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:
Add an additional option relativeStoppingTolerance which is used in place of the magic constant 0.01. This is a no-brainer.
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.)
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.
This issue addresses a small road bump with the
remeshfunction, 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
remeshisEven though the quantity
flowDistis 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
maxIterationsoption, since the optimizer will quit as soon asflowDistis less than0.01.Proposed Solution
Three possibilities come to mind:
relativeStoppingTolerancewhich is used in place of the magic constant0.01. This is a no-brainer.minIterationsthat 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.