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circle_fitting.py
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138 lines (98 loc) · 3.44 KB
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"""
Object shape recognition with circle fitting
author: Atsushi Sakai (@Atsushi_twi)
"""
import matplotlib.pyplot as plt
import math
import random
import numpy as np
show_animation = True
def circle_fitting(x, y):
"""
Circle Fitting with least squared
input: point x-y positions
output cxe x center position
cye y center position
re radius of circle
error: prediction error
"""
sumx = sum(x)
sumy = sum(y)
sumx2 = sum([ix ** 2 for ix in x])
sumy2 = sum([iy ** 2 for iy in y])
sumxy = sum([ix * iy for (ix, iy) in zip(x, y)])
F = np.array([[sumx2, sumxy, sumx],
[sumxy, sumy2, sumy],
[sumx, sumy, len(x)]])
G = np.array([[-sum([ix ** 3 + ix * iy ** 2 for (ix, iy) in zip(x, y)])],
[-sum([ix ** 2 * iy + iy ** 3 for (ix, iy) in zip(x, y)])],
[-sum([ix ** 2 + iy ** 2 for (ix, iy) in zip(x, y)])]])
T = np.linalg.inv(F).dot(G)
cxe = float(T[0] / -2)
cye = float(T[1] / -2)
re = math.sqrt(cxe**2 + cye**2 - T[2])
error = sum([np.hypot(cxe - ix, cye - iy) - re for (ix, iy) in zip(x, y)])
return (cxe, cye, re, error)
def get_sample_points(cx, cy, cr, angle_reso):
x, y, angle, r = [], [], [], []
# points sampling
for theta in np.arange(0.0, 2.0 * math.pi, angle_reso):
nx = cx + cr * math.cos(theta)
ny = cy + cr * math.sin(theta)
nangle = math.atan2(ny, nx)
nr = math.hypot(nx, ny) * random.uniform(0.95, 1.05)
x.append(nx)
y.append(ny)
angle.append(nangle)
r.append(nr)
# ray casting filter
rx, ry = ray_casting_filter(x, y, angle, r, angle_reso)
return rx, ry
def ray_casting_filter(xl, yl, thetal, rangel, angle_reso):
rx, ry = [], []
rangedb = [float("inf") for _ in range(
int(math.floor((math.pi * 2.0) / angle_reso)) + 1)]
for i in range(len(thetal)):
angleid = math.floor(thetal[i] / angle_reso)
if rangedb[angleid] > rangel[i]:
rangedb[angleid] = rangel[i]
for i in range(len(rangedb)):
t = i * angle_reso
if rangedb[i] != float("inf"):
rx.append(rangedb[i] * math.cos(t))
ry.append(rangedb[i] * math.sin(t))
return rx, ry
def plot_circle(x, y, size, color="-b"):
deg = list(range(0, 360, 5))
deg.append(0)
xl = [x + size * math.cos(math.radians(d)) for d in deg]
yl = [y + size * math.sin(math.radians(d)) for d in deg]
plt.plot(xl, yl, color)
def main():
# simulation parameters
simtime = 15.0 # simulation time
dt = 1.0 # time tick
cx = -2.0 # initial x position of obstacle
cy = -8.0 # initial y position of obstacle
cr = 1.0 # obstacle radious
theta = math.radians(30.0) # obstacle moving direction
angle_reso = math.radians(3.0) # sensor angle resolution
time = 0.0
while time <= simtime:
time += dt
cx += math.cos(theta)
cy += math.cos(theta)
x, y = get_sample_points(cx, cy, cr, angle_reso)
ex, ey, er, error = circle_fitting(x, y)
print("Error:", error)
if show_animation:
plt.cla()
plt.axis("equal")
plt.plot(0.0, 0.0, "*r")
plot_circle(cx, cy, cr)
plt.plot(x, y, "xr")
plot_circle(ex, ey, er, "-r")
plt.pause(dt)
print("Done")
if __name__ == '__main__':
main()