Quality Mesh Smoothing via Local Surface Fitting and Optimum Projection.

Area of Science:

• Computer Graphics
• Computational Geometry
• Scientific Visualization

Background:

• Surface mesh quality is critical for applications like visualization and numerical simulation.
• Existing methods often focus on either smoothness or angle quality, but not both.
• Noise and poor angle quality in meshes hinder downstream processing accuracy.

Purpose of the Study:

• To present a novel surface mesh processing method that simultaneously reduces noise and improves angle quality.
• To enhance the overall
• goodness
• of surface meshes for various computational tasks.

Main Methods:

• Local surface fitting around each vertex using least squares minimization.
• Determining the new vertex position via the maximum inscribed circle (MIC) of the surrounding polygon.
• Projecting the MIC center onto the analytically fitted surface iteratively until convergence.

Main Results:

• Significant improvement in mesh smoothness through combined surface fitting and projection.
• Enhanced angle quality achieved by the MIC-based projection scheme.
• Demonstrated effectiveness across diverse geometric mesh models.

Conclusions:

• The proposed method offers a robust solution for improving both mesh smoothness and angle quality.
• This technique is valuable for applications requiring high-fidelity geometric representations.
• The novel approach provides a unified strategy for comprehensive surface mesh enhancement.