(b) An imaging process under perspective projection has its lens center at the origin of the X-Y-Z coordinate system. The image plane is at Z = -a. The origin of the image coordinate system x-y is at the upper-left corner. The size of the image plane is d x d. Derive the equations that maps a 3D point P (X, Y, Z) to a 2D pixel p (x, y) (c) Given the 3D coordinates of points A: [2, 12, 8], and B: [31, 20, 14] on an object, calculate the 2D coordinates on an image, with respect to (1) A perspective projection (assuming the lens center is at point (0, 0, 1) and center of image plane is at (0, 0, 0) (2) An isometric parallel projection. (b) An imaging process under perspective projection has its lens center at the origin of the X-Y-Z coordinate system. The image plane is at Z = -a. The origin of the image coordinate system x-y is at the upper-left corner. The size of the image plane is d x d. Derive the equations that maps a 3D point P (X, Y, Z) to a 2D pixel p (x, y) (c) Given the 3D coordinates of points A: [2, 12, 8], and B: [31, 20, 14] on an object, calculate the 2D coordinates on an image, with respect to (1) A perspective projection (assuming the lens center is at point (0, 0, 1) and center of image plane is at (0, 0, 0) (2) An isometric parallel projection