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Tools for triangular grids.
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Define basic tools for triangular mesh analysis and improvement.
A TriAnalyzer encapsulates a `.Triangulation` object and provides basic
tools for mesh analysis and mesh improvement.
Attributes
----------
scale_factors
Parameters
----------
triangulation : `~matplotlib.tri.Triangulation`
The encapsulated triangulation to analyze.
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Factors to rescale the triangulation into a unit square.
Returns
-------
(float, float)
Scaling factors (kx, ky) so that the triangulation
``[triangulation.x * kx, triangulation.y * ky]``
fits exactly inside a unit square.
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Return a measure of the triangulation triangles flatness.
The ratio of the incircle radius over the circumcircle radius is a
widely used indicator of a triangle flatness.
It is always ``<= 0.5`` and ``== 0.5`` only for equilateral
triangles. Circle ratios below 0.01 denote very flat triangles.
To avoid unduly low values due to a difference of scale between the 2
axis, the triangular mesh can first be rescaled to fit inside a unit
square with `scale_factors` (Only if *rescale* is True, which is
its default value).
Parameters
----------
rescale : bool, default: True
If True, internally rescale (based on `scale_factors`), so that the
(unmasked) triangles fit exactly inside a unit square mesh.
Returns
-------
masked array
Ratio of the incircle radius over the circumcircle radius, for
each 'rescaled' triangle of the encapsulated triangulation.
Values corresponding to masked triangles are masked out.
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Eliminate excessively flat border triangles from the triangulation.
Returns a mask *new_mask* which allows to clean the encapsulated
triangulation from its border-located flat triangles
(according to their :meth:`circle_ratios`).
This mask is meant to be subsequently applied to the triangulation
using `.Triangulation.set_mask`.
*new_mask* is an extension of the initial triangulation mask
in the sense that an initially masked triangle will remain masked.
The *new_mask* array is computed recursively; at each step flat
triangles are removed only if they share a side with the current mesh
border. Thus no new holes in the triangulated domain will be created.
Parameters
----------
min_circle_ratio : float, default: 0.01
Border triangles with incircle/circumcircle radii ratio r/R will
be removed if r/R < *min_circle_ratio*.
rescale : bool, default: True
If True, first, internally rescale (based on `scale_factors`) so
that the (unmasked) triangles fit exactly inside a unit square
mesh. This rescaling accounts for the difference of scale which
might exist between the 2 axis.
Returns
-------
array of bool
Mask to apply to encapsulated triangulation.
All the initially masked triangles remain masked in the
*new_mask*.
Notes
-----
The rationale behind this function is that a Delaunay
triangulation - of an unstructured set of points - sometimes contains
almost flat triangles at its border, leading to artifacts in plots
(especially for high-resolution contouring).
Masked with computed *new_mask*, the encapsulated
triangulation would contain no more unmasked border triangles
with a circle ratio below *min_circle_ratio*, thus improving the
mesh quality for subsequent plots or interpolation.
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Compress (if masked) the encapsulated triangulation.
Returns minimal-length triangles array (*compressed_triangles*) and
coordinates arrays (*compressed_x*, *compressed_y*) that can still
describe the unmasked triangles of the encapsulated triangulation.
Returns
-------
compressed_triangles : array-like
the returned compressed triangulation triangles
compressed_x : array-like
the returned compressed triangulation 1st coordinate
compressed_y : array-like
the returned compressed triangulation 2nd coordinate
tri_renum : int array
renumbering table to translate the triangle numbers from the
encapsulated triangulation into the new (compressed) renumbering.
-1 for masked triangles (deleted from *compressed_triangles*).
node_renum : int array
renumbering table to translate the point numbers from the
encapsulated triangulation into the new (compressed) renumbering.
-1 for unused points (i.e. those deleted from *compressed_x* and
*compressed_y*).
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Parameters
----------
valid : 1D bool array
Validity mask.
Returns
-------
int array
Array so that (`valid_array` being a compressed array
based on a `masked_array` with mask ~*valid*):
- For all i with valid[i] = True:
valid_array[renum[i]] = masked_array[i]
- For all i with valid[i] = False:
renum[i] = -1 (invalid value)
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