Output details

An RBF-Based Reparameterization Method for Constrained Texture Mapping

Originality: Surface parameterisation is a geometric process of unfolding and flattening 3D shapes to make them ease to paint. It is widely utilised in computer aided design, computer graphics and animation, for tasks such as texture mapping. A current research focus is how to unfold shapes while maintaining certain user defined constraints. For example, we may want to prevent an flattened shape from folding over like scrunching paper, or we may want the shape to resemble a particular target shape to make it easy to paint. Our research presents an algorithm that guarantees the removal of undesirable artefacts for texture mapping subject to user-defined constraints.

Rigour: In addition to the mathematical derivation which underpins our technique, we give a proof of the convergence of the algorithm and compare the computational complexity with other approaches. Experiments and analysis also demonstrate the advantages of our algorithm.

Significance: The main contribution is to propose a mathematical condition which guarantees that no foldover occurs in a mesh structure during deformation including animation. The distinct advantage of our method is that there is no post-process necessary, and it makes sure the meshes are sufficiently smooth, i.e. free from unwanted sharp edges and corners. We have successfully applied this technique to the deformation and visualisation of different geometric data.