Globally optimal direction fields energy

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Assessment

Difficulty
5/5
Estimated time
Over a week
Newbie friendliness
35/100
Issue type
Bug
Clarity
Mostly clear
Activity status
Stale
Tech stack
cpp
Domain
computer-graphics

Research direction

Read the smoothest vertex direction fields algorithms documentation and the Globally Optimal Direction Fields paper, especially the FEM energy in Eqn 18. Compare that formulation with the current connection-Laplacian approach, then validate the proper energy using a curvature-aligned cross field on a uniform sphere.

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Description

good first issue

Currently, the smoothest vertex direction fields algorithms do not precisely implement the energy from the Globally Optimal Direction Fields paper; they use a slightly different, simpler algorithm.

The Globally Optimal Direction Fields paper carefully derives a FEM expression which incorporates curvature (Eqn 18). The geometry-central implementation instead just uses a simple connection Laplacian which does not really incorporate curvature properly. This is mostly fine most of the time, but some examples expose the distinction. For instance, try computing a curvature-aligned cross field on a uniform sphere.

Fix: implement the proper energy.

Dominant language
C++
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