Possible Chess Moves

The lines indicates a piece's control over all the squares through which the line runs. The power of a piece ends at the square the arrow indicates. For clarity, the origin of some knight moves have solid red circles. Unlike other pieces, the knight must move to the square indicated by the arrow. Other pieces can move to any square the line runs through.

As complicated as it looks, there is one important simplifying factor. The "lines of force" of chess pieces do not interfere with one another. This is unlike real physical phenomenon in which the influence of different forces on one another complicate analysis immensely. For example, the interaction of gravitational forces make the three body problem very difficult to solve.

The above diagram is based on the position below.