Foldover-Free Mesh Warping for Constrained Texture Mapping

Mapping texture onto 3D meshes with positional constraints is a popular technique that can effectively enhance the visual realism of geometric models. Such a process usually requires constructing a valid mesh embedding satisfying a set of positional constraints, which is known to be a challenging problem. This paper presents a novel algorithm for computing a foldover-free piecewise linear mapping with exact positional constraints. The algorithm begins with an unconstrained planar embedding, followed by iterative constrained mesh transformations. At the heart of the algorithm are radial basis function (RBF)-based warping and the longest edge bisection (LEB)-based refinement. A delicate integration of the RBF-based warping and the LEB-based refinement provides a provably-foldover-free, smooth constrained mesh warping, which can handle a large number of constraints and output a visually pleasing mapping result without extra smoothing optimization. The experiments demonstrate the effectiveness of the proposed algorithm.