Texture mapping has long been used in computer graphics to \udenhance the realism of virtual scenes. However, to match the 3D model feature points with the corresponding pixels in a texture image, surface parameterization must satisfy specific positional constraints. However, despite numerous \udresearch efforts, the construction of a mathematically robust, foldover‐free parameterization that is subject to \udpositional constraints continues to be a challenge. In the \udpresent paper, this foldover problem is addressed by developing radial basis function (RBF) based reparameterization. Given initial 2D embedding of a 3D \udsurface, the proposed method can reparameterize 2D embedding into a foldover ‐free 2D mesh, satisfying a set \udof user‐specified constraint points. In addition, this approach is mesh‐free. Therefore, generating smooth texture \udmapping results is possible without extra smoothing optimization.
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