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import math
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import ticker
orders = [2, 3]
fig, axes = plt.subplots(1, len(orders), figsize=(11, 5))
n_cells = 7 # grid will be size (n_cells, n_cells)
# desired interpolation coordinate (xi, yi)
xi, yi = 3.3, 3.7
def get_start(cc, order):
if order % 1 == 0:
start = math.floor(cc) - order // 2
else:
start = math.floor(cc + 0.5) - order // 2
return start
for ax, order in zip(axes, orders):
# draw open circles at the locations of pixel centers
for n in range(n_cells):
ax.plot(np.arange(n_cells), -np.full(n_cells, n), 'ko',
fillstyle='none')
# draw pixel borders
for n in range(n_cells + 1):
ax.plot([n - 0.5, n - 0.5], [0.5, -n_cells + .5], 'k-')
ax.plot([-0.5, n_cells - .5], [-n + 0.5, -n + 0.5], 'k-')
# plot an example coordinate location to interpolate
ax.plot([xi], [-yi], 'rx')
# plot filled circles for the points that will be involved in the
# interpolation
startx = get_start(xi, order)
starty = get_start(yi, order)
xc = np.tile(np.arange(startx, startx + order + 1)[:, np.newaxis],
(1, order + 1)).ravel()
yc = np.tile(np.arange(starty, starty + order + 1)[np.newaxis, :],
(order + 1, 1)).ravel()
ax.plot(xc, -yc, 'ko')
ax.set_title(f"Interpolation (order = {order})",
fontdict=dict(size=16, weight='bold'))
# set limits and ticks for 0, 0 voxel at upper left
ax.axis('square')
ax.set_xticks(np.arange(n_cells + 1))
ax.xaxis.tick_top()
ax.xaxis.set_label_position('top')
yticks = ticker.FixedLocator(-np.arange(n_cells, -1, -1))
ax.yaxis.set_major_locator(yticks)
yticklabels = ticker.FixedFormatter(np.arange(n_cells, -1, -1))
ax.yaxis.set_major_formatter(yticklabels)
ax.set_ylim([-n_cells + 0.5, 0.5])
ax.set_xlim([-0.5, n_cells - 0.5])
plt.tight_layout()
plt.plot()
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