gluLookAt(GLdouble eyex, GLdouble eyey, GLdouble eyez, GLdouble centrex, GLdouble centrey, GLdouble centrez, GLdouble upx, GLdouble upy, GLdouble upz);eye = (eyex,eyey,eyez) is the centre of projection, centre = (centrex,centrey,centrez) is a reference point, and up = (upx, upy, upz) is the up-vector. Derive the matrix that transforms a World Coordinate (WC) point into the 'viewing coordinate system' (or 'eye coordinate system') specified by eye, centre and up. (Remember that OpenGL operates a right-handed coordinate system throughout).
1(b) Suppose that eye=(0,0,0), centre = (3,0,4) and up = (0,0,1). What coordinates in the viewing coordinate system would the WC point (0,1,2) have?
1(c) The view plane is 1 unit along the positive z axis. To what point on the view plane will the WC point (0,1,2) be projected?
1(d) Suppose the view plane window is between -4 and 4 in both x and y, and the display window size is 1000 by 1000 pixels. To what actual pixel will the WC point (0,1,2) be projected?
2. A camera is modelled as follows: the View Reference Point is at
(-3,1,5), the camera is pointing at the centre of the cube defined by
A,B,C,D,E,F,G,H in the following diagram, and the View Up Vector is
(0,1,0). Where does the point A map to in camera coordinates?
3. (Harder, refer to Chapter 11) Calculate which faces of the cube
A,B,C,D,E,F,G,H are visible to the camera that was defined in question
2?