8000 Merge pull request #1582 from ianthomas23/1521_linear_tri_interpolator · matplotlib/matplotlib@e4d4984 · GitHub
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Merge pull request #1582 from ianthomas23/1521_linear_tri_interpolator
Linear tri interpolator
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‎CHANGELOG

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2012-12-22 Added classes for interpolation within triangular grids
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(LinearTriInterpolator) and to find the triangles in which points
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lie (TrapezoidMapTriFinder) to matplotlib.tri module. - IMT
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2012-12-05 Added MatplotlibDeprecationWarning class for signaling deprecation.
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Matplotlib developers can use this class as follows:
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‎doc/api/tri_api.rst

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:mod:`matplotlib.tri`
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=====================
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.. automodule:: matplotlib.tri
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:members: Triangulation
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.. autoclass:: matplotlib.tri.Triangulation
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:members:
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.. autoclass:: matplotlib.tri.TriFinder
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:members:
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.. autoclass:: matplotlib.tri.TrapezoidMapTriFinder
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:members: __call__
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.. autoclass:: matplotlib.tri.TriInterpolator
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:members:
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.. autoclass:: matplotlib.tri.LinearTriInterpolator
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:members: __call__

‎doc/users/whats_new.rst

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`svg` please note that you'll have to disable the default text-to-path
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conversion (`mpl.rc('svg', fonttype='none')`).
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Triangular grid interpolation
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-----------------------------
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Ian Thomas added classes to perform interpolation within triangular grids
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(:class:`~matplotlib.tri.LinearTriInterpolator`) and a utility class to find
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the triangles in which points lie (
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:class:`~matplotlib.tri.TrapezoidMapTriFinder`).
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.. _whats-new-1-2:
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new in matplotlib-1.2
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fig, axes_list = plt.subplots(2, 1)
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for ax in axes_list.flat:
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ax.set(xlabel="x-label", ylabel="y-label", title="before tight_layout")
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ax.locator_params(nbins=3)
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ax.locator_params(nbins=3)
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plt.show()
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fig, axes_list = plt.subplots(2, 1)
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for ax in axes_list.flat:
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ax.set(xlabel="x-label", ylabel="y-label", title="after tight_layout")
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ax.locator_params(nbins=3)
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ax.locator_params(nbins=3)
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plt.tight_layout()
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plt.show()

‎examples/event_handling/trifinder_event_demo.py

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"""
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Example showing the use of a TriFinder object. As the mouse is moved over the
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triangulation, the triangle under the cursor is highlighted and the index of
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the triangle is displayed in the plot title.
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"""
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import matplotlib.pyplot as plt
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from matplotlib.tri import Triangulation
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from matplotlib.patches import Polygon
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import numpy as np
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import math
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def update_polygon(tri):
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if tri == -1:
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points = [0, 0, 0]
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else:
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points = triangulation.triangles[tri]
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xs = triangulation.x[points]
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ys = triangulation.y[points]
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polygon.set_xy(zip(xs, ys))
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def motion_notify(event):
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if event.inaxes is None:
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tri = -1
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else:
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tri = trifinder(event.xdata, event.ydata)
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update_polygon(tri)
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plt.title('In triangle %i' % tri)
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event.canvas.draw()
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# Create a Triangulation.
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n_angles = 16
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n_radii = 5
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min_radius = 0.25
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radii = np.linspace(min_radius, 0.95, n_radii)
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angles = np.linspace(0, 2*math.pi, n_angles, endpoint=False)
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angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1)
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angles[:, 1::2] += math.pi / n_angles
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x = (radii*np.cos(angles)).flatten()
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y = (radii*np.sin(angles)).flatten()
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triangulation = Triangulation(x, y)
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xmid = x[triangulation.triangles].mean(axis=1)
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ymid = y[triangulation.triangles].mean(axis=1)
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mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0)
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triangulation.set_mask(mask)
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# Use the triangulation's default TriFinder object.
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trifinder = triangulation.get_trifinder()
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# Setup plot and callbacks.
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plt.subplot(111, aspect='equal')
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plt.triplot(triangulation, 'bo-')
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polygon = Polygon([[0, 0], [0, 0]], facecolor='y') # dummy data for xs,ys
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update_polygon(-1)
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plt.gca().add_patch(polygon)
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plt.gcf().canvas.mpl_connect('motion_notify_event', motion_notify)
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plt.show()

‎examples/pylab_examples/triinterp_demo.py

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"""
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Interpolation from triangular grid to quad grid.
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"""
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import matplotlib.pyplot as plt
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import matplotlib.tri as mtri
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import numpy as np
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# Create triangulation.
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x = np.asarray([0, 1, 2, 3, 0.5, 1.5, 2.5, 1, 2, 1.5])
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y = np.asarray([0, 0, 0, 0, 1, 1, 1, 2, 2, 3])
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triangles = [[0, 1, 4], [1, 2, 5], [2, 3, 6], [1, 5, 4], [2, 6, 5], [4, 5, 7],
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[5, 6, 8], [5, 8, 7], [7, 8, 9]]
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triang = mtri.Triangulation(x, y, triangles)
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# Interpolate to regularly-spaced quad grid.
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z = np.cos(1.5*x)*np.cos(1.5*y)
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interp = mtri.LinearTriInterpolator(triang, z)
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xi, yi = np.meshgrid(np.linspace(0, 3, 20), np.linspace(0, 3, 20))
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zi = interp(xi, yi)
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# Plot the triangulation.
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plt.subplot(121)
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plt.tricontourf(triang, z)
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plt.triplot(triang, 'ko-')
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plt.title('Triangular grid')
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# Plot interpolation to quad grid.
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plt.subplot(122)
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plt.contourf(xi, yi, zi)
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plt.plot(xi, yi, 'k-', alpha=0.5)
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plt.plot(xi.T, yi.T, 'k-', alpha=0.5)
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plt.title('Linear interpolation')
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plt.show()

‎lib/matplotlib/tests/test_triangulation.py

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tri = mtri.Triangulation(points[:,0], points[:,1], triangles)
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edges = tri.edges
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assert_array_equal(old_triangles, triangles)
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def test_trifinder():
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# Test points within triangles of masked triangulation.
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x, y = np.meshgrid(np.arange(4), np.arange(4))
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x = x.ravel()
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y = y.ravel()
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triangles = [[0, 1, 4], [1, 5, 4], [1, 2, 5], [2, 6, 5], [2, 3, 6],
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[3, 7, 6], [4, 5, 8], [5, 9, 8], [5, 6, 9], [6, 10, 9],
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[6, 7, 10], [7, 11, 10], [8, 9, 12], [9, 13, 12], [9, 10, 13],
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[10, 14, 13], [10, 11, 14], [11, 15, 14]]
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mask = np.zeros(len(triangles))
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mask[8:10] = 1
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triang = mtri.Triangulation(x, y, triangles, mask)
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trifinder = triang.get_trifinder()
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xs = [0.25, 1.25, 2.25, 3.25]
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ys = [0.25, 1.25, 2.25, 3.25]
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xs, ys = np.meshgrid(xs, ys)
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xs = xs.ravel()
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ys = ys.ravel()
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tris = trifinder(xs, ys)
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assert_array_equal(tris, [0, 2, 4, -1, 6, -1, 10, -1,
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12, 14, 16, -1, -1, -1, -1, -1])
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tris = trifinder(xs-0.5, ys-0.5)
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assert_array_equal(tris, [-1, -1, -1, -1, -1, 1, 3, 5,
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-1, 7, -1, 11, -1, 13, 15, 17])
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# Test points exactly on boundary edges of masked triangulation.
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xs = [0.5, 1.5, 2.5, 0.5, 1.5, 2.5, 1.5, 1.5, 0.0, 1.0, 2.0, 3.0]
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ys = [0.0, 0.0, 0.0, 3.0, 3.0, 3.0, 1.0, 2.0, 1.5, 1.5, 1.5, 1.5]
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tris = trifinder(xs, ys)
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assert_array_equal(tris, [0, 2, 4, 13, 15, 17, 3, 14, 6, 7, 10, 11])
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# Test points exactly on boundary corners of masked triangulation.
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xs = [0.0, 3.0]
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ys = [0.0, 3.0]
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tris = trifinder(xs, ys)
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assert_array_equal(tris, [0, 17])
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# Test triangles with horizontal colinear points. These are not valid
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# triangulations, but we try to deal with the simplest violations.
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delta = 0.0 # If +ve, triangulation is OK, if -ve triangulation invalid,
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# if zero have colinear points but should pass tests anyway.
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x = [1.5, 0, 1, 2, 3, 1.5, 1.5]
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y = [-1, 0, 0, 0, 0, delta, 1]
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triangles = [[0, 2, 1], [0, 3, 2], [0, 4, 3], [1, 2, 5], [2, 3, 5],
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[3, 4, 5], [1, 5, 6], [4, 6, 5]]
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triang = mtri.Triangulation(x, y, triangles)
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trifinder = triang.get_trifinder()
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xs = [-0.1, 0.4, 0.9, 1.4, 1.9, 2.4, 2.9]
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ys = [-0.1, 0.1]
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xs, ys = np.meshgrid(xs, ys)
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tris = trifinder(xs, ys)
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assert_array_equal(tris, [[-1, 0, 0, 1, 1, 2, -1],
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[-1, 6, 6, 6, 7, 7, -1]])
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# Test triangles with vertical colinear points. These are not valid
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# triangulations, but we try to deal with the simplest violations.
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delta = 0.0 # If +ve, triangulation is OK, if -ve triangulation invalid,
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# if zero have colinear points but should pass tests anyway.
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x = [-1, -delta, 0, 0, 0, 0, 1]
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y = [1.5, 1.5, 0, 1, 2, 3, 1.5]
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triangles = [[0, 1, 2], [0, 1, 5], [1, 2, 3], [1, 3, 4], [1, 4, 5],
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[2, 6, 3], [3, 6, 4], [4, 6, 5]]
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triang = mtri.Triangulation(x, y, triangles)
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trifinder = triang.get_trifinder()
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xs = [-0.1, 0.1]
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ys = [-0.1, 0.4, 0.9, 1.4, 1.9, 2.4, 2.9]
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xs, ys = np.meshgrid(xs, ys)
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tris = trifinder(xs, ys)
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assert_array_equal(tris, [[-1, -1], [0, 5], [0, 5], [0, 6], [1, 6], [1, 7],
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[-1, -1]])
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# Test that changing triangulation by setting a mask causes the trifinder
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# to be reinitialised.
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x = [0, 1, 0, 1]
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y = [0, 0, 1, 1]
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triangles = [[0, 1, 2], [1, 3, 2]]
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triang = mtri.Triangulation(x, y, triangles)
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trifinder = triang.get_trifinder()
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xs = [-0.2, 0.2, 0.8, 1.2]
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ys = [0.5, 0.5, 0.5, 0.5]
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tris = trifinder(xs, ys)
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assert_array_equal(tris, [-1, 0, 1, -1])
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triang.set_mask([1, 0])
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assert_equal(trifinder, triang.get_trifinder())
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tris = trifinder(xs, ys)
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assert_array_equal(tris, [-1, -1, 1, -1])
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def test_triinterp():
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# Test points within triangles of masked triangulation.
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x, y = np.meshgrid(np.arange(4), np.arange(4))
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x = x.ravel()
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y = y.ravel()
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z = 1.23*x - 4.79*y
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triangles = [[0, 1, 4], [1, 5, 4], [1, 2, 5], [2, 6, 5], [2, 3, 6],
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[3, 7, 6], [4, 5, 8], [5, 9, 8], [5, 6, 9], [6, 10, 9],
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[6, 7, 10], [7, 11, 10], [8, 9, 12], [9, 13, 12], [9, 10, 13],
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[10, 14, 13], [10, 11, 14], [11, 15, 14]]
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mask = np.zeros(len(triangles))
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mask[8:10] = 1
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triang = mtri.Triangulation(x, y, triangles, mask)
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linear_interp = mtri.LinearTriInterpolator(triang, z)
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xs = np.linspace(0.25, 2.75, 6)
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ys = [0.25, 0.75, 2.25, 2.75]
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xs, ys = np.meshgrid(xs, ys)
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xs = xs.ravel()
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ys = ys.ravel()
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zs = linear_interp(xs, ys)
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assert_array_almost_equal(zs, (1.23*xs - 4.79*ys))
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# Test points outside triangulation.
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xs = [-0.25, 1.25, 1.75, 3.25]
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ys = xs
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xs, ys = np.meshgrid(xs, ys)
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xs = xs.ravel()
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ys = ys.ravel()
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zs = linear_interp(xs, ys)
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assert_array_equal(zs.mask, [True]*16)

‎lib/matplotlib/tri/__init__.py

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from __future__ import print_function
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from triangulation import *
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from tricontour import *
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from trifinder import *
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from triinterpolate import *
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from tripcolor import *
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from triplot import *

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