Robust Coarse Cage Construction With Small Approximation Errors.

Area of Science:

• Computer Graphics
• Computational Geometry
• Geometric Modeling

Background:

• Constructing accurate and robust manifold cages for 3D triangular meshes is a challenging problem in computer graphics.
• Existing methods often struggle with robustness, self-intersections, and maintaining tightness while enclosing complex geometries.

Purpose of the Study:

• To propose a novel, robust, and automatic method for generating manifold cages for 3D triangular meshes.
• To ensure generated cages tightly enclose input meshes without self-intersections.
• To enhance the robustness and performance of cage generation algorithms.

Main Methods:

• The algorithm employs a two-phase approach: constructing initial manifold cages and then reducing mesh complexity.
• Phase 1 combines conformal tetrahedral meshing and tetrahedral mesh subdivision to satisfy tightness, enclosure, and intersection-free requirements.
• Phase 2 utilizes constrained remeshing with explicit checks, employing a hybrid coordinate representation (rational and floating-point numbers) with exact arithmetic and filtering for robustness.

Main Results:

• The method successfully generates manifold cages that tightly enclose 3D triangular meshes without self-intersections.
• Extensive testing on over 8500 models demonstrated the method's robustness and performance.
• The proposed technique exhibits significantly stronger robustness compared to existing state-of-the-art methods.

Conclusions:

• The developed method provides a robust and automatic solution for constructing manifold cages for 3D triangular meshes.
• The combination of advanced meshing techniques and robust geometric predicates ensures reliable cage generation.
• This approach advances the state-of-the-art in geometric modeling and mesh processing.