Improve stopping conditions in surface meshing (and throughout GC)

Open
#141 0 comments 0 reactions 1 assignee View on GitHub

@MarkGillespie is already working on this.

Since Jan 21, 2023.

Assessment

This issue has not been assessed yet.

Description

design-decision

This issue addresses a small road bump with the remesh function, but is more generally something good to think about throughout the design of GC: how should stopping criteria be determined, and what control should be provided to the user?

Issue

Currently the stopping condition in remesh is

    if ((nFlips == 0) && (flowDist < 0.01)) break;

Even though the quantity flowDist is normalized by the number of mesh vertices, the constant (0.01) is pretty arbitrary and often does not yield the desired/expected behavior.

Especially annoying is that one can't get more smoothing by increasing the maxIterations option, since the optimizer will quit as soon as flowDist is less than 0.01.

Proposed Solution

Three possibilities come to mind:

  1. Add an additional option relativeStoppingTolerance which is used in place of the magic constant 0.01. This is a no-brainer.
  2. Measure the relative norm of the gradient. This requires us to assign a variational interpretation to the smoothing operations, but that seems reasonably straightforward: Laplacian smoothing is minimizing Dirichlet energy, restricted to tangential motions; circumcentric smoothing is likewise minimizing the optimal Delaunay energy among tangential motions. (I believe de Goes et al discuss how to think about ODT in terms of energy minimization in the non-flat case.)
  3. Add an additional option minIterations that forces the optimizer to take at least this many iterations. In general, such a parameter is good to have: no matter how careful you are with designing stopping criteria, there tend to be cases where this automatic condition stopped to early—or at very least, the user would like to see what happens if you "just keep on going." For instance, in the remeshing case, it's clear just from looking at the output meshes that they are not always as smooth/regular as they could be.
Dominant language
C++
Stars
1.3k
Forks
183
No merged PRs in 30d

Contributor guide

No contributing guide indexed for this repository

First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

More from nmwsharp/geometry-central

All issues in nmwsharp/geometry-central

Similar issues

More C++ issues

Get new issues in your inbox

A short digest of beginner-friendly GitHub issues.