POLYOMINO_MULTIHEDRAL_TILING_PLOT
Plot Solutions of Polyomino Multihedral Tiling

POLYOMINO_MULTIHEDRAL_TILING_PLOT, a MATLAB library which is given matrices defining a region R and a set of polyominoes P, and a vector X, computed by POLYOMINO_MULTIHEDRAL, which represent a tiling of R by the polyominoes in P. The task is to plot a representation of that tiling.

The problem being solved is discussed in the documentation for POLYOMINO_MULTIHEDRAL. Briefly, a region R is to be tiled by one or more copies of polyominoes stored in P. The solution procedure treats as "variables" all distinct rotation, reflections, and translations of the polyominoes that fit exactly onto some portion of R. The solution is a binary list that indicates a selection of these variables that tile R completely.

This function takes the solution vector of selected variables, such as:

  1 0 1 0 1 0 0 1 0 0

  1  1   
  8  3  3
  8  5  3

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

polyomino_multihedral_tiling_plot is available in a MATLAB version.

Related Data and Programs:

polyomino_multihedral_tiling_plot_test

Source Code:

• filename_inc.m numerically "increments" a file name.
• polyomino_condense.m, cleans up a matrix that represents a polyomino by setting all nonzero entries to 1, and removing initial and final rows and columns of zeros.
• polyomino_embed_list.m, for each possible embedding, lists the translation necessary to to apply to the polyomino.
• polyomino_embed_number.m, reports the number of ways a polyomino can be embedded in a region.
• polyomino_index.m, computes an index for each nonzero polyomino entry.
• polyomino_multihedral_matrix.m, determines the matrix and right hand side for a polyomino multihedral problem.
• polyomino_multihedral_tiling_plot.m, is given matrices defining a region R and a set of polyominoes P, and a vector X, computed by POLYOMINO_MULTIHEDRAL, which represents a tiling of R by the polyominoes in P, and plots a representation of that tiling.
• polyomino_multihedral_variants.m, carries out reflections and rotations of all the polyominoes in a set P to determine which transformations yield distinct variants.
• polyomino_print.m, prints a polyomino.
• polyomino_transform.m, carries out reflections and rotations of a polyomino.
• timestamp.m, prints the YMDHMS date as a timestamp.