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pixel_delta.py

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+from math import *
+import matplotlib.pyplot as plt
+import numpy as np
+	
+# alpha is half of vertical fov
+# sigma is angle between laser plane and camera center vector
+# phi is angle between camera center vector and target pixel vector
+# d is distance between laser plane and camera
+# h is vertical pixel count
+alpha = pi/6
+sigma = pi/3
+d = 5
+h = 1000
+
+def get_phi(y, h, alpha):
+	# get phi of pixel row y
+	return atan(tan(alpha)*(2*y/h - 1))
+
+def crunch(alpha, sigma, phi, d, h):
+	# depth delta approximation
+	da = 2*d*tan(alpha)*cos(phi)/(h*sin(sigma+phi)**2)
+	# te is tan(epsilon)
+	# epsilon is angle increment in phi across one pixel
+	te = (2*tan(alpha)*cos(phi)**2/(h + 2*tan(alpha)*sin(phi)*cos(phi)))
+	# exact depth delta
+	#de = d/sin(sigma+phi)*te/(sin(sigma+phi) + te*sin(sigma+phi))
+	de = 2*d*tan(alpha)*cos(phi)*(cos(phi) - sin(phi)*te)/(h*sin(sigma+phi)*(sin(sigma+phi) + cos(sigma+phi)*te))
+	return {'da':da, 'te':te, 'de':de, 'ea':de-da, 'er':(de-da)/de}
+
+def nprint(phi_text, phi):
+	nums = crunch(alpha, sigma, phi, d, h)
+	print(phi_text)
+	print(f"Delta approx.:    {nums['da']}")
+	print(f"Tan(eps):         {nums['te']}")
+	print(f"Delta exact:      {nums['de']}")
+	print(f"Error (absolute): {nums['ea']}")
+	print(f"Error (relative): {nums['er']}")
+	print("")
+
+nprint('Maximal phi', alpha)
+nprint('Zero phi', 0)
+nprint('Minimal phi', -alpha)
+
+print(f"phi at y = 50 is {get_phi(50, h, alpha)}")
+
+# make data
+xpoints = []
+dapoints = []
+depoints = []
+epoints = []
+aspan = 0
+espan = 0
+tspan = d*(1/tan(sigma-alpha) - 1/tan(sigma+alpha))
+for y in range(h):
+	xpoints.append(y)
+	cronch = crunch(alpha, sigma, get_phi(y, h, alpha), d, h)
+	dapoints.append(cronch['da'])
+	aspan += cronch['da']
+	depoints.append(cronch['de'])
+	espan += cronch['de']
+	epoints.append(cronch['er'])
+
+print('approximate segment sum', aspan)
+print('exact segment sum', espan)
+print('expected sum', tspan)
+
+xpoints = np.array(xpoints)
+dapoints = np.array(dapoints)
+depoints = np.array(depoints)
+plt.plot(xpoints, dapoints, label = 'approx')
+plt.plot(xpoints, depoints, label = 'exact')
+plt.legend()
+plt.show()
+plt.plot(xpoints, epoints, label = 'error')
+plt.legend()
+plt.show()