Module aoc::year2022::day22

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§Monkey Map

Parses any arbitrary cube map calculating the transitions between faces dynamically using 3D vectors.

We build the transitions with a BFS over the connected cube map. The first face we find is labelled A in the diagram below. For each face we define 3 vectors:

  • i Horizontal from left to right in the plane of the face.
  • j Vertical from top to bottom in the plane of the face.
  • k Perpendicular to the face pointing into the body of the cube.
             k (0, 0, 1)
            ^
           /
          /
         -------------+
        /            /|
       /    B       / |
      /            /  |
     +------------+---->i (1, 0, 0)
     |            | C |
     |     A      |  /
     |            | /
     |            |/
     +------------+
     |
     |
     v
     j (0, 1, 0)

Then for each neighbouring face we can find its i, j and k vectors depending on which edge it shares in common. For example if we move from face A to face B along the top edge then the new vectors are:

  • i (1, 0, 0) Remains unchanged
  • j (0, 0, -1) Minus previous k
  • k (0, 1, 0) Previous j

If face B and C are connected then the vectors for face C are:

  • i (0, 1, 0)
  • j (0, 0, -1)
  • k (-1, 0, 0)

However if A and C were connected then the vectors for face C are:

  • i (0, 0, 1)
  • j (0, 1, 0)
  • k (-1, 0, 0)

The really neat part is that when we leave the edge of a cube face the next 3D vector is always k no matter which edge. We can find the new direction by comparing the previous k against the new i and j vectors.

For example say we transition from face A to face B. Our k is (0, 1, 0) which is equal to minus the new j, so we know that we’re travelling upwards from the bottom edge. Then we can use this information to figure out the two dimensional offsets into the new face.

Structs§

  • Face 🔒
    2D coordinates of the top left corner plus 3D vectors for the cube face.
  • Grid
  • Input
  • Vector 🔒
    Minimal 3D vector implementation

Enums§

Functions§