In [15]:

    

import matplotlib.pyplot as plt
import numpy as np

import matplotlib.style

matplotlib.style.available

%matplotlib inline


    

In [16]:

    

X, Y = np.mgrid[0:5, 0:5]
X, Y = np.meshgrid(sorted(np.random.random(5)), sorted(np.random.random(4)))
# X, Y = np.meshgrid()


    

In [17]:

    

def grid2enclosure(X, Y):
    """Generate cell boundaries """
    # compute gradients in X and Y
    Xx, Xy = np.gradient(X)
    Yx, Yy = np.gradient(Y)
    
    print(Xx.any(), Xy.any())

    # lower left
    ll = np.c_[(X - 0.5*Xx - 0.5*Xy).ravel(), (Y - 0.5*Yy - 0.5*Yx).ravel()]
    # lower right
    lr = np.c_[(X + 0.5*Xx - 0.5*Xy).ravel(), (Y - 0.5*Yy + 0.5*Yx).ravel()]
    # upper left
    ul = np.c_[(X - 0.5*Xx + 0.5*Xy).ravel(), (Y + 0.5*Yy - 0.5*Yx).ravel()]
    # upper right
    ur = np.c_[(X + 0.5*Xx + 0.5*Xy).ravel(), (Y + 0.5*Yy + 0.5*Yx).ravel()]

    # number of cells x 5 points/cell x 2 (x,y)
    verts = np.hstack(
        [
            ll[:,np.newaxis,:], 
            lr[:,np.newaxis,:], 
            ur[:,np.newaxis,:], 
            ul[:,np.newaxis,:],
            ll[:,np.newaxis,:] 

        ]
    )
    return verts
verts = grid2enclosure(X, Y)


    

    




False True

In [18]:

    

plt.plot(X.ravel(), Y.ravel(), 'k.')
for vert in verts:
    plt.fill(vert[:,0], vert[:,1], edgecolor='none', alpha=0.2)


    

In [19]:

    

import matplotlib.transforms


    

In [20]:

    

T = matplotlib.transforms.Affine2D()
T.rotate_around(1, 1, 0.1 * np.pi)


    

    
Out[20]:





Affine2D(array([[ 0.95105652, -0.30901699,  0.35796048],
       [ 0.30901699,  0.95105652, -0.26007351],
       [ 0.        ,  0.        ,  1.        ]]))

In [21]:

    

XY_t = T.transform(np.c_[X.ravel(), Y.ravel()])
X_t, Y_t = XY_t[:,0].reshape(X.shape), XY_t[:,1].reshape(Y.shape)
vert_t = [T.transform(vert) for vert in verts]
vert_t = grid2enclosure(X_t, Y_t)

plt.plot(X_t, Y_t, 'k.')
for vert in vert_t:
    plt.fill(vert[:,0], vert[:,1], edgecolor='none', alpha=0.2)


    

    




True True






    

In [22]:

    

T.skew(0.8, 0.3)


    

    
Out[22]:





Affine2D(array([[ 1.26923233,  0.67022746,  0.09017876],
       [ 0.60321325,  0.85546636, -0.14934336],
       [ 0.        ,  0.        ,  1.        ]]))

In [23]:

    

XY_t = T.transform(np.c_[X.ravel(), Y.ravel()])
X_t, Y_t = XY_t[:,0].reshape(X.shape), XY_t[:,1].reshape(Y.shape)
vert_t = [T.transform(vert) for vert in verts]
vert_t = grid2enclosure(X_t, Y_t)

plt.plot(X_t, Y_t, 'k.')
for vert in vert_t:
    plt.fill(vert[:,0], vert[:,1], edgecolor='none', alpha=0.2)


    

    




True True






    

In [24]:

    

# note that this has 1 cell less
mesh = plt.pcolormesh(X_t, Y_t, X_t)


    

In [25]:

    

import scipy.spatial


    

In [28]:

    

vor = scipy.spatial.Voronoi(np.c_[X_t.ravel(), Y_t.ravel()])
scipy.spatial.voronoi_plot_2d(vor)


    

    
Out[28]:












    

In [29]:

    

X = [1, 2, 4, 7]
Xx = np.gradient( [1, 2, 4, 7])
l = X - 0.5 * Xx
r = X + 0.5 * Xx


    

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