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zo7Z?ffd3^C|N8mC^TXkOXNCztz3boeCm%s^c=z&UYZ43o!N-qnu_! z?C<-rc;Qywk|jq(=RSHq|5yca%k$E|w2)H0P;uygPX5)!n;HN7??2o4)Wv^B=F?sL zGkE?#jm1U%Z}ur={!aBz!1GV_`-F|3D$J)M_=!sV#fv`S;wN1E#JqDpiGzQH(kF@a zr)d0yi=S}u6E6NA#>JP(;bUfIOO_u$;vM{to%4UVyZ;Zn7&mM(pO%fhJ3KgG_fhj7 Z_dR`t;S-a4_}J+aM=_YRkLNyq{u_k|W2OKA literal 0 HcmV?d00001 diff --git a/pixel_delta.py b/pixel_delta.py new file mode 100644 index 0000000..732839b --- /dev/null +++ b/pixel_delta.py @@ -0,0 +1,76 @@ +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()