Progressive Conversion from B-rep to BSP for Streaming Geometric Modeling.

Area of Science:

• Computer-Aided Design (CAD)
• Computational Geometry
• Geometric Modeling

Background:

• Boundary representations (B-rep) are standard for 3D models.
• Generating Binary Space Partition (BSP) trees and cell decompositions from B-rep is computationally intensive.
• Progressive Level of Detail (LOD) generation is crucial for efficient visualization and design.

Purpose of the Study:

• To introduce a novel progressive approach for generating BSP trees and convex cell decomposition from B-rep.
• To enable the generation of solid models at progressive levels of detail.
• To integrate these processes within a streaming computational framework for real-time performance.

Main Methods:

• Utilized fast calculation of surface inertia for BSP tree and cell decomposition generation.
• Employed a variation of standard BSP tree generation with "in, out, and fuzzy" cell labeling.
• Integrated the algorithm into a streaming computational framework with four dataflow process types.
• Incorporated diverse geometric modeling techniques, including polygonal, spline, solid, and heterogeneous modeling.

Main Results:

• Successfully generated BSP trees and convex cell decompositions for arbitrary B-rep inputs.
• Achieved real-time B-rep to BSP streaming, demonstrating significant performance improvements.
• Produced solid models at progressive levels of detail.
• Demonstrated the comprehensive representation of solids as Hasse diagrams of cell complexes.

Conclusions:

• The novel progressive approach offers a significant advancement in geometric modeling.
• The streaming framework facilitates the unification of rapid conceptual and detailed shape design.
• This method paves the way for more efficient and integrated CAD workflows.