A Triangular Mesh Library

PolyMLib™ is a stand-alone, object oriented library that provides a set of objects and corresponding methods to repair, optimize, edit, and analyze triangle mesh models. PolyMLib™ is well suited to post-process triangular meshes emerging from a tessellator or from a 3D scanning process. These meshes often contain topological inconsistencies, geometric artifacts, degenerate triangles, disproportioned triangles, and/or unnecessary complexity. PolyMLib™ can be used to repair, smooth, reduce, and/or optimize surface meshes. This document and this slideshow describe many features found in PolyMLib™. This short video demonstrates some of the editing features of PolyMLib™.

Key Features

  • Mesh Repair – Detect and fix topology inconsistencies, gaps, holes, degenerate triangles, and disproportionate triangles.

  • Mesh Optimization – Smoothing, decimation, and remeshing.

  • Mesh Quality Control – Inspect and compare smoothness and curvature.

  • Shape Editing – Redefine region, modify tangency, deformations.

Summary of Functions

Mesh Repair

• Fix Topology
• Mesh statistics
• Detect/Remove short edges
• Detect/Remove caps (triangles with very large angle)
• Detect/Remove Valence 3 vertices
• Detect/Remove Skinny triangles
• Detect Fold-overs
• Flip orientation
• Snap Boundary

• Manual Fixes
• Delete/Add/Split face
• Delete/Flip/Split edge

• Remove Degeneracy
• Short edges
• Caps
• Valence 3 vertices
• Hole Repair
• Detect
• Fill
• Smoothly interpolate hole boundary
• Avoid self-intersections
• Adapt vertex density to hole boundary
• Construct regular tessellation to fill-in patch

Mesh Optimization

• Smoothing
• Hinged membrane approach (soap film)
• Clamped thin plate approach (avoid high bending)
• Geometric smoothness
• Parametric smoothness

• Decimation
• Distance tolerance
• Normal deviation
• Edge Length
• Aspect Ratio
• Number of triangles

• Re-meshing
• Isotropic
• Target edge length control
• Uniform vertex distribution
• Close to equilateral triangles
• Regular tessellation (mostly valence 6 vertices)

Mesh Quality Control

• Compare
• Distance comparison
• Normal comparison
• Curvature comparison
• Close to equilateral triangles
• Regular tessellation (mostly valence 6 vertices)

• Inspect
• Smoothness
• Reflection Lines
• Realistic Material rendering
• Interactive Slicing
• Curvature
• Minimum and Maximum curvature
• Mean curvature
• Gaussian curvature
• Visualization
• Flat shading
• Gouraud shading
• Phong shading

Shape Editing

• Region Definition
• Define Deformable Area
• Define Handle
• Translate, Rotate, Scale

• Distance Surface Behavior
• Tangent continuity maintained
• Isotropic or Anisotropic deformations
• Maintain small surface detail