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This article introduces new techniques for non-distorted texture mapping on complex triangulated meshes. Texture coordinates are assigned to the vertices of the triangulation by using an iterative op- timization algorithm, honoring a set of constraints minimizing the distortions. As compared to other global optimization techniques, our method allows the user to specify the surface zones where dis- tortions should be minimized in order of preference. The modular approach described in this paper results in a highly flexible method, facilitating a customized mapping construction. For instance, it is easy to align the texture on the surface with a set of user defined isoparametric curves. Moreover, the mapping can be made con- tinuous through cuts, allowing to parametrize in one go complex cut surfaces. It is easy to specify other constraints to be honored by the so-constructed mappings, as soon as they can be expressed by linear (or linearizable) relations. This method has been inte- grated successfully within a widely used C.A.D. software dedicated to geosciences. In this context, applications of the method com- prise numerical computations of physical properties stored in fine grids within texture space, unfolding geological layers and generat- ing grids that are suitable for finite element analysis. The impact of the method could be also important for 3D paint systems.

Non-distorted texture mapping for sheared triangulated meshes