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Commite4d4984

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Merge pull request#1582 from ianthomas23/1521_linear_tri_interpolator
Linear tri interpolator
2 parents24c1417 +88dc57e commite4d4984

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12 files changed

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-29
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12 files changed

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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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@@ -5,6 +5,17 @@ triangular grids
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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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@@ -49,6 +49,13 @@ using Inkscape for example, while preserving their intended position. For
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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
@@ -298,7 +305,7 @@ to address the most common layout issues.
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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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@@ -308,7 +315,7 @@ to address the most common layout issues.
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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()
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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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importmatplotlib.pyplotasplt
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frommatplotlib.triimportTriangulation
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frommatplotlib.patchesimportPolygon
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importnumpyasnp
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importmath
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defupdate_polygon(tri):
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iftri==-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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defmotion_notify(event):
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ifevent.inaxesisNone:
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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()
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"""
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Interpolation from triangular grid to quad grid.
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"""
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importmatplotlib.pyplotasplt
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importmatplotlib.triasmtri
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importnumpyasnp
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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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@@ -131,3 +131,127 @@ def test_no_modify():
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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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deftest_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)
182+
trifinder=triang.get_trifinder()
183+
184+
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)
187+
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,
194+
# 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)
200+
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
210+
# to be reinitialised.
211+
x= [0,1,0,1]
212+
y= [0,0,1,1]
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triangles= [[0,1,2], [1,3,2]]
214+
triang=mtri.Triangulation(x,y,triangles)
215+
trifinder=triang.get_trifinder()
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217+
xs= [-0.2,0.2,0.8,1.2]
218+
ys= [0.5,0.5,0.5,0.5]
219+
tris=trifinder(xs,ys)
220+
assert_array_equal(tris, [-1,0,1,-1])
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triang.set_mask([1,0])
223+
assert_equal(trifinder,triang.get_trifinder())
224+
tris=trifinder(xs,ys)
225+
assert_array_equal(tris, [-1,-1,1,-1])
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deftest_triinterp():
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# Test points within triangles of masked triangulation.
229+
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
233+
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))
238+
mask[8:10]=1
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triang=mtri.Triangulation(x,y,triangles,mask)
240+
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]
244+
xs,ys=np.meshgrid(xs,ys)
245+
xs=xs.ravel()
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ys=ys.ravel()
247+
zs=linear_interp(xs,ys)
248+
assert_array_almost_equal(zs, (1.23*xs-4.79*ys))
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# Test points outside triangulation.
251+
xs= [-0.25,1.25,1.75,3.25]
252+
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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@@ -5,5 +5,7 @@
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from __future__importprint_function
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fromtriangulationimport*
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fromtricontourimport*
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fromtrifinderimport*
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fromtriinterpolateimport*
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fromtripcolorimport*
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fromtriplotimport*

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