This paper introduces new techniques for interactive piecewise flattening of parametric 3-D surfaces, leading to a non-distorted, hence realistic, texture mapping. Cuts are allowed on the mapped texture and we make a compromise between discontinuities and distortions. These techniques are based on results from differential geometry, more precisely on the notion of "geodesic curvature": isoparametric curves of the surface are mapped, in a constructive way, onto curves in the texture plane with preservation of geodesic curvature at each point. As an application, we give a concrete example which is a first step towards an efficient and robust CAD tool for shoe modeling.

This paper presents a new method for synthesizing hierarchical textures on 3-D surfaces. This method utilizes both a mapping technique for rendering the macroscopic structure on the surface and a generalization of the direct 3-D microscopic synthesis algorithms (presented in earlier publications) for generating a homogeneous texture inside each pattern. To produce the macroscopic structure on the 3-D shape a new mapping technique is proposed. With this technique patterns distortion is minimized locally. Finally a solution to the aliasing problem adapted to our mapping is given.