Tekigo terminology

The metric

As the meshing is ultimately performed by MMG, the inputs need to be tailored to its needs. A “future edge size” field is what MMG bases its refinement on. HIP relies instead on a parameter called the metric which is more intuitive than the latter field and internally generates the “correct” input for MMG. Similar to any other field variable, the metric (and also the future edge size ) has a value assigned to each mesh node. Requirements are that

• the metric values have to be ∈ [0.5, 4] with

  • < 1: refine

  • = 1: do nothing

  • > 1: coarsen

• and where

  • 0.5: implies that the target edge length will be half of the current one

  • 4: implies that the target edge length will be 4 times larger that the current one

MMG cannot guarantee that nodes with a metric value of 1 assigned to them will not be affected by the refinement, as multiple parameters come into play. The same comment is valid for other values. The refinement procedure tries to comply as much as possible with the metric field values.

The criterion

Tekigo also works with the concept of a criterion (or criteria), and is relevant to the indirect adaptation introduced further below. Similarly to the metric, it is a field variable with a value assigned to each node.

• A criterion has to be ∈ [-1, - 1] with

  • 1: maximum refinement

  • 0: do nothing

  • -1: maximum coarsening

Through the intermediary of the calibrate_metric() function, a criterion is converted into a metric, complying with the previously mentioned requirements, as to enable the use of MMG.

A criterion can best be understood as being a mask, where one specifies whether one wishes to refine, coarsen or do nothing. The amount of refinement is then controlled by the mixing of the criteria.