Skeleton-Based Parametric 2-D Region Representation: Disk B-Spline Curves.

Area of Science:

• Computer Graphics
• Geometric Modeling
• Computational Geometry

Background:

• The skeleton (medial axis) is a crucial feature for understanding 2-D shapes.
• Existing shape representations often lack explicit skeleton information.
• Disk B-spline curves (DBSCs) are a skeleton-based parametric freeform 2-D region representation.

Purpose of the Study:

• To thoroughly investigate the fundamental theory and algorithms of DBSCs.
• To derive explicit evaluation and derivative formulas for DBSC-represented 2-D regions.
• To introduce methods for modeling and interactive design of heterogeneous objects using DBSCs.

Main Methods:

• Derivation of explicit evaluation and derivative formulas for DBSC regions.
• Application of the de Boor algorithm to DBSCs.
• Development of modeling and interactive design techniques for heterogeneous objects.

Main Results:

• Explicit formulas for evaluating points and derivatives within DBSC regions.
• A method for representing heterogeneous materials within DBSC regions.
• Introduction of interactive design tools for DBSC-based objects.

Conclusions:

• DBSCs provide a robust framework for representing 2-D regions with explicit skeleton information.
• The derived formulas and design methods consolidate DBSC theory and enable new applications.
• This work supports advanced uses in animation, simulation, error estimation, and heterogeneous object design.