What is riged body transformation matrix, Computer Graphics

What is riged body transformation matrix? Show that the composition lf two rotation is additive by concatenating the matrix representation of r (theta2) = R (theta1 + theta2) to obtain.

A general rigid body transformation matrix involving only translation and rotations can be expressed as: Where the four elements are the multiplicative rotation terms and elements and are the translational terms. A rigid body change in coordinate position is also sometimes referred to as a rigid motion transformation. All angles and distances between coordinate positions are unchanged by the transformation.   

 

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