Drawing Collision on Screen

In general, each vertex is the intersection of three planes. Additionally, each vertex you want to draw needs to be on the correct side of all remaining planes. This may be an annoying combinatorial description of the problem, but with a kDop, at least it's a fixed-size problem...

To get a bit more clever about it, you should look at some Linear Programming math. Specifically, once you have a valid vertex (i.e., an intersection of 3 planes that is on the correct side of the remaining planes), you can slide along each edge to the next valid vertex. You can recursively explore the entire graph of valid vertices and edges this way: do a breadth-first search of the graph, keeping track of which vertices you've explored -- and once you've exhausted the possibilities (finite, remember!) you've got what you want to draw.

Oh, and to calculate the actual vertices based on the planes, check out this mathworld page.

[edit:] -- Actually, you may be able to simplify your search quite a lot, if you know for sure that none of your planes are redundant (i.e., if none of them are entirely outside your kDop). In that case, your kDop has a standard structure, with each polygon having a fixed configuration of neighbors; in that case, you can just plug your planes in, compute your fixed set of vertices, and draw your standard figure with them. You could easily (if somewhat tediously) work out all the details by hand.

You might want to watch out for degenerate cases, though -- e.g. if you put an oriented cube in your kDop, so that most of your facets are zero-sized.

[edit2:] -- On further consideration, I'm thinking your configuration may not be entirely fixed. For example, say there are 4 nearby planes; and based on their depth, the edge between them may go one way or another, like so:

plane A     |    plane B
            |
           / \
          /   \
         /     \
________/       \
        |        \
        |         \
plane C | plane D  \

        vs.

plane A |    plane B
        |
        |
________|
         \
          \
          |\
          | \
          |  \
          |   \
          |    \
          |     \
          |      \
          |       \
          |        \
plane C   | plane D \

However, I think you can still simplify your setup somewhat. You will still need to check whether your vertices are valid or not, but you can reduce both the number of vertices and the number of planes to check by considering your particular plane configuration.