Consider the 3D unit cube that has vertices at (0,0,0), (0,0,1), (0,1,0), (0,1,1), (1,0,0), (1,0,1), (1,1,0), and (1,1,1). Suppose you first apply a translation by (.5, .5, 0), then a rotation by 72 counterclockwise around the z-axis, then a scaling by 5 in the zdirection (leaving the other directions as they are), then a translation by (100, 50, 80), then a projection onto the z = 0 plane with the center of projection (i.e., the eye position) at (0, 0, 35). What are the coordinates of all the vertices of the cube after all these transformations? Keep your answer as a floating point number, i.e., do not round to the nearest integer.

To answer this, do the following:

(a) Enter each transformation into Matlab separately (remember you might need to convert degrees to radians) as a 4 4 matrix.

(b) Multiply all these matrices together (in the appropriate order) to get a matrix for the overall transformation.

(c) Multiply each cube vertex by the matrix from (b). To do this, put all the points together into a matrix as shown:

V = [0 0 0 0 1 1 1 1; 0 0 1 1 0 0 1 1; 4 0 1 0 1 0 1 0 1; 1 1 1 1 1 1 1 1] Note each column is the homogeneous form of one of the cube vertices.

(d) If the final coordinate of any vertices is not 1, then divide all the coordinates for that vertex by the final coordinates value to get the final coordinates.