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.

介绍了一种新的自我交叉消除算法TransforMesh和基于此算法的网格演化框架，可以处理高度变形的网格表面同时保持其流形性质，解决了传统方法中自交和拓扑变化等问题。

适应拓扑结构的网格变形算法在表面演变、变形和多视图重建中的应用