boundary_word_square
boundary_word_square,
a MATLAB code which
describes the outline of an object on a grid of squares,
using a string of symbols that represent the sequence of steps
tracing out the boundary.
The symbols might be 'u', 'd', 'r', and 'l', indicating that the boundary is
to be drawn by a succession of movements of unit length, that are up, down,
right or left.
In image processing, boundary words are known as "chain codes".
Licensing:
The computer code and data files made available on this web page
are distributed under
the MIT license
Languages:
boundary_word_square is available in
a MATLAB version and
an Octave version and
a Python version.
Related Data and Programs:
boundary_word_square_test
boundary_word_drafter,
a MATLAB code which
describes the outline of an object on a grid of drafters,
or 306090 triangles, using a string of symbols that represent
the sequence of steps tracing out the boundary.
boundary_word_equilateral,
a MATLAB code which
describes the outline of an object on a grid of equilateral triangles,
using a string of symbols that represent the sequence of steps
tracing out the boundary.
boundary_word_hexagon,
a MATLAB code which
describes the outline of an object on a grid of hexagons,
using a string of symbols that represent the sequence of steps
tracing out the boundary.
boundary_word_right,
a MATLAB code which
describes the outline of an object on a grid of isoceles right triangles,
using a string of symbols that represent the sequence of steps
tracing out the boundary.
eternity,
a MATLAB code which
considers the eternity puzzle, which considers an irregular dodecagon
shape that is to be tiled by 209 distinct pieces, each formed by 36
contiguous 306090 triangles, known as polydrafters.
pariomino,
a MATLAB code which
considers pariominoes, which are polyominoes with a checkerboard parity.
polyomino_parity,
a MATLAB code which
uses parity considerations to determine whether a given set of
polyominoes can tile a specified region.
polyominoes,
a MATLAB code which
defines, solves, and plots a variety of polyomino tiling problems,
which are solved by a direct algebraic approach involving the
reduced row echelon form (RREF) of a specific matrix, instead of the
more typical bruteforce or backtracking methods.
Reference:

George Bell,
The dynamics of spinning polyominoes,
Gathering for Gardner, G4G13.

Srecko Briek, Gilbert Labelle, Ariane Lacasse,
Algorithms for polyominoes based on the discrete Green theorem,
Discrete Applied Mathematics,
Volume 147, pages 187205, 2005.
Source Code:

boundary_word_area.m,
returns the area of a polyomino defined by a boundary word.

boundary_word_boundary.m,
returns the boundary of a polyomino defined by a boundary word.

boundary_word_boundary_plot.m,
plots the boundary of a polyomino defined by a boundary word.

boundary_word_centroid.m,
returns the centroid of a polyomino defined by a boundary word.

boundary_word_check.m,
checks that a boundary word is valid.

boundary_word_is_convex.m,
is TRUE if the boundary word describes a convex shape.

boundary_word_moment.m,
determines the moment of inertia of a polyomino defined by a boundary word.

boundary_word_parity.m,
determines the parity of a polyomino defined by a boundary word.

boundary_word_perimeter.m,
determines the perimeter of a polyomino defined by a boundary word.

boundary_word_plot.m,
plots a polyomino defined by a boundary word.

boundary_word_range.m,
determines the range of a polyomino defined by a boundary word.

boundary_word_representative.m,
returns the representative for a boundary word, the lexically first
member of the equivalence class.

boundary_word_sense.m,
determines the sense of a polyomino defined by a boundary word,
which is +1 for a counterclockwise boundary, 1 otherwise.

boundary_word_transform.m,
returns the boundary word of a polyomino after reflections and
rotations.

chvec_eq.m,
is TRUE if c1=c2, where c1 and c2 are character strings.

chvec_lt.m,
is TRUE if c1

chvec_reduce.m,
reduces a string of repeated characters to a single occurrence.

is_octave.m,
is TRUE if Octave is executing.

pentomino_index.m,
returns the symbol of any of the 12 pentominoes.

pentomino_moment.m,
returns the moment of inertia of any of the 12 pentominoes.

pentomino_symbol.m,
returns the symbol of the ith pentomino.

pentomino_to_boundary_word.m,
returns the boundary_word describing any of the 12 pentominoes.

polygon_contains_point.m,
is TRUE if a point is contained in a polygon.

polyomino_boundary_word.m,
returns the boundary_word of a polyomino.

polyomino_boundary_step.m,
takes one step along the boundary of a polyomino, to compute the
boundary word.

polyomino_print.m,
prints a polyomino.

r8mat_print.m,
prints an R8MAT.

r8mat_print_some.m,
prints some of an R8MAT.

r8vec2_print.m,
prints a pair of R8VEC's side by side.
Last modified on 21 June 2021.