z interpolation#
Interpolation of z
values occurs in two situations:
When calculating how far along the edge of a quad (or corner-masked corner) a contour line intersects it.
When calculating the
z
value of the central point of quad. This is needed for all quads ifquad_as_tri=True
or just saddle quads ifquad_as_tri=False
(see Algorithm description about saddle quads).
The default for all algorithms is linear z-interpolation, but serial
and threaded
support
the use of a ZInterp
enum that contains other possibilities.
mpl2005 |
mpl2014 |
serial |
threaded |
|
---|---|---|---|---|
supports_z_interp |
Yes |
Yes |
Note
Currently the only members of ZInterp
are ZInterp.Linear
and
ZInterp.Log
.
To use alternative z-interpolation, pass the z_interp
keyword argument to
contour_generator()
. A string name can be used instead of the enum member so the
following are equivalent:
>>> contour_generator(z_interp="Log", ...)
>>> contour_generator(z_interp=ZInterp.Log, ...)
When might logarithmic z-interpolation be appropriate? When contour levels are exponentially distributed, as exponential and logarithm are inverse transforms.
The example below has a coarse rotated grid where z = np.exp(6*y)
and the contour levels
[0.3, 1, 3, 10, 30, 100]
increase exponentially. Using linear z-interpolation the contour lines
are jagged, using logarithmic z-interpolation the contour lines are straight and at constant y
,
as expected.
from contourpy import contour_generator, ZInterp
from contourpy.util.mpl_renderer import MplRenderer as Renderer
import numpy as np
n = 4
angle = 0.4 # Radians.
# Rotated grid.
x, y = np.meshgrid(np.linspace(0.0, 1.0, n), np.linspace(0.0, 1.0, n))
rot = [[np.cos(angle), np.sin(angle)], [-np.sin(angle), np.cos(angle)]]
x, y = np.einsum('ji,mni->jmn', rot, np.dstack([x, y]))
# z is exponential in y.
z = np.exp(6*y)
levels = [0.3, 1, 3, 10, 30, 100]
renderer = Renderer(ncols=2, figsize=(8, 4))
for ax, z_interp in enumerate([ZInterp.Linear, ZInterp.Log]):
renderer.grid(x, y, ax=ax, color="gray", alpha=0.2)
cont_gen = contour_generator(x, y, z, z_interp=z_interp)
for i, level in enumerate(levels):
lines = cont_gen.lines(level)
renderer.lines(lines, cont_gen.line_type, ax=ax, color=f"C{i}", linewidth=2)
renderer.z_values(x, y, z, ax=ax)
renderer.title(z_interp, ax=ax)
renderer.show()
Note
The difference is much less pronounced on a finer (higher resolution) grid, which can be
confirmed by increasing the grid resolution n
.