Parametric Surfaces with Displacement and Deformation

Parametric surfaces are widely used for modeling in CAD systems. However, they pose problems when representing complex macrogeometric features. In order to solve these problems we introduce an extension to parametric surface models that incorporates displacements and deformations. Our extended model retains its original parametric properties, thus allowing easy texture mapping together with a better macrogeometric representation. We allow both two-dimensional and three-dimensional functions to generate displacements that can be applied along directions different from the normal, allowing a continuous level of detail variation, as a function of distance to the viewer. Additionally, we compute deformations using geometric transformations that produce global effects on an entire object. We present object-space algorithms that allow direct rendering of the parametric surfaces without conversion to polygonal approximation, and smooth transitions between bump rendering algorithms. Our paper includes applications of our method to tree modeling and ceramic tile design.