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