Structured Volume Decomposition via Generalized Sweeping.

Area of Science:

• Computer Graphics
• Computational Geometry
• Geometric Modeling

Background:

• Generating high-quality hexahedral meshes from complex 3D models is challenging.
• Existing methods often struggle with feature alignment and T-junctions, complicating downstream applications like data fitting.

Purpose of the Study:

• To introduce a robust volumetric partitioning strategy for seamless decomposition of triangle meshes into deformed cuboids.
• To simplify hexahedral mesh generation and facilitate trivariate B-spline fitting.

Main Methods:

• A generalized sweeping framework guides volume decomposition using a user-defined volumetric harmonic function.
• Skeletal structures are extracted for level sets, aligned with object features, and connected to form a skeletal surface.
• The skeletal surface partitions the volume into T-junction-free deformed cuboids.

Main Results:

• The proposed method successfully partitions various 3D objects into deformed cuboids without T-junctions.
• This decomposition significantly simplifies hexahedral mesh generation and trivariate B-spline fitting.
• Intersections of skeletal surfaces identify singular edges in the resulting hex-meshes.

Conclusions:

• The volumetric partitioning strategy offers an effective approach for hexahedral mesh generation from triangle meshes.
• The T-junction-free cuboid decomposition benefits data fitting applications by providing a structured representation.
• This method enhances the process of converting complex geometric data for simulation and analysis.