Visualize for a moment that we have software that displays the game of
Prince on binocular-vision LCD glasses. The glasses superimpose images
onto a transparent view of the wearer's real environment-- not virtual
reality, but augmented reality. Imagine also that we have two telemetry
gloves. The index finger and thumb are tracked in 3D and 'mouse click'
when they touch-- the two fingertips are displayed as two cursors floating
in the image. I would want to play this game.

Since a computer simulation has no gravity, we do not need surfaces on
which to rest pieces. Each piece sits on an intersection of three
translucent lines, one for each dimension, in an eight-by-eight cube.
Grasping and pulling any edge of the cube allows free rotation. The cube
should fill half the visual field, since the user's reach can be
transposed on a huge scale, or the user can also change to the size of the
pieces and stand inside the cube when desired. Ideally though, the glasses
would be tracked with telemetry so that the cube would always float in the
same space in the user's real environment while the user moved around it.
In this mode the whole cube should fit within easy reach, perhaps three
feet to a side.

Without gravity there is no reason for pieces to be stable pedestals with
radial symmetry along only one axis as they are in 2-D chess. The shapes
that represent one-dimensional ranged movers could be 3-D stars. The piece
is formed of arms extending from the intersection it occupies, and
dwindling to tips before reaching adjacent intersections. Each arm points
out toward an intersection to which the piece could move if it weren't
obstructed. So, a rook looks like a thickening of bright, bold opacity
along the three translucent board-lines of its intersection. Arms of
bishops and merchants do not lie along the board lines; they reach across
the gap toward adjacent line segments and intersections respectively.
Leaper pieces have thinner, threadlike arms, that fork into Y's tipped
with spheres. Two-dimensional movers are formed of a set of intersecting
surfaces. Pawns are half-spheres. Kings are large spheres.

For a game this complex, no one should complain if there is as much
graphical computer assistance as possible. All pieces glow when under
threat. A large crown symbol appears outside the cube when check is given.
When a piece is grasped and dragged, the intersections to which it can
legally move light up. Moving an index finger onto a piece, without
touching the fingers together on it, causes its name and animated graphic
description to display in the space above the cube. The piece on the board
grows without thickening its arms: the arms stretch as far as they can
without being blocked, to show all the intersections to which it can
legally move. At the option of the user, all pieces on the board
simultaneously extend their arms/spheres/surfaces as ghostly fogs of
color. Since the sides are red and blue, they blend into purple where they
cross. This represents threat from the red and blue sides, and varies with
intensity based on how many pieces have a line of sight to the
intersection.