Orientations
This is a naming scheme for piece orientations.
We need to precisely describe orientations to describe puzzle solutions.
Axes
The legs of the piece below show the directions of the X, Y, Z axes.
- Positive X goes to the viewer's right.
- Positive Y goes toward the viewer and is the shortest leg.
- Positive Z goes upward and is the longest leg.
X, Y, Z axes.
Orientation Names
Orientation names have two parts:
- A letter indicating the face that faces down (A,N,E,W,S,U). A means the bottom faces down. N, E, W, S are named after compass directions, where each of these sides face down. U is the upside-down orientation, equivalent to applying the E or W transform twice.
- A digit indicating the number of 90ยบ clockwise turns around the Z axis (0,1,2,3)
Thus, A0 is the identity orientation (no change).
A0 orientation
A1 orientation
A2 orientation
A3 orientation
N0 orientation
N1 orientation
N2 orientation
N3 orientation
E0 orientation
E1 orientation
E2 orientation
E3 orientation
W0 orientation
W1 orientation
W2 orientation
W3 orientation
S0 orientation
S1 orientation
S2 orientation
S3 orientation
U0 orientation
U1 orientation
U2 orientation
U3 orientation
Evaluating Piece Orientations
- Which orientations have overhangs?
- Which orientations are 2D (height=1)?
- What is the footprint of each orientation? (useful for pruning the decision tree when solving)
- Which orientations are duplicates? Which footprints are?