Before revision:  We propose a new algorithm to compute that transform of an image represented by unit (pixel/voxel) basis functions , for various two-dimensional (2D)/three-dimensional (3D) scanning geometries, such as 2D/3D parallel beam, 2D fan beam, 3D circular/helical cone beam, etc. Since the transform is acting as a line integral, the fundamental task is to calculate this integral of the unit basis functions, which is equivalently the intersection length of the ray with the associated unit.
After revision:  We propose a new algorithm to compute that transform of an image represented by unit (pixel/voxel) basis functions . The fundamental issue is equivalently calculating the intersection lengths of the ray with the associated unit.