Given is a cube in the range [0 , 1]³ . One looks through glm::lookAt(0.5, 0.5, 3.0, 0.5, 0.5, 1.0, 0.0, 1.0, 0.0) to the center of the front face (z = 1).

a) Determine the parameters of a perspective projection with glm::frustum(...), so that the cube is half the size of the window (half the width and half the height) and centered in the middle of the window. Set near = 1 and f ar = 4. Sketch the view pyramid from above.

b) What are the coordinates of the cube vertices [ 1 1 0 1 ]^T and [1 1 1 1] ^T in the camera coordinate system and in the canonical volume (cube from -1 to +1)? Sketch the cube in the canonical volume from above. (Note: The conversion into the canonical volume is done with the glm::frustum matrix, the coordinates of the remaining cube vertices can be determined by symmetries).