“Constrained texture mapping for polygonal meshes” by Levy

Recently, time and effort have been devoted to automatic texture mapping. It is possible to study the parameterization function and to describe the texture mapping process in terms of a functional optimization problem. Several methods of this type have been proposed to minimize deformations. However, these existing methods suffer from several limitations. For instance, it is difficult to put details of the texture in correspondence with features of the model, since most of the existing methods can only constrain iso-parametric curves.
We introduce in this paper a new optimization-based method for parameterizing polygonal meshes with minimum deformations, while enabling the user to interactively define and edit a set of constraints. Each user-defined constraint consists of a relation linking a 3D point picked on the surface and a 2D point of the texture. Moreover, the non-deformation criterion introduced here can act as an extrapolator, thus making it unnecessary to constrain the border of the surface, in contrast with classic methods. To minimize the criterion, a conjugate gradient algorithm is combined with a compressed representation of sparse matrices, making it possible to achieve a fast convergence.

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