  Triangulated meshes have become ubiquitous discrete-surface representations.
In this paper we address the problem of how to maintain the manifold properties
of a surface while it undergoes strong deformations that may cause topological
changes. We introduce a new self-intersection removal algorithm, TransforMesh,
and we propose a mesh evolution framework based on this algorithm. Numerous
shape modelling applications use surface evolution in order to improve shape
properties, such as appearance or accuracy. Both explicit and implicit
representations can be considered for that purpose. However, explicit mesh
representations, while allowing for accurate surface modelling, suffer from the
inherent difficulty of reliably dealing with self-intersections and topological
changes such as merges and splits. As a consequence, a majority of methods rely
on implicit representations of surfaces, e.g. level-sets, that naturally
overcome these issues. Nevertheless, these methods are based on volumetric
discretizations, which introduce an unwanted precision-complexity trade-off.
The method that we propose handles topological changes in a robust manner and
removes self intersections, thus overcoming the traditional limitations of
mesh-based approaches. To illustrate the effectiveness of TransforMesh, we
describe two challenging applications, namely surface morphing and 3-D
reconstruction.
