Analyzing and Improving the Parameterization Quality of Catmull-Clark Solids for Isogeometric Analysis

Area of Science:

• Computer Graphics
• Computational Science
• Geometric Modeling

Background:

• Physically based simulation relies on high-quality models for accurate results and efficient algorithms.
• In isogeometric analysis with spline or subdivision models, parameterization quality is as critical as control mesh geometry.
• Existing methods often overlook parameterization quality, impacting simulation outcomes.

Purpose of the Study:

• To introduce a novel parameterization quality metric specifically for Catmull-Clark (CC) solids.
• To identify and address local distortions and singularities in CC solid parameterizations.
• To improve the quality of simulation models without incurring additional computational expense.

Main Methods:

• Developed a parameterization quality metric based on conformal mapping quality measures.
• Applied the metric to assess the limit volume quality of CC solids.
• Introduced topological operations to resolve identified singularities by splitting boundary cells.

Main Results:

• The proposed metric effectively reveals local distortions and singularities in CC solid parameterizations.
• Topological operations successfully resolved singularities in interactively designed CC solid models.
• Improved parameterization quality led to enhanced simulation results.

Conclusions:

• The new metric provides a robust measure of parameterization quality for CC solids.
• Topological modifications enhance model quality and simulation accuracy without added computational load.
• This work advances the quality and efficiency of physically based simulations using CC solids.