CV Radial Lens Map

Polynomial radial (lens) distortion, like ImageMagick's barrel distort: scales each coordinate's distance to the center by a*r^3 + b*r^2 + c*r + d (r normalized so r = 1 at the nearest edge). Positive b bulges the center outward (barrel/fisheye look), negative b pinches it (pincushion); mixing signs of a and b gives mustache distortion. The inverse form undoes the polynomial with the SAME coefficients (it solves r' * P(r') = r per pixel with a few Newton steps, the technique cv2.undistortPoints uses) - chain both to round-trip a distortion to sub-pixel accuracy. Where the polynomial is not monotonic (extreme coefficients fold the image onto itself) the inverse clamps to the last invertible radius instead of blowing up.