A. Homogeneous coordinates serve two purposes. First, they give us a way to express translation via matrix multiplication. That helps us compose sequences of rotations and translations into single modeling transformation M. Second, the perspective projection uses homogeneous coordinates in an essential way. This projection, when combined with homogeneous division, causes objects near the camera to appear larger than objects far away.

B. At this point in the course, an XYZ vertex obtained from the mesh is typically transformed by a modeling transformation M, then the projection P, then homogeneous division, then the viewport V. The M and P steps are done in the vertex shader. The division and V steps are done after the vertex shader, for reasons that are not yet clear.

C. One algorithm is to loop through the triangles. For each triangle, transform the three vertices (meaning, apply the vertex shader, homogeneous division, and viewport to them), and pass the transformed vertices to the rasterizer-interpolator code. This algorithm uses no extra memory and is easy to implement, but it probably results in many vertices being transformed multiple times (because they appear in multiple triangles).

Another algorithm begins by looping through the vertices, transforming each one. Then the algorithm loops over the triangles, passing the triangle's transformed vertices to the rasterizer-interpolator. This algorithm transforms each vertex only once, but it requires the temporary allocation of extra memory to hold the transformed vertices.

D. The answer that I expected was: You don't see anything. Before the introduction of the camera isometry, the camera is implicitly situated at the origin. So it is inside the sphere. So it views the sphere's triangles from their back sides, and they are culled by backface culling.

A truer answer, which did not earn more points because it used material not officially covered by the exam, was: You might see the sphere. For example, if you are using an orthographic projection, then you won't see the back faces in front of the camera, but you will see the front faces behind the camera, because we have not yet introduced clipping to prevent that.