An Augmented Lagrangian Method for Locally Injective Mapping

The generation of piecewise linear maps has received a lot of attention from the scientific community. In particular, locally injective maps are very important in many fields, from geometry processing and shape modelling to computer games and movies. We propose a mesh-based method for computing positionally constrained piece-wise linear maps which are locally injective and have low distortion. The main advantage of our approach is that it can recover both from violations of positional constraints as well as from violations of the injectivity constraints. This flexibility makes it suitable for difficult problems where other state-of-the-art methods fail. Our method is very general and can be used to augment any existing mapping algorithm to enforce local injectivity.