Spherical mirror forward and backward projection

The function cam2world allows to solve the backward projection problem: given the 2D coordinates of a pixel, it returns the 3D coordinates of the reflection point and the 3D direction of the reflected line passing from the imaged point.
The funciton world2cam allows to solve the forward projection problem: given the 3D coordinates of a point, it returns the 3D coordinates of the reflection point and the 2D coordinates of the corresponding pixel in the image plane.
Both the functions implement a closed form analytical solution of the refleciton problem.
Please refer to the paper:
"Omnidirectional vision sensor based on a spherical mirror catadioptric system", S. Barone, M. Carulli, P. Neri, A. Paoli and A.V. Razionale, Sensors, 2018
for the detailed reflection model description software implementation.
Please note that this function needs Camera calibration toolbox for matlab, by Bouguet, J.Y., 2015. Available for download at: http://www.vision.caltech.edu/bouguetj/calib_doc/