Section 3 provide simple means to reduce undesired texture distortion in rendering parametric surfaces. To the authors' knowledge, no previous literature exists on the subject. Instead of applying no texture mapping function at all (here called uniform rectangle mapping), as seems to be the general practice, the adaptive rectangle function provides a much better default for parametric surface visualization. The surface flattening method described in Section 4 gives very good results for optimally minimizing the texturing distortion. The method is fast, flexible, and easy to use. The only required parameter is the area-distance weighting factor applied with the flatness norm, which allows the flattening to be tuned according to requirements of the application. The presented norm produces superior results compared to other norms the authors have tested. Finally, they believe the results are not restricted only to computer graphics but they apply equally well to many other surface flattening tasks.