Correct distortion figure in calib3d documentation

[catree]

This pullrequest changes

Related #12958
To be merged after #12958

Second figure shows that barrel distorted image is smaller than the original one (thus k1 < 0), thing that I was not aware. I hope that it will be useful for other people too.

Ugly code to generate the second figure:

import numpy as np
import cv2 as cv

img = np.ones((480, 640, 3), dtype=np.uint8)*255

xmin = 100
xmax = 640-xmin
ymin = 80
ymax = 480-ymin

def distort(pt):
  u = pt[0]
  v = pt[1]

  fx = 600.0
  fy = 600.0
  cx = 640.0/2.0
  cy = 480.0/2.0
  x = (u - cx) / fx
  y = (v - cy) / fy

  k1 = -1.5
  r2 = x**2 + y**2
  x_dist = x * (1.0 + k1*r2)
  y_dist = y * (1.0 + k1*r2)

  u_dist = x_dist*fx + cx
  v_dist = y_dist*fy + cy

  return (int(u_dist), int(v_dist))

step = 1
for x in range(xmin, xmax, step):
  pt1 = (x, ymin)
  pt2 = (x+step, ymin)
  cv.line(img, pt1, pt2, (0,0,255), 2)

  pt1_dist = distort(pt1)
  pt2_dist = distort(pt2)
  cv.line(img, pt1_dist, pt2_dist, (255,0,0), 2)

  pt1 = (x, ymax)
  pt2 = (x+step, ymax)
  cv.line(img, pt1, pt2, (0,0,255), 2)

  pt1_dist = distort(pt1)
  pt2_dist = distort(pt2)
  cv.line(img, pt1_dist, pt2_dist, (255,0,0), 2)


for y in range(ymin, ymax, step):
  pt1 = (xmin, y)
  pt2 = (xmin, y+step)
  cv.line(img, pt1, pt2, (0,0,255), 2)

  pt1_dist = distort(pt1)
  pt2_dist = distort(pt2)
  cv.line(img, pt1_dist, pt2_dist, (255,0,0), 2)

  pt1 = (xmax, y)
  pt2 = (xmax, y+step)
  cv.line(img, pt1, pt2, (0,0,255), 2)

  pt1_dist = distort(pt1)
  pt2_dist = distort(pt2)
  cv.line(img, pt1_dist, pt2_dist, (255,0,0), 2)

cv.imshow('img', img)
cv.imwrite('img_distortion.png', img)
cv.waitKey(0)

[alalek]

Rebased due merge conflicts. Please take a look.

[vpisarev]

@catree, thank you! 👍