← the explorer · watch it built · geometry → twin trees

Read the twin trees from the mosaic.

The permutation makes the floorplan. After that, the two trees are recovered from the room corners and T-junctions alone.

MFTB trace

The mosaic is ready.

τ+ upper-right corners and C+ edges ×τ− lower-left corners and C− edges
empty overlayframe 0 / 1finished

the geometric rules

Mosaic floorplan → twin trees

Every room becomes one node in each tree. The two copies are anchored at opposite corners of the same room.

  1. Put a circle at the room's upper-right corner. This is its node in τ+.
  2. Put a cross at the room's lower-left corner. This is its node in τ−.
  3. At the upper-right T-junction, follow the non-crossing segment to the C+-parent. The child is left when that parent is on the right, and right otherwise.
  4. At the lower-left T-junction, follow the non-crossing segment to the C−-parent. The child is right when that parent is on the left, and left otherwise.

The upper-right room is the root of τ+; the bottom-left room is the root of τ−. No permutation values are used in these steps.