Smooth Feature Lines on Surface Meshes

-- based on the paper by K. Hildebrandt, K. Polthier and M. Wardetzky

Background

Feature lines on a mesh carry the visually most prominent characteristics of the mesh. This paper introduces a way to detect the feature lines on a mesh based on utilizing discrete differential operators on piecewise linear meshes.

Objective

• Detect “salient ridges” on meshes
• Compute points with extreme principal curvatures
  • Under certain conditions, these form feature curves
  • Checking these conditions requires computing 1st and 2nd derivatives of curvatures

Procedures

• Compute principal curvatures
• Compute discrete extremalities
• Smooth discrete extremalities
• Determine regularity for each triangle
• Trace feature lines in regular triangles
• Process singular triangles

Library used

• Libigl

Results

• Direction of principal curvatures on a half cylinder
• Color map of the extramalities on a bumpy cube
  • e max (absolute values)
  • e min (absolute values)
• Singular triangles on a hand
• Feature lines
  • on a camel head
  • on a bumpy cube
  • on a bumpy plane

Todo

• Remove small ridges by a threshold