Piecewise Surface Flattening for Non - Distorted

This paper introduces new techniques for interactive piecewise at-tening of parametric3-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 diierential 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 rst step towards an eecient and robust CAD tool for shoe modeling.