(quad_as_tri)=

# Quad as triangles

A contour line within a quad is, by default, a straight line between points on two of its edges.
The `quad_as_tri` option divides each quad into four triangles using a virtual point at the
centre (mean x, y of the corner points) and extra contour points are inserted where the contour
level intersects the diagonals so that contour lines are piecewise linear within the triangles.

The `z` value of the central point is calculated depending on the {ref}`z_interp` setting; for
the default `z_interp=ZInterp.Linear` this is the mean of the `z` values of the corner points.
Corner masked triangles are not affected by this setting, only full unmasked quads.

```{name_supports}
:filter: quad_as_tri
```

`quad_as_tri` is available for the {ref}`serial` and {ref}`threaded` algorithms.  It is always
disabled by default, so if required it must be explicitly requested:

```python
>>> cont_gen = contour_generator(quad_as_tri=True, ...)
```

```{note}
   `quad_as_tri` produces more detailed contours, but not necessarily smoother ones.
```

Here is an example of the difference between `quad_as_tri=False` and `True` for `z` values on
a coarse grid that are given by `z = np.sqrt(x**2 + y**2)`. On a finer grid the contours would be
semicircular.

```{plot}
:separate-modes:
:source-position: below

from contourpy import contour_generator
from contourpy.util.mpl_renderer import MplRenderer as Renderer
import numpy as np

x, y = np.meshgrid([-2, -1, 0, 1, 2], [0, 1, 2])
z = np.sqrt(x**2 + y**2)

renderer = Renderer(ncols=2, figsize=(8, 2.4))
for ax in range(2):
   quad_as_tri = bool(ax)
   renderer.grid(x, y, ax=ax, color="gray", alpha=0.2, quad_as_tri_alpha=ax*0.1)
   renderer.title(f"quad_as_tri={quad_as_tri}", ax=ax)

   cont_gen = contour_generator(x, y, z, quad_as_tri=quad_as_tri)
   multi_lines = cont_gen.multi_lines(np.arange(0.5, 2.51, 0.5))
   renderer.multi_lines(multi_lines, cont_gen.line_type, ax=ax, linewidth=2)

   renderer.z_values(x, y, z, ax=ax, quad_as_tri=quad_as_tri, fmt="0.2f")

renderer.show()
```

Another situation in which `quad_as_tri` may be useful is shown below. The quad has three corners
at the same `z` level so without `quad_as_tri` contour lines cut across diagonally.

```{plot}
:separate-modes:
:source-position: below

from contourpy import contour_generator
from contourpy.util.mpl_renderer import MplRenderer as Renderer
import numpy as np

x = y = [0, 1]
z = [[0, 0], [0, 4]]

renderer = Renderer(ncols=2, figsize=(6, 3))
for ax in range(2):
   quad_as_tri = bool(ax)
   renderer.grid(x, y, ax=ax, color="gray", alpha=0.2, quad_as_tri_alpha=ax*0.1)
   renderer.title(f"quad_as_tri={quad_as_tri}", ax=ax)

   cont_gen = contour_generator(x, y, z, quad_as_tri=quad_as_tri)
   multi_lines = cont_gen.multi_lines(np.arange(0.0, 4.0, 0.4))
   renderer.multi_lines(multi_lines, cont_gen.line_type, ax=ax, linewidth=2)

   renderer.z_values(x, y, z, ax=ax, quad_as_tri=quad_as_tri)

renderer.show()
```

```{note}
   `quad_as_tri=True` produces contour lines and filled contours typically containing about three
   times as many points as `quad_as_tri=False`.
```