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"""
This module provides Axes3Ds ("Axes3D Spatial"), a drop-in replacement for
Axes3D which incorporates the improvements proposed by eric-wieser in matplotlib
issue #8896.
The purpose is to reduce the distortion when projecting 3D scenes into the 2D
image. For example, the projection of a sphere will be (closer to) a circle.
"""
"""
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=========================================================
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"""
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d import proj3d
# Patch note: An update of the original implementation in proj3d.py.
def world_transformation(xmin, xmax,
ymin, ymax,
zmin, zmax, pb_aspect=None):
"""
produce a matrix that scales homogenous coords in the specified ranges
to [0, 1], or [0, pb_aspect[i]] if the plotbox aspect ratio is specified
"""
dx = xmax - xmin
dy = ymax - ymin
dz = zmax - zmin
if pb_aspect is not None:
ax, ay, az = pb_aspect
dx /= ax
dy /= ay
dz /= az
return np.array([[1/dx, 0, 0, -xmin/dx],
[0, 1/dy, 0, -ymin/dy],
[0, 0, 1/dz, -zmin/dz],
[0, 0, 0, 1]])
class Axes3Ds(Axes3D):
"""
Class Axes3Ds ("Axes3D Spatial") is a drop-in replacement for Axes3D which
incorporates the improvements proposed by eric-wieser in matplotlib issue
#8896.
"""
# Patch note: A new function.
def apply_aspect(self, position=None):
if position is None:
position = self.get_position(original=True)
# in the superclass, we would go through and actually deal with axis
# scales and box/datalim. Those are all irrelevant - all we need to do
# is make sure our coordinate system is square.
figW, figH = self.get_figure().get_size_inches()
fig_aspect = figH / figW
box_aspect = 1
pb = position.frozen()
pb1 = pb.shrunk_to_aspect(box_aspect, pb, fig_aspect)
self.set_position(pb1.anchored(self.get_anchor(), pb), 'active')
# Patch note: Overwritten to use the updated version of world_transformation
# and the new pb_aspect value.
def get_proj(self):
"""
Create the projection matrix from the current viewing position.
elev stores the elevation angle in the z plane
azim stores the azimuth angle in the x,y plane
dist is the distance of the eye viewing point from the object
point.
"""
# chosen for similarity with the initial view before gh-8896
pb_aspect = np.array([4, 4, 3]) / 3.5
relev, razim = np.pi * self.elev/180, np.pi * self.azim/180
xmin, xmax = self.get_xlim3d()
ymin, ymax = self.get_ylim3d()
zmin, zmax = self.get_zlim3d()
# transform to uniform world coordinates 0-1.0,0-1.0,0-1.0
worldM = world_transformation(xmin, xmax,
ymin, ymax,
zmin, zmax, pb_aspect=pb_aspect)
# look into the middle of the new coordinates
R = pb_aspect / 2
xp = R[0] + np.cos(razim) * np.cos(relev) * self.dist
yp = R[1] + np.sin(razim) * np.cos(relev) * self.dist
zp = R[2] + np.sin(relev) * self.dist
E = np.array((xp, yp, zp))
self.eye = E
self.vvec = R - E
self.vvec = self.vvec / np.linalg.norm(self.vvec)
if abs(relev) > np.pi/2:
# upside down
V = np.array((0, 0, -1))
else:
V = np.array((0, 0, 1))
zfront, zback = -self.dist, self.dist
viewM = proj3d.view_transformation(E, R, V)
projM = self._projection(zfront, zback)
M0 = np.dot(viewM, worldM)
M = np.dot(projM, M0)
return M