Practical Integer-Constrained Cone Construction for Conformal Parameterizations.

Area of Science:

• Computer Graphics
• Computational Geometry
• Geometric Modeling

Background:

• Conformal parameterizations are crucial in graphics and geometry processing.
• Constructing parameterizations with sparse integer-constrained cone singularities is a challenging combinatorial problem.
• Existing methods often result in high distortion or an excessive number of singularities.

Purpose of the Study:

• To develop a practical and robust method for generating sparse integer-constrained cone singularities.
• To minimize both the number of cone singularities and the resulting parameterization distortion.
• To provide a state-of-the-art solution for conformal parameterization challenges.

Main Methods:

• A two-stage procedure: 1) enhancing sparsity for initialization, 2) optimizing cone reduction and distortion.
• Progressive determination of combinatorial variables (number, location, angle) in the first stage.
• Adaptive cone relocation and merging in the second stage for iterative optimization.

Main Results:

• The proposed method demonstrates practical robustness and performance across a dataset of 3885 models.
• Achieved a significant reduction in the number of cone singularities compared to prior methods.
• Demonstrated lower parameterization distortion than state-of-the-art techniques.

Conclusions:

• The developed method offers an effective solution for constructing sparse integer-constrained cone singularities.
• It provides a significant improvement in reducing both singularity count and distortion in conformal parameterizations.
• The approach is validated for its practical applicability and superior performance.