ref: 0af537d2c0a56dc99f90d581341317a607531ff0
parent: 8d6647548f7d0051221374ad6eb2b6dd32e2a3ed
author: Simon Tatham <anakin@pobox.com>
date: Mon Mar 27 05:17:51 EDT 2023
Rename the 'aux' subdirectory to avoid Windows restrictions. James Harvey points out that Windows still forbids calling a file 'aux' in any context. Even a directory. Gaaah.
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -264,7 +264,7 @@
OBJECTIVE "Reposition the points so that the lines do not cross.")
add_subdirectory(unfinished)
-add_subdirectory(aux)
+add_subdirectory(auxiliary)
cliprogram(obfusc obfusc.c)
cliprogram(latincheck latin.c COMPILE_DEFINITIONS STANDALONE_LATIN_TEST)
--- a/aux/CMakeLists.txt
+++ /dev/null
@@ -1,1 +1,0 @@
-cliprogram(hatgen hatgen.c COMPILE_DEFINITIONS TEST_HAT)
--- a/aux/doc/arrow.svg
+++ /dev/null
@@ -1,4 +1,0 @@
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--- a/aux/doc/expanded-F.svg
+++ /dev/null
@@ -1,84 +1,0 @@
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--- a/aux/doc/hat-kites.svg
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-</svg>
--- a/aux/doc/hatmaps.html
+++ /dev/null
@@ -1,62 +1,0 @@
-<html>
-<head>
-<meta http-equiv="Content-type" content="text/html; charset=UTF-8" />
-<title>Kitemaps and metamaps for the hat tiling generator</title>
-<style type="text/css">
- table, tbody, tr, td, th {- border: 1px solid rgba(0, 0, 0, 0.3);
- border-collapse: collapse;
- }
- table.noborder, table.noborder tbody, table.noborder td,
- table.noborder th, table.noborder tr { border: none; }- table {- margin: 1em;
- }
- th, td {- padding: 0.5em;
- }
-</style>
-</head>
-<body>
- <h1>Kitemaps and metamaps for the hat tiling generator</h1>
- <p>See <a href="hats.html">hats.html</a> for the full explanation.</p>
- <p>Here's the full set of kitemaps and metamaps for all the tile
- types:</p>
- <table>
- <tr>
- <th>Tile name</th>
- <th>Original tile</th>
- <th>First-order expansion</th>
- <th>Kitemap</th>
- <th>Metamap</th>
- <tr>
- <td>H</td>
- <td><img src="single-H.svg"></td>
- <td><img src="expanded-H.svg"></td>
- <td><img src="kitemap-H.svg"></td>
- <td><img src="metamap-H.svg"></td>
- </tr>
- <tr>
- <td>T</td>
- <td><img src="single-T.svg"></td>
- <td><img src="expanded-T.svg"></td>
- <td><img src="kitemap-T.svg"></td>
- <td><img src="metamap-T.svg"></td>
- </tr>
- <tr>
- <td>P</td>
- <td><img src="single-P.svg"></td>
- <td><img src="expanded-P.svg"></td>
- <td><img src="kitemap-P.svg"></td>
- <td><img src="metamap-P.svg"></td>
- </tr>
- <tr>
- <td>F</td>
- <td><img src="single-F.svg"></td>
- <td><img src="expanded-F.svg"></td>
- <td><img src="kitemap-F.svg"></td>
- <td><img src="metamap-F.svg"></td>
- </tr>
- </table>
-</body>
-</html>
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--- a/aux/doc/hats-single-H.svg
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-</svg>
--- a/aux/doc/hats-single-T.svg
+++ /dev/null
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-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="81" height="110">
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-</svg>
--- a/aux/doc/hats.html
+++ /dev/null
@@ -1,258 +1,0 @@
-<html>
-<head>
-<meta http-equiv="Content-type" content="text/html; charset=UTF-8" />
-<title>Generating hat tilings for Loopy</title>
-<style type="text/css">
- table, tbody, tr, td, th {- border: 1px solid rgba(0, 0, 0, 0.3);
- border-collapse: collapse;
- }
- table.noborder, table.noborder tbody, table.noborder td,
- table.noborder th, table.noborder tr { border: none; }- table {- margin: 1em;
- }
- th, td {- padding: 0.5em;
- }
-</style>
-</head>
-<body>
- <h1>Generating hat tilings for Loopy</h1>
- <p>The <a href="https://arxiv.org/abs/2303.10798">original paper</a>
- describes a method for generating hat tilings from a system of four
- 'metatiles'. You can start with any one of the four tiles, and then
- recursively apply a set of expansion rules that turn each tile into
- a collection of smaller tiles from the same set.</p>
- <p>This table shows the four tiles, with their one-letter names as
- given in the paper, and how each one is expanded.</p>
- <p>All the tiles have a significant orientation. The H, T and P
- tiles are marked with arrows to indicate the orientation. The F tile
- is asymmetric, so no arrow is needed.</p>
- <p>I've assigned each tile in each expansion a number, which Loopy
- will use for its coordinate system.</p>
- <table>
- <tr>
- <th>Tile name</th>
- <th>Single tile</th>
- <th>Expansion</th>
- <tr>
- <td>H</td>
- <td><img src="single-H.svg"></td>
- <td><img src="expanded-H.svg"></td>
- </tr>
- <tr>
- <td>T</td>
- <td><img src="single-T.svg"></td>
- <td><img src="expanded-T.svg"></td>
- </tr>
- <tr>
- <td>P</td>
- <td><img src="single-P.svg"></td>
- <td><img src="expanded-P.svg"></td>
- </tr>
- <tr>
- <td>F</td>
- <td><img src="single-F.svg"></td>
- <td><img src="expanded-F.svg"></td>
- </tr>
- </table>
- <p><strong>Note that these expansions overlap</strong>. When two
- adjacent metatiles are expanded, the outer layer of P and F tiles in
- their expansions must be placed so that they overlap each other. The
- original paper suggests a set of tiles to remove from these
- expansions so that each metatile expands to a <em>disjoint</em> set
- of smaller tiles. In our implementation, however, we prefer to keep
- the overlap, because our coordinate system will use it.</p>
- <p>Once you've generated a large enough patch of metatiles for your
- needs, the final step is to convert it into the actual hat tiles.
- The expansion of each metatile into hats is shown here. Again, I've
- assigned numbers to each hat for coordinate-system purposes:</p>
- <table>
- <tr>
- <th>Tile name</th>
- <th>Conversion into hats</th>
- <tr>
- <td>H</td>
- <td><img src="single-H.svg"></td>
- <td><img src="hats-single-H.svg"></td>
- </tr>
- <tr>
- <td>T</td>
- <td><img src="single-T.svg"></td>
- <td><img src="hats-single-T.svg"></td>
- </tr>
- <tr>
- <td>P</td>
- <td><img src="single-P.svg"></td>
- <td><img src="hats-single-P.svg"></td>
- </tr>
- <tr>
- <td>F</td>
- <td><img src="single-F.svg"></td>
- <td><img src="hats-single-F.svg"></td>
- </tr>
- </table>
- <p>(The hat in the middle of the H is shaded to indicate that it's
- one of the rare reflected ones. All the other hats are rotations of
- each other.)</p>
- <p>Given all of this, an obvious approach to generating a random
- patch of hat tiling would be to start with a single metatile,
- iterate the expansion process a few times until you have a tiled
- area much larger than you need, and then pick a subrectangle of
- it at random.</p>
- <p>Loopy's algorithm for generating Penrose tilings (which admit a
- similar, though less complicated, expansion system) works in exactly
- this way.</p>
- <p>One problem with that algorithm is that it spends a lot of effort
- on generating huge areas of tiles that aren't actually needed. So
- you'd prefer to adjust the algorithm so that at every stage of
- expansion it spots tiles completely outside the target rectangle,
- and throws them away <em>before</em> spending 5 iterations on
- exponentially expanding them into huge amounts of detail that will
- only be thrown away anyway later.</p>
- <p>That works well for Penrose tilings, because there, the expansion
- procedure is geometrically precise: coordinates in the expanded
- tiling are scaled up by an exact factor from coordinates in the
- original tiling. So at every stage it's easy to know exactly where
- your target rectangle <em>is</em>, and discard things that don't
- overlap it.</p>
- <p>But the metatiles shown here don't have that property. The tiles
- distort slightly as they expand. The <em>topological</em> properties
- of the expanded tiling match the original (which expanded tiles
- connect to each other), but the geometry (precise distances) is
- different. So it would be harder to implement the pruning for this
- tiling. The target rectangle might not even be rectangular in every
- iteration!</p>
- <p>Instead, I came up with a completely different mechanism, by
- devising a coordinate system to track our position within multiple
- layers of tile expansion. This allows us to generate precisely the
- area of tiling we need, and waste no effort at all on anything
- outside the target region.</p>
- <p>We begin by assigning an integer index to each kite making up an
- individual hat:</p>
- <img src="hat-kites.svg">
- <p>(For a reflected hat, these indices work in mirror image, so that
- for example 5 is still the kite in the middle.)</p>
- <p>Together with the indices we've assigned to hats within each
- metatile, and to metatiles in the expansion of another metatile,
- this gives us a coordinate system that can identify an individual
- kite in an n-times-expanded metatile. For each large metatile
- expansion, you can give the index of the smaller metatile selected
- from its expansion; when we reach the last layer of metatiles and
- expand them into hats, we can give the index of the hat in that
- metatile; finally we can index the kite in that hat.</p>
- <p><strong>But note that a kite can have multiple
- coordinates</strong>, because of the overlap between the expansions
- of adjacent metatiles. This will be useful!</p>
- <p>Our next step is to unambiguously name the four directions in
- which you can move from one kite to an adjacent kite. The directions
- should be independent of the orientation of the kite. I've chosen to
- name them from the viewpoint of someone standing at the pointy end
- of the kite and looking towards the blunt end:</p>
- <dl>
- <dt><strong>Left</strong></dt>
- <dd>Rotate 60° anticlockwise about the pointy end of the kite. For
- example, in the above hat, going 'left' from kite 5 takes you to
- kite 4.</dd>
- <dt><strong>Right</strong></dt>
- <dd>Rotate 60° clockwise about the pointy end. From kite 5, this
- would take you to kite 6.</dd>
- <dt><strong>Forward left</strong></dt>
- <dd>Head forwards and slightly left, to the kite sharing the
- left-hand one of this kite's short edges (as seen from the
- centre). Equivalently, rotate 120° <em>clockwise</em> about the
- blunt end. From kite 5, this takes you to kite 2.</dd>
- <dt><strong>Forward right</strong></dt>
- <dd>Head forwards and slightly right. Or rotate 120° anticlockwise
- about the blunt end, if you prefer to think of it that way. From
- kite 5, this takes you to kite 1.</dd>
- </dl>
- <p>The idea is that if we know how to transform the coordinates of a
- single kite into the coordinates of each of those four adjacent
- kites, then we can iterate that over a whole area and determine the
- coordinates of every kite in the whole tiling.</p>
- <p>Having done that, it's easy to identify each individual kite, by
- several different methods. For example, you could iterate over edges
- of the tiling to see whether the kites on each side have coordinates
- differing only in the kite index; if so, they're part of the same
- hat, and if not, not. Or a completely different approach (in fact
- the one Loopy actually uses) would be to trace round the boundary of
- each hat by starting from its kite #0 and just knowing what shape a
- hat is.</p>
- <p>So now we have to come up with an algorithm that lets us
- transform a kite coordinate by making one of the four permitted
- moves. To do this, we use two multilevel types of map.</p>
- <p>The <strong>kitemap</strong> for a given metatile type is made by
- expanding the metatile once into more metatiles, and then into hats.
- For example, the T tile:</p>
- <table class="noborder">
- <tr>
- <td><img src="single-T.svg"></td>
- <td><img src="arrow.svg"></td>
- <td><img src="expanded-T.svg" height="200px"></td>
- <td><img src="arrow.svg"></td>
- <td><img src="kitemap-T.svg" height="500px"></td>
- </tr>
- </table>
- <p>In each kite, we show a three-part coordinate, in little-endian
- fashion (because that matches the order the coordinates are stored
- in an array in the code that actually generates the tilings). For
- example, 7.3.0 means kite 7 in hat 3 of metatile 0 of the
- expansion.</p>
- <p>This map can be converted into a lookup table, indexed by those
- three-part coordinates and also the four move directions, which
- allows you to look up that (for example) going Left from kite 7.3.0
- goes to 0.0.0, or going Forward Left from 7.3.0 goes to 3.1.3.</p>
- <p>But if you're at the very edge of the kitemap, this isn't enough.
- For example, kite 0.0.4 right at the top can go Left to 1.0.4, but
- if it wants to go in any of the other three directions, this map
- doesn't help at all.</p>
- <p>This is where the overlap between the metatile expansions comes
- in. If you're in kite 0.0.4, then in particular, you're in the F
- tile numbered 4 in the expansion of a larger T metatile. And that F
- tile is <em>also</em> part of the expansion of at least one other
- second-order metatile – maybe two of them – which means that there
- are other equivalent coordinates describing the same kite, which
- will place it in a different kitemap where it <em>isn't</em> right
- on the edge,</p>
- <p>In order to find those equivalent coordinates, we create a second
- map for each metatile type, called the <strong>metamap</strong>.
- This one arises from expanding the metatile twice into other
- metatiles, instead of into hats:</p>
- <table class="noborder">
- <tr>
- <td><img src="single-T.svg"></td>
- <td><img src="arrow.svg"></td>
- <td><img src="expanded-T.svg" height="200px"></td>
- <td><img src="arrow.svg"></td>
- <td><img src="metamap-T.svg" height="500px"></td>
- </tr>
- </table>
- <p>Again, the coordinates are little-end first, so that 7.4 means
- the 7th smallest-size tile expanded from the 4th medium-sized tile
- expanded from the original single large tile.</p>
- <p>Unlike the kitemap, the metamap is not used for <em>moving
- around</em> the tiling to a different kite. It's used for rewriting
- the coordinates of the current kite into equivalent forms. So each
- the small tile in the metamap that's part of the expansion
- of <em>more than one</em> medium-sized tile has more than one
- coordinate pair. For example, tile 5.2 is also tile 5.4, and tile
- 7.0 is also 8.3 <em>and</em> also 4.5 (because it's where three
- medium-tile expansions meet).</p>
- <p>Using both of these maps (converted into appropriate lookup
- tables in the code), you can always eventually find a valid
- coordinate representation of whichever kite you like adjacent to
- your current one. If the kitemap corresponding to the current
- coordinates doesn't tell you the coordinates of the next kite, then
- you can try rewriting the two least-significant metatile indices
- (using the metamap corresponding to the type of the next-larger
- metatile still) and then see if that gives you a new kitemap that
- works. If even that doesn't work, you can move another level up, and
- try a metamap rewrite on the 2nd and 3rd smallest metatile levels,
- or the 3rd and 4th, etc. And eventually, you find something you can
- do.</p>
- <p>The full set of kitemaps and metamaps for all the tile
- types is in <a href="hatmaps.html">hatmaps.html</a>.</p>
-</body>
-</html>
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-</svg>
--- a/aux/doc/single-F.svg
+++ /dev/null
@@ -1,9 +1,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="66" height="162">
-<path style="fill: none; stroke: black; stroke-width: 2.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 2.000000 140.564056
-L 32.000000 157.884567
-L 62.000000 140.564056
-L 62.000000 2.000000
-L 2.000000 36.641014
-z" />
-</svg>
--- a/aux/doc/single-H.svg
+++ /dev/null
@@ -1,11 +1,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="156" height="180">
-<path style="fill: none; stroke: black; stroke-width: 2.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 2.000000 157.884567
-L 32.000000 175.205078
-L 152.000000 105.923050
-L 152.000000 71.282021
-L 32.000000 2.000000
-L 2.000000 19.320511
-z" />
-<path style="fill: none; stroke: black; stroke-width: 9.000000; stroke-opacity: 0.2; stroke-linejoin: round; stroke-linecap: round; " d="M 32.000000 36.641014 L 77.000000 114.583298 L 81.392305 98.190992 M 77.000000 114.583298 L 60.607695 110.190993 " />
-</svg>
--- a/aux/doc/single-P.svg
+++ /dev/null
@@ -1,9 +1,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="66" height="180">
-<path style="fill: none; stroke: black; stroke-width: 2.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 2.000000 175.205093
-L 62.000000 140.564087
-L 62.000000 2.000000
-L 2.000000 36.641037
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-<path style="fill: none; stroke: black; stroke-width: 9.000000; stroke-opacity: 0.2; stroke-linejoin: round; stroke-linecap: round; " d="M 14.000000 88.602562 L 50.000000 88.602554 L 37.999997 76.602557 M 50.000000 88.602554 L 38.000003 100.602557 " />
-</svg>
--- a/aux/doc/single-T.svg
+++ /dev/null
@@ -1,8 +1,0 @@
-<?xml version="1.0" encoding="UTF-8" standalone="no"?>
-<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="96" height="110">
-<path style="fill: none; stroke: black; stroke-width: 2.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 2.000000 105.923042
-L 92.000000 53.961521
-L 2.000000 2.000000
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-</svg>
--- a/aux/hatgen-images.sh
+++ /dev/null
@@ -1,23 +1,0 @@
-#!/bin/sh
-
-# Regenerate all the SVG images in the aux/doc directory for hats.html
-# and hatmap.html.
-
-set -e
-
-hatgen=$1
-
-if ! test -x "$hatgen"; then
- echo "Provide pathname to hatgen as an argument" >&2
- exit 1
-fi
-
-for tile in H T P F; do
- "$hatgen" "$tile" > single-"$tile".svg
- "$hatgen" c"$tile" > expanded-"$tile".svg
- "$hatgen" h"$tile" > hats-single-"$tile".svg
- "$hatgen" H"$tile" > kitemap-"$tile".svg
- "$hatgen" C"$tile" > metamap-"$tile".svg
-done
-
-"$hatgen" --hat > hat-kites.svg
--- a/aux/hatgen.c
+++ /dev/null
@@ -1,1713 +1,0 @@
-/*
- * Generate patches of tiling by the 'hat' aperiodic monotile
- * discovered in 2023.
- *
- * This implementation of hat-tiling generation was intended to be the
- * basis for generating hat grids for Loopy. However, it turned out
- * that I found a better strategy, so this source file isn't used by
- * the main puzzle system. I've kept it anyway because I ended up
- * adapting it to generate the file hat-tables.h containing the lookup
- * tables for the algorithm I _did_ end up using. It also generates
- * diagrams that are useful for understanding that algorithm, and for
- * debugging it if anything still turns out to be wrong with it.
- *
- * Discoverers' website: https://cs.uwaterloo.ca/~csk/hat/
- * Preprint of paper: https://arxiv.org/abs/2303.10798
- */
-
-#include <assert.h>
-#include <math.h>
-#include <stdbool.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-
-#include "puzzles.h"
-#include "tree234.h"
-#include "hat.h"
-
-/*
- * General strategy:
- *
- * We construct the hat tiling by means of a substitution system of
- * 'metatiles' which come in four types, called H,T,P,F. A (valid)
- * tiling of these metatiles can be expanded to a larger one by a set
- * of recursive subdivision rules. Once we have a large enough patch
- * of metatiles, we apply a final transformation that converts each
- * metatile into 1, 2 or 4 instances of the aperiodically tiling
- * 'hat'.
- *
- * Unlike the similar substitution system for Penrose tilings, the
- * expansion rules are not geometrically precise: the larger versions
- * of each metatile fit together combinatorially in the same way, but
- * their shapes are distorted slightly. So we must construct our
- * expanded meta-tiling by breadth-first search out from a starting
- * metatile, because we won't quite know the coordinates of the
- * expanded version of each metatile until we know one of the ones
- * next to it.
- */
-
-/*
- * Coordinate system:
- *
- * Everything in this code lives on the tiling known to grid.c as
- * 'Kites', which can be viewed as a tiling of hexagons each of which
- * is subdivided into six kites sharing their pointy vertex, or
- * (equivalently) a tiling of equilateral triangles each subdivided
- * into three kits sharing their blunt vertex.
- *
- * We express coordinates in this system relative to the basis (1, r)
- * where r = (1 + sqrt(3)i) / 2 is a primitive 6th root of unity. This
- * gives us a system in which two integer coordinates can address any
- * grid point, provided we scale up so that the side length of the
- * equilateral triangles in the tiling is 6.
- */
-
-typedef struct Point {- int x, y; /* represents x + yr */
-} Point;
-
-static inline Point left6(Point p)
-{- /* r satisfies the equation r^2 = r-1. Hence, multiplying by r
- * (achieving a rotation anticlockwise by 1/6 turn) transforms
- * x+yr into xr+yr^2 = xr+y(r-1) = (-y) + (x+y)r.
- *
- * It's easy to check that iterating this transformation six times
- * gives you back the same coordinates you started with. */
- Point q = { -p.y, p.x + p.y };- return q;
-}
-
-static inline Point right6(Point p)
-{- /* Conversely, 1/r = 1 - r, so dividing by r turns x+yr into x/r+y
- * = x(1-r) + y = (x+y) + (-x)r. */
- Point q = { p.x + p.y, -p.x };- return q;
-}
-
-typedef enum MetatileType { MT_H, MT_T, MT_P, MT_F } MetatileType;-typedef struct Metatile Metatile;
-typedef struct MetaCoord {- Metatile *parent;
- int index;
-} MetaCoord;
-
-struct Metatile {- /* Data fields describing the metatile and its position. */
- MetatileType type;
- Point start, orientation;
-
- MetaCoord coords[4];
- size_t ncoords;
-
- /* Auxiliary fields used to store the progress of the expansion
- * algorithm. */
- bool queued;
- Metatile *qnext;
-};
-
-#define MT_MAXVERT 6 /* largest number of vertices of any metatile */
-#define MT_MAXVDEGREE 3 /* largest degree of any vertex of a meta-tiling */
-#define MT_MAXEXPAND 13 /* largest number of metatiles in any expansion */
-#define MT_MAXHAT 4 /* largest number of hats in a metatile */
-#define HAT_NVERT 14 /* vertices of a single hat (counting the straight one) */
-#define HAT_NKITE 8 /* kites in a single hat */
-
-static int metatile_cmp(void *av, void *bv)
-{- Metatile *a = (Metatile *)av, *b = (Metatile *)bv;
- if (a->type < b->type) return -1;
- if (a->type > b->type) return +1;
- if (a->start.x < b->start.x) return -1;
- if (a->start.x > b->start.x) return +1;
- if (a->start.y < b->start.y) return -1;
- if (a->start.y > b->start.y) return +1;
- if (a->orientation.x < b->orientation.x) return -1;
- if (a->orientation.x > b->orientation.x) return +1;
- if (a->orientation.y < b->orientation.y) return -1;
- if (a->orientation.y > b->orientation.y) return +1;
- return 0;
-}
-
-/*
- * Return the coordinates of the vertices of a metatile, given the
- * coordinates of the vertex we deem to be distinguished, and a vector
- * of Euclidean length 1 showing its direction.
- *
- * If 'expanded' is true, we instead return the coordinates of the
- * corresponding vertices of the expanded version of the same
- * metatile.
- */
-static size_t metatile_vertices(Metatile m, Point *out, bool expanded)
-{- static const Point vertices_H[] = {- {0, 0}, {4, -2}, {12, 6}, {10, 10}, {-6, 18}, {-8, 16},- };
- static const Point vertices_T[] = {- {0, 0}, {6, 6}, {-6, 12},- };
- static const Point vertices_P[] = {- {0, 0}, {4, 4}, {-4, 20}, {-8, 16},- };
- static const Point vertices_F[] = {- {0, 0}, {4, -2}, {6, 0}, {-2, 16}, {-6, 12},- };
-
- static const Point expanded_H[] = {- {0, 0}, {12, -6}, {30, 12}, {24, 24}, {-12, 42}, {-18, 36},- };
- static const Point expanded_T[] = {- {0, 0}, {12, 12}, {-12, 24},- };
- static const Point expanded_P[] = {- {0, 0}, {14, 8}, {-4, 44}, {-18, 36},- };
- static const Point expanded_F[] = {- {0, 0}, {14, -4}, {18, 6}, {0, 42}, {-14, 34},- };
-
- const Point *vertices;
- size_t nvertices;
- size_t i;
-
- switch (m.type) {- case MT_H:
- vertices = expanded ? expanded_H : vertices_H;
- nvertices = lenof(vertices_H);
- break;
- case MT_T:
- vertices = expanded ? expanded_T : vertices_T;
- nvertices = lenof(vertices_T);
- break;
- case MT_P:
- vertices = expanded ? expanded_P : vertices_P;
- nvertices = lenof(vertices_P);
- break;
- default /* case MT_F */:
- vertices = expanded ? expanded_F : vertices_F;
- nvertices = lenof(vertices_F);
- break;
- }
- assert(nvertices <= MT_MAXVERT);
-
- Point orientation_r = left6(m.orientation);
- for (i = 0; i < nvertices; i++) {- Point v = vertices[i];
- out[i].x = m.start.x + v.x * m.orientation.x + v.y * orientation_r.x;
- out[i].y = m.start.y + v.x * m.orientation.y + v.y * orientation_r.y;
- }
- return nvertices;
-}
-
-/*
- * Return a list of metatiles that arise from expanding a given tile.
- */
-static size_t metatile_expand(Metatile m, Metatile *out)
-{- static const Metatile tiles_H[] = {- {MT_H, {-4, 20}, {1, 0}},- {MT_H, {2, 2}, {1, 0}},- {MT_H, {8, 26}, {0, -1}},- {MT_T, {6, 24}, {-1, 0}},- {MT_P, {-8, 16}, {1, 0}},- {MT_P, {4, 34}, {0, -1}},- {MT_P, {6, 0}, {1, -1}},- {MT_F, {-10, 38}, {-1, 1}},- {MT_F, {-10, 44}, {0, -1}},- {MT_F, {-4, 2}, {1, 0}},- {MT_F, {2, 2}, {0, -1}},- {MT_F, {26, 14}, {1, 0}},- {MT_F, {32, 8}, {-1, 1}},- };
- static const Metatile tiles_T[] = {- {MT_H, {10, 10}, {-1, 1}},- {MT_P, {-6, 0}, {1, 0}},- {MT_P, {8, 14}, {0, 1}},- {MT_P, {18, 6}, {-1, 1}},- {MT_F, {-14, 34}, {-1, 0}},- {MT_F, {-8, -2}, {1, -1}},- {MT_F, {22, 4}, {0, 1}},- };
- static const Metatile tiles_P[] = {- {MT_H, {4, 22}, {0, 1}},- {MT_H, {10, 10}, {-1, 1}},- {MT_P, {-6, 0}, {1, 0}},- {MT_P, {6, 24}, {1, 0}},- {MT_P, {8, 14}, {0, 1}},- {MT_F, {-20, 40}, {1, -1}},- {MT_F, {-14, 34}, {-1, 0}},- {MT_F, {-8, -2}, {1, -1}},- {MT_F, {4, 46}, {-1, 1}},- {MT_F, {10, 10}, {1, 0}},- {MT_F, {16, 4}, {-1, 1}},- };
- static const Metatile tiles_F[] = {- {MT_H, {8, 20}, {0, 1}},- {MT_H, {14, 8}, {-1, 1}},- {MT_P, {10, 22}, {1, 0}},- {MT_P, {12, 12}, {0, 1}},- {MT_F, {-16, 38}, {1, -1}},- {MT_F, {-10, 32}, {-1, 0}},- {MT_F, {-4, 2}, {1, 0}},- {MT_F, {2, 2}, {0, -1}},- {MT_F, {8, 44}, {-1, 1}},- {MT_F, {14, 8}, {1, 0}},- {MT_F, {20, 2}, {-1, 1}},- };
-
- const Metatile *tiles;
- size_t ntiles;
- size_t i;
-
- switch (m.type) {- case MT_H:
- tiles = tiles_H;
- ntiles = lenof(tiles_H);
- break;
- case MT_T:
- tiles = tiles_T;
- ntiles = lenof(tiles_T);
- break;
- case MT_P:
- tiles = tiles_P;
- ntiles = lenof(tiles_P);
- break;
- default /* case MT_F */:
- tiles = tiles_F;
- ntiles = lenof(tiles_F);
- break;
- }
- assert(ntiles <= MT_MAXEXPAND);
-
- Point orientation_r = left6(m.orientation);
- for (i = 0; i < ntiles; i++) {- Metatile t = tiles[i];
- out[i].type = t.type;
- out[i].start.x = (m.start.x + t.start.x * m.orientation.x +
- t.start.y * orientation_r.x);
- out[i].start.y = (m.start.y + t.start.x * m.orientation.y +
- t.start.y * orientation_r.y);
- out[i].orientation.x = (t.orientation.x * m.orientation.x +
- t.orientation.y * orientation_r.x);
- out[i].orientation.y = (t.orientation.x * m.orientation.y +
- t.orientation.y * orientation_r.y);
- }
- return ntiles;
-}
-
-/* Store data about each vertex during an expansion. */
-typedef struct VertexMapping {- Point in;
-
- /* Metatiles sharing this vertex */
- Metatile *tiles[MT_MAXVDEGREE];
- size_t ntiles;
-
- /* The expanded coordinates of this vertex, if known */
- bool mapped;
- Point out;
-} VertexMapping;
-
-static int vertexmapping_cmp(void *av, void *bv)
-{- VertexMapping *a = (VertexMapping *)av, *b = (VertexMapping *)bv;
- if (a->in.x < b->in.x) return -1;
- if (a->in.x > b->in.x) return +1;
- if (a->in.y < b->in.y) return -1;
- if (a->in.y > b->in.y) return +1;
- return 0;
-}
-
-static int vertexmapping_find(void *av, void *bv)
-{- Point *a = (Point *)av;
- VertexMapping *b = (VertexMapping *)bv;
- if (a->x < b->in.x) return -1;
- if (a->x > b->in.x) return +1;
- if (a->y < b->in.y) return -1;
- if (a->y > b->in.y) return +1;
- return 0;
-}
-
-typedef struct MetatileSet {- /* The tiles in the set */
- tree234 *tiles;
-
- /*
- * Bounding box of a rectangular region within the original single
- * tile this set was expanded from. We need this in order to pick
- * a random chunk out of the tiling to return to our client: this
- * box is the limit of where we might select our chunk from.
- *
- * The box is obtained by starting from the two obtuse vertices of
- * the starting P metatile, and then mapping those two vertices
- * through each expansion pass. This wouldn't work for the _other_
- * two vertices of the P metatile, which end up in the middle of
- * another metatile after the first expansion, so that the next
- * expansion wouldn't find that point in its VertexMapping. But
- * luckily the two inner P vertices do continue working: they
- * alternate in subsequent expansions between vertex 1 and vertex
- * 4 of an F metatile. And those are the ones we need to define a
- * reliable bounding box - phew!
- */
- Point vertices[2];
- size_t nvertices;
-} MetatileSet;
-
-static MetatileSet *metatile_initial_set(MetatileType type)
-{- MetatileSet *s;
- Metatile *m;
- Point vertices[MT_MAXVERT];
- size_t nv;
-
- s = snew(MetatileSet);
- s->tiles = newtree234(metatile_cmp);
-
- m = snew(Metatile);
- m->type = type;
- m->start.x = 0;
- m->start.y = 0;
- m->orientation.x = 1;
- m->orientation.y = 0;
- m->ncoords = 0;
- add234(s->tiles, m);
-
- if (type == MT_P) {- nv = metatile_vertices(*m, vertices, false);
- assert(nv == 4);
- s->vertices[0] = vertices[1];
- s->vertices[1] = vertices[3];
- s->nvertices = 2;
- } else {- s->nvertices = 0;
- }
-
- return s;
-}
-
-static void metatile_free_set(MetatileSet *s)
-{- Metatile *m;
-
- while ((m = delpos234(s->tiles, 0)) != NULL)
- sfree(m);
- freetree234(s->tiles);
- sfree(s);
-}
-
-typedef struct Queue {- Metatile *head, *tail;
-} Queue;
-
-static void map_vertex(VertexMapping *vm, Point out, Queue *queue)
-{- size_t i;
-
- debug(("map_vertex %d,%d -> %d,%d", vm->in.x, vm->in.y, out.x, out.y));- if (vm->mapped) {- debug((" (already done)\n"));- return;
- }
- debug(("\n"));-
- vm->mapped = true;
- vm->out = out;
-
- for (i = 0; i < vm->ntiles; i++) {- Metatile *t = vm->tiles[i];
- if (!t->queued) {- t->queued = true;
- t->qnext = NULL;
- if (queue->tail)
- queue->tail->qnext = t;
- else
- queue->head = t;
- queue->tail = t;
- debug(("queued %c @ %d,%d d=%d,%d\n", "HTPF"[t->type], t->start.x,- t->start.y, t->orientation.x, t->orientation.y));
- }
- }
-}
-
-/*
- * Expand a set of metatiles into its next-generation set. Returns the
- * new set. The old set is not freed, but the auxiliary fields of its
- * Metatile structures will be used as intermediate storage.
- */
-static MetatileSet *metatile_set_expand(MetatileSet *si)
-{- tree234 *vmap;
- VertexMapping *vm;
- Metatile *m;
- Queue queue = { NULL, NULL };- size_t i, j;
- MetatileSet *so = snew(MetatileSet);
-
- so->tiles = newtree234(metatile_cmp);
-
- /*
- * Enumerate all the vertices in our tiling, and store the set of
- * tiles they belong to.
- */
- vmap = newtree234(vertexmapping_cmp);
- for (i = 0; (m = index234(si->tiles, i)) != NULL; i++) {- Point vertices[MT_MAXVERT];
- size_t nv = metatile_vertices(*m, vertices, false);
-
- for (j = 0; j < nv; j++) {- VertexMapping *newvm = snew(VertexMapping);
- newvm->in = vertices[j];
- newvm->ntiles = 0;
- newvm->mapped = false;
-
- vm = add234(vmap, newvm);
- if (vm != newvm)
- sfree(newvm);
-
- assert(vm->ntiles < MT_MAXVDEGREE);
- vm->tiles[vm->ntiles++] = m;
- }
-
- m->queued = false;
- }
-
- for (i = 0; (vm = index234(vmap, i)) != NULL; i++) {- debug(("vertex @ %d,%d {", vm->in.x, vm->in.y));- for (j = 0; j < vm->ntiles; j++) {- m = vm->tiles[j];
- debug(("%s%c @ %d,%d d=%d,%d", j?", ":"", "HTPF"[m->type],- m->start.x, m->start.y, m->orientation.x,
- m->orientation.y));
- }
- debug(("}\n"));- }
-
- /*
- * Initialise an arbitrary vertex to a known location.
- */
- {- Point p = {0, 0};- m = index234(si->tiles, 0);
- vm = find234(vmap, &m->start, vertexmapping_find);
- map_vertex(vm, p, &queue);
- }
-
- /*
- * Now process the queue of tiles to be expanded.
- */
- debug(("-- start\n"));- while (queue.head) {- Metatile *m, m_moved;
- Metatile t[MT_MAXEXPAND];
- Point vi[MT_MAXVERT], vo[MT_MAXVERT];
- size_t nv, nt;
-
- m = queue.head;
- queue.head = queue.head->qnext;
- if (!queue.head)
- queue.tail = NULL;
-
- debug(("unqueued %c @ %d,%d d=%d,%d\n", "HTPF"[m->type],- m->start.x, m->start.y, m->orientation.x, m->orientation.y));
-
- nv = metatile_vertices(*m, vi, false);
- metatile_vertices(*m, vo, true);
-
- /* Find a vertex of this tile that's already mapped, and use
- * it to determine the placement. */
- int dx, dy;
- for (i = 0; i < nv; i++) {- vm = find234(vmap, &vi[i], vertexmapping_find);
- assert(vm);
- if (vm->mapped) {- dx = vm->out.x - vo[i].x;
- dy = vm->out.y - vo[i].y;
- debug(("found mapped vertex %d,%d -> %d,%d: "- "offset=%d,%d\n",
- vm->in.x, vm->in.y, vm->out.x, vm->out.y, dx, dy));
- break;
- }
- }
- assert(i < nv && "Why was this tile queued without a mapped vertex?");
-
- /* Now map all the rest of the vertices of the tile. */
- for (i = 0; i < nv; i++) {- vm = find234(vmap, &vi[i], vertexmapping_find);
- vo[i].x += dx;
- vo[i].y += dy;
- map_vertex(vm, vo[i], &queue);
- }
-
- /* And expand it, substituting in its new starting coordinate. */
- m_moved = *m; /* structure copy */
- m_moved.start = vo[0];
- nt = metatile_expand(m_moved, t);
- for (i = 0; i < nt; i++) {- Metatile *newmt = snew(Metatile);
- *newmt = t[i]; /* structure copy */
- newmt->ncoords = 0;
- debug(("expanded %c @ %d,%d d=%d,%d\n", "HTPF"[newmt->type],- newmt->start.x, newmt->start.y, newmt->orientation.x,
- newmt->orientation.y));
-
- Metatile *added = add234(so->tiles, newmt);
- if (added != newmt)
- sfree(newmt);
- assert(added->ncoords < lenof(added->coords));
- added->coords[added->ncoords].parent = m;
- added->coords[added->ncoords].index = i;
- added->ncoords++;
- }
- }
-
- for (i = 0; (m = index234(si->tiles, i)) != NULL; i++) {- if (!m->queued)
- debug(("OMITTED %c @ %d,%d d=%d,%d\n", "HTPF"[m->type],- m->start.x, m->start.y, m->orientation.x,
- m->orientation.y));
- }
-
- /*
- * Write out the remapped versions of the tile set's bounding
- * vertices.
- */
- for (i = 0; i < si->nvertices; i++) {- vm = find234(vmap, &si->vertices[i], vertexmapping_find);
- so->vertices[i] = vm->out;
- }
- so->nvertices = si->nvertices;
-
- while ((vm = delpos234(vmap, 0)) != NULL)
- sfree(vm);
- freetree234(vmap);
-
- return so;
-}
-
-typedef struct Hat {- Point start, orientation;
- bool reversed;
- const Metatile *parent;
- int index;
-} Hat;
-
-static size_t metatile_hats(const Metatile *m, Hat *out)
-{- static const Hat hats_H[] = {- {{6, 0}, {1, 0}, false},- {{6, 6}, {0, -1}, false},- {{0, 12}, {1, 0}, false},- {{0, 6}, {-1, 0}, true},- };
- static const Hat hats_T[] = {- {{-2, 10}, {-1, 1}, false},- };
- static const Hat hats_P[] = {- {{-2, 10}, {-1, 1}, false},- {{-2, 16}, {0, 1}, false},- };
- static const Hat hats_F[] = {- {{0, 6}, {-1, 1}, false},- {{0, 12}, {0, 1}, false},- };
-
- const Hat *hats;
- size_t nhats;
- size_t i;
-
- switch (m->type) {- case MT_H:
- hats = hats_H;
- nhats = lenof(hats_H);
- break;
- case MT_T:
- hats = hats_T;
- nhats = lenof(hats_T);
- break;
- case MT_P:
- hats = hats_P;
- nhats = lenof(hats_P);
- break;
- default /* case MT_F */:
- hats = hats_F;
- nhats = lenof(hats_F);
- break;
- }
- assert(nhats <= MT_MAXHAT);
-
- Point orientation_r = left6(m->orientation);
- for (i = 0; i < nhats; i++) {- Hat h = hats[i];
- out[i].parent = m;
- out[i].index = i;
- out[i].start.x = (m->start.x + h.start.x * m->orientation.x +
- h.start.y * orientation_r.x);
- out[i].start.y = (m->start.y + h.start.x * m->orientation.y +
- h.start.y * orientation_r.y);
- out[i].orientation.x = (h.orientation.x * m->orientation.x +
- h.orientation.y * orientation_r.x);
- out[i].orientation.y = (h.orientation.x * m->orientation.y +
- h.orientation.y * orientation_r.y);
- out[i].reversed = h.reversed;
- }
- return nhats;
-}
-
-static size_t hat_vertices(Hat h, Point *out)
-{- static const Point reference_hat[] = {- {0, 0}, {3, 0}, {2, 2}, {0, 3}, {-2, 4}, {-3, 3}, {-6, 6}, {-9, 6},- {-8, 4}, {-6, 3}, {-6, 0}, {-3, -3}, {-2, -2}, {0, -3},- };
-
- size_t i;
-
- Point orientation_r;
- if (h.reversed)
- orientation_r = right6(h.orientation);
- else
- orientation_r = left6(h.orientation);
- assert(lenof(reference_hat) == HAT_NVERT);
-
- for (i = 0; i < lenof(reference_hat); i++) {- Point v = reference_hat[h.reversed ? HAT_NVERT-1-i : i];
- out[i].x = h.start.x + v.x * h.orientation.x + v.y * orientation_r.x;
- out[i].y = h.start.y + v.x * h.orientation.y + v.y * orientation_r.y;
- }
- return lenof(reference_hat);
-}
-
-typedef struct BoundingBox {- Point bl, tr;
-} BoundingBox;
-
-static bool point_in_bbox(Point p, const BoundingBox *bbox)
-{- int xl, xr, x;
-
- if (!bbox)
- return true;
-
- /*
- * Bounding boxes have vertical edges, not aligned with our basis
- * vector r. So the 'true' x coordinate of (x,y) is proportional
- * to 2x+y.
- */
- if (p.y < bbox->bl.y || p.y > bbox->tr.y)
- return false;
-
- xl = 2*bbox->bl.x + bbox->bl.y;
- xr = 2*bbox->tr.x + bbox->tr.y;
- x = 2*p.x + p.y;
-
- if (x < xl || x > xr)
- return false;
-
- return true;
-}
-
-static bool hat_in_bbox(Hat h, const BoundingBox *bbox)
-{- Point p[HAT_NVERT];
- size_t i, np;
-
- if (!bbox)
- return true;
-
- np = hat_vertices(h, p);
- for (i = 0; i < np; i++)
- if (!point_in_bbox(p[i], bbox))
- return false;
-
- return true;
-}
-
-static Hat *metatile_set_to_hats(MetatileSet *s, size_t *nhats,
- const BoundingBox *bbox)
-{- Metatile *m;
- size_t i, j, k, n;
- Hat *h;
-
- n = 0;
- for (i = 0; (m = index234(s->tiles, i)) != NULL; i++) {- Hat htmp[MT_MAXHAT];
- size_t nthis = metatile_hats(m, htmp);
- for (k = 0; k < nthis; k++)
- if (hat_in_bbox(htmp[k], bbox))
- n++;
- }
-
- *nhats = n;
- h = snewn(n, Hat);
-
- j = 0;
- for (i = 0; (m = index234(s->tiles, i)) != NULL; i++) {- Hat htmp[MT_MAXHAT];
- size_t nthis = metatile_hats(m, htmp);
- for (k = 0; k < nthis; k++) {- if (hat_in_bbox(htmp[k], bbox)) {- assert(j < n);
- h[j++] = htmp[k]; /* structure copy */
- }
- }
- }
-
- assert(j == n);
- return h;
-}
-
-#if 0
-void hat_tiling_randomise(struct HatPatchParams *params, random_state *rs)
-{- MetatileSet *s, *s2;
- int x0, x1, y0, y1;
-
- /*
- * Iterate until we have a good-sized patch to select a rectangle
- * from.
- */
- s = metatile_initial_set(MT_P);
- params->iterations = 0;
-
- while (true) {- x0 = 2 * s->vertices[0].x + s->vertices[0].y;
- x1 = 2 * s->vertices[1].x + s->vertices[1].y;
- if (x1 < x0) {- int t = x1;
- x1 = x0;
- x0 = t;
- }
- y0 = s->vertices[0].y;
- y1 = s->vertices[1].y;
- if (y1 < y0) {- int t = y1;
- y1 = y0;
- y0 = t;
- }
-
- if (50*params->w <= x1-x0 && 50*params->h <= y1-y0)
- break;
-
- params->iterations++;
- s2 = metatile_set_expand(s);
- metatile_free_set(s);
- s = s2;
- }
-
- /*
- * Now select that rectangle.
- */
- params->x = x0 + random_upto(rs, x1 - x0 - params->w + 1);
- params->y = y0 + random_upto(rs, y1 - y0 - params->h + 1);
-}
-
-void hat_tiling_generate(struct HatPatchParams *params,
- hat_tile_callback_fn cb, void *cbctx)
-{- MetatileSet *s, *s2;
- unsigned i;
- size_t j, nh;
- BoundingBox bbox;
- Hat *hats;
-
- s = metatile_initial_set(MT_P);
- for (i = 0; i < params->iterations; i++) {- s2 = metatile_set_expand(s);
- metatile_free_set(s);
- s = s2;
- }
-
- bbox.bl.x = (params->x - params->y) / 2;
- bbox.tr.x = ((params->x + params->w) - (params->y + params->h)) / 2;
- bbox.bl.y = params->y;
- bbox.tr.y = params->y + params->h;
- hats = metatile_set_to_hats(s, &nh, &bbox);
- for (j = 0; j < nh; j++) {- Point vertices[HAT_NVERT];
- size_t nv = hat_vertices(hats[j], vertices);
- int out[2 * HAT_NVERT];
- size_t k;
-
- for (k = 0; k < nv; k++) {- out[2*k] = 2 * vertices[k].x + vertices[k].y;
- out[2*k+1] = vertices[k].y;
- }
-
- cb(cbctx, nv, out);
- }
- sfree(hats);
-
- metatile_free_set(s);
-}
-
-#endif
-
-#ifdef TEST_HAT
-
-/*
- * Assortment of test modes that output Postscript diagrams.
- */
-
-static size_t hat_kite_centres(Hat h, Point *out)
-{- static const Point reference_hat[] = {- {-7,5},{-5,4},{-5,1},{-4,-1},{-1,-1},{-2,1},{-1,2},{1,1},- };
-
- size_t i;
-
- Point orientation_r;
- if (h.reversed)
- orientation_r = right6(h.orientation);
- else
- orientation_r = left6(h.orientation);
- assert(lenof(reference_hat) == HAT_NKITE);
-
- for (i = 0; i < lenof(reference_hat); i++) {- Point v = reference_hat[i];
- out[i].x = h.start.x + v.x * h.orientation.x + v.y * orientation_r.x;
- out[i].y = h.start.y + v.x * h.orientation.y + v.y * orientation_r.y;
- }
- return lenof(reference_hat);
-}
-
-static inline int round6(int x)
-{- int sign = x<0 ? -1 : +1;
- x *= sign;
- x += 3;
- x /= 6;
- x *= 6;
- x *= sign;
- return x;
-}
-
-static inline Point kite_left(Point k)
-{- Point centre = { round6(k.x), round6(k.y) };- Point offset = { k.x - centre.x, k.y - centre.y };- offset = left6(offset);
- Point r = { centre.x + offset.x, centre.y + offset.y };- return r;
-}
-
-static inline Point kite_right(Point k)
-{- Point centre = { round6(k.x), round6(k.y) };- Point offset = { k.x - centre.x, k.y - centre.y };- offset = right6(offset);
- Point r = { centre.x + offset.x, centre.y + offset.y };- return r;
-}
-
-static inline Point kite_forward_left(Point k)
-{- Point centre = { round6(k.x), round6(k.y) };- Point offset = { k.x - centre.x, k.y - centre.y };- Point rotate = left6(offset);
- Point r = { k.x + rotate.x + offset.x, k.y + rotate.y + offset.y };- return r;
-}
-
-static inline Point kite_forward_right(Point k)
-{- Point centre = { round6(k.x), round6(k.y) };- Point offset = { k.x - centre.x, k.y - centre.y };- Point rotate = right6(offset);
- Point r = { k.x + rotate.x + offset.x, k.y + rotate.y + offset.y };- return r;
-}
-
-typedef struct pspoint {- float x, y;
-} pspoint;
-
-static inline pspoint pscoords(Point p)
-{- pspoint q = { p.x + p.y / 2.0F, p.y * sqrt(0.75) };- return q;
-}
-
-typedef struct psbbox {- bool started;
- pspoint bl, tr;
-} psbbox;
-
-static inline void psbbox_add(psbbox *bbox, pspoint p)
-{- if (!bbox->started || bbox->bl.x > p.x)
- bbox->bl.x = p.x;
- if (!bbox->started || bbox->tr.x < p.x)
- bbox->tr.x = p.x;
- if (!bbox->started || bbox->bl.y > p.y)
- bbox->bl.y = p.y;
- if (!bbox->started || bbox->tr.y < p.y)
- bbox->tr.y = p.y;
- bbox->started = true;
-}
-
-static void draw_metatiles_svg(const Metatile *tiles, size_t n,
- const Point *bounds, bool coords)
-{- size_t i, j;
- psbbox bbox = { false };-
- for (i = 0; i < n; i++) {- Point vertices[MT_MAXVERT];
- size_t nv = metatile_vertices(tiles[i], vertices, false);
- for (j = 0; j < nv; j++)
- psbbox_add(&bbox, pscoords(vertices[j]));
- }
-
- float ascale = 10, xscale = ascale, yscale = -ascale;
- float border = 0.2 * ascale; /* leave room for strokes at the edges */
- float ox = -xscale * bbox.bl.x + border;
- float oy = -yscale * bbox.tr.y + border;
-
- printf("<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n");- printf("<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\" "- "width=\"%g\" height=\"%g\">\n",
- ceil(ox + xscale * bbox.tr.x + 2*border),
- ceil(oy + yscale * bbox.bl.y + 2*border));
-
- for (i = 0; i < n; i++) {- Point vertices[MT_MAXVERT];
- size_t nv = metatile_vertices(tiles[i], vertices, false);
- pspoint pp[MT_MAXVERT];
-
- for (j = 0; j < nv; j++) {- pp[j] = pscoords(vertices[j]);
- pp[j].x = ox + xscale * pp[j].x;
- pp[j].y = oy + yscale * pp[j].y;
- }
-
- printf("<path style=\""- "fill: none; "
- "stroke: black; "
- "stroke-width: %f; "
- "stroke-linejoin: round; "
- "stroke-linecap: round; "
- "\" d=\"", 0.2 * ascale);
- for (j = 0; j < nv; j++)
- printf("%s %f %f \n", j ? "L" : "M", pp[j].x, pp[j].y);- printf("z\" />\n");-
- if (tiles[i].type != MT_F) {- /*
- * Mark arrows on three of the metatile types (H, T, P),
- * following the diagrams in the paper. (The metatile
- * shapes other than F each have some symmetry, but their
- * roles in the metatile substitution system are not
- * similarly symmetric, so for diagnostic diagrams you
- * want to mark their orientation.)
- */
- pspoint lstart, lend;
- pspoint astart, aend, aforward, aleft;
- double d;
-
- /*
- * Determine endpoints of a line crossing the polygon in
- * the appropriate direction, by case analysis on the
- * individual tile types.
- */
- switch (tiles[i].type) {- case MT_H:
- lstart.x = (pp[4].x + pp[5].x) / 2;
- lstart.y = (pp[4].y + pp[5].y) / 2;
- lend.x = (pp[1].x + pp[2].x) / 2;
- lend.y = (pp[1].y + pp[2].y) / 2;
- break;
- case MT_T:
- lstart = pp[0];
- lend.x = (pp[1].x + pp[2].x) / 2;
- lend.y = (pp[1].y + pp[2].y) / 2;
- break;
- default /* case MT_P */:
- lstart.x = (5*pp[3].x + 3*pp[0].x) / 8;
- lstart.y = (5*pp[3].y + 3*pp[0].y) / 8;
- lend.x = (5*pp[1].x + 3*pp[2].x) / 8;
- lend.y = (5*pp[1].y + 3*pp[2].y) / 8;
- break;
- }
-
- /*
- * Now shorten that line a little and give it an arrowhead.
- */
- astart.x = (4 * lstart.x + lend.x) / 5;
- astart.y = (4 * lstart.y + lend.y) / 5;
- aend.x = (lstart.x + 4 * lend.x) / 5;
- aend.y = (lstart.y + 4 * lend.y) / 5;
- aforward.x = aend.x - astart.x;
- aforward.y = aend.y - astart.y;
- d = sqrt(aforward.x*aforward.x + aforward.y*aforward.y);
- aforward.x /= d;
- aforward.y /= d;
- aleft.x = -aforward.y;
- aleft.y = +aforward.x;
-
- printf("<path style=\""- "fill: none; "
- "stroke: black; "
- "stroke-width: %f; "
- "stroke-opacity: 0.2; "
- "stroke-linejoin: round; "
- "stroke-linecap: round; "
- "\" d=\"", 0.9 * ascale);
-
- printf("M %f %f L %f %f ", astart.x, astart.y,- aend.x, aend.y);
- printf("L %f %f ",- aend.x - 1.2 * ascale * (aforward.x + aleft.x),
- aend.y - 1.2 * ascale * (aforward.y + aleft.y));
- printf("M %f %f L %f %f ", aend.x, aend.y,- aend.x - 1.2 * ascale * (aforward.x - aleft.x),
- aend.y - 1.2 * ascale * (aforward.y - aleft.y));
- printf("\" />\n");- }
-
- if (coords) {- /*
- * Print each tile's coordinates.
- */
- pspoint centre;
- size_t j;
-
- switch (tiles[i].type) {- case MT_H:
- centre.x = (pp[0].x + pp[2].x + pp[4].x) / 3;
- centre.y = (pp[0].y + pp[2].y + pp[4].y) / 3;
- break;
- case MT_T:
- centre.x = (pp[0].x + pp[1].x + pp[2].x) / 3;
- centre.y = (pp[0].y + pp[1].y + pp[2].y) / 3;
- break;
- case MT_P:
- centre.x = (pp[0].x + pp[2].x) / 2;
- centre.y = (pp[0].y + pp[2].y) / 2;
- break;
- default /* case MT_F */:
- centre.x = (pp[2].x + pp[4].x) / 2;
- centre.y = (pp[2].y + pp[4].y) / 2;
- break;
- }
-
- double lineheight = ascale * 1.5;
- double charheight = lineheight * 0.6; /* close enough */
- double allheight = lineheight * (tiles[i].ncoords-1) + charheight;
-
- for (j = 0; j < tiles[i].ncoords; j++) {- const Metatile *it;
- unsigned cindex;
-
- printf("<text style=\""- "fill: black; "
- "font-family: Sans; "
- "font-size: %g; "
- "text-anchor: middle; "
- "text-align: center; "
- "\" x=\"%g\" y=\"%g\">", lineheight,
- centre.x,
- centre.y - allheight/2 + charheight + lineheight*j);
-
- it = &tiles[i];
- cindex = j;
- while (cindex < it->ncoords) {- if (it != &tiles[i])
- printf(".");- printf("%d", (int)it->coords[cindex].index);-
- it = it->coords[cindex].parent;
- cindex = 0; /* BODGING AHOY */
- }
-
- printf("</text>\n");- }
- }
-
- }
-
- printf("</svg>\n");-}
-
-static void draw_metatile_set_svg(
- MetatileSet *tiles, const Point *bounds, bool coords)
-{- /*
- * Slurp the tree234 of tiles into an array for display.
- * Tedious, but this test code doesn't have to be particularly
- * efficient.
- */
- size_t nt = count234(tiles->tiles);
- Metatile *t = snewn(nt, Metatile);
- size_t i;
- for (i = 0; i < nt; i++) {- Metatile *m = index234(tiles->tiles, i);
- t[i] = *m; /* structure copy */
- }
- draw_metatiles_svg(t, nt, bounds, coords);
- sfree(t);
-}
-
-static void draw_hats_svg(const Hat *hats, size_t n,
- const Point *bounds, bool kites, char coordtype)
-{- size_t i, j;
- psbbox bbox = { false };-
- for (i = 0; i < n; i++) {- Point vertices[HAT_NVERT];
- size_t nv = hat_vertices(hats[i], vertices);
- for (j = 0; j < nv; j++)
- psbbox_add(&bbox, pscoords(vertices[j]));
- }
-
- float ascale = (coordtype == 'k' || coordtype == 'K' ? 20 : 10);
- float xscale = ascale, yscale = -ascale;
- float border = 0.2 * ascale; /* leave room for strokes at the edges */
- float ox = -xscale * bbox.bl.x + border;
- float oy = -yscale * bbox.tr.y + border;
-
- printf("<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n");- printf("<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\" "- "width=\"%g\" height=\"%g\">\n",
- ceil(ox + xscale * bbox.tr.x + 2*border),
- ceil(oy + yscale * bbox.bl.y + 2*border));
-
- for (i = 0; i < n; i++) {- Point vertices[HAT_NVERT];
- pspoint psvs[HAT_NVERT];
- size_t nv = hat_vertices(hats[i], vertices);
- int is = hats[i].reversed ? -1 : +1;
- int io = hats[i].reversed ? 13 : 0;
-
- printf("<path style=\""- "fill: %s; "
- "stroke: black; "
- "stroke-width: %f; "
- "stroke-linejoin: round; "
- "stroke-linecap: round; "
- "\" d=\"",
- hats[i].reversed ? "rgba(0,0,0,0.2)" : "none",
- 0.2 * ascale);
- for (j = 0; j < nv; j++) {- psvs[j] = pscoords(vertices[j]);
- printf("%s %f %f\n", j ? "L" : "M",- ox + xscale * psvs[j].x, oy + yscale * psvs[j].y);
- }
- printf("z\" />\n");-
- if (kites) {- /*
- * Draw internal lines within each hat dividing it into
- * kites. This is done in a rather bodgy way, sorry.
- */
- const char *fmt = "<path style=\""
- "fill: none; "
- "stroke: rgba(0,0,0,0.2); "
- "stroke-width: %f; "
- "stroke-linejoin: round; "
- "stroke-linecap: round; "
- "\" d=\"M %f %f L %f %f\" />\n";
- float strokewidth = 0.1 * ascale;
-
- printf(fmt, strokewidth,
- ox + xscale * psvs[io+is*0].x,
- oy + yscale * psvs[io+is*0].y,
- ox + xscale * psvs[io+is*3].x,
- oy + yscale * psvs[io+is*3].y);
-
- printf(fmt, strokewidth,
- ox + xscale * psvs[io+is*0].x,
- oy + yscale * psvs[io+is*0].y,
- ox + xscale * psvs[io+is*5].x,
- oy + yscale * psvs[io+is*5].y);
-
- printf(fmt, strokewidth,
- ox + xscale * psvs[io+is*6].x,
- oy + yscale * psvs[io+is*6].y,
- ox + xscale * psvs[io+is*9].x,
- oy + yscale * psvs[io+is*9].y);
-
- printf(fmt, strokewidth,
- ox + xscale * psvs[io+is*0].x,
- oy + yscale * psvs[io+is*0].y,
- ox + xscale * psvs[io+is*10].x,
- oy + yscale * psvs[io+is*10].y);
-
- printf(fmt, strokewidth,
- ox + xscale * psvs[io+is*9].x,
- oy + yscale * psvs[io+is*9].y,
- ox + xscale * (psvs[io+is*6].x + psvs[io+is*12].x) / 2,
- oy + yscale * (psvs[io+is*6].y + psvs[io+is*12].y) / 2);
-
- printf(fmt, strokewidth,
- ox + xscale * psvs[io+is*5].x,
- oy + yscale * psvs[io+is*5].y,
- ox + xscale * (psvs[io+is*6].x + psvs[io+is*12].x) / 2,
- oy + yscale * (psvs[io+is*6].y + psvs[io+is*12].y) / 2);
-
- printf(fmt, strokewidth,
- ox + xscale * psvs[io+is*12].x,
- oy + yscale * psvs[io+is*12].y,
- ox + xscale * (psvs[io+is*6].x + psvs[io+is*12].x) / 2,
- oy + yscale * (psvs[io+is*6].y + psvs[io+is*12].y) / 2);
- }
-
- if (coordtype == 'h') {- double lineheight = ascale * 2;
- double charheight = lineheight * 0.6; /* close enough */
-
- printf("<text style=\""- "fill: black; "
- "font-family: Sans; "
- "font-size: %gpx; "
- "text-anchor: middle; "
- "text-align: center; "
- "\" x=\"%g\" y=\"%g\">", lineheight,
- ox + xscale * (psvs[io+is*0].x + psvs[io+is*10].x) / 2,
- oy + yscale * (psvs[io+is*0].y + psvs[io+is*10].y) / 2
- + charheight/2);
- printf("%d", (int)i);- printf("</text>\n");- } else if (coordtype == 'k') {- Point kites[HAT_NKITE];
- size_t nk = hat_kite_centres(hats[i], kites);
-
- double lineheight = ascale * 0.5;
- double charheight = lineheight * 0.6; /* close enough */
-
- for (j = 0; j < nk; j++) {- pspoint p = pscoords(kites[j]);
-
- printf("<text style=\""- "fill: black; "
- "font-family: Sans; "
- "font-size: %gpx; "
- "text-anchor: middle; "
- "text-align: center; "
- "\" x=\"%g\" y=\"%g\">", lineheight,
- ox + xscale * p.x,
- oy + yscale * p.y + charheight/2);
-
- printf("%d.%d.%d", (int)j, hats[i].index,- hats[i].parent->coords[0].index);
-
- printf("</text>\n");- }
- } else if (coordtype == 'K') {- Point kites[HAT_NKITE];
- size_t nk = hat_kite_centres(hats[i], kites);
-
- double lineheight = ascale * 1.1;
- double charheight = lineheight * 0.6; /* close enough */
-
- for (j = 0; j < nk; j++) {- pspoint p = pscoords(kites[j]);
-
- printf("<text style=\""- "fill: black; "
- "font-family: Sans; "
- "font-size: %gpx; "
- "text-anchor: middle; "
- "text-align: center; "
- "\" x=\"%g\" y=\"%g\">", lineheight,
- ox + xscale * p.x,
- oy + yscale * p.y + charheight/2);
- printf("%d", (int)j);- printf("</text>\n");- }
- }
- }
-
- printf("</svg>\n");-}
-
-typedef enum KiteStep { KS_LEFT, KS_RIGHT, KS_F_LEFT, KS_F_RIGHT } KiteStep;-
-static inline Point kite_step(Point k, KiteStep step)
-{- switch (step) {- case KS_LEFT: return kite_left(k);
- case KS_RIGHT: return kite_right(k);
- case KS_F_LEFT: return kite_forward_left(k);
- default /* case KS_F_RIGHT */: return kite_forward_right(k);
- }
-}
-
-int main(int argc, char **argv)
-{- if (argc <= 1) {- printf("usage: hat-test <mode>\n");- printf("modes: H,T,P,F display a single unexpanded tile\n");- printf(" xH,xT,xP,xF display the expansion of one tile\n");- printf(" cH,cT,cP,cF display expansion with tile coords\n");- printf(" CH,CT,CP,CF display double expansion with coords\n");- printf(" hH,hT,hP,hF display the hats from one tile\n");- printf(" HH,HT,HP,HF hats from an expansion, with coords\n");- printf(" m1, m2, ... nth expansion of one H metatile\n");- printf(" M1, M2, ... nth expansion turned into real hats\n");- printf(" --hat show the kites in a single hat\n");- printf(" --tables generate hat-tables.h for hat.c\n");- return 0;
- }
-
- if (!strcmp(argv[1], "H") || !strcmp(argv[1], "T") ||
- !strcmp(argv[1], "P") || !strcmp(argv[1], "F")) {- MetatileType type = (argv[1][0] == 'H' ? MT_H :
- argv[1][0] == 'T' ? MT_T :
- argv[1][0] == 'P' ? MT_P : MT_F);
- Metatile m = {type, {0, 0}, {1, 0}};- draw_metatiles_svg(&m, 1, NULL, false);
- return 0;
- }
-
- if (!strcmp(argv[1], "xH") || !strcmp(argv[1], "xT") ||
- !strcmp(argv[1], "xP") || !strcmp(argv[1], "xF")) {- MetatileType type = (argv[1][1] == 'H' ? MT_H :
- argv[1][1] == 'T' ? MT_T :
- argv[1][1] == 'P' ? MT_P : MT_F);
- Metatile m = {type, {0, 0}, {1, 0}};- Metatile t[MT_MAXEXPAND];
- size_t nt = metatile_expand(m, t);
- draw_metatiles_svg(t, nt, NULL, false);
- return 0;
- }
-
- if (argv[1][0] && argv[1][1] &&
- strchr("cC", argv[1][0]) && strchr("HTPF", argv[1][1])) {- MetatileType type = (argv[1][1] == 'H' ? MT_H :
- argv[1][1] == 'T' ? MT_T :
- argv[1][1] == 'P' ? MT_P : MT_F);
- MetatileSet *t[3];
- int nsets = (argv[1][0] == 'c' ? 2 : 3);
- int i;
-
- t[0] = metatile_initial_set(type);
- for (i = 1; i < nsets; i++)
- t[i] = metatile_set_expand(t[i-1]);
- draw_metatile_set_svg(t[nsets-1], NULL, true);
- for (i = 0; i < nsets; i++)
- metatile_free_set(t[i]);
- return 0;
- }
-
- if (!strcmp(argv[1], "hH") || !strcmp(argv[1], "hT") ||
- !strcmp(argv[1], "hP") || !strcmp(argv[1], "hF")) {- MetatileType type = (
- !strcmp(argv[1], "hH") ? MT_H :
- !strcmp(argv[1], "hT") ? MT_T :
- !strcmp(argv[1], "hP") ? MT_P : MT_F);
- Metatile m = {type, {0, 0}, {1, 0}};- Hat h[MT_MAXHAT];
- size_t nh = metatile_hats(&m, h);
- draw_hats_svg(h, nh, NULL, false, 'h');
- return 0;
- }
-
- if (!strcmp(argv[1], "--hat")) {- Hat h = { { 0, 0 }, { 1, 0 }, false, NULL, 0 };- draw_hats_svg(&h, 1, NULL, true, 'K');
- return 0;
- }
-
- if (argv[1][0] == 'H' && argv[1][1] && strchr("HTPF", argv[1][1])) {- MetatileType type = (argv[1][1] == 'H' ? MT_H :
- argv[1][1] == 'T' ? MT_T :
- argv[1][1] == 'P' ? MT_P : MT_F);
- MetatileSet *t[2];
- size_t i, nh;
-
- t[0] = metatile_initial_set(type);
- t[1] = metatile_set_expand(t[0]);
- Hat *h = metatile_set_to_hats(t[1], &nh, NULL);
- draw_hats_svg(h, nh, NULL, true, 'k');
- sfree(h);
- for (i = 0; i < 2; i++)
- metatile_free_set(t[i]);
- return 0;
- }
-
- if (argv[1][0] == 'm' || argv[1][0] == 'M') {- int niter = atoi(argv[1] + 1);
- MetatileSet *tiles = metatile_initial_set(MT_P);
-
- while (niter-- > 0) {- MetatileSet *t2 = metatile_set_expand(tiles);
- metatile_free_set(tiles);
- tiles = t2;
- }
-
- if (argv[1][0] == 'M') {- size_t nh;
- Hat *h = metatile_set_to_hats(tiles, &nh, NULL);
- draw_hats_svg(h, nh, tiles->vertices, false, 0);
- sfree(h);
- } else {- draw_metatile_set_svg(tiles, tiles->vertices, false);
- }
-
- metatile_free_set(tiles);
-
- return 0;
- }
-
- if (!strcmp(argv[1], "--tables")) {- size_t i, j, k;
-
- printf("/*\n"- " * Header file autogenerated by aux/hatgen.c\n"
- " *\n"
- " * To regenerate, run 'hatgen --tables > hat-tables.h'\n"
- " */\n\n");
-
- static const char HTPF[] = "HTPF";
-
- printf("static const unsigned hats_in_metatile[] = {");- for (i = 0; i < 4; i++) {- Metatile m = {i, {0, 0}, {1, 0}};- Hat h[MT_MAXHAT];
- size_t nh = metatile_hats(&m, h);
- printf(" %zu,", nh);- }
- printf(" };\n\n");-
- {- struct Parent {- MetatileType t;
- unsigned index;
- } parents[4][4*MT_MAXEXPAND];
- size_t psizes[4] = {0, 0, 0, 0};- size_t csizes[4] = {0, 0, 0, 0};-
- for (i = 0; i < 4; i++) {- Metatile m = {i, {0, 0}, {1, 0}};- Metatile t[MT_MAXEXPAND];
- size_t nt = metatile_expand(m, t);
-
- printf("static const TileType children_%c[] = {\n"- " ", HTPF[i]);
- for (j = 0; j < nt; j++) {- MetatileType c = t[j].type;
- parents[c][psizes[c]].t = i;
- parents[c][psizes[c]].index = j;
- psizes[c]++;
- csizes[i]++;
- printf(" TT_%c,", HTPF[c]);- }
- printf("\n};\n");- }
-
- printf("static const TileType *const children[] = {\n");- for (i = 0; i < 4; i++)
- printf(" children_%c,\n", HTPF[i]);- printf("};\n");- printf("static const size_t nchildren[] = {\n");- for (i = 0; i < 4; i++)
- printf(" %u,\n", (unsigned)csizes[i]);- printf("};\n\n");-
- for (i = 0; i < 4; i++) {- printf("static const MetatilePossibleParent "- "permitted_parents_%c[] = {\n", HTPF[i]);- for (j = 0; j < psizes[i]; j++)
- printf(" { TT_%c, %u },\n", HTPF[parents[i][j].t],- parents[i][j].index);
- printf("};\n");- }
-
- printf("static const MetatilePossibleParent *const "- "permitted_parents[] = {\n");- for (i = 0; i < 4; i++)
- printf(" permitted_parents_%c,\n", HTPF[i]);- printf("};\n");-
- printf("static const size_t n_permitted_parents[] = {\n");- for (i = 0; i < 4; i++)
- printf(" %u,\n", (unsigned)psizes[i]);- printf("};\n\n");- }
-
- {- for (i = 0; i < 4; i++) {- MetatileSet *t[2];
- size_t j, k, nh, nmeta, ti;
- struct list {- Point kite;
- unsigned ik, ih, im;
- } list[8*MT_MAXHAT*MT_MAXEXPAND];
- size_t len = 0;
-
- t[0] = metatile_initial_set(i);
- t[1] = metatile_set_expand(t[0]);
- Hat *h = metatile_set_to_hats(t[1], &nh, NULL);
-
- printf("static const KitemapEntry kitemap_%c[] = {\n",- HTPF[i]);
-
- Point origin = h[0].start;
- for (j = 0; j < nh; j++) {- Point kites[HAT_NKITE];
- size_t nk = hat_kite_centres(h[j], kites);
- for (k = 0; k < nk; k++) {- struct list *le = &list[len++];
- le->kite.x = kites[k].x - origin.x;
- le->kite.y = kites[k].y - origin.y;
- le->ik = k;
- le->ih = h[j].index;
- le->im = h[j].parent->coords[0].index;
-#if 0
- printf("// %d,%d = %u.%u.%u\n", le->kite.x, le->kite.y, le->ik, le->ih, le->im);-#endif
- }
- }
-
- nmeta = count234(t[1]->tiles);
- for (ti = 0; ti < 8 * 4 * nmeta; ti++) {- unsigned ik = ti % 8;
- unsigned ih = ti / 8 % 4;
- unsigned im = ti / (8*4);
- struct list *src = NULL, *dst = NULL;
- int istep;
-
- for (j = 0; j < len; j++) {- struct list *tmp = &list[j];
- if (tmp->ik == ik && tmp->ih == ih && tmp->im == im) {- src = tmp;
- break;
- }
- }
- if (ik == 0) {- printf(" /* hat #%u in metatile #%u (type %c)",- ih, im, HTPF[((Metatile *)index234(
- t[1]->tiles, im))->type]);
- if (!src)
- printf(" does not exist");- printf(" */\n");- }
-#if 0
- if (src)
- printf(" // src=%d,%d\n", src->kite.x, src->kite.y);-#endif
- printf(" ");-
- for (istep = 0; istep < 4; istep++) {- KiteStep step = istep;
- dst = NULL;
- if (src) {- Point pdst = kite_step(src->kite, step);
-#if 0
- printf(" /* dst=%d,%d */", pdst.x, pdst.y);-#endif
- for (k = 0; k < len; k++) {- struct list *tmp = &list[k];
- if (tmp->kite.x == pdst.x &&
- tmp->kite.y == pdst.y) {- dst = tmp;
- break;
- }
- }
- }
- if (!dst) {- printf(" {-1,-1,-1},");- } else {- printf(" {%u,%u,%u},", dst->ik, dst->ih, dst->im);- }
- }
- printf("\n");- }
- printf("};\n");-
- sfree(h);
- for (j = 0; j < 2; j++)
- metatile_free_set(t[j]);
- }
-
- printf("static const KitemapEntry *const "- "kitemap[] = {\n");- for (i = 0; i < 4; i++)
- printf(" kitemap_%c,\n", HTPF[i]);- printf("};\n\n");-
- }
-
- {- for (i = 0; i < 4; i++) {- MetatileSet *t[3];
- Metatile *m;
- int map[MT_MAXEXPAND * MT_MAXEXPAND];
- size_t maplen;
-
- for (j = 0; j < lenof(map); j++)
- map[j] = -1;
-
- t[0] = metatile_initial_set(i);
- for (j = 1; j < 3; j++)
- t[j] = metatile_set_expand(t[j-1]);
-
- for (j = 0; (m = index234(t[2]->tiles, j)) != NULL; j++) {- unsigned coords[4];
- size_t ncoords = 0;
- int cindex;
-
-#if 0
- printf("// ***\n");-#endif
- for (cindex = 0; cindex < m->ncoords; cindex++) {-#if 0
- printf("// %d.%d\n", (int)m->coords[cindex].index,- (int)m->coords[cindex].parent->coords[0].index);
-#endif
- coords[ncoords++] = (
- m->coords[cindex].index + MT_MAXEXPAND *
- m->coords[cindex].parent->coords[0].index);
- }
-
- unsigned prev = ncoords-1;
- for (k = 0; k < ncoords; k++) {- map[coords[prev]] = coords[k];
- prev = k;
- }
- }
-
- printf("static const MetamapEntry metamap_%c[] = {\n",- HTPF[i]);
- maplen = MT_MAXEXPAND * count234(t[1]->tiles);
- for (j = 0; j < maplen; j++) {- printf(" /* %u, %u -> */ ",- (unsigned)(j % MT_MAXEXPAND),
- (unsigned)(j / MT_MAXEXPAND));
- if (map[j] == -1) {- printf("{-1,-1}, /* does not exist */\n");- } else {- printf("{%u, %u},",- (unsigned)(map[j] % MT_MAXEXPAND),
- (unsigned)(map[j] / MT_MAXEXPAND));
- if (map[j] == j)
- printf(" /* no alternatives */");- printf("\n");- }
- }
- printf("};\n");-
- for (j = 0; j < 3; j++)
- metatile_free_set(t[j]);
- }
-
- printf("static const MetamapEntry *const "- "metamap[] = {\n");- for (i = 0; i < 4; i++)
- printf(" metamap_%c,\n", HTPF[i]);- printf("};\n");- }
-
- return 0;
- }
-
- fprintf(stderr, "unknown test mode '%s'\n", argv[1]);
- return 1;
-}
-#endif
--- /dev/null
+++ b/auxiliary/CMakeLists.txt
@@ -1,0 +1,1 @@
+cliprogram(hatgen hatgen.c COMPILE_DEFINITIONS TEST_HAT)
--- /dev/null
+++ b/auxiliary/doc/arrow.svg
@@ -1,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="110" height="200">
+<path style="fill: none; stroke: black; stroke-width: 9.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 10 100 L 100 100 L 70 70 M 100 100 L 70 130" />
+</svg>
--- /dev/null
+++ b/auxiliary/doc/expanded-F.svg
@@ -1,0 +1,84 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="336" height="543">
+<path style="fill: none; stroke: black; stroke-width: 2.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 212.000000 261.807617
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+<text style="fill: black; font-family: Sans; font-size: 15; text-anchor: middle; text-align: center; " x="182" y="179.705">0</text>
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+<text style="fill: black; font-family: Sans; font-size: 22px; text-anchor: middle; text-align: center; " x="34" y="131.844">3</text>
+<text style="fill: black; font-family: Sans; font-size: 22px; text-anchor: middle; text-align: center; " x="94" y="131.844">4</text>
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+<text style="fill: black; font-family: Sans; font-size: 22px; text-anchor: middle; text-align: center; " x="124" y="79.882">6</text>
+<text style="fill: black; font-family: Sans; font-size: 22px; text-anchor: middle; text-align: center; " x="154" y="97.2025">7</text>
+</svg>
--- /dev/null
+++ b/auxiliary/doc/hatmaps.html
@@ -1,0 +1,62 @@
+<html>
+<head>
+<meta http-equiv="Content-type" content="text/html; charset=UTF-8" />
+<title>Kitemaps and metamaps for the hat tiling generator</title>
+<style type="text/css">
+ table, tbody, tr, td, th {+ border: 1px solid rgba(0, 0, 0, 0.3);
+ border-collapse: collapse;
+ }
+ table.noborder, table.noborder tbody, table.noborder td,
+ table.noborder th, table.noborder tr { border: none; }+ table {+ margin: 1em;
+ }
+ th, td {+ padding: 0.5em;
+ }
+</style>
+</head>
+<body>
+ <h1>Kitemaps and metamaps for the hat tiling generator</h1>
+ <p>See <a href="hats.html">hats.html</a> for the full explanation.</p>
+ <p>Here's the full set of kitemaps and metamaps for all the tile
+ types:</p>
+ <table>
+ <tr>
+ <th>Tile name</th>
+ <th>Original tile</th>
+ <th>First-order expansion</th>
+ <th>Kitemap</th>
+ <th>Metamap</th>
+ <tr>
+ <td>H</td>
+ <td><img src="single-H.svg"></td>
+ <td><img src="expanded-H.svg"></td>
+ <td><img src="kitemap-H.svg"></td>
+ <td><img src="metamap-H.svg"></td>
+ </tr>
+ <tr>
+ <td>T</td>
+ <td><img src="single-T.svg"></td>
+ <td><img src="expanded-T.svg"></td>
+ <td><img src="kitemap-T.svg"></td>
+ <td><img src="metamap-T.svg"></td>
+ </tr>
+ <tr>
+ <td>P</td>
+ <td><img src="single-P.svg"></td>
+ <td><img src="expanded-P.svg"></td>
+ <td><img src="kitemap-P.svg"></td>
+ <td><img src="metamap-P.svg"></td>
+ </tr>
+ <tr>
+ <td>F</td>
+ <td><img src="single-F.svg"></td>
+ <td><img src="expanded-F.svg"></td>
+ <td><img src="kitemap-F.svg"></td>
+ <td><img src="metamap-F.svg"></td>
+ </tr>
+ </table>
+</body>
+</html>
--- /dev/null
+++ b/auxiliary/doc/hats-single-F.svg
@@ -1,0 +1,35 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="96" height="171">
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+<text style="fill: black; font-family: Sans; font-size: 20px; text-anchor: middle; text-align: center; " x="62" y="68.6218">1</text>
+</svg>
--- /dev/null
+++ b/auxiliary/doc/hats-single-H.svg
@@ -1,0 +1,67 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="171" height="188">
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+</svg>
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+++ b/auxiliary/doc/hats-single-P.svg
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+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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+</svg>
--- /dev/null
+++ b/auxiliary/doc/hats-single-T.svg
@@ -1,0 +1,19 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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+</svg>
--- /dev/null
+++ b/auxiliary/doc/hats.html
@@ -1,0 +1,258 @@
+<html>
+<head>
+<meta http-equiv="Content-type" content="text/html; charset=UTF-8" />
+<title>Generating hat tilings for Loopy</title>
+<style type="text/css">
+ table, tbody, tr, td, th {+ border: 1px solid rgba(0, 0, 0, 0.3);
+ border-collapse: collapse;
+ }
+ table.noborder, table.noborder tbody, table.noborder td,
+ table.noborder th, table.noborder tr { border: none; }+ table {+ margin: 1em;
+ }
+ th, td {+ padding: 0.5em;
+ }
+</style>
+</head>
+<body>
+ <h1>Generating hat tilings for Loopy</h1>
+ <p>The <a href="https://arxiv.org/abs/2303.10798">original paper</a>
+ describes a method for generating hat tilings from a system of four
+ 'metatiles'. You can start with any one of the four tiles, and then
+ recursively apply a set of expansion rules that turn each tile into
+ a collection of smaller tiles from the same set.</p>
+ <p>This table shows the four tiles, with their one-letter names as
+ given in the paper, and how each one is expanded.</p>
+ <p>All the tiles have a significant orientation. The H, T and P
+ tiles are marked with arrows to indicate the orientation. The F tile
+ is asymmetric, so no arrow is needed.</p>
+ <p>I've assigned each tile in each expansion a number, which Loopy
+ will use for its coordinate system.</p>
+ <table>
+ <tr>
+ <th>Tile name</th>
+ <th>Single tile</th>
+ <th>Expansion</th>
+ <tr>
+ <td>H</td>
+ <td><img src="single-H.svg"></td>
+ <td><img src="expanded-H.svg"></td>
+ </tr>
+ <tr>
+ <td>T</td>
+ <td><img src="single-T.svg"></td>
+ <td><img src="expanded-T.svg"></td>
+ </tr>
+ <tr>
+ <td>P</td>
+ <td><img src="single-P.svg"></td>
+ <td><img src="expanded-P.svg"></td>
+ </tr>
+ <tr>
+ <td>F</td>
+ <td><img src="single-F.svg"></td>
+ <td><img src="expanded-F.svg"></td>
+ </tr>
+ </table>
+ <p><strong>Note that these expansions overlap</strong>. When two
+ adjacent metatiles are expanded, the outer layer of P and F tiles in
+ their expansions must be placed so that they overlap each other. The
+ original paper suggests a set of tiles to remove from these
+ expansions so that each metatile expands to a <em>disjoint</em> set
+ of smaller tiles. In our implementation, however, we prefer to keep
+ the overlap, because our coordinate system will use it.</p>
+ <p>Once you've generated a large enough patch of metatiles for your
+ needs, the final step is to convert it into the actual hat tiles.
+ The expansion of each metatile into hats is shown here. Again, I've
+ assigned numbers to each hat for coordinate-system purposes:</p>
+ <table>
+ <tr>
+ <th>Tile name</th>
+ <th>Conversion into hats</th>
+ <tr>
+ <td>H</td>
+ <td><img src="single-H.svg"></td>
+ <td><img src="hats-single-H.svg"></td>
+ </tr>
+ <tr>
+ <td>T</td>
+ <td><img src="single-T.svg"></td>
+ <td><img src="hats-single-T.svg"></td>
+ </tr>
+ <tr>
+ <td>P</td>
+ <td><img src="single-P.svg"></td>
+ <td><img src="hats-single-P.svg"></td>
+ </tr>
+ <tr>
+ <td>F</td>
+ <td><img src="single-F.svg"></td>
+ <td><img src="hats-single-F.svg"></td>
+ </tr>
+ </table>
+ <p>(The hat in the middle of the H is shaded to indicate that it's
+ one of the rare reflected ones. All the other hats are rotations of
+ each other.)</p>
+ <p>Given all of this, an obvious approach to generating a random
+ patch of hat tiling would be to start with a single metatile,
+ iterate the expansion process a few times until you have a tiled
+ area much larger than you need, and then pick a subrectangle of
+ it at random.</p>
+ <p>Loopy's algorithm for generating Penrose tilings (which admit a
+ similar, though less complicated, expansion system) works in exactly
+ this way.</p>
+ <p>One problem with that algorithm is that it spends a lot of effort
+ on generating huge areas of tiles that aren't actually needed. So
+ you'd prefer to adjust the algorithm so that at every stage of
+ expansion it spots tiles completely outside the target rectangle,
+ and throws them away <em>before</em> spending 5 iterations on
+ exponentially expanding them into huge amounts of detail that will
+ only be thrown away anyway later.</p>
+ <p>That works well for Penrose tilings, because there, the expansion
+ procedure is geometrically precise: coordinates in the expanded
+ tiling are scaled up by an exact factor from coordinates in the
+ original tiling. So at every stage it's easy to know exactly where
+ your target rectangle <em>is</em>, and discard things that don't
+ overlap it.</p>
+ <p>But the metatiles shown here don't have that property. The tiles
+ distort slightly as they expand. The <em>topological</em> properties
+ of the expanded tiling match the original (which expanded tiles
+ connect to each other), but the geometry (precise distances) is
+ different. So it would be harder to implement the pruning for this
+ tiling. The target rectangle might not even be rectangular in every
+ iteration!</p>
+ <p>Instead, I came up with a completely different mechanism, by
+ devising a coordinate system to track our position within multiple
+ layers of tile expansion. This allows us to generate precisely the
+ area of tiling we need, and waste no effort at all on anything
+ outside the target region.</p>
+ <p>We begin by assigning an integer index to each kite making up an
+ individual hat:</p>
+ <img src="hat-kites.svg">
+ <p>(For a reflected hat, these indices work in mirror image, so that
+ for example 5 is still the kite in the middle.)</p>
+ <p>Together with the indices we've assigned to hats within each
+ metatile, and to metatiles in the expansion of another metatile,
+ this gives us a coordinate system that can identify an individual
+ kite in an n-times-expanded metatile. For each large metatile
+ expansion, you can give the index of the smaller metatile selected
+ from its expansion; when we reach the last layer of metatiles and
+ expand them into hats, we can give the index of the hat in that
+ metatile; finally we can index the kite in that hat.</p>
+ <p><strong>But note that a kite can have multiple
+ coordinates</strong>, because of the overlap between the expansions
+ of adjacent metatiles. This will be useful!</p>
+ <p>Our next step is to unambiguously name the four directions in
+ which you can move from one kite to an adjacent kite. The directions
+ should be independent of the orientation of the kite. I've chosen to
+ name them from the viewpoint of someone standing at the pointy end
+ of the kite and looking towards the blunt end:</p>
+ <dl>
+ <dt><strong>Left</strong></dt>
+ <dd>Rotate 60° anticlockwise about the pointy end of the kite. For
+ example, in the above hat, going 'left' from kite 5 takes you to
+ kite 4.</dd>
+ <dt><strong>Right</strong></dt>
+ <dd>Rotate 60° clockwise about the pointy end. From kite 5, this
+ would take you to kite 6.</dd>
+ <dt><strong>Forward left</strong></dt>
+ <dd>Head forwards and slightly left, to the kite sharing the
+ left-hand one of this kite's short edges (as seen from the
+ centre). Equivalently, rotate 120° <em>clockwise</em> about the
+ blunt end. From kite 5, this takes you to kite 2.</dd>
+ <dt><strong>Forward right</strong></dt>
+ <dd>Head forwards and slightly right. Or rotate 120° anticlockwise
+ about the blunt end, if you prefer to think of it that way. From
+ kite 5, this takes you to kite 1.</dd>
+ </dl>
+ <p>The idea is that if we know how to transform the coordinates of a
+ single kite into the coordinates of each of those four adjacent
+ kites, then we can iterate that over a whole area and determine the
+ coordinates of every kite in the whole tiling.</p>
+ <p>Having done that, it's easy to identify each individual kite, by
+ several different methods. For example, you could iterate over edges
+ of the tiling to see whether the kites on each side have coordinates
+ differing only in the kite index; if so, they're part of the same
+ hat, and if not, not. Or a completely different approach (in fact
+ the one Loopy actually uses) would be to trace round the boundary of
+ each hat by starting from its kite #0 and just knowing what shape a
+ hat is.</p>
+ <p>So now we have to come up with an algorithm that lets us
+ transform a kite coordinate by making one of the four permitted
+ moves. To do this, we use two multilevel types of map.</p>
+ <p>The <strong>kitemap</strong> for a given metatile type is made by
+ expanding the metatile once into more metatiles, and then into hats.
+ For example, the T tile:</p>
+ <table class="noborder">
+ <tr>
+ <td><img src="single-T.svg"></td>
+ <td><img src="arrow.svg"></td>
+ <td><img src="expanded-T.svg" height="200px"></td>
+ <td><img src="arrow.svg"></td>
+ <td><img src="kitemap-T.svg" height="500px"></td>
+ </tr>
+ </table>
+ <p>In each kite, we show a three-part coordinate, in little-endian
+ fashion (because that matches the order the coordinates are stored
+ in an array in the code that actually generates the tilings). For
+ example, 7.3.0 means kite 7 in hat 3 of metatile 0 of the
+ expansion.</p>
+ <p>This map can be converted into a lookup table, indexed by those
+ three-part coordinates and also the four move directions, which
+ allows you to look up that (for example) going Left from kite 7.3.0
+ goes to 0.0.0, or going Forward Left from 7.3.0 goes to 3.1.3.</p>
+ <p>But if you're at the very edge of the kitemap, this isn't enough.
+ For example, kite 0.0.4 right at the top can go Left to 1.0.4, but
+ if it wants to go in any of the other three directions, this map
+ doesn't help at all.</p>
+ <p>This is where the overlap between the metatile expansions comes
+ in. If you're in kite 0.0.4, then in particular, you're in the F
+ tile numbered 4 in the expansion of a larger T metatile. And that F
+ tile is <em>also</em> part of the expansion of at least one other
+ second-order metatile – maybe two of them – which means that there
+ are other equivalent coordinates describing the same kite, which
+ will place it in a different kitemap where it <em>isn't</em> right
+ on the edge,</p>
+ <p>In order to find those equivalent coordinates, we create a second
+ map for each metatile type, called the <strong>metamap</strong>.
+ This one arises from expanding the metatile twice into other
+ metatiles, instead of into hats:</p>
+ <table class="noborder">
+ <tr>
+ <td><img src="single-T.svg"></td>
+ <td><img src="arrow.svg"></td>
+ <td><img src="expanded-T.svg" height="200px"></td>
+ <td><img src="arrow.svg"></td>
+ <td><img src="metamap-T.svg" height="500px"></td>
+ </tr>
+ </table>
+ <p>Again, the coordinates are little-end first, so that 7.4 means
+ the 7th smallest-size tile expanded from the 4th medium-sized tile
+ expanded from the original single large tile.</p>
+ <p>Unlike the kitemap, the metamap is not used for <em>moving
+ around</em> the tiling to a different kite. It's used for rewriting
+ the coordinates of the current kite into equivalent forms. So each
+ the small tile in the metamap that's part of the expansion
+ of <em>more than one</em> medium-sized tile has more than one
+ coordinate pair. For example, tile 5.2 is also tile 5.4, and tile
+ 7.0 is also 8.3 <em>and</em> also 4.5 (because it's where three
+ medium-tile expansions meet).</p>
+ <p>Using both of these maps (converted into appropriate lookup
+ tables in the code), you can always eventually find a valid
+ coordinate representation of whichever kite you like adjacent to
+ your current one. If the kitemap corresponding to the current
+ coordinates doesn't tell you the coordinates of the next kite, then
+ you can try rewriting the two least-significant metatile indices
+ (using the metamap corresponding to the type of the next-larger
+ metatile still) and then see if that gives you a new kitemap that
+ works. If even that doesn't work, you can move another level up, and
+ try a metamap rewrite on the 2nd and 3rd smallest metatile levels,
+ or the 3rd and 4th, etc. And eventually, you find something you can
+ do.</p>
+ <p>The full set of kitemaps and metamaps for all the tile
+ types is in <a href="hatmaps.html">hatmaps.html</a>.</p>
+</body>
+</html>
--- /dev/null
+++ b/auxiliary/doc/kitemap-F.svg
@@ -1,0 +1,783 @@
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+</svg>
--- /dev/null
+++ b/auxiliary/doc/single-F.svg
@@ -1,0 +1,9 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="66" height="162">
+<path style="fill: none; stroke: black; stroke-width: 2.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 2.000000 140.564056
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+L 62.000000 140.564056
+L 62.000000 2.000000
+L 2.000000 36.641014
+z" />
+</svg>
--- /dev/null
+++ b/auxiliary/doc/single-H.svg
@@ -1,0 +1,11 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="156" height="180">
+<path style="fill: none; stroke: black; stroke-width: 2.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 2.000000 157.884567
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+</svg>
--- /dev/null
+++ b/auxiliary/doc/single-P.svg
@@ -1,0 +1,9 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="66" height="180">
+<path style="fill: none; stroke: black; stroke-width: 2.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 2.000000 175.205093
+L 62.000000 140.564087
+L 62.000000 2.000000
+L 2.000000 36.641037
+z" />
+<path style="fill: none; stroke: black; stroke-width: 9.000000; stroke-opacity: 0.2; stroke-linejoin: round; stroke-linecap: round; " d="M 14.000000 88.602562 L 50.000000 88.602554 L 37.999997 76.602557 M 50.000000 88.602554 L 38.000003 100.602557 " />
+</svg>
--- /dev/null
+++ b/auxiliary/doc/single-T.svg
@@ -1,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg xmlns="http://www.w3.org/2000/svg" version="1.1" width="96" height="110">
+<path style="fill: none; stroke: black; stroke-width: 2.000000; stroke-linejoin: round; stroke-linecap: round; " d="M 2.000000 105.923042
+L 92.000000 53.961521
+L 2.000000 2.000000
+z" />
+<path style="fill: none; stroke: black; stroke-width: 9.000000; stroke-opacity: 0.2; stroke-linejoin: round; stroke-linecap: round; " d="M 11.000000 90.334587 L 38.000000 43.569218 L 21.607695 47.961522 M 38.000000 43.569218 L 42.392305 59.961523 " />
+</svg>
--- /dev/null
+++ b/auxiliary/hatgen-images.sh
@@ -1,0 +1,23 @@
+#!/bin/sh
+
+# Regenerate all the SVG images in the aux/doc directory for hats.html
+# and hatmap.html.
+
+set -e
+
+hatgen=$1
+
+if ! test -x "$hatgen"; then
+ echo "Provide pathname to hatgen as an argument" >&2
+ exit 1
+fi
+
+for tile in H T P F; do
+ "$hatgen" "$tile" > single-"$tile".svg
+ "$hatgen" c"$tile" > expanded-"$tile".svg
+ "$hatgen" h"$tile" > hats-single-"$tile".svg
+ "$hatgen" H"$tile" > kitemap-"$tile".svg
+ "$hatgen" C"$tile" > metamap-"$tile".svg
+done
+
+"$hatgen" --hat > hat-kites.svg
--- /dev/null
+++ b/auxiliary/hatgen.c
@@ -1,0 +1,1713 @@
+/*
+ * Generate patches of tiling by the 'hat' aperiodic monotile
+ * discovered in 2023.
+ *
+ * This implementation of hat-tiling generation was intended to be the
+ * basis for generating hat grids for Loopy. However, it turned out
+ * that I found a better strategy, so this source file isn't used by
+ * the main puzzle system. I've kept it anyway because I ended up
+ * adapting it to generate the file hat-tables.h containing the lookup
+ * tables for the algorithm I _did_ end up using. It also generates
+ * diagrams that are useful for understanding that algorithm, and for
+ * debugging it if anything still turns out to be wrong with it.
+ *
+ * Discoverers' website: https://cs.uwaterloo.ca/~csk/hat/
+ * Preprint of paper: https://arxiv.org/abs/2303.10798
+ */
+
+#include <assert.h>
+#include <math.h>
+#include <stdbool.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "puzzles.h"
+#include "tree234.h"
+#include "hat.h"
+
+/*
+ * General strategy:
+ *
+ * We construct the hat tiling by means of a substitution system of
+ * 'metatiles' which come in four types, called H,T,P,F. A (valid)
+ * tiling of these metatiles can be expanded to a larger one by a set
+ * of recursive subdivision rules. Once we have a large enough patch
+ * of metatiles, we apply a final transformation that converts each
+ * metatile into 1, 2 or 4 instances of the aperiodically tiling
+ * 'hat'.
+ *
+ * Unlike the similar substitution system for Penrose tilings, the
+ * expansion rules are not geometrically precise: the larger versions
+ * of each metatile fit together combinatorially in the same way, but
+ * their shapes are distorted slightly. So we must construct our
+ * expanded meta-tiling by breadth-first search out from a starting
+ * metatile, because we won't quite know the coordinates of the
+ * expanded version of each metatile until we know one of the ones
+ * next to it.
+ */
+
+/*
+ * Coordinate system:
+ *
+ * Everything in this code lives on the tiling known to grid.c as
+ * 'Kites', which can be viewed as a tiling of hexagons each of which
+ * is subdivided into six kites sharing their pointy vertex, or
+ * (equivalently) a tiling of equilateral triangles each subdivided
+ * into three kits sharing their blunt vertex.
+ *
+ * We express coordinates in this system relative to the basis (1, r)
+ * where r = (1 + sqrt(3)i) / 2 is a primitive 6th root of unity. This
+ * gives us a system in which two integer coordinates can address any
+ * grid point, provided we scale up so that the side length of the
+ * equilateral triangles in the tiling is 6.
+ */
+
+typedef struct Point {+ int x, y; /* represents x + yr */
+} Point;
+
+static inline Point left6(Point p)
+{+ /* r satisfies the equation r^2 = r-1. Hence, multiplying by r
+ * (achieving a rotation anticlockwise by 1/6 turn) transforms
+ * x+yr into xr+yr^2 = xr+y(r-1) = (-y) + (x+y)r.
+ *
+ * It's easy to check that iterating this transformation six times
+ * gives you back the same coordinates you started with. */
+ Point q = { -p.y, p.x + p.y };+ return q;
+}
+
+static inline Point right6(Point p)
+{+ /* Conversely, 1/r = 1 - r, so dividing by r turns x+yr into x/r+y
+ * = x(1-r) + y = (x+y) + (-x)r. */
+ Point q = { p.x + p.y, -p.x };+ return q;
+}
+
+typedef enum MetatileType { MT_H, MT_T, MT_P, MT_F } MetatileType;+typedef struct Metatile Metatile;
+typedef struct MetaCoord {+ Metatile *parent;
+ int index;
+} MetaCoord;
+
+struct Metatile {+ /* Data fields describing the metatile and its position. */
+ MetatileType type;
+ Point start, orientation;
+
+ MetaCoord coords[4];
+ size_t ncoords;
+
+ /* Auxiliary fields used to store the progress of the expansion
+ * algorithm. */
+ bool queued;
+ Metatile *qnext;
+};
+
+#define MT_MAXVERT 6 /* largest number of vertices of any metatile */
+#define MT_MAXVDEGREE 3 /* largest degree of any vertex of a meta-tiling */
+#define MT_MAXEXPAND 13 /* largest number of metatiles in any expansion */
+#define MT_MAXHAT 4 /* largest number of hats in a metatile */
+#define HAT_NVERT 14 /* vertices of a single hat (counting the straight one) */
+#define HAT_NKITE 8 /* kites in a single hat */
+
+static int metatile_cmp(void *av, void *bv)
+{+ Metatile *a = (Metatile *)av, *b = (Metatile *)bv;
+ if (a->type < b->type) return -1;
+ if (a->type > b->type) return +1;
+ if (a->start.x < b->start.x) return -1;
+ if (a->start.x > b->start.x) return +1;
+ if (a->start.y < b->start.y) return -1;
+ if (a->start.y > b->start.y) return +1;
+ if (a->orientation.x < b->orientation.x) return -1;
+ if (a->orientation.x > b->orientation.x) return +1;
+ if (a->orientation.y < b->orientation.y) return -1;
+ if (a->orientation.y > b->orientation.y) return +1;
+ return 0;
+}
+
+/*
+ * Return the coordinates of the vertices of a metatile, given the
+ * coordinates of the vertex we deem to be distinguished, and a vector
+ * of Euclidean length 1 showing its direction.
+ *
+ * If 'expanded' is true, we instead return the coordinates of the
+ * corresponding vertices of the expanded version of the same
+ * metatile.
+ */
+static size_t metatile_vertices(Metatile m, Point *out, bool expanded)
+{+ static const Point vertices_H[] = {+ {0, 0}, {4, -2}, {12, 6}, {10, 10}, {-6, 18}, {-8, 16},+ };
+ static const Point vertices_T[] = {+ {0, 0}, {6, 6}, {-6, 12},+ };
+ static const Point vertices_P[] = {+ {0, 0}, {4, 4}, {-4, 20}, {-8, 16},+ };
+ static const Point vertices_F[] = {+ {0, 0}, {4, -2}, {6, 0}, {-2, 16}, {-6, 12},+ };
+
+ static const Point expanded_H[] = {+ {0, 0}, {12, -6}, {30, 12}, {24, 24}, {-12, 42}, {-18, 36},+ };
+ static const Point expanded_T[] = {+ {0, 0}, {12, 12}, {-12, 24},+ };
+ static const Point expanded_P[] = {+ {0, 0}, {14, 8}, {-4, 44}, {-18, 36},+ };
+ static const Point expanded_F[] = {+ {0, 0}, {14, -4}, {18, 6}, {0, 42}, {-14, 34},+ };
+
+ const Point *vertices;
+ size_t nvertices;
+ size_t i;
+
+ switch (m.type) {+ case MT_H:
+ vertices = expanded ? expanded_H : vertices_H;
+ nvertices = lenof(vertices_H);
+ break;
+ case MT_T:
+ vertices = expanded ? expanded_T : vertices_T;
+ nvertices = lenof(vertices_T);
+ break;
+ case MT_P:
+ vertices = expanded ? expanded_P : vertices_P;
+ nvertices = lenof(vertices_P);
+ break;
+ default /* case MT_F */:
+ vertices = expanded ? expanded_F : vertices_F;
+ nvertices = lenof(vertices_F);
+ break;
+ }
+ assert(nvertices <= MT_MAXVERT);
+
+ Point orientation_r = left6(m.orientation);
+ for (i = 0; i < nvertices; i++) {+ Point v = vertices[i];
+ out[i].x = m.start.x + v.x * m.orientation.x + v.y * orientation_r.x;
+ out[i].y = m.start.y + v.x * m.orientation.y + v.y * orientation_r.y;
+ }
+ return nvertices;
+}
+
+/*
+ * Return a list of metatiles that arise from expanding a given tile.
+ */
+static size_t metatile_expand(Metatile m, Metatile *out)
+{+ static const Metatile tiles_H[] = {+ {MT_H, {-4, 20}, {1, 0}},+ {MT_H, {2, 2}, {1, 0}},+ {MT_H, {8, 26}, {0, -1}},+ {MT_T, {6, 24}, {-1, 0}},+ {MT_P, {-8, 16}, {1, 0}},+ {MT_P, {4, 34}, {0, -1}},+ {MT_P, {6, 0}, {1, -1}},+ {MT_F, {-10, 38}, {-1, 1}},+ {MT_F, {-10, 44}, {0, -1}},+ {MT_F, {-4, 2}, {1, 0}},+ {MT_F, {2, 2}, {0, -1}},+ {MT_F, {26, 14}, {1, 0}},+ {MT_F, {32, 8}, {-1, 1}},+ };
+ static const Metatile tiles_T[] = {+ {MT_H, {10, 10}, {-1, 1}},+ {MT_P, {-6, 0}, {1, 0}},+ {MT_P, {8, 14}, {0, 1}},+ {MT_P, {18, 6}, {-1, 1}},+ {MT_F, {-14, 34}, {-1, 0}},+ {MT_F, {-8, -2}, {1, -1}},+ {MT_F, {22, 4}, {0, 1}},+ };
+ static const Metatile tiles_P[] = {+ {MT_H, {4, 22}, {0, 1}},+ {MT_H, {10, 10}, {-1, 1}},+ {MT_P, {-6, 0}, {1, 0}},+ {MT_P, {6, 24}, {1, 0}},+ {MT_P, {8, 14}, {0, 1}},+ {MT_F, {-20, 40}, {1, -1}},+ {MT_F, {-14, 34}, {-1, 0}},+ {MT_F, {-8, -2}, {1, -1}},+ {MT_F, {4, 46}, {-1, 1}},+ {MT_F, {10, 10}, {1, 0}},+ {MT_F, {16, 4}, {-1, 1}},+ };
+ static const Metatile tiles_F[] = {+ {MT_H, {8, 20}, {0, 1}},+ {MT_H, {14, 8}, {-1, 1}},+ {MT_P, {10, 22}, {1, 0}},+ {MT_P, {12, 12}, {0, 1}},+ {MT_F, {-16, 38}, {1, -1}},+ {MT_F, {-10, 32}, {-1, 0}},+ {MT_F, {-4, 2}, {1, 0}},+ {MT_F, {2, 2}, {0, -1}},+ {MT_F, {8, 44}, {-1, 1}},+ {MT_F, {14, 8}, {1, 0}},+ {MT_F, {20, 2}, {-1, 1}},+ };
+
+ const Metatile *tiles;
+ size_t ntiles;
+ size_t i;
+
+ switch (m.type) {+ case MT_H:
+ tiles = tiles_H;
+ ntiles = lenof(tiles_H);
+ break;
+ case MT_T:
+ tiles = tiles_T;
+ ntiles = lenof(tiles_T);
+ break;
+ case MT_P:
+ tiles = tiles_P;
+ ntiles = lenof(tiles_P);
+ break;
+ default /* case MT_F */:
+ tiles = tiles_F;
+ ntiles = lenof(tiles_F);
+ break;
+ }
+ assert(ntiles <= MT_MAXEXPAND);
+
+ Point orientation_r = left6(m.orientation);
+ for (i = 0; i < ntiles; i++) {+ Metatile t = tiles[i];
+ out[i].type = t.type;
+ out[i].start.x = (m.start.x + t.start.x * m.orientation.x +
+ t.start.y * orientation_r.x);
+ out[i].start.y = (m.start.y + t.start.x * m.orientation.y +
+ t.start.y * orientation_r.y);
+ out[i].orientation.x = (t.orientation.x * m.orientation.x +
+ t.orientation.y * orientation_r.x);
+ out[i].orientation.y = (t.orientation.x * m.orientation.y +
+ t.orientation.y * orientation_r.y);
+ }
+ return ntiles;
+}
+
+/* Store data about each vertex during an expansion. */
+typedef struct VertexMapping {+ Point in;
+
+ /* Metatiles sharing this vertex */
+ Metatile *tiles[MT_MAXVDEGREE];
+ size_t ntiles;
+
+ /* The expanded coordinates of this vertex, if known */
+ bool mapped;
+ Point out;
+} VertexMapping;
+
+static int vertexmapping_cmp(void *av, void *bv)
+{+ VertexMapping *a = (VertexMapping *)av, *b = (VertexMapping *)bv;
+ if (a->in.x < b->in.x) return -1;
+ if (a->in.x > b->in.x) return +1;
+ if (a->in.y < b->in.y) return -1;
+ if (a->in.y > b->in.y) return +1;
+ return 0;
+}
+
+static int vertexmapping_find(void *av, void *bv)
+{+ Point *a = (Point *)av;
+ VertexMapping *b = (VertexMapping *)bv;
+ if (a->x < b->in.x) return -1;
+ if (a->x > b->in.x) return +1;
+ if (a->y < b->in.y) return -1;
+ if (a->y > b->in.y) return +1;
+ return 0;
+}
+
+typedef struct MetatileSet {+ /* The tiles in the set */
+ tree234 *tiles;
+
+ /*
+ * Bounding box of a rectangular region within the original single
+ * tile this set was expanded from. We need this in order to pick
+ * a random chunk out of the tiling to return to our client: this
+ * box is the limit of where we might select our chunk from.
+ *
+ * The box is obtained by starting from the two obtuse vertices of
+ * the starting P metatile, and then mapping those two vertices
+ * through each expansion pass. This wouldn't work for the _other_
+ * two vertices of the P metatile, which end up in the middle of
+ * another metatile after the first expansion, so that the next
+ * expansion wouldn't find that point in its VertexMapping. But
+ * luckily the two inner P vertices do continue working: they
+ * alternate in subsequent expansions between vertex 1 and vertex
+ * 4 of an F metatile. And those are the ones we need to define a
+ * reliable bounding box - phew!
+ */
+ Point vertices[2];
+ size_t nvertices;
+} MetatileSet;
+
+static MetatileSet *metatile_initial_set(MetatileType type)
+{+ MetatileSet *s;
+ Metatile *m;
+ Point vertices[MT_MAXVERT];
+ size_t nv;
+
+ s = snew(MetatileSet);
+ s->tiles = newtree234(metatile_cmp);
+
+ m = snew(Metatile);
+ m->type = type;
+ m->start.x = 0;
+ m->start.y = 0;
+ m->orientation.x = 1;
+ m->orientation.y = 0;
+ m->ncoords = 0;
+ add234(s->tiles, m);
+
+ if (type == MT_P) {+ nv = metatile_vertices(*m, vertices, false);
+ assert(nv == 4);
+ s->vertices[0] = vertices[1];
+ s->vertices[1] = vertices[3];
+ s->nvertices = 2;
+ } else {+ s->nvertices = 0;
+ }
+
+ return s;
+}
+
+static void metatile_free_set(MetatileSet *s)
+{+ Metatile *m;
+
+ while ((m = delpos234(s->tiles, 0)) != NULL)
+ sfree(m);
+ freetree234(s->tiles);
+ sfree(s);
+}
+
+typedef struct Queue {+ Metatile *head, *tail;
+} Queue;
+
+static void map_vertex(VertexMapping *vm, Point out, Queue *queue)
+{+ size_t i;
+
+ debug(("map_vertex %d,%d -> %d,%d", vm->in.x, vm->in.y, out.x, out.y));+ if (vm->mapped) {+ debug((" (already done)\n"));+ return;
+ }
+ debug(("\n"));+
+ vm->mapped = true;
+ vm->out = out;
+
+ for (i = 0; i < vm->ntiles; i++) {+ Metatile *t = vm->tiles[i];
+ if (!t->queued) {+ t->queued = true;
+ t->qnext = NULL;
+ if (queue->tail)
+ queue->tail->qnext = t;
+ else
+ queue->head = t;
+ queue->tail = t;
+ debug(("queued %c @ %d,%d d=%d,%d\n", "HTPF"[t->type], t->start.x,+ t->start.y, t->orientation.x, t->orientation.y));
+ }
+ }
+}
+
+/*
+ * Expand a set of metatiles into its next-generation set. Returns the
+ * new set. The old set is not freed, but the auxiliary fields of its
+ * Metatile structures will be used as intermediate storage.
+ */
+static MetatileSet *metatile_set_expand(MetatileSet *si)
+{+ tree234 *vmap;
+ VertexMapping *vm;
+ Metatile *m;
+ Queue queue = { NULL, NULL };+ size_t i, j;
+ MetatileSet *so = snew(MetatileSet);
+
+ so->tiles = newtree234(metatile_cmp);
+
+ /*
+ * Enumerate all the vertices in our tiling, and store the set of
+ * tiles they belong to.
+ */
+ vmap = newtree234(vertexmapping_cmp);
+ for (i = 0; (m = index234(si->tiles, i)) != NULL; i++) {+ Point vertices[MT_MAXVERT];
+ size_t nv = metatile_vertices(*m, vertices, false);
+
+ for (j = 0; j < nv; j++) {+ VertexMapping *newvm = snew(VertexMapping);
+ newvm->in = vertices[j];
+ newvm->ntiles = 0;
+ newvm->mapped = false;
+
+ vm = add234(vmap, newvm);
+ if (vm != newvm)
+ sfree(newvm);
+
+ assert(vm->ntiles < MT_MAXVDEGREE);
+ vm->tiles[vm->ntiles++] = m;
+ }
+
+ m->queued = false;
+ }
+
+ for (i = 0; (vm = index234(vmap, i)) != NULL; i++) {+ debug(("vertex @ %d,%d {", vm->in.x, vm->in.y));+ for (j = 0; j < vm->ntiles; j++) {+ m = vm->tiles[j];
+ debug(("%s%c @ %d,%d d=%d,%d", j?", ":"", "HTPF"[m->type],+ m->start.x, m->start.y, m->orientation.x,
+ m->orientation.y));
+ }
+ debug(("}\n"));+ }
+
+ /*
+ * Initialise an arbitrary vertex to a known location.
+ */
+ {+ Point p = {0, 0};+ m = index234(si->tiles, 0);
+ vm = find234(vmap, &m->start, vertexmapping_find);
+ map_vertex(vm, p, &queue);
+ }
+
+ /*
+ * Now process the queue of tiles to be expanded.
+ */
+ debug(("-- start\n"));+ while (queue.head) {+ Metatile *m, m_moved;
+ Metatile t[MT_MAXEXPAND];
+ Point vi[MT_MAXVERT], vo[MT_MAXVERT];
+ size_t nv, nt;
+
+ m = queue.head;
+ queue.head = queue.head->qnext;
+ if (!queue.head)
+ queue.tail = NULL;
+
+ debug(("unqueued %c @ %d,%d d=%d,%d\n", "HTPF"[m->type],+ m->start.x, m->start.y, m->orientation.x, m->orientation.y));
+
+ nv = metatile_vertices(*m, vi, false);
+ metatile_vertices(*m, vo, true);
+
+ /* Find a vertex of this tile that's already mapped, and use
+ * it to determine the placement. */
+ int dx, dy;
+ for (i = 0; i < nv; i++) {+ vm = find234(vmap, &vi[i], vertexmapping_find);
+ assert(vm);
+ if (vm->mapped) {+ dx = vm->out.x - vo[i].x;
+ dy = vm->out.y - vo[i].y;
+ debug(("found mapped vertex %d,%d -> %d,%d: "+ "offset=%d,%d\n",
+ vm->in.x, vm->in.y, vm->out.x, vm->out.y, dx, dy));
+ break;
+ }
+ }
+ assert(i < nv && "Why was this tile queued without a mapped vertex?");
+
+ /* Now map all the rest of the vertices of the tile. */
+ for (i = 0; i < nv; i++) {+ vm = find234(vmap, &vi[i], vertexmapping_find);
+ vo[i].x += dx;
+ vo[i].y += dy;
+ map_vertex(vm, vo[i], &queue);
+ }
+
+ /* And expand it, substituting in its new starting coordinate. */
+ m_moved = *m; /* structure copy */
+ m_moved.start = vo[0];
+ nt = metatile_expand(m_moved, t);
+ for (i = 0; i < nt; i++) {+ Metatile *newmt = snew(Metatile);
+ *newmt = t[i]; /* structure copy */
+ newmt->ncoords = 0;
+ debug(("expanded %c @ %d,%d d=%d,%d\n", "HTPF"[newmt->type],+ newmt->start.x, newmt->start.y, newmt->orientation.x,
+ newmt->orientation.y));
+
+ Metatile *added = add234(so->tiles, newmt);
+ if (added != newmt)
+ sfree(newmt);
+ assert(added->ncoords < lenof(added->coords));
+ added->coords[added->ncoords].parent = m;
+ added->coords[added->ncoords].index = i;
+ added->ncoords++;
+ }
+ }
+
+ for (i = 0; (m = index234(si->tiles, i)) != NULL; i++) {+ if (!m->queued)
+ debug(("OMITTED %c @ %d,%d d=%d,%d\n", "HTPF"[m->type],+ m->start.x, m->start.y, m->orientation.x,
+ m->orientation.y));
+ }
+
+ /*
+ * Write out the remapped versions of the tile set's bounding
+ * vertices.
+ */
+ for (i = 0; i < si->nvertices; i++) {+ vm = find234(vmap, &si->vertices[i], vertexmapping_find);
+ so->vertices[i] = vm->out;
+ }
+ so->nvertices = si->nvertices;
+
+ while ((vm = delpos234(vmap, 0)) != NULL)
+ sfree(vm);
+ freetree234(vmap);
+
+ return so;
+}
+
+typedef struct Hat {+ Point start, orientation;
+ bool reversed;
+ const Metatile *parent;
+ int index;
+} Hat;
+
+static size_t metatile_hats(const Metatile *m, Hat *out)
+{+ static const Hat hats_H[] = {+ {{6, 0}, {1, 0}, false},+ {{6, 6}, {0, -1}, false},+ {{0, 12}, {1, 0}, false},+ {{0, 6}, {-1, 0}, true},+ };
+ static const Hat hats_T[] = {+ {{-2, 10}, {-1, 1}, false},+ };
+ static const Hat hats_P[] = {+ {{-2, 10}, {-1, 1}, false},+ {{-2, 16}, {0, 1}, false},+ };
+ static const Hat hats_F[] = {+ {{0, 6}, {-1, 1}, false},+ {{0, 12}, {0, 1}, false},+ };
+
+ const Hat *hats;
+ size_t nhats;
+ size_t i;
+
+ switch (m->type) {+ case MT_H:
+ hats = hats_H;
+ nhats = lenof(hats_H);
+ break;
+ case MT_T:
+ hats = hats_T;
+ nhats = lenof(hats_T);
+ break;
+ case MT_P:
+ hats = hats_P;
+ nhats = lenof(hats_P);
+ break;
+ default /* case MT_F */:
+ hats = hats_F;
+ nhats = lenof(hats_F);
+ break;
+ }
+ assert(nhats <= MT_MAXHAT);
+
+ Point orientation_r = left6(m->orientation);
+ for (i = 0; i < nhats; i++) {+ Hat h = hats[i];
+ out[i].parent = m;
+ out[i].index = i;
+ out[i].start.x = (m->start.x + h.start.x * m->orientation.x +
+ h.start.y * orientation_r.x);
+ out[i].start.y = (m->start.y + h.start.x * m->orientation.y +
+ h.start.y * orientation_r.y);
+ out[i].orientation.x = (h.orientation.x * m->orientation.x +
+ h.orientation.y * orientation_r.x);
+ out[i].orientation.y = (h.orientation.x * m->orientation.y +
+ h.orientation.y * orientation_r.y);
+ out[i].reversed = h.reversed;
+ }
+ return nhats;
+}
+
+static size_t hat_vertices(Hat h, Point *out)
+{+ static const Point reference_hat[] = {+ {0, 0}, {3, 0}, {2, 2}, {0, 3}, {-2, 4}, {-3, 3}, {-6, 6}, {-9, 6},+ {-8, 4}, {-6, 3}, {-6, 0}, {-3, -3}, {-2, -2}, {0, -3},+ };
+
+ size_t i;
+
+ Point orientation_r;
+ if (h.reversed)
+ orientation_r = right6(h.orientation);
+ else
+ orientation_r = left6(h.orientation);
+ assert(lenof(reference_hat) == HAT_NVERT);
+
+ for (i = 0; i < lenof(reference_hat); i++) {+ Point v = reference_hat[h.reversed ? HAT_NVERT-1-i : i];
+ out[i].x = h.start.x + v.x * h.orientation.x + v.y * orientation_r.x;
+ out[i].y = h.start.y + v.x * h.orientation.y + v.y * orientation_r.y;
+ }
+ return lenof(reference_hat);
+}
+
+typedef struct BoundingBox {+ Point bl, tr;
+} BoundingBox;
+
+static bool point_in_bbox(Point p, const BoundingBox *bbox)
+{+ int xl, xr, x;
+
+ if (!bbox)
+ return true;
+
+ /*
+ * Bounding boxes have vertical edges, not aligned with our basis
+ * vector r. So the 'true' x coordinate of (x,y) is proportional
+ * to 2x+y.
+ */
+ if (p.y < bbox->bl.y || p.y > bbox->tr.y)
+ return false;
+
+ xl = 2*bbox->bl.x + bbox->bl.y;
+ xr = 2*bbox->tr.x + bbox->tr.y;
+ x = 2*p.x + p.y;
+
+ if (x < xl || x > xr)
+ return false;
+
+ return true;
+}
+
+static bool hat_in_bbox(Hat h, const BoundingBox *bbox)
+{+ Point p[HAT_NVERT];
+ size_t i, np;
+
+ if (!bbox)
+ return true;
+
+ np = hat_vertices(h, p);
+ for (i = 0; i < np; i++)
+ if (!point_in_bbox(p[i], bbox))
+ return false;
+
+ return true;
+}
+
+static Hat *metatile_set_to_hats(MetatileSet *s, size_t *nhats,
+ const BoundingBox *bbox)
+{+ Metatile *m;
+ size_t i, j, k, n;
+ Hat *h;
+
+ n = 0;
+ for (i = 0; (m = index234(s->tiles, i)) != NULL; i++) {+ Hat htmp[MT_MAXHAT];
+ size_t nthis = metatile_hats(m, htmp);
+ for (k = 0; k < nthis; k++)
+ if (hat_in_bbox(htmp[k], bbox))
+ n++;
+ }
+
+ *nhats = n;
+ h = snewn(n, Hat);
+
+ j = 0;
+ for (i = 0; (m = index234(s->tiles, i)) != NULL; i++) {+ Hat htmp[MT_MAXHAT];
+ size_t nthis = metatile_hats(m, htmp);
+ for (k = 0; k < nthis; k++) {+ if (hat_in_bbox(htmp[k], bbox)) {+ assert(j < n);
+ h[j++] = htmp[k]; /* structure copy */
+ }
+ }
+ }
+
+ assert(j == n);
+ return h;
+}
+
+#if 0
+void hat_tiling_randomise(struct HatPatchParams *params, random_state *rs)
+{+ MetatileSet *s, *s2;
+ int x0, x1, y0, y1;
+
+ /*
+ * Iterate until we have a good-sized patch to select a rectangle
+ * from.
+ */
+ s = metatile_initial_set(MT_P);
+ params->iterations = 0;
+
+ while (true) {+ x0 = 2 * s->vertices[0].x + s->vertices[0].y;
+ x1 = 2 * s->vertices[1].x + s->vertices[1].y;
+ if (x1 < x0) {+ int t = x1;
+ x1 = x0;
+ x0 = t;
+ }
+ y0 = s->vertices[0].y;
+ y1 = s->vertices[1].y;
+ if (y1 < y0) {+ int t = y1;
+ y1 = y0;
+ y0 = t;
+ }
+
+ if (50*params->w <= x1-x0 && 50*params->h <= y1-y0)
+ break;
+
+ params->iterations++;
+ s2 = metatile_set_expand(s);
+ metatile_free_set(s);
+ s = s2;
+ }
+
+ /*
+ * Now select that rectangle.
+ */
+ params->x = x0 + random_upto(rs, x1 - x0 - params->w + 1);
+ params->y = y0 + random_upto(rs, y1 - y0 - params->h + 1);
+}
+
+void hat_tiling_generate(struct HatPatchParams *params,
+ hat_tile_callback_fn cb, void *cbctx)
+{+ MetatileSet *s, *s2;
+ unsigned i;
+ size_t j, nh;
+ BoundingBox bbox;
+ Hat *hats;
+
+ s = metatile_initial_set(MT_P);
+ for (i = 0; i < params->iterations; i++) {+ s2 = metatile_set_expand(s);
+ metatile_free_set(s);
+ s = s2;
+ }
+
+ bbox.bl.x = (params->x - params->y) / 2;
+ bbox.tr.x = ((params->x + params->w) - (params->y + params->h)) / 2;
+ bbox.bl.y = params->y;
+ bbox.tr.y = params->y + params->h;
+ hats = metatile_set_to_hats(s, &nh, &bbox);
+ for (j = 0; j < nh; j++) {+ Point vertices[HAT_NVERT];
+ size_t nv = hat_vertices(hats[j], vertices);
+ int out[2 * HAT_NVERT];
+ size_t k;
+
+ for (k = 0; k < nv; k++) {+ out[2*k] = 2 * vertices[k].x + vertices[k].y;
+ out[2*k+1] = vertices[k].y;
+ }
+
+ cb(cbctx, nv, out);
+ }
+ sfree(hats);
+
+ metatile_free_set(s);
+}
+
+#endif
+
+#ifdef TEST_HAT
+
+/*
+ * Assortment of test modes that output Postscript diagrams.
+ */
+
+static size_t hat_kite_centres(Hat h, Point *out)
+{+ static const Point reference_hat[] = {+ {-7,5},{-5,4},{-5,1},{-4,-1},{-1,-1},{-2,1},{-1,2},{1,1},+ };
+
+ size_t i;
+
+ Point orientation_r;
+ if (h.reversed)
+ orientation_r = right6(h.orientation);
+ else
+ orientation_r = left6(h.orientation);
+ assert(lenof(reference_hat) == HAT_NKITE);
+
+ for (i = 0; i < lenof(reference_hat); i++) {+ Point v = reference_hat[i];
+ out[i].x = h.start.x + v.x * h.orientation.x + v.y * orientation_r.x;
+ out[i].y = h.start.y + v.x * h.orientation.y + v.y * orientation_r.y;
+ }
+ return lenof(reference_hat);
+}
+
+static inline int round6(int x)
+{+ int sign = x<0 ? -1 : +1;
+ x *= sign;
+ x += 3;
+ x /= 6;
+ x *= 6;
+ x *= sign;
+ return x;
+}
+
+static inline Point kite_left(Point k)
+{+ Point centre = { round6(k.x), round6(k.y) };+ Point offset = { k.x - centre.x, k.y - centre.y };+ offset = left6(offset);
+ Point r = { centre.x + offset.x, centre.y + offset.y };+ return r;
+}
+
+static inline Point kite_right(Point k)
+{+ Point centre = { round6(k.x), round6(k.y) };+ Point offset = { k.x - centre.x, k.y - centre.y };+ offset = right6(offset);
+ Point r = { centre.x + offset.x, centre.y + offset.y };+ return r;
+}
+
+static inline Point kite_forward_left(Point k)
+{+ Point centre = { round6(k.x), round6(k.y) };+ Point offset = { k.x - centre.x, k.y - centre.y };+ Point rotate = left6(offset);
+ Point r = { k.x + rotate.x + offset.x, k.y + rotate.y + offset.y };+ return r;
+}
+
+static inline Point kite_forward_right(Point k)
+{+ Point centre = { round6(k.x), round6(k.y) };+ Point offset = { k.x - centre.x, k.y - centre.y };+ Point rotate = right6(offset);
+ Point r = { k.x + rotate.x + offset.x, k.y + rotate.y + offset.y };+ return r;
+}
+
+typedef struct pspoint {+ float x, y;
+} pspoint;
+
+static inline pspoint pscoords(Point p)
+{+ pspoint q = { p.x + p.y / 2.0F, p.y * sqrt(0.75) };+ return q;
+}
+
+typedef struct psbbox {+ bool started;
+ pspoint bl, tr;
+} psbbox;
+
+static inline void psbbox_add(psbbox *bbox, pspoint p)
+{+ if (!bbox->started || bbox->bl.x > p.x)
+ bbox->bl.x = p.x;
+ if (!bbox->started || bbox->tr.x < p.x)
+ bbox->tr.x = p.x;
+ if (!bbox->started || bbox->bl.y > p.y)
+ bbox->bl.y = p.y;
+ if (!bbox->started || bbox->tr.y < p.y)
+ bbox->tr.y = p.y;
+ bbox->started = true;
+}
+
+static void draw_metatiles_svg(const Metatile *tiles, size_t n,
+ const Point *bounds, bool coords)
+{+ size_t i, j;
+ psbbox bbox = { false };+
+ for (i = 0; i < n; i++) {+ Point vertices[MT_MAXVERT];
+ size_t nv = metatile_vertices(tiles[i], vertices, false);
+ for (j = 0; j < nv; j++)
+ psbbox_add(&bbox, pscoords(vertices[j]));
+ }
+
+ float ascale = 10, xscale = ascale, yscale = -ascale;
+ float border = 0.2 * ascale; /* leave room for strokes at the edges */
+ float ox = -xscale * bbox.bl.x + border;
+ float oy = -yscale * bbox.tr.y + border;
+
+ printf("<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n");+ printf("<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\" "+ "width=\"%g\" height=\"%g\">\n",
+ ceil(ox + xscale * bbox.tr.x + 2*border),
+ ceil(oy + yscale * bbox.bl.y + 2*border));
+
+ for (i = 0; i < n; i++) {+ Point vertices[MT_MAXVERT];
+ size_t nv = metatile_vertices(tiles[i], vertices, false);
+ pspoint pp[MT_MAXVERT];
+
+ for (j = 0; j < nv; j++) {+ pp[j] = pscoords(vertices[j]);
+ pp[j].x = ox + xscale * pp[j].x;
+ pp[j].y = oy + yscale * pp[j].y;
+ }
+
+ printf("<path style=\""+ "fill: none; "
+ "stroke: black; "
+ "stroke-width: %f; "
+ "stroke-linejoin: round; "
+ "stroke-linecap: round; "
+ "\" d=\"", 0.2 * ascale);
+ for (j = 0; j < nv; j++)
+ printf("%s %f %f \n", j ? "L" : "M", pp[j].x, pp[j].y);+ printf("z\" />\n");+
+ if (tiles[i].type != MT_F) {+ /*
+ * Mark arrows on three of the metatile types (H, T, P),
+ * following the diagrams in the paper. (The metatile
+ * shapes other than F each have some symmetry, but their
+ * roles in the metatile substitution system are not
+ * similarly symmetric, so for diagnostic diagrams you
+ * want to mark their orientation.)
+ */
+ pspoint lstart, lend;
+ pspoint astart, aend, aforward, aleft;
+ double d;
+
+ /*
+ * Determine endpoints of a line crossing the polygon in
+ * the appropriate direction, by case analysis on the
+ * individual tile types.
+ */
+ switch (tiles[i].type) {+ case MT_H:
+ lstart.x = (pp[4].x + pp[5].x) / 2;
+ lstart.y = (pp[4].y + pp[5].y) / 2;
+ lend.x = (pp[1].x + pp[2].x) / 2;
+ lend.y = (pp[1].y + pp[2].y) / 2;
+ break;
+ case MT_T:
+ lstart = pp[0];
+ lend.x = (pp[1].x + pp[2].x) / 2;
+ lend.y = (pp[1].y + pp[2].y) / 2;
+ break;
+ default /* case MT_P */:
+ lstart.x = (5*pp[3].x + 3*pp[0].x) / 8;
+ lstart.y = (5*pp[3].y + 3*pp[0].y) / 8;
+ lend.x = (5*pp[1].x + 3*pp[2].x) / 8;
+ lend.y = (5*pp[1].y + 3*pp[2].y) / 8;
+ break;
+ }
+
+ /*
+ * Now shorten that line a little and give it an arrowhead.
+ */
+ astart.x = (4 * lstart.x + lend.x) / 5;
+ astart.y = (4 * lstart.y + lend.y) / 5;
+ aend.x = (lstart.x + 4 * lend.x) / 5;
+ aend.y = (lstart.y + 4 * lend.y) / 5;
+ aforward.x = aend.x - astart.x;
+ aforward.y = aend.y - astart.y;
+ d = sqrt(aforward.x*aforward.x + aforward.y*aforward.y);
+ aforward.x /= d;
+ aforward.y /= d;
+ aleft.x = -aforward.y;
+ aleft.y = +aforward.x;
+
+ printf("<path style=\""+ "fill: none; "
+ "stroke: black; "
+ "stroke-width: %f; "
+ "stroke-opacity: 0.2; "
+ "stroke-linejoin: round; "
+ "stroke-linecap: round; "
+ "\" d=\"", 0.9 * ascale);
+
+ printf("M %f %f L %f %f ", astart.x, astart.y,+ aend.x, aend.y);
+ printf("L %f %f ",+ aend.x - 1.2 * ascale * (aforward.x + aleft.x),
+ aend.y - 1.2 * ascale * (aforward.y + aleft.y));
+ printf("M %f %f L %f %f ", aend.x, aend.y,+ aend.x - 1.2 * ascale * (aforward.x - aleft.x),
+ aend.y - 1.2 * ascale * (aforward.y - aleft.y));
+ printf("\" />\n");+ }
+
+ if (coords) {+ /*
+ * Print each tile's coordinates.
+ */
+ pspoint centre;
+ size_t j;
+
+ switch (tiles[i].type) {+ case MT_H:
+ centre.x = (pp[0].x + pp[2].x + pp[4].x) / 3;
+ centre.y = (pp[0].y + pp[2].y + pp[4].y) / 3;
+ break;
+ case MT_T:
+ centre.x = (pp[0].x + pp[1].x + pp[2].x) / 3;
+ centre.y = (pp[0].y + pp[1].y + pp[2].y) / 3;
+ break;
+ case MT_P:
+ centre.x = (pp[0].x + pp[2].x) / 2;
+ centre.y = (pp[0].y + pp[2].y) / 2;
+ break;
+ default /* case MT_F */:
+ centre.x = (pp[2].x + pp[4].x) / 2;
+ centre.y = (pp[2].y + pp[4].y) / 2;
+ break;
+ }
+
+ double lineheight = ascale * 1.5;
+ double charheight = lineheight * 0.6; /* close enough */
+ double allheight = lineheight * (tiles[i].ncoords-1) + charheight;
+
+ for (j = 0; j < tiles[i].ncoords; j++) {+ const Metatile *it;
+ unsigned cindex;
+
+ printf("<text style=\""+ "fill: black; "
+ "font-family: Sans; "
+ "font-size: %g; "
+ "text-anchor: middle; "
+ "text-align: center; "
+ "\" x=\"%g\" y=\"%g\">", lineheight,
+ centre.x,
+ centre.y - allheight/2 + charheight + lineheight*j);
+
+ it = &tiles[i];
+ cindex = j;
+ while (cindex < it->ncoords) {+ if (it != &tiles[i])
+ printf(".");+ printf("%d", (int)it->coords[cindex].index);+
+ it = it->coords[cindex].parent;
+ cindex = 0; /* BODGING AHOY */
+ }
+
+ printf("</text>\n");+ }
+ }
+
+ }
+
+ printf("</svg>\n");+}
+
+static void draw_metatile_set_svg(
+ MetatileSet *tiles, const Point *bounds, bool coords)
+{+ /*
+ * Slurp the tree234 of tiles into an array for display.
+ * Tedious, but this test code doesn't have to be particularly
+ * efficient.
+ */
+ size_t nt = count234(tiles->tiles);
+ Metatile *t = snewn(nt, Metatile);
+ size_t i;
+ for (i = 0; i < nt; i++) {+ Metatile *m = index234(tiles->tiles, i);
+ t[i] = *m; /* structure copy */
+ }
+ draw_metatiles_svg(t, nt, bounds, coords);
+ sfree(t);
+}
+
+static void draw_hats_svg(const Hat *hats, size_t n,
+ const Point *bounds, bool kites, char coordtype)
+{+ size_t i, j;
+ psbbox bbox = { false };+
+ for (i = 0; i < n; i++) {+ Point vertices[HAT_NVERT];
+ size_t nv = hat_vertices(hats[i], vertices);
+ for (j = 0; j < nv; j++)
+ psbbox_add(&bbox, pscoords(vertices[j]));
+ }
+
+ float ascale = (coordtype == 'k' || coordtype == 'K' ? 20 : 10);
+ float xscale = ascale, yscale = -ascale;
+ float border = 0.2 * ascale; /* leave room for strokes at the edges */
+ float ox = -xscale * bbox.bl.x + border;
+ float oy = -yscale * bbox.tr.y + border;
+
+ printf("<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n");+ printf("<svg xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\" "+ "width=\"%g\" height=\"%g\">\n",
+ ceil(ox + xscale * bbox.tr.x + 2*border),
+ ceil(oy + yscale * bbox.bl.y + 2*border));
+
+ for (i = 0; i < n; i++) {+ Point vertices[HAT_NVERT];
+ pspoint psvs[HAT_NVERT];
+ size_t nv = hat_vertices(hats[i], vertices);
+ int is = hats[i].reversed ? -1 : +1;
+ int io = hats[i].reversed ? 13 : 0;
+
+ printf("<path style=\""+ "fill: %s; "
+ "stroke: black; "
+ "stroke-width: %f; "
+ "stroke-linejoin: round; "
+ "stroke-linecap: round; "
+ "\" d=\"",
+ hats[i].reversed ? "rgba(0,0,0,0.2)" : "none",
+ 0.2 * ascale);
+ for (j = 0; j < nv; j++) {+ psvs[j] = pscoords(vertices[j]);
+ printf("%s %f %f\n", j ? "L" : "M",+ ox + xscale * psvs[j].x, oy + yscale * psvs[j].y);
+ }
+ printf("z\" />\n");+
+ if (kites) {+ /*
+ * Draw internal lines within each hat dividing it into
+ * kites. This is done in a rather bodgy way, sorry.
+ */
+ const char *fmt = "<path style=\""
+ "fill: none; "
+ "stroke: rgba(0,0,0,0.2); "
+ "stroke-width: %f; "
+ "stroke-linejoin: round; "
+ "stroke-linecap: round; "
+ "\" d=\"M %f %f L %f %f\" />\n";
+ float strokewidth = 0.1 * ascale;
+
+ printf(fmt, strokewidth,
+ ox + xscale * psvs[io+is*0].x,
+ oy + yscale * psvs[io+is*0].y,
+ ox + xscale * psvs[io+is*3].x,
+ oy + yscale * psvs[io+is*3].y);
+
+ printf(fmt, strokewidth,
+ ox + xscale * psvs[io+is*0].x,
+ oy + yscale * psvs[io+is*0].y,
+ ox + xscale * psvs[io+is*5].x,
+ oy + yscale * psvs[io+is*5].y);
+
+ printf(fmt, strokewidth,
+ ox + xscale * psvs[io+is*6].x,
+ oy + yscale * psvs[io+is*6].y,
+ ox + xscale * psvs[io+is*9].x,
+ oy + yscale * psvs[io+is*9].y);
+
+ printf(fmt, strokewidth,
+ ox + xscale * psvs[io+is*0].x,
+ oy + yscale * psvs[io+is*0].y,
+ ox + xscale * psvs[io+is*10].x,
+ oy + yscale * psvs[io+is*10].y);
+
+ printf(fmt, strokewidth,
+ ox + xscale * psvs[io+is*9].x,
+ oy + yscale * psvs[io+is*9].y,
+ ox + xscale * (psvs[io+is*6].x + psvs[io+is*12].x) / 2,
+ oy + yscale * (psvs[io+is*6].y + psvs[io+is*12].y) / 2);
+
+ printf(fmt, strokewidth,
+ ox + xscale * psvs[io+is*5].x,
+ oy + yscale * psvs[io+is*5].y,
+ ox + xscale * (psvs[io+is*6].x + psvs[io+is*12].x) / 2,
+ oy + yscale * (psvs[io+is*6].y + psvs[io+is*12].y) / 2);
+
+ printf(fmt, strokewidth,
+ ox + xscale * psvs[io+is*12].x,
+ oy + yscale * psvs[io+is*12].y,
+ ox + xscale * (psvs[io+is*6].x + psvs[io+is*12].x) / 2,
+ oy + yscale * (psvs[io+is*6].y + psvs[io+is*12].y) / 2);
+ }
+
+ if (coordtype == 'h') {+ double lineheight = ascale * 2;
+ double charheight = lineheight * 0.6; /* close enough */
+
+ printf("<text style=\""+ "fill: black; "
+ "font-family: Sans; "
+ "font-size: %gpx; "
+ "text-anchor: middle; "
+ "text-align: center; "
+ "\" x=\"%g\" y=\"%g\">", lineheight,
+ ox + xscale * (psvs[io+is*0].x + psvs[io+is*10].x) / 2,
+ oy + yscale * (psvs[io+is*0].y + psvs[io+is*10].y) / 2
+ + charheight/2);
+ printf("%d", (int)i);+ printf("</text>\n");+ } else if (coordtype == 'k') {+ Point kites[HAT_NKITE];
+ size_t nk = hat_kite_centres(hats[i], kites);
+
+ double lineheight = ascale * 0.5;
+ double charheight = lineheight * 0.6; /* close enough */
+
+ for (j = 0; j < nk; j++) {+ pspoint p = pscoords(kites[j]);
+
+ printf("<text style=\""+ "fill: black; "
+ "font-family: Sans; "
+ "font-size: %gpx; "
+ "text-anchor: middle; "
+ "text-align: center; "
+ "\" x=\"%g\" y=\"%g\">", lineheight,
+ ox + xscale * p.x,
+ oy + yscale * p.y + charheight/2);
+
+ printf("%d.%d.%d", (int)j, hats[i].index,+ hats[i].parent->coords[0].index);
+
+ printf("</text>\n");+ }
+ } else if (coordtype == 'K') {+ Point kites[HAT_NKITE];
+ size_t nk = hat_kite_centres(hats[i], kites);
+
+ double lineheight = ascale * 1.1;
+ double charheight = lineheight * 0.6; /* close enough */
+
+ for (j = 0; j < nk; j++) {+ pspoint p = pscoords(kites[j]);
+
+ printf("<text style=\""+ "fill: black; "
+ "font-family: Sans; "
+ "font-size: %gpx; "
+ "text-anchor: middle; "
+ "text-align: center; "
+ "\" x=\"%g\" y=\"%g\">", lineheight,
+ ox + xscale * p.x,
+ oy + yscale * p.y + charheight/2);
+ printf("%d", (int)j);+ printf("</text>\n");+ }
+ }
+ }
+
+ printf("</svg>\n");+}
+
+typedef enum KiteStep { KS_LEFT, KS_RIGHT, KS_F_LEFT, KS_F_RIGHT } KiteStep;+
+static inline Point kite_step(Point k, KiteStep step)
+{+ switch (step) {+ case KS_LEFT: return kite_left(k);
+ case KS_RIGHT: return kite_right(k);
+ case KS_F_LEFT: return kite_forward_left(k);
+ default /* case KS_F_RIGHT */: return kite_forward_right(k);
+ }
+}
+
+int main(int argc, char **argv)
+{+ if (argc <= 1) {+ printf("usage: hat-test <mode>\n");+ printf("modes: H,T,P,F display a single unexpanded tile\n");+ printf(" xH,xT,xP,xF display the expansion of one tile\n");+ printf(" cH,cT,cP,cF display expansion with tile coords\n");+ printf(" CH,CT,CP,CF display double expansion with coords\n");+ printf(" hH,hT,hP,hF display the hats from one tile\n");+ printf(" HH,HT,HP,HF hats from an expansion, with coords\n");+ printf(" m1, m2, ... nth expansion of one H metatile\n");+ printf(" M1, M2, ... nth expansion turned into real hats\n");+ printf(" --hat show the kites in a single hat\n");+ printf(" --tables generate hat-tables.h for hat.c\n");+ return 0;
+ }
+
+ if (!strcmp(argv[1], "H") || !strcmp(argv[1], "T") ||
+ !strcmp(argv[1], "P") || !strcmp(argv[1], "F")) {+ MetatileType type = (argv[1][0] == 'H' ? MT_H :
+ argv[1][0] == 'T' ? MT_T :
+ argv[1][0] == 'P' ? MT_P : MT_F);
+ Metatile m = {type, {0, 0}, {1, 0}};+ draw_metatiles_svg(&m, 1, NULL, false);
+ return 0;
+ }
+
+ if (!strcmp(argv[1], "xH") || !strcmp(argv[1], "xT") ||
+ !strcmp(argv[1], "xP") || !strcmp(argv[1], "xF")) {+ MetatileType type = (argv[1][1] == 'H' ? MT_H :
+ argv[1][1] == 'T' ? MT_T :
+ argv[1][1] == 'P' ? MT_P : MT_F);
+ Metatile m = {type, {0, 0}, {1, 0}};+ Metatile t[MT_MAXEXPAND];
+ size_t nt = metatile_expand(m, t);
+ draw_metatiles_svg(t, nt, NULL, false);
+ return 0;
+ }
+
+ if (argv[1][0] && argv[1][1] &&
+ strchr("cC", argv[1][0]) && strchr("HTPF", argv[1][1])) {+ MetatileType type = (argv[1][1] == 'H' ? MT_H :
+ argv[1][1] == 'T' ? MT_T :
+ argv[1][1] == 'P' ? MT_P : MT_F);
+ MetatileSet *t[3];
+ int nsets = (argv[1][0] == 'c' ? 2 : 3);
+ int i;
+
+ t[0] = metatile_initial_set(type);
+ for (i = 1; i < nsets; i++)
+ t[i] = metatile_set_expand(t[i-1]);
+ draw_metatile_set_svg(t[nsets-1], NULL, true);
+ for (i = 0; i < nsets; i++)
+ metatile_free_set(t[i]);
+ return 0;
+ }
+
+ if (!strcmp(argv[1], "hH") || !strcmp(argv[1], "hT") ||
+ !strcmp(argv[1], "hP") || !strcmp(argv[1], "hF")) {+ MetatileType type = (
+ !strcmp(argv[1], "hH") ? MT_H :
+ !strcmp(argv[1], "hT") ? MT_T :
+ !strcmp(argv[1], "hP") ? MT_P : MT_F);
+ Metatile m = {type, {0, 0}, {1, 0}};+ Hat h[MT_MAXHAT];
+ size_t nh = metatile_hats(&m, h);
+ draw_hats_svg(h, nh, NULL, false, 'h');
+ return 0;
+ }
+
+ if (!strcmp(argv[1], "--hat")) {+ Hat h = { { 0, 0 }, { 1, 0 }, false, NULL, 0 };+ draw_hats_svg(&h, 1, NULL, true, 'K');
+ return 0;
+ }
+
+ if (argv[1][0] == 'H' && argv[1][1] && strchr("HTPF", argv[1][1])) {+ MetatileType type = (argv[1][1] == 'H' ? MT_H :
+ argv[1][1] == 'T' ? MT_T :
+ argv[1][1] == 'P' ? MT_P : MT_F);
+ MetatileSet *t[2];
+ size_t i, nh;
+
+ t[0] = metatile_initial_set(type);
+ t[1] = metatile_set_expand(t[0]);
+ Hat *h = metatile_set_to_hats(t[1], &nh, NULL);
+ draw_hats_svg(h, nh, NULL, true, 'k');
+ sfree(h);
+ for (i = 0; i < 2; i++)
+ metatile_free_set(t[i]);
+ return 0;
+ }
+
+ if (argv[1][0] == 'm' || argv[1][0] == 'M') {+ int niter = atoi(argv[1] + 1);
+ MetatileSet *tiles = metatile_initial_set(MT_P);
+
+ while (niter-- > 0) {+ MetatileSet *t2 = metatile_set_expand(tiles);
+ metatile_free_set(tiles);
+ tiles = t2;
+ }
+
+ if (argv[1][0] == 'M') {+ size_t nh;
+ Hat *h = metatile_set_to_hats(tiles, &nh, NULL);
+ draw_hats_svg(h, nh, tiles->vertices, false, 0);
+ sfree(h);
+ } else {+ draw_metatile_set_svg(tiles, tiles->vertices, false);
+ }
+
+ metatile_free_set(tiles);
+
+ return 0;
+ }
+
+ if (!strcmp(argv[1], "--tables")) {+ size_t i, j, k;
+
+ printf("/*\n"+ " * Header file autogenerated by aux/hatgen.c\n"
+ " *\n"
+ " * To regenerate, run 'hatgen --tables > hat-tables.h'\n"
+ " */\n\n");
+
+ static const char HTPF[] = "HTPF";
+
+ printf("static const unsigned hats_in_metatile[] = {");+ for (i = 0; i < 4; i++) {+ Metatile m = {i, {0, 0}, {1, 0}};+ Hat h[MT_MAXHAT];
+ size_t nh = metatile_hats(&m, h);
+ printf(" %zu,", nh);+ }
+ printf(" };\n\n");+
+ {+ struct Parent {+ MetatileType t;
+ unsigned index;
+ } parents[4][4*MT_MAXEXPAND];
+ size_t psizes[4] = {0, 0, 0, 0};+ size_t csizes[4] = {0, 0, 0, 0};+
+ for (i = 0; i < 4; i++) {+ Metatile m = {i, {0, 0}, {1, 0}};+ Metatile t[MT_MAXEXPAND];
+ size_t nt = metatile_expand(m, t);
+
+ printf("static const TileType children_%c[] = {\n"+ " ", HTPF[i]);
+ for (j = 0; j < nt; j++) {+ MetatileType c = t[j].type;
+ parents[c][psizes[c]].t = i;
+ parents[c][psizes[c]].index = j;
+ psizes[c]++;
+ csizes[i]++;
+ printf(" TT_%c,", HTPF[c]);+ }
+ printf("\n};\n");+ }
+
+ printf("static const TileType *const children[] = {\n");+ for (i = 0; i < 4; i++)
+ printf(" children_%c,\n", HTPF[i]);+ printf("};\n");+ printf("static const size_t nchildren[] = {\n");+ for (i = 0; i < 4; i++)
+ printf(" %u,\n", (unsigned)csizes[i]);+ printf("};\n\n");+
+ for (i = 0; i < 4; i++) {+ printf("static const MetatilePossibleParent "+ "permitted_parents_%c[] = {\n", HTPF[i]);+ for (j = 0; j < psizes[i]; j++)
+ printf(" { TT_%c, %u },\n", HTPF[parents[i][j].t],+ parents[i][j].index);
+ printf("};\n");+ }
+
+ printf("static const MetatilePossibleParent *const "+ "permitted_parents[] = {\n");+ for (i = 0; i < 4; i++)
+ printf(" permitted_parents_%c,\n", HTPF[i]);+ printf("};\n");+
+ printf("static const size_t n_permitted_parents[] = {\n");+ for (i = 0; i < 4; i++)
+ printf(" %u,\n", (unsigned)psizes[i]);+ printf("};\n\n");+ }
+
+ {+ for (i = 0; i < 4; i++) {+ MetatileSet *t[2];
+ size_t j, k, nh, nmeta, ti;
+ struct list {+ Point kite;
+ unsigned ik, ih, im;
+ } list[8*MT_MAXHAT*MT_MAXEXPAND];
+ size_t len = 0;
+
+ t[0] = metatile_initial_set(i);
+ t[1] = metatile_set_expand(t[0]);
+ Hat *h = metatile_set_to_hats(t[1], &nh, NULL);
+
+ printf("static const KitemapEntry kitemap_%c[] = {\n",+ HTPF[i]);
+
+ Point origin = h[0].start;
+ for (j = 0; j < nh; j++) {+ Point kites[HAT_NKITE];
+ size_t nk = hat_kite_centres(h[j], kites);
+ for (k = 0; k < nk; k++) {+ struct list *le = &list[len++];
+ le->kite.x = kites[k].x - origin.x;
+ le->kite.y = kites[k].y - origin.y;
+ le->ik = k;
+ le->ih = h[j].index;
+ le->im = h[j].parent->coords[0].index;
+#if 0
+ printf("// %d,%d = %u.%u.%u\n", le->kite.x, le->kite.y, le->ik, le->ih, le->im);+#endif
+ }
+ }
+
+ nmeta = count234(t[1]->tiles);
+ for (ti = 0; ti < 8 * 4 * nmeta; ti++) {+ unsigned ik = ti % 8;
+ unsigned ih = ti / 8 % 4;
+ unsigned im = ti / (8*4);
+ struct list *src = NULL, *dst = NULL;
+ int istep;
+
+ for (j = 0; j < len; j++) {+ struct list *tmp = &list[j];
+ if (tmp->ik == ik && tmp->ih == ih && tmp->im == im) {+ src = tmp;
+ break;
+ }
+ }
+ if (ik == 0) {+ printf(" /* hat #%u in metatile #%u (type %c)",+ ih, im, HTPF[((Metatile *)index234(
+ t[1]->tiles, im))->type]);
+ if (!src)
+ printf(" does not exist");+ printf(" */\n");+ }
+#if 0
+ if (src)
+ printf(" // src=%d,%d\n", src->kite.x, src->kite.y);+#endif
+ printf(" ");+
+ for (istep = 0; istep < 4; istep++) {+ KiteStep step = istep;
+ dst = NULL;
+ if (src) {+ Point pdst = kite_step(src->kite, step);
+#if 0
+ printf(" /* dst=%d,%d */", pdst.x, pdst.y);+#endif
+ for (k = 0; k < len; k++) {+ struct list *tmp = &list[k];
+ if (tmp->kite.x == pdst.x &&
+ tmp->kite.y == pdst.y) {+ dst = tmp;
+ break;
+ }
+ }
+ }
+ if (!dst) {+ printf(" {-1,-1,-1},");+ } else {+ printf(" {%u,%u,%u},", dst->ik, dst->ih, dst->im);+ }
+ }
+ printf("\n");+ }
+ printf("};\n");+
+ sfree(h);
+ for (j = 0; j < 2; j++)
+ metatile_free_set(t[j]);
+ }
+
+ printf("static const KitemapEntry *const "+ "kitemap[] = {\n");+ for (i = 0; i < 4; i++)
+ printf(" kitemap_%c,\n", HTPF[i]);+ printf("};\n\n");+
+ }
+
+ {+ for (i = 0; i < 4; i++) {+ MetatileSet *t[3];
+ Metatile *m;
+ int map[MT_MAXEXPAND * MT_MAXEXPAND];
+ size_t maplen;
+
+ for (j = 0; j < lenof(map); j++)
+ map[j] = -1;
+
+ t[0] = metatile_initial_set(i);
+ for (j = 1; j < 3; j++)
+ t[j] = metatile_set_expand(t[j-1]);
+
+ for (j = 0; (m = index234(t[2]->tiles, j)) != NULL; j++) {+ unsigned coords[4];
+ size_t ncoords = 0;
+ int cindex;
+
+#if 0
+ printf("// ***\n");+#endif
+ for (cindex = 0; cindex < m->ncoords; cindex++) {+#if 0
+ printf("// %d.%d\n", (int)m->coords[cindex].index,+ (int)m->coords[cindex].parent->coords[0].index);
+#endif
+ coords[ncoords++] = (
+ m->coords[cindex].index + MT_MAXEXPAND *
+ m->coords[cindex].parent->coords[0].index);
+ }
+
+ unsigned prev = ncoords-1;
+ for (k = 0; k < ncoords; k++) {+ map[coords[prev]] = coords[k];
+ prev = k;
+ }
+ }
+
+ printf("static const MetamapEntry metamap_%c[] = {\n",+ HTPF[i]);
+ maplen = MT_MAXEXPAND * count234(t[1]->tiles);
+ for (j = 0; j < maplen; j++) {+ printf(" /* %u, %u -> */ ",+ (unsigned)(j % MT_MAXEXPAND),
+ (unsigned)(j / MT_MAXEXPAND));
+ if (map[j] == -1) {+ printf("{-1,-1}, /* does not exist */\n");+ } else {+ printf("{%u, %u},",+ (unsigned)(map[j] % MT_MAXEXPAND),
+ (unsigned)(map[j] / MT_MAXEXPAND));
+ if (map[j] == j)
+ printf(" /* no alternatives */");+ printf("\n");+ }
+ }
+ printf("};\n");+
+ for (j = 0; j < 3; j++)
+ metatile_free_set(t[j]);
+ }
+
+ printf("static const MetamapEntry *const "+ "metamap[] = {\n");+ for (i = 0; i < 4; i++)
+ printf(" metamap_%c,\n", HTPF[i]);+ printf("};\n");+ }
+
+ return 0;
+ }
+
+ fprintf(stderr, "unknown test mode '%s'\n", argv[1]);
+ return 1;
+}
+#endif