Topology-adaptive mesh deformation for surface evolution, morphing, and multiview reconstruction.

Area of Science:

• Computer Graphics
• Computational Geometry
• Geometric Modeling

Background:

• Triangulated meshes are standard for discrete surface representation.
• Deforming meshes can lead to self-intersections and topological changes (merges/splits).
• Existing methods often rely on implicit representations (e.g., level sets), trading precision for complexity.

Purpose of the Study:

• To develop a robust mesh evolution framework that maintains manifold properties under strong deformations.
• To introduce a novel self-intersection removal algorithm for explicit mesh representations.
• To overcome limitations of traditional mesh-based approaches in handling topological changes.

Main Methods:

• A new self-intersection removal algorithm named TransforMesh is introduced.
• A mesh evolution framework is proposed, built upon the TransforMesh algorithm.
• The method is designed to handle topological changes and remove self-intersections in triangulated surfaces.

Main Results:

• TransforMesh effectively removes self-intersections in deforming meshes.
• The proposed framework robustly manages topological changes, maintaining surface manifold properties.
• Demonstrated effectiveness in challenging applications like surface morphing and 3D reconstruction.

Conclusions:

• The TransforMesh algorithm and framework provide a robust solution for mesh evolution with topological changes.
• This approach overcomes the limitations of traditional explicit mesh representations.
• Enables accurate and complex shape modeling without the precision-complexity trade-off of implicit methods.