Sharpen&Bend: recovering curved sharp edges in triangle meshes produced by feature-insensitive sampling

Area of Science:

• Computer Graphics
• Geometric Modeling
• 3D Shape Analysis

Background:

• Current 3D shape sampling methods often ignore surface features like sharp edges.
• Uniform sampling leads to inaccurate triangle meshes that chamfer features and increase error.
• Existing resampling techniques struggle to preserve geometric fidelity, especially around critical features.

Purpose of the Study:

• To introduce novel postprocessing filters for improving the quality of resampled 3D models.
• To address the limitations of feature-insensitive sampling in 3D shape acquisition and analysis.
• To reduce geometric distortion and enhance feature representation in reconstructed 3D meshes.

Main Methods:

• Developed 'EdgeSharpener' filter to restore sharp edges by re-calculating vertex positions.
• Introduced 'Bender' filter using an interpolating subdivision scheme to refine meshes and smooth curves.
• Combined 'EdgeSharpener' and 'Bender' filters for comprehensive postprocessing (Sharpen&Bend).

Main Results:

• EdgeSharpener alone reduced mean-squared distortion by up to 80% for SwingWrapper compressor output.
• The combined Sharpen&Bend approach further reduced error by an additional 60% for models with curved regions.
• Significant improvements in mesh accuracy and feature preservation were observed compared to standard resampling.

Conclusions:

• The Sharpen&Bend postprocessing effectively mitigates errors introduced by uniform sampling of 3D shapes.
• These filters provide a robust solution for enhancing the quality of 3D models derived from various acquisition methods.
• The proposed methods significantly improve geometric fidelity, particularly for models with sharp and curved features.