Rigid motion transformation

Description

Computes the rigid motion transformation Y = R*X+T.

INPUTS:

X: 3D structure in the world coordinate frame (3xN matrix for N points)
(om,T): rigid motion parameters between world coordinate frame and camera reference frame
om: rotation vector (3×1 vector); T: translation vector (3×1 vector)

OUTPUTS:

Y: 3D coordinates of the structure points in the camera reference frame (3xN matrix for N points)
dYdom: derivative of Y with respect to om ((3N)x3 matrix)
dYdT: derivative of Y with respect to T ((3N)x3 matrix)

DEFINITIONS:

Let P be a point in 3D of coordinates X in the world reference frame (stored in the matrix X).
The coordinate vector of P in the camera reference frame is Xc = R*X + T,
where R is the rotation matrix corresponding to the rotation vector om: 

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