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Improved non-uniform subdivision scheme with modified Eigen-polyhedron.

Jingjing Zhang¹, Yufeng Tian², Xin Li³

¹School of Mathematical Sciences, Anhui University, Hefei, 230601, Anhui, China.

Visual Computing for Industry, Biomedicine, and Art

|July 12, 2022

Summary

This study introduces a new refinement method for non-uniform Catmull-Clark subdivision surfaces. It enhances surface quality at extraordinary points (EPs) using a modified eigenpolyhedron approach.

Keywords:

Eigen polyhedron Non-uniform Catmull-Clark surface Subdivision surface

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Area of Science:

Computer Graphics
Geometric Modeling
Surface Parameterization

Background:

Catmull-Clark subdivision surfaces are widely used in computer graphics for creating smooth surfaces.
Non-uniform parameterization and extraordinary points (EPs) pose challenges to surface quality.
Existing methods often struggle to maintain high-quality surfaces at EPs under non-uniform conditions.

Purpose of the Study:

To develop a systematic refinement method for non-uniform Catmull-Clark subdivision surfaces.
To specifically address and improve surface quality at extraordinary points (EPs).
To enhance the performance and robustness of subdivision surfaces in non-uniform parameterization scenarios.

Main Methods:

A novel systematic refinement method was developed.
The core of the method involves modifying the eigenpolyhedron.
Specific focus was placed on designing angles between adjacent edges containing an EP.
Refinement rules were formulated based on the modified eigenpolyhedron.

Main Results:

The developed method significantly improves the quality of subdivision surfaces at EPs.
Numerical experiments demonstrated enhanced performance for non-uniform parameterization.
The approach effectively handles the complexities introduced by non-uniformity and EPs.

Conclusions:

The proposed refinement method offers a robust solution for improving non-uniform Catmull-Clark subdivision surfaces.
It provides better control and quality at extraordinary points.
This advancement is beneficial for applications requiring high-fidelity surface modeling.