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Larry Smith wrote on Fri, Aug 28, 2009 12:15 AM EDT:
Planar moves are translations from one corner position of a plane to its opposite corner position. The plane is defined by two distinct axes. There must be no other pieces located on positions within this plane.

For example, an orthogonal planar move from b3 to d7 could be performed if b4, b5, b6, b7, c3, c4, c5, c6, c7, d3, d4, d5 and d6 are vacant.

8 [ ][ ][ ][ ][ ][ ][ ][ ]
7 [ ][-][-][x][ ][ ][ ][ ]
6 [ ][-][-][-][ ][ ][ ][ ]
5 [ ][-][-][-][ ][ ][ ][ ]
4 [ ][-][-][-][ ][ ][ ][ ]
3 [ ][o][-][-][ ][ ][ ][ ]
2 [ ][ ][ ][ ][ ][ ][ ][ ]
1 [ ][ ][ ][ ][ ][ ][ ][ ]
   a  b  c  d  e  f  g  h

This a translation within a 3x5 plane. And, of course, these planes can be of various dimensions.

The diagonal planar move can prove a little difficult for the new player to visualize. The same translation from b3 to d7 could be accomplished if a4, b5, c4, c6, d5 and e6 are vacant. A 2x4 plane. Note that b4, c5 and d6 are NOT part of this diagonal pattern.

8 [ ][ ][ ][ ][ ][ ][ ][ ]
7 [ ][ ][ ][x][ ][ ][ ][ ]
6 [ ][ ][-][ ][-][ ][ ][ ]
5 [ ][-][ ][-][ ][ ][ ][ ]
4 [-][ ][-][ ][ ][ ][ ][ ]
3 [ ][o][ ][ ][ ][ ][ ][ ]
2 [ ][ ][ ][ ][ ][ ][ ][ ]
1 [ ][ ][ ][ ][ ][ ][ ][ ]
   a  b  c  d  e  f  g  h

The simple linear slide can be considered a planar move with one axis being only one position wide. And planar pieces can also perform this form of movement.

Okay, that is the short version. I hope that it was illuminating. I've included an empty field variant with the Zillions implementation(for those who have the program) so that a player can check out the dynamics of this form of play.

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