This week I decided to give the stragglers more time to finish things up and polish up assignments that aren't quite working, so I'm giving you an extremely easy assignment, mainly a matter of putting together two pieces.

Using the example Phong-shader applet that I implemented in class, replace the fake sphere by a sphere made from an actual polygonal mesh.

For this first step, don't need to do any matrix transformations before you do the shading calculation. In other words, keep your unit sphere as a unit sphere. Before shading, your sphere mesh should look something like the one in the figure below.

Note that when you scan-convert this mesh, you will end up with two triangles for each polygon that is not at the north pole, so your scan-converter will need to split any four-sided polygon into two triangles, and separately render each triangle. The figure below shows one way to split each four-sided polygon into two triangles:

For this week's assignment, you can just generate a "northern hemisphere" - ie: make your latitude parameter range from the equator to the north pole (ie: from 0 to π/2), so that the z coordinate ranges from 0.0 to 1.0.

The sequence of your algorithm should be as follows:

   • For each vertex:
      • Use the Phong algorithm and the normal vector at that vertex to compute r,g,b

   • For each polygon:
      • Split the polygon into triangles as needed.
      • For each triangle:
         • Scan convert, while interpolating r,g,b from each of the three vertices.

In the special case of the unit sphere, the normal vector is very simple - it's just the same as the (x,y,z) coordinates of the vertex itself.

Notice that scan-conversion of a full-color triangle is very much the same as what you did last week - split your triangle into two trapezoids, and then interpolate values from the four corners of a trapezoid down to each pixel. The only difference is that in addition to linearly interpolating x and y, you also linearly interpolate each of r,g,b.

For the assignment, I'd like you to try your own combinations of surface material and lights. Do not duplicate the surface materials or lights I use in - come up with your own.

This assignment will be due Wednesday April 1.