z interpolation

Interpolation of z values occurs in two situations:

1. When calculating how far along the edge of a quad (or corner-masked corner) a contour line intersects it.

2. When calculating the z value of the central point of quad. This is needed for all quads if quad_as_tri=True or just saddle quads if quad_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			✔️	✔️

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)
   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.