Weighted Squared Volume Minimization (WSVM) for Generating Uniform Tetrahedral Meshes.

Area of Science:

• Computational geometry
• Computer graphics
• Scientific visualization

Background:

• Generating high-quality tetrahedral meshes is crucial for various scientific and engineering simulations.
• Existing methods often struggle with mesh uniformity and sliver elements, impacting simulation accuracy.
• Automated, parameter-free meshing algorithms are highly desirable.

Purpose of the Study:

• To introduce a novel algorithm, Weighted Squared Volume Minimization (WSVM), for generating high-quality tetrahedral meshes from closed triangle meshes.
• To achieve uniform element volumes and dihedral angles within the generated tetrahedral mesh.
• To provide a fully automatic and parameter-free meshing solution.

Main Methods:

• WSVM utilizes a new energy function based on weighted squared volumes of tetrahedral elements.
• The algorithm iteratively minimizes volume-oriented and dihedral angle-oriented energies.
• Mesh connectivity is refined by alternating vertex position optimization and iterative refinement.

Main Results:

• WSVM consistently produces tetrahedral meshes with enhanced uniformity compared to existing methods.
• The algorithm effectively reduces the occurrence of sliver elements in the generated meshes.
• Evaluations on diverse 3D models confirm the high quality of WSVM-generated meshes.

Conclusions:

• Weighted Squared Volume Minimization (WSVM) offers a robust and automated approach for high-quality tetrahedral mesh generation.
• The method's ability to control both element volume and dihedral angles leads to superior mesh quality.
• WSVM presents a significant advancement for applications requiring accurate and efficient tetrahedral meshes.