first version

Author: danieldugas

.gitignore

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+CMap2D.cpp
+CMap2D.html
+*.pyc
+build/

CMap2D.pyx

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+import numpy as np
+from timeit import default_timer as timer
+
+
+def make_circular_index(pixel_radius, sample_factor=10):
+    """ Creates a circular index around the point at index 0, 0
+    This method is sample-based and therefore not precise. 
+    Solution is found by sampling at regular interval along the circle
+    and storing the resulting points in 2d grid of resolution 1.
+    Points are returned in order, forming a 2d grid circular path."""
+    px_r = pixel_radius # radius of the circle in pixels
+
+    # ensures sample_factor samples per angular pixel.
+    kNSamples = max(12, 2 * np.pi * px_r * sample_factor) 
+
+    theta = np.arange(0, kNSamples) * 2 * np.pi / kNSamples
+    x = px_r * np.cos(theta)
+    y = px_r * np.sin(theta)
+    i = np.round(x).astype(int)
+    j = np.round(y).astype(int)
+    ij = np.vstack([i,j])
+    unique_id = np.sort(np.unique(ij, axis=1, return_index=True)[1])
+    i = ij[0, unique_id]
+    j = ij[1, unique_id]
+    return i, j
+
+def index_to_grid(i, j, gridsize=None):
+    """ Converts the circle from index format to 2d-grid format """
+    size = gridsize
+    if gridsize is None:
+        size_i = max(i) - min(i) + 3
+        size_j = max(j) - min(j) + 3
+        size = max(size_i, size_j)
+    mid = int((size - 1) / 2)
+    grid = np.zeros((size, size))
+    grid[(i+mid, j+mid)] = 1
+    return grid
+
+class CircularIndexCreator(object):
+    """ Allows creating circular indices for given radii,
+    and stores the results in a lookup table to avoid repeat computation """
+    def __init__(self):
+        self.px_r_archive = {}
+        self.indices_archive = {}
+
+    def make_circular_index(self, radius, resolution=1.):
+        r = radius # [m]
+        res = resolution # [m / px]
+        px_r = radius / resolution # pixel-radius of circle [px]
+
+        if px_r in self.px_r_archive:
+            i, j = self.px_r_archive[px_r]
+            return i, j
+
+        i, j = make_circular_index(px_r)
+        # store result in lookup table
+        self.px_r_archive[px_r] = (i, j)
+        return i, j
+
+if __name__ == "__main__":
+    from matplotlib import pyplot as plt
+    N_CIRCLES = 1000
+    PLOT_RADII = False
+    PLOT_EVOLUTION = True
+    px_radii = np.linspace(0, 100, N_CIRCLES)
+    cc = CircularIndexCreator()
+    circle_lengths = []
+    t_st = timer()
+    for px_r in px_radii:
+        i, j = cc.make_circular_index(px_r, 1)
+        circle_lengths.append(len(i))
+    t_end = timer()
+    print("First-time computation of {} circles took {} seconds.".format(N_CIRCLES, t_end - t_st))
+    t_st = timer()
+    for px_r in px_radii:
+        i, j = cc.make_circular_index(px_r, 1)
+    t_end = timer()
+    print("Second-time computation of {} circles took {} seconds.".format(N_CIRCLES, t_end - t_st))
+    if PLOT_RADII:
+        plt.figure()
+        for px_r in px_radii:
+            i, j = cc.make_circular_index(px_r, 1)
+            plt.plot(i, j, '-x')
+        plt.show()
+        plt.figure()
+        plt.plot(px_radii, circle_lengths, '-x')
+        plt.show()
+    if PLOT_EVOLUTION:
+        print("Plotting evolution of circles with radius")
+        N = 20
+        px_radii = np.logspace(np.log(0.5),np.log10(N-1),200)
+        for px_r in px_radii:
+            i, j = cc.make_circular_index(px_r, 1)
+        plt.ion()
+        plt.figure()
+        for px_r in px_radii:
+            plt.gca().clear()
+            i, j = cc.make_circular_index(px_r, 1)
+            grid = index_to_grid(i, j, 2*N+1)
+            plt.imshow(1-grid, cmap='gray')
+            plt.gca().add_patch(plt.Circle((N,N), radius=px_r, color='white', fill=False))
+            plt.pause(0.005)
+        plt.ioff()