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Loopy / grid.c: support the new Spectre monotiling.

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This uses a tile shape very similar to the hat, but the tiling
_structure_ is totally changed so that there aren't any reflected
copies of the tile.

I'm not sure how much difference this makes to gameplay: the two
tilings are very similar for Loopy purposes. But the code was fun to
write, and I think the Spectre shape is noticeably prettier, so I'm
adding this to the collection anyway.

The test programs also generate a pile of SVG images used in the
companion article on my website.
This commit is contained in:
Simon Tatham
2023-06-16 18:30:53 +01:00
parent c82537b457
commit a33d9fad02
15 changed files with 4691 additions and 1 deletions
Download Patch File Download Diff File Expand all files Collapse all files

2
CMakeLists.txt
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@ -10,7 +10,7 @@ add_library(core_obj OBJECT
laydomino.c loopgen.c malloc.c matching.c midend.c misc.c penrose.c
ps.c random.c sort.c tdq.c tree234.c version.c ${platform_common_sources})
add_library(core $<TARGET_OBJECTS:core_obj>)
add_library(common $<TARGET_OBJECTS:core_obj> hat.c)
add_library(common $<TARGET_OBJECTS:core_obj> hat.c spectre.c)
include_directories(${CMAKE_CURRENT_SOURCE_DIR})

2
auxiliary/CMakeLists.txt
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@ -7,4 +7,6 @@ cliprogram(matching matching.c)
cliprogram(obfusc obfusc.c)
cliprogram(penrose-test penrose-test.c)
cliprogram(sort-test sort-test.c)
cliprogram(spectre-gen spectre-gen.c spectre-help.c CORE_LIB)
cliprogram(spectre-test spectre-test.c spectre-help.c)
cliprogram(tree234-test tree234-test.c)

709
auxiliary/spectre-gen.c Normal file
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@ -0,0 +1,709 @@
/*
* Generate the lookup tables used by the Spectre tiling.
*/
#include <assert.h>
#include <errno.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include "puzzles.h"
#include "tree234.h"
#include "spectre-internal.h"
#include "spectre-tables-manual.h"
#include "spectre-tables-extra.h"
#include "spectre-help.h"
struct HexData {
const Hex *subhexes;
const unsigned *orientations;
const int *edges;
Point hex_outline_start, hex_outline_direction;
unsigned spectre_outline_start_spec, spectre_outline_start_vertex;
};
static const struct HexData hexdata[] = {
#define HEXDATA_ENTRY(x) { subhexes_##x, orientations_##x, edges_##x, \
HEX_OUTLINE_START_##x, SPEC_OUTLINE_START_##x },
HEX_LETTERS(HEXDATA_ENTRY)
#undef HEXDATA_ENTRY
};
/*
* Store information about an edge of the hexagonal tiling.
*/
typedef struct EdgeData {
/* Edges are regarded as directed, so that we can store
* information separately about what's on each side of one. The
* names 'start' and 'finish' indicate a direction of travel,
* which is taken to be anticlockwise around a hexagon, i.e. if
* you walk from 'start' to 'finish' then the hexagon in question
* is the one on your left. */
Point start, finish;
/* Whether this edge is internal (i.e. owned by a hexagon). */
bool internal;
/*
* High- and low-order parts of the edge identity.
*
* If the edge is internal, then 'hi' indexes the hexagon it's an
* edge of, and 'lo' identifies one of its edges.
*
* If it's external, then 'hi' is the index of the edge segment
* corresponding to a particular edge of the superhex, and 'lo'
* the sub-index within that segment.
*/
unsigned hi, lo;
} EdgeData;
static int edge_cmp(void *av, void *bv)
{
const EdgeData *a = (const EdgeData *)av;
const EdgeData *b = (const EdgeData *)bv;
size_t i;
for (i = 0; i < 4; i++) {
if (a->start.coeffs[i] < b->start.coeffs[i])
return -1;
if (a->start.coeffs[i] > b->start.coeffs[i])
return +1;
}
for (i = 0; i < 4; i++) {
if (a->finish.coeffs[i] < b->finish.coeffs[i])
return -1;
if (a->finish.coeffs[i] > b->finish.coeffs[i])
return +1;
}
return 0;
}
static void lay_out_hexagons(Hex h, Graphics *gr, FILE *hdr)
{
size_t i, j;
tree234 *edge_map = newtree234(edge_cmp);
EdgeData *edge;
EdgeData *intmap[48], *extmap[22];
unsigned edgestarts[7];
const struct HexData *hd = h == NO_HEX ? NULL : &hexdata[h];
/*
* Iterate over all hexagons and enter their edges into the edge
* map.
*/
for (i = 0; i < (h == NO_HEX ? 8 : num_subhexes(h)); i++) {
Point centre = hex_centres[i];
Point vrel = {{ -2, 0, 4, 0 }};
Point vertices[6];
if (hd)
vrel = point_mul(vrel, point_rot(2*hd->orientations[i]));
for (j = 0; j < 6; j++) {
Point vrelnext = point_mul(vrel, point_rot(2));
edge = snew(EdgeData);
edge->start = point_add(centre, vrel);
edge->finish = point_add(centre, vrelnext);
edge->internal = true;
edge->hi = i;
edge->lo = j;
add234(edge_map, edge);
intmap[6*i + j] = edge;
vertices[j] = edge->start;
vrel = vrelnext;
}
gr_draw_hex(gr, gr->jigsaw_mode ? -1 : i,
hd ? hd->subhexes[i] : NO_HEX, vertices);
}
/*
* Trace round the exterior outline of the hex expansion,
* following the list of edge types.
*/
if (hd) {
Point pos, dir;
size_t mappos = 0;
pos = hd->hex_outline_start;
dir = hd->hex_outline_direction;
for (i = 0; i < 6; i++) {
int edge_type = hd->edges[i];
int sign = edge_type < 0 ? -1 : +1;
const int *edge_shape = hex_edge_shapes[abs(edge_type)];
size_t len = hex_edge_lengths[abs(edge_type)];
size_t index = sign < 0 ? len-2 : 0;
if (gr->vertex_blobs)
gr_draw_blob(gr, (i == 0 ? "startpoint" : "edgesep"),
gr_logcoords(pos), (i == 0 ? 0.6 : 0.3));
edgestarts[i] = mappos;
for (j = 0; j < len; j++) {
Point posnext = point_add(pos, dir);
if (j < len-1) {
dir = point_mul(dir, point_rot(sign * edge_shape[index]));
index += sign;
}
edge = snew(EdgeData);
edge->start = pos;
edge->finish = posnext;
edge->internal = false;
edge->hi = i;
edge->lo = j;
add234(edge_map, edge);
assert(mappos < lenof(extmap));
extmap[mappos++] = edge;
pos = posnext;
}
/*
* In the hex expansion, every pair of edges meet at a
* 60-degree left turn.
*/
dir = point_mul(dir, point_rot(-2));
}
edgestarts[i] = mappos; /* record end position */
for (i = 0; i < 4; i++)
assert(pos.coeffs[i] == hd->hex_outline_start.coeffs[i]);
}
/*
* Draw the labels on the edges.
*/
if (gr->number_edges) {
for (i = 0; (edge = index234(edge_map, i)) != NULL; i++) {
char buf[64];
double textheight = 0.8, offset = textheight * 0.2;
GrCoords start = gr_logcoords(edge->start);
GrCoords finish = gr_logcoords(edge->finish);
GrCoords len = { finish.x - start.x, finish.y - start.y };
GrCoords perp = { -len.y, +len.x };
GrCoords mid = { (start.x+finish.x)/2, (start.y+finish.y)/2 };
if (edge->internal) {
sprintf(buf, "%u", edge->lo);
} else {
sprintf(buf, "%u.%u", edge->lo, edge->hi);
offset = textheight * 0.3;
}
{
GrCoords pos = {
mid.x + offset * perp.x,
mid.y + offset * perp.y,
};
gr_draw_text(gr, pos, textheight, buf);
}
}
}
/*
* Write out C array declarations for the machine-readable version
* of the maps we just generated.
*/
if (hdr) {
fprintf(hdr, "static const struct MapEntry hexmap_%s[] = {\n",
hex_names[h]);
for (i = 0; i < 6 * num_subhexes(h); i++) {
EdgeData *our_edge = intmap[i];
EdgeData key, *rev_edge;
key.finish = our_edge->start;
key.start = our_edge->finish;
rev_edge = find234(edge_map, &key, NULL);
assert(rev_edge);
fprintf(hdr, " { %-6s %u, %u }, /* edge %u of hex %u (%s) */\n",
rev_edge->internal ? "true," : "false,",
rev_edge->hi, rev_edge->lo,
our_edge->lo, our_edge->hi,
hex_names[hd->subhexes[our_edge->hi]]);
}
fprintf(hdr, "};\n");
fprintf(hdr, "static const struct MapEdge hexedges_%s[] = {\n",
hex_names[h]);
for (i = 0; i < 6; i++)
fprintf(hdr, " { %2u, %u },\n", edgestarts[i],
edgestarts[i+1] - edgestarts[i]);
fprintf(hdr, "};\n");
fprintf(hdr, "static const struct MapEntry hexin_%s[] = {\n",
hex_names[h]);
for (i = 0; i < edgestarts[6]; i++) {
EdgeData *our_edge = extmap[i];
EdgeData key, *rev_edge;
key.finish = our_edge->start;
key.start = our_edge->finish;
rev_edge = find234(edge_map, &key, NULL);
assert(rev_edge);
fprintf(hdr, " { %-6s %u, %u }, /* subedge %u of edge %u */\n",
rev_edge->internal ? "true," : "false,",
rev_edge->hi, rev_edge->lo,
our_edge->lo, our_edge->hi);
}
fprintf(hdr, "};\n");
}
while ((edge = delpos234(edge_map, 0)) != NULL)
sfree(edge);
freetree234(edge_map);
}
static void lay_out_spectres(Hex h, Graphics *gr, FILE *hdr)
{
size_t i, j;
tree234 *edge_map = newtree234(edge_cmp);
EdgeData *edge;
EdgeData *intmap[28], *extmap[24];
Point vertices[28];
unsigned edgestarts[7];
const struct HexData *hd = (h == NO_HEX ? NULL : &hexdata[h]);
/*
* Iterate over the Spectres in a hex (usually only one), and enter
* their edges into the edge map.
*/
for (i = 0; i < (h == NO_HEX ? 2 : num_spectres(h)); i++) {
Point start = {{ 0, 0, 0, 0 }};
Point pos = start;
Point diag = {{ 2, 0, 0, 2 }};
Point dir = point_mul(diag, point_rot(5));
/*
* Usually the single Spectre in each map is oriented in the
* same place. For spectre #1 in the G map, however, we orient
* it manually in a different location. (There's no point
* making an organised lookup table for just this one
* exceptional case.)
*/
if (i == 1) {
Point unusual_start = {{ 2, 6, 2, 0 }};
pos = unusual_start;
dir = point_mul(dir, point_rot(+1));
}
for (j = 0; j < 14; j++) {
edge = snew(EdgeData);
edge->start = pos;
edge->finish = point_add(pos, dir);
edge->internal = true;
edge->hi = i;
edge->lo = j;
add234(edge_map, edge);
intmap[14*i + j] = edge;
vertices[14*i + j] = edge->start;
pos = edge->finish;
dir = point_mul(dir, point_rot(spectre_angles[(j+1) % 14]));
}
gr_draw_spectre(gr, h, i, vertices + 14*i);
}
/*
* Trace round the exterior outline of the hex expansion,
* following the list of edge types. Due to the confusing
* reflection of all the expansions, we end up doing this in the
* reverse order to the hexes code above.
*/
if (hd) {
Point start, pos, dir;
size_t mappos = lenof(extmap);
start = pos = vertices[14 * hd->spectre_outline_start_spec +
hd->spectre_outline_start_vertex];
edgestarts[6] = mappos;
for (i = 0; i < 6; i++) {
int edge_type = hd->edges[5-i];
int sign = edge_type < 0 ? -1 : +1;
const int *edge_shape = spec_edge_shapes[abs(edge_type)];
size_t len = spec_edge_lengths[abs(edge_type)];
size_t index = sign < 0 ? len-2 : 0;
if (gr->vertex_blobs)
gr_draw_blob(gr, (i == 0 ? "startpoint" : "edgesep"),
gr_logcoords(pos), (i == 0 ? 0.6 : 0.3));
if (h == HEX_S && i >= 4) {
/*
* Two special cases
*/
if (i == 4)
/* leave dir from last time */;
else
dir = point_mul(dir, point_rot(6)); /* reverse */
} else {
/*
* Determine the direction of the first sub-edge of
* this edge expansion, by iterating over all the
* edges in edge_map starting at this point and
* finding one whose reverse isn't in the map (hence,
* it's an exterior edge).
*/
EdgeData dummy, *iter, *found = NULL;
dummy.start = pos;
for (j = 0; j < 4; j++)
dummy.finish.coeffs[j] = INT_MIN;
for (iter = findrel234(edge_map, &dummy, NULL, REL234_GE);
iter != NULL && point_equal(iter->start, pos);
iter = findrel234(edge_map, iter, NULL, REL234_GT)) {
EdgeData *rev;
dummy.finish = iter->start;
dummy.start = iter->finish;
rev = find234(edge_map, &dummy, NULL);
if (!rev) {
found = iter;
break;
}
}
assert(found);
dir = point_sub(found->finish, found->start);
}
for (j = 0; j < len; j++) {
Point posnext = point_add(pos, dir);
if (j < len-1) {
dir = point_mul(dir, point_rot(sign * edge_shape[index]));
index += sign;
}
edge = snew(EdgeData);
edge->start = posnext;
edge->finish = pos;
edge->internal = false;
edge->hi = 5-i;
edge->lo = len-1-j;
add234(edge_map, edge);
assert(mappos > 0);
extmap[--mappos] = edge;
pos = posnext;
}
edgestarts[5-i] = mappos;
}
assert(point_equal(pos, start));
}
/*
* Draw the labels on the edges.
*/
if (gr->number_edges) {
for (i = 0; (edge = index234(edge_map, i)) != NULL; i++) {
char buf[64];
double textheight = 0.8, offset = textheight * 0.2;
GrCoords start = gr_logcoords(edge->start);
GrCoords finish = gr_logcoords(edge->finish);
GrCoords len = { finish.x - start.x, finish.y - start.y };
GrCoords perp = { +len.y, -len.x };
GrCoords mid = { (start.x+finish.x)/2, (start.y+finish.y)/2 };
if (edge->internal) {
sprintf(buf, "%u", edge->lo);
} else {
sprintf(buf, "%u.%u", edge->lo, edge->hi);
textheight = 0.6;
}
if (strlen(buf) > 1)
offset = textheight * 0.35;
{
GrCoords pos = {
mid.x + offset * perp.x,
mid.y + offset * perp.y,
};
gr_draw_text(gr, pos, textheight, buf);
}
}
}
/*
* Write out C array declarations for the machine-readable version
* of the maps we just generated.
*
* Also, because it's easier than having a whole extra iteration,
* draw lines for the extraordinary edges outside the S diagram.
*/
if (hdr) {
fprintf(hdr, "static const struct MapEntry specmap_%s[] = {\n",
hex_names[h]);
for (i = 0; i < 14 * num_spectres(h); i++) {
EdgeData *our_edge = intmap[i];
EdgeData key, *rev_edge;
key.finish = our_edge->start;
key.start = our_edge->finish;
rev_edge = find234(edge_map, &key, NULL);
assert(rev_edge);
fprintf(hdr, " { %-6s %u, %2u }, /* edge %2u of Spectre %u */\n",
rev_edge->internal ? "true," : "false,",
rev_edge->hi, rev_edge->lo,
our_edge->lo, our_edge->hi);
}
fprintf(hdr, "};\n");
fprintf(hdr, "static const struct MapEdge specedges_%s[] = {\n",
hex_names[h]);
for (i = 0; i < 6; i++)
fprintf(hdr, " { %2u, %u },\n", edgestarts[i] - edgestarts[0],
edgestarts[i+1] - edgestarts[i]);
fprintf(hdr, "};\n");
fprintf(hdr, "static const struct MapEntry specin_%s[] = {\n",
hex_names[h]);
for (i = edgestarts[0]; i < edgestarts[6]; i++) {
EdgeData *our_edge = extmap[i];
EdgeData key, *rev_edge;
key.finish = our_edge->start;
key.start = our_edge->finish;
rev_edge = find234(edge_map, &key, NULL);
assert(rev_edge);
fprintf(hdr, " { %-6s %u, %2u }, /* subedge %u of edge %u */\n",
rev_edge->internal ? "true," : "false,",
rev_edge->hi, rev_edge->lo,
our_edge->lo, our_edge->hi);
if (!our_edge->internal && !rev_edge->internal)
gr_draw_extra_edge(gr, key.start, key.finish);
}
fprintf(hdr, "};\n");
}
while ((edge = delpos234(edge_map, 0)) != NULL)
sfree(edge);
freetree234(edge_map);
}
static void draw_base_hex(Hex h, Graphics *gr)
{
size_t i;
Point vertices[6];
/*
* Plot the points of the hex.
*/
for (i = 0; i < 6; i++) {
Point startvertex = {{ -2, 0, 4, 0 }};
vertices[i] = point_mul(startvertex, point_rot(2*i));
}
/*
* Draw the hex itself.
*/
gr_draw_hex(gr, -1, h, vertices);
if (gr->vertex_blobs) {
/*
* Draw edge-division blobs on all vertices, to match the ones on
* the expansion diagrams.
*/
for (i = 0; i < 6; i++) {
gr_draw_blob(gr, (i == 0 ? "startpoint" : "edgesep"),
gr_logcoords(vertices[i]), (i == 0 ? 0.6 : 0.3));
}
}
if (gr->number_edges) {
/*
* Draw the labels on its edges.
*/
for (i = 0; i < 6; i++) {
char buf[64];
double textheight = 0.8, offset = textheight * 0.2;
GrCoords start = gr_logcoords(vertices[i]);
GrCoords finish = gr_logcoords(vertices[(i+1) % 6]);
GrCoords len = { finish.x - start.x, finish.y - start.y };
GrCoords perp = { -len.y, +len.x };
GrCoords mid = { (start.x+finish.x)/2, (start.y+finish.y)/2 };
sprintf(buf, "%zu", i);
{
GrCoords pos = {
mid.x + offset * perp.x,
mid.y + offset * perp.y,
};
gr_draw_text(gr, pos, textheight, buf);
}
}
}
}
static void draw_one_spectre(Graphics *gr)
{
size_t i, j;
Point vertices[14];
{
Point start = {{ 0, 0, 0, 0 }};
Point pos = start;
Point diag = {{ 2, 0, 0, 2 }};
Point dir = point_mul(diag, point_rot(9));
for (j = 0; j < 14; j++) {
vertices[j] = pos;
pos = point_add(pos, dir);
dir = point_mul(dir, point_rot(spectre_angles[(j+1) % 14]));
}
gr_draw_spectre(gr, NO_HEX, -1, vertices);
}
/*
* Draw the labels on the edges.
*/
if (gr->number_edges) {
for (i = 0; i < 14; i++) {
char buf[64];
double textheight = 0.8, offset = textheight * 0.2;
GrCoords start = gr_logcoords(vertices[i]);
GrCoords finish = gr_logcoords(vertices[(i+1) % 14]);
GrCoords len = { finish.x - start.x, finish.y - start.y };
GrCoords perp = { +len.y, -len.x };
GrCoords mid = { (start.x+finish.x)/2, (start.y+finish.y)/2 };
sprintf(buf, "%zu", i);
if (strlen(buf) > 1)
offset = textheight * 0.35;
{
GrCoords pos = {
mid.x + offset * perp.x,
mid.y + offset * perp.y,
};
gr_draw_text(gr, pos, textheight, buf);
}
}
}
}
static void make_parent_tables(FILE *fp)
{
size_t i, j, k;
for (i = 0; i < 9; i++) {
fprintf(fp, "static const struct Possibility poss_%s[] = {\n",
hex_names[i]);
for (j = 0; j < 9; j++) {
for (k = 0; k < num_subhexes(j); k++) {
if (hexdata[j].subhexes[k] == i) {
fprintf(fp, " { HEX_%s, %zu, PROB_%s },\n",
hex_names[j], k, hex_names[j]);
}
}
}
fprintf(fp, "};\n");
}
fprintf(fp, "static const struct Possibility poss_spectre[] = {\n");
for (j = 0; j < 9; j++) {
for (k = 0; k < num_spectres(j); k++) {
fprintf(fp, " { HEX_%s, %zu, PROB_%s },\n",
hex_names[j], k, hex_names[j]);
}
}
fprintf(fp, "};\n");
}
int main(void)
{
size_t i;
FILE *fp = fopen("spectre-tables-auto.h", "w");
fprintf(fp,
"/*\n"
" * Autogenerated transition tables for the Spectre tiling.\n"
" * Generated by auxiliary/spectre-gen.c.\n"
" */\n\n");
for (i = 0; i < 9; i++) {
char buf[64];
sprintf(buf, "hexmap_%s.svg", hex_names[i]);
Graphics *gr = gr_new(buf, -11, +11, -20, +4.5, 13);
lay_out_hexagons(i, gr, fp);
gr_free(gr);
}
for (i = 0; i < 9; i++) {
char buf[64];
sprintf(buf, "specmap_%s.svg", hex_names[i]);
Graphics *gr = gr_new(buf, (i == HEX_S ? -14 : -11.5),
(i == HEX_G ? +10 : 0.5),
-2, +12, 15);
lay_out_spectres(i, gr, fp);
gr_free(gr);
}
for (i = 0; i < 9; i++) {
char buf[64];
sprintf(buf, "basehex_%s.svg", hex_names[i]);
Graphics *gr = gr_new(buf, -4, +4, -4.2, +4.5, 15);
draw_base_hex(i, gr);
gr_free(gr);
}
for (i = 0; i < 9; i++) {
char buf[64];
sprintf(buf, "jigsawhex_%s.svg", hex_names[i]);
Graphics *gr = gr_new(buf, -4, +4, -4.2, +4.5, 20);
gr->jigsaw_mode = true;
gr->vertex_blobs = false;
gr->number_edges = false;
draw_base_hex(i, gr);
gr_free(gr);
}
{
Graphics *gr = gr_new("basehex_null.svg", -4, +4, -4.2, +4.5, 20);
gr->vertex_blobs = false;
draw_base_hex(NO_HEX, gr);
gr_free(gr);
}
{
Graphics *gr = gr_new("basespec_null.svg", -7, +6, -14, +1, 15);
gr->vertex_blobs = false;
draw_one_spectre(gr);
gr_free(gr);
}
{
Graphics *gr = gr_new("hexmap_null.svg", -11, +11, -20, +4.5, 10);
gr->vertex_blobs = false;
gr->number_edges = false;
gr->hex_arrows = false;
lay_out_hexagons(NO_HEX, gr, NULL);
gr_free(gr);
}
{
Graphics *gr = gr_new("specmap_null.svg", -11.5, +10, -2, +12, 15);
gr->vertex_blobs = false;
gr->number_edges = false;
gr->hex_arrows = false;
lay_out_spectres(NO_HEX, gr, NULL);
gr_free(gr);
}
for (i = 0; i < 2; i++) {
char buf[64];
sprintf(buf, "jigsawexpand_%s.svg", hex_names[i]);
Graphics *gr = gr_new(buf, -11, +11, -20, +4.5, 10);
gr->jigsaw_mode = true;
gr->vertex_blobs = false;
gr->number_edges = false;
lay_out_hexagons(i, gr, fp);
gr_free(gr);
}
make_parent_tables(fp);
fclose(fp);
return 0;
}

417
auxiliary/spectre-help.c Normal file
View File

@ -0,0 +1,417 @@
/*
* Common code between spectre-test and spectre-gen, since both of
* them want to output SVG graphics.
*/
#include <assert.h>
#include <errno.h>
#include <math.h>
#include <stdio.h>
#include <string.h>
#include "puzzles.h"
#include "tree234.h"
#include "spectre-internal.h"
#include "spectre-tables-extra.h"
#include "spectre-help.h"
struct HexData {
const int *edges;
};
static const struct HexData hexdata[] = {
#define HEXDATA_ENTRY(x) { edges_##x },
HEX_LETTERS(HEXDATA_ENTRY)
#undef HEXDATA_ENTRY
};
const char *hex_names[10] = {
"G", "D", "J", "L", "X", "P", "S", "F", "Y",
"" /* NO_HEX */
};
Graphics *gr_new(const char *filename, double xmin, double xmax,
double ymin, double ymax, double scale)
{
Graphics *gr = snew(Graphics);
if (!strcmp(filename, "-")) {
gr->fp = stdout;
gr->close_file = false;
} else {
gr->fp = fopen(filename, "w");
if (!gr->fp) {
fprintf(stderr, "%s: open: %s\n", filename, strerror(errno));
exit(1);
}
gr->close_file = true;
}
fprintf(gr->fp, "<?xml version=\"1.0\" encoding=\"UTF-8\" "
"standalone=\"no\"?>\n");
fprintf(gr->fp, "<svg xmlns=\"http://www.w3.org/2000/svg\" "
"version=\"1.1\" width=\"%f\" height=\"%f\">\n",
(xmax - xmin) * scale, (ymax - ymin) * scale);
gr->absscale = fabs(scale);
gr->xoff = -xmin * scale;
gr->xscale = scale;
/* invert y axis for SVG top-down coordinate system */
gr->yoff = ymax * scale;
gr->yscale = -scale;
/* Defaults, which can be overridden by the caller immediately
* after this constructor returns */
gr->jigsaw_mode = false;
gr->vertex_blobs = true;
gr->number_cells = true;
gr->four_colour = false;
gr->arcs = false;
gr->linewidth = 1.5;
gr->started = false;
return gr;
}
void gr_free(Graphics *gr)
{
if (!gr)
return;
fprintf(gr->fp, "</svg>\n");
if (gr->close_file)
fclose(gr->fp);
sfree(gr);
}
static void gr_ensure_started(Graphics *gr)
{
if (gr->started)
return;
fprintf(gr->fp, "<style type=\"text/css\">\n");
fprintf(gr->fp, "path { fill: none; stroke: black; stroke-width: %f; "
"stroke-linejoin: round; stroke-linecap: round; }\n",
gr->linewidth);
fprintf(gr->fp, "text { fill: black; font-family: Sans; "
"text-anchor: middle; text-align: center; }\n");
if (gr->four_colour) {
fprintf(gr->fp, ".c0 { fill: rgb(255, 178, 178); }\n");
fprintf(gr->fp, ".c1 { fill: rgb(255, 255, 178); }\n");
fprintf(gr->fp, ".c2 { fill: rgb(178, 255, 178); }\n");
fprintf(gr->fp, ".c3 { fill: rgb(153, 153, 255); }\n");
} else {
fprintf(gr->fp, ".G { fill: rgb(255, 128, 128); }\n");
fprintf(gr->fp, ".G1 { fill: rgb(255, 64, 64); }\n");
fprintf(gr->fp, ".F { fill: rgb(255, 192, 128); }\n");
fprintf(gr->fp, ".Y { fill: rgb(255, 255, 128); }\n");
fprintf(gr->fp, ".S { fill: rgb(128, 255, 128); }\n");
fprintf(gr->fp, ".D { fill: rgb(128, 255, 255); }\n");
fprintf(gr->fp, ".P { fill: rgb(128, 128, 255); }\n");
fprintf(gr->fp, ".X { fill: rgb(192, 128, 255); }\n");
fprintf(gr->fp, ".J { fill: rgb(255, 128, 255); }\n");
fprintf(gr->fp, ".L { fill: rgb(128, 128, 128); }\n");
fprintf(gr->fp, ".optional { stroke-dasharray: 5; }\n");
fprintf(gr->fp, ".arrow { fill: rgba(0, 0, 0, 0.2); "
"stroke: none; }\n");
}
fprintf(gr->fp, "</style>\n");
gr->started = true;
}
/* Logical coordinates in our mathematical space */
GrCoords gr_logcoords(Point p)
{
double rt3o2 = sqrt(3) / 2;
GrCoords r = {
p.coeffs[0] + rt3o2 * p.coeffs[1] + 0.5 * p.coeffs[2],
p.coeffs[3] + rt3o2 * p.coeffs[2] + 0.5 * p.coeffs[1],
};
return r;
}
/* Physical coordinates in the output image */
GrCoords gr_log2phys(Graphics *gr, GrCoords c)
{
c.x = gr->xoff + gr->xscale * c.x;
c.y = gr->yoff + gr->yscale * c.y;
return c;
}
GrCoords gr_physcoords(Graphics *gr, Point p)
{
return gr_log2phys(gr, gr_logcoords(p));
}
void gr_draw_text(Graphics *gr, GrCoords logpos, double logheight,
const char *text)
{
GrCoords pos;
double height;
if (!gr)
return;
gr_ensure_started(gr);
pos = gr_log2phys(gr, logpos);
height = gr->absscale * logheight;
fprintf(gr->fp, "<text style=\"font-size: %fpx\" x=\"%f\" y=\"%f\">"
"%s</text>\n", height, pos.x, pos.y + 0.35 * height, text);
}
void gr_draw_path(Graphics *gr, const char *classes, const GrCoords *phys,
size_t n, bool closed)
{
size_t i;
if (!gr)
return;
gr_ensure_started(gr);
fprintf(gr->fp, "<path class=\"%s\" d=\"", classes);
for (i = 0; i < n; i++) {
GrCoords c = phys[i];
if (i == 0)
fprintf(gr->fp, "M %f %f", c.x, c.y);
else if (gr->arcs)
fprintf(gr->fp, "A %f %f 10 0 %zu %f %f",
gr->absscale, gr->absscale, i&1, c.x, c.y);
else
fprintf(gr->fp, "L %f %f", c.x, c.y);
}
if (gr->arcs) {
/* Explicitly return to the starting point so as to curve the
* final edge */
fprintf(gr->fp, "A %f %f 10 0 0 %f %f",
gr->absscale, gr->absscale, phys[0].x, phys[0].y);
}
if (closed)
fprintf(gr->fp, " z");
fprintf(gr->fp, "\"/>\n");
}
void gr_draw_blob(Graphics *gr, const char *classes, GrCoords log,
double logradius)
{
GrCoords centre;
if (!gr)
return;
gr_ensure_started(gr);
centre = gr_log2phys(gr, log);
fprintf(gr->fp, "<circle class=\"%s\" cx=\"%f\" cy=\"%f\" r=\"%f\"/>\n",
classes, centre.x, centre.y, gr->absscale * logradius);
}
void gr_draw_hex(Graphics *gr, unsigned index, Hex htype,
const Point *vertices)
{
size_t i;
Point centre;
if (!gr)
return;
gr_ensure_started(gr);
/* Draw the actual hexagon, in its own colour */
if (!gr->jigsaw_mode) {
GrCoords phys[6];
for (i = 0; i < 6; i++)
phys[i] = gr_physcoords(gr, vertices[i]);
gr_draw_path(gr, (index == 7 && htype == NO_HEX ?
"optional" : hex_names[htype]), phys, 6, true);
} else {
GrCoords phys[66];
size_t pos = 0;
const struct HexData *hd = &hexdata[htype];
for (i = 0; i < 6; i++) {
int edge_type = hd->edges[i];
int sign = edge_type < 0 ? -1 : +1;
int edge_abs = abs(edge_type);
int left_sign = (edge_abs & 4) ? sign : edge_type == 0 ? +1 : 0;
int mid_sign = (edge_abs & 2) ? sign : 0;
int right_sign = (edge_abs & 1) ? sign : edge_type == 0 ? -1 : 0;
GrCoords start = gr_physcoords(gr, vertices[i]);
GrCoords end = gr_physcoords(gr, vertices[(i+1) % 6]);
GrCoords x = { (end.x - start.x) / 7, (end.y - start.y) / 7 };
GrCoords y = { -x.y, +x.x };
#define addpoint(X, Y) do { \
GrCoords p = { \
start.x + (X) * x.x + (Y) * y.x, \
start.y + (X) * x.y + (Y) * y.y, \
}; \
phys[pos++] = p; \
} while (0)
if (sign < 0) {
int tmp = right_sign;
right_sign = left_sign;
left_sign = tmp;
}
addpoint(0, 0);
if (left_sign) {
addpoint(1, 0);
addpoint(2, left_sign);
addpoint(2, 0);
}
if (mid_sign) {
addpoint(3, 0);
addpoint(3, mid_sign);
addpoint(4, mid_sign);
addpoint(4, 0);
}
if (right_sign) {
addpoint(5, 0);
addpoint(5, right_sign);
addpoint(6, 0);
}
#undef addpoint
}
gr_draw_path(gr, hex_names[htype], phys, pos, true);
}
/* Find the centre of the hex */
for (i = 0; i < 4; i++)
centre.coeffs[i] = 0;
for (i = 0; i < 6; i++)
centre = point_add(centre, vertices[i]);
for (i = 0; i < 4; i++)
centre.coeffs[i] /= 6;
/* Draw an arrow towards vertex 0 of the hex */
if (gr->hex_arrows) {
double ext = 0.6;
double headlen = 0.3, thick = 0.08, headwid = 0.25;
GrCoords top = gr_physcoords(gr, vertices[0]);
GrCoords bot = gr_physcoords(gr, vertices[3]);
GrCoords mid = gr_physcoords(gr, centre);
GrCoords base = { mid.x + ext * (bot.x - mid.x),
mid.y + ext * (bot.y - mid.y) };
GrCoords tip = { mid.x + ext * (top.x - mid.x),
mid.y + ext * (top.y - mid.y) };
GrCoords len = { tip.x - base.x, tip.y - base.y };
GrCoords perp = { -len.y, +len.x };
GrCoords basep = { base.x+perp.x*thick, base.y+perp.y*thick };
GrCoords basen = { base.x-perp.x*thick, base.y-perp.y*thick };
GrCoords hbase = { tip.x-len.x*headlen, tip.y-len.y*headlen };
GrCoords headp = { hbase.x+perp.x*thick, hbase.y+perp.y*thick };
GrCoords headn = { hbase.x-perp.x*thick, hbase.y-perp.y*thick };
GrCoords headP = { hbase.x+perp.x*headwid, hbase.y+perp.y*headwid };
GrCoords headN = { hbase.x-perp.x*headwid, hbase.y-perp.y*headwid };
GrCoords phys[] = {
basep, headp, headP, tip, headN, headn, basen
};
gr_draw_path(gr, "arrow", phys, lenof(phys), true);
}
/*
* Label the hex with its index and type.
*/
if (gr->number_cells) {
char buf[64];
if (index == (unsigned)-1) {
if (htype == NO_HEX)
buf[0] = '\0';
else
strcpy(buf, hex_names[htype]);
} else {
if (htype == NO_HEX)
sprintf(buf, "%u", index);
else
sprintf(buf, "%u (%s)", index, hex_names[htype]);
}
if (buf[0])
gr_draw_text(gr, gr_logcoords(centre), 1.2, buf);
}
}
void gr_draw_spectre(Graphics *gr, Hex container, unsigned index,
const Point *vertices)
{
size_t i;
GrCoords log[14];
GrCoords centre;
if (!gr)
return;
gr_ensure_started(gr);
for (i = 0; i < 14; i++)
log[i] = gr_logcoords(vertices[i]);
/* Draw the actual Spectre */
{
GrCoords phys[14];
char class[16];
for (i = 0; i < 14; i++)
phys[i] = gr_log2phys(gr, log[i]);
if (gr->four_colour) {
sprintf(class, "c%u", index);
} else if (index == 1 && container == NO_HEX) {
sprintf(class, "optional");
} else {
sprintf(class, "%s%.0u", hex_names[container], index);
}
gr_draw_path(gr, class, phys, 14, true);
}
/* Pick a point to use as the centre of the Spectre for labelling */
centre.x = (log[5].x + log[6].x + log[11].x + log[12].x) / 4;
centre.y = (log[5].y + log[6].y + log[11].y + log[12].y) / 4;
/*
* Label the hex with its index and type.
*/
if (gr->number_cells && index != (unsigned)-1) {
char buf[64];
sprintf(buf, "%u", index);
gr_draw_text(gr, centre, 1.2, buf);
}
}
void gr_draw_spectre_from_coords(Graphics *gr, SpectreCoords *sc,
const Point *vertices)
{
Hex h;
unsigned index;
if (!gr)
return;
gr_ensure_started(gr);
if (gr->four_colour) {
h = NO_HEX;
if (sc->index == 1)
index = 3; /* special colour for odd G1 Spectres */
else
index = sc->hex_colour;
} else if (sc) {
h = sc->c[0].type;
index = sc->index;
} else {
h = NO_HEX;
index = -1;
}
gr_draw_spectre(gr, h, index, vertices);
}
void gr_draw_extra_edge(Graphics *gr, Point a, Point b)
{
GrCoords phys[2];
if (!gr)
return;
gr_ensure_started(gr);
phys[0] = gr_physcoords(gr, a);
phys[1] = gr_physcoords(gr, b);
gr_draw_path(gr, "extraedge", phys, 2, false);
}

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/*
* Header for spectre-help.c
*/
/* Dummy value indicating no specific hexagon, used in some diagrams
* for the accompanying article. */
#define NO_HEX (Hex)9
/*
* String constants for the hex names, including an extra entry
* mapping NO_HEX to the empty string.
*/
extern const char *hex_names[10];
typedef struct Graphics {
FILE *fp;
bool close_file; /* if it's not stdout */
bool started; /* have we written the header yet? */
double xoff, xscale, yoff, yscale, absscale, linewidth;
bool jigsaw_mode; /* draw protrusions on hex edges */
bool vertex_blobs; /* draw blobs marking hex vertices */
bool hex_arrows; /* draw arrows orienting each hex */
bool number_edges; /* number the edges of everything */
bool number_cells; /* number the things themselves */
bool four_colour; /* four-colour Spectres instead of semantically */
bool arcs; /* draw Spectre edges as arcs */
} Graphics;
typedef struct GrCoords {
double x, y;
} GrCoords;
Graphics *gr_new(const char *filename, double xmin, double xmax,
double ymin, double ymax, double scale);
void gr_free(Graphics *gr);
GrCoords gr_logcoords(Point p);
GrCoords gr_log2phys(Graphics *gr, GrCoords c);
GrCoords gr_physcoords(Graphics *gr, Point p);
void gr_draw_text(Graphics *gr, GrCoords logpos, double logheight,
const char *text);
void gr_draw_path(Graphics *gr, const char *classes, const GrCoords *phys,
size_t n, bool closed);
void gr_draw_blob(Graphics *gr, const char *classes, GrCoords log,
double logradius);
void gr_draw_hex(Graphics *gr, unsigned index, Hex htype,
const Point *vertices);
void gr_draw_spectre(Graphics *gr, Hex container, unsigned index,
const Point *vertices);
void gr_draw_spectre_from_coords(Graphics *gr, SpectreCoords *sc,
const Point *vertices);
void gr_draw_extra_edge(Graphics *gr, Point a, Point b);

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/*
* Further data tables used to generate the final transition maps.
*/
/*
* Locations in the plane of the centres of the 8 hexagons in the
* expansion of each hex.
*
* We take the centre-to-centre distance to be 6 units, so that other
* locations in the hex tiling (e.g. edge midpoints and vertices) will
* still have integer coefficients.
*
* These locations are represented using the same Point type used for
* the whole tiling, but all our angles are 60 degrees, so we don't
* ever need the coefficients of d or d^3, only of 1 and d^2.
*/
static const Point hex_centres[] = {
{{0, 0, 0, 0}}, {{6, 0, 0, 0}}, /* 0 1 */
{{0, 0, -6, 0}}, {{6, 0, -6, 0}}, /* 2 3 */
{{0, 0, -12, 0}}, {{6, 0, -12, 0}}, {{12, 0, -12, 0}}, /* 4 5 6 */
{{12, 0, -18, 0}}, /* 7 */
};
/*
* Orientations of all the sub-hexes in the expansion of each hex.
* Measured anticlockwise (that is, as a power of s) from 0, where 0
* means the hex is upright, with its own vertex #0 at the top.
*/
static const unsigned orientations_G[] = {
2, /* HEX_F */
1, /* HEX_X */
0, /* HEX_G */
1, /* HEX_S */
4, /* HEX_P */
5, /* HEX_D */
0, /* HEX_J */
/* hex #7 is not present for this tile */
};
static const unsigned orientations_D[] = {
2, /* HEX_F */
1, /* HEX_P */
0, /* HEX_G */
1, /* HEX_S */
4, /* HEX_X */
5, /* HEX_D */
0, /* HEX_F */
5, /* HEX_X */
};
static const unsigned orientations_J[] = {
2, /* HEX_F */
1, /* HEX_P */
0, /* HEX_G */
1, /* HEX_S */
4, /* HEX_Y */
5, /* HEX_D */
0, /* HEX_F */
5, /* HEX_P */
};
static const unsigned orientations_L[] = {
2, /* HEX_F */
1, /* HEX_P */
0, /* HEX_G */
1, /* HEX_S */
4, /* HEX_Y */
5, /* HEX_D */
0, /* HEX_F */
5, /* HEX_X */
};
static const unsigned orientations_X[] = {
2, /* HEX_F */
1, /* HEX_Y */
0, /* HEX_G */
1, /* HEX_S */
4, /* HEX_Y */
5, /* HEX_D */
0, /* HEX_F */
5, /* HEX_P */
};
static const unsigned orientations_P[] = {
2, /* HEX_F */
1, /* HEX_Y */
0, /* HEX_G */
1, /* HEX_S */
4, /* HEX_Y */
5, /* HEX_D */
0, /* HEX_F */
5, /* HEX_X */
};
static const unsigned orientations_S[] = {
2, /* HEX_L */
1, /* HEX_P */
0, /* HEX_G */
1, /* HEX_S */
4, /* HEX_X */
5, /* HEX_D */
0, /* HEX_F */
5, /* HEX_X */
};
static const unsigned orientations_F[] = {
2, /* HEX_F */
1, /* HEX_P */
0, /* HEX_G */
1, /* HEX_S */
4, /* HEX_Y */
5, /* HEX_D */
0, /* HEX_F */
5, /* HEX_Y */
};
static const unsigned orientations_Y[] = {
2, /* HEX_F */
1, /* HEX_Y */
0, /* HEX_G */
1, /* HEX_S */
4, /* HEX_Y */
5, /* HEX_D */
0, /* HEX_F */
5, /* HEX_Y */
};
/*
* For each hex type, indicate the point on the boundary of the
* expansion that corresponds to vertex 0 of the superhex. Also,
* indicate the initial direction we head in to go round the edge.
*/
#define HEX_OUTLINE_START_COMMON {{ -4, 0, -10, 0 }}, {{ +2, 0, +2, 0 }}
#define HEX_OUTLINE_START_RARE {{ -2, 0, -14, 0 }}, {{ -2, 0, +4, 0 }}
#define HEX_OUTLINE_START_G HEX_OUTLINE_START_COMMON
#define HEX_OUTLINE_START_D HEX_OUTLINE_START_RARE
#define HEX_OUTLINE_START_J HEX_OUTLINE_START_COMMON
#define HEX_OUTLINE_START_L HEX_OUTLINE_START_COMMON
#define HEX_OUTLINE_START_X HEX_OUTLINE_START_COMMON
#define HEX_OUTLINE_START_P HEX_OUTLINE_START_COMMON
#define HEX_OUTLINE_START_S HEX_OUTLINE_START_RARE
#define HEX_OUTLINE_START_F HEX_OUTLINE_START_COMMON
#define HEX_OUTLINE_START_Y HEX_OUTLINE_START_COMMON
/*
* Similarly, for each hex type, indicate the point on the boundary of
* its Spectre expansion that corresponds to hex vertex 0.
*
* This time, it's easiest just to indicate which vertex of which
* sub-Spectre we take in each case, because the Spectre outlines
* don't take predictable turns between the edge expansions, so the
* routine consuming this data will have to look things up in its
* edgemap anyway.
*/
#define SPEC_OUTLINE_START_COMMON 0, 9
#define SPEC_OUTLINE_START_RARE 0, 8
#define SPEC_OUTLINE_START_G SPEC_OUTLINE_START_COMMON
#define SPEC_OUTLINE_START_D SPEC_OUTLINE_START_RARE
#define SPEC_OUTLINE_START_J SPEC_OUTLINE_START_COMMON
#define SPEC_OUTLINE_START_L SPEC_OUTLINE_START_COMMON
#define SPEC_OUTLINE_START_X SPEC_OUTLINE_START_COMMON
#define SPEC_OUTLINE_START_P SPEC_OUTLINE_START_COMMON
#define SPEC_OUTLINE_START_S SPEC_OUTLINE_START_RARE
#define SPEC_OUTLINE_START_F SPEC_OUTLINE_START_COMMON
#define SPEC_OUTLINE_START_Y SPEC_OUTLINE_START_COMMON
/*
* The paper also defines a set of 8 different classes of edges for
* the hexagons. (You can imagine these as different shapes of
* jigsaw-piece tab, constraining how the hexes can fit together). So
* for each hex, we need a list of its edge types.
*
* Most edge types come in two matching pairs, which the paper labels
* with the same lowercase Greek letter and a + or - superscript, e.g.
* alpha^+ and alpha^-. The usual rule is that when two edges meet,
* they have to be the + and - versions of the same letter. The
* exception to this rule is the 'eta' edge, which has no sign: it's
* symmetric, so any two eta edges can validly meet.
*
* We express this here by defining an enumeration in which eta = 0
* and all other edge types have positive values, so that integer
* negation can be used to indicate the other edge that fits with this
* one (and for eta, it doesn't change the value).
*/
enum Edge {
edge_eta = 0,
edge_alpha,
edge_beta,
edge_gamma,
edge_delta,
edge_epsilon,
edge_zeta,
edge_theta,
};
/*
* Edge types for each hex are specified anticlockwise, starting from
* the top vertex, so that edge #0 is the top-left diagonal edge, edge
* #1 the left-hand vertical edge, etc.
*/
static const int edges_G[6] = {
-edge_beta, -edge_alpha, +edge_alpha,
-edge_gamma, -edge_delta, +edge_beta,
};
static const int edges_D[6] = {
-edge_zeta, +edge_gamma, +edge_beta,
-edge_epsilon, +edge_alpha, -edge_gamma,
};
static const int edges_J[6] = {
-edge_beta, +edge_gamma, +edge_beta,
+edge_theta, +edge_beta, edge_eta,
};
static const int edges_L[6] = {
-edge_beta, +edge_gamma, +edge_beta,
-edge_epsilon, +edge_alpha, -edge_theta,
};
static const int edges_X[6] = {
-edge_beta, -edge_alpha, +edge_epsilon,
+edge_theta, +edge_beta, edge_eta,
};
static const int edges_P[6] = {
-edge_beta, -edge_alpha, +edge_epsilon,
-edge_epsilon, +edge_alpha, -edge_theta,
};
static const int edges_S[6] = {
+edge_delta, +edge_zeta, +edge_beta,
-edge_epsilon, +edge_alpha, -edge_gamma,
};
static const int edges_F[6] = {
-edge_beta, +edge_gamma, +edge_beta,
-edge_epsilon, +edge_epsilon, edge_eta,
};
static const int edges_Y[6] = {
-edge_beta, -edge_alpha, +edge_epsilon,
-edge_epsilon, +edge_epsilon, edge_eta,
};
/*
* Now specify the actual shape of each edge type, in terms of the
* angles of turns as you traverse the edge.
*
* Edges around the outline of a hex expansion are traversed
* _clockwise_, because each expansion step flips the handedness of
* the whole system.
*
* Each array has one fewer element than the number of sub-edges in
* the edge shape (for the usual reason - n edges in a path have only
* n-1 vertices separating them).
*
* These arrays show the positive version of each edge type. The
* negative version is obtained by reversing the order of the turns
* and also the sign of each turn.
*/
static const int hex_edge_shape_eta[] = { +2, +2, -2, -2 };
static const int hex_edge_shape_alpha[] = { +2, -2 };
static const int hex_edge_shape_beta[] = { -2 };
static const int hex_edge_shape_gamma[] = { +2, -2, -2, +2 };
static const int hex_edge_shape_delta[] = { -2, +2, -2, +2 };
static const int hex_edge_shape_epsilon[] = { +2, -2, -2 };
static const int hex_edge_shape_zeta[] = { -2, +2 };
static const int hex_edge_shape_theta[] = { +2, +2, -2, -2, +2 };
static const int *const hex_edge_shapes[] = {
hex_edge_shape_eta,
hex_edge_shape_alpha,
hex_edge_shape_beta,
hex_edge_shape_gamma,
hex_edge_shape_delta,
hex_edge_shape_epsilon,
hex_edge_shape_zeta,
hex_edge_shape_theta,
};
static const size_t hex_edge_lengths[] = {
lenof(hex_edge_shape_eta) + 1,
lenof(hex_edge_shape_alpha) + 1,
lenof(hex_edge_shape_beta) + 1,
lenof(hex_edge_shape_gamma) + 1,
lenof(hex_edge_shape_delta) + 1,
lenof(hex_edge_shape_epsilon) + 1,
lenof(hex_edge_shape_zeta) + 1,
lenof(hex_edge_shape_theta) + 1,
};
static const int spec_edge_shape_eta[] = { 0 };
static const int spec_edge_shape_alpha[] = { -2, +3 };
static const int spec_edge_shape_beta[] = { +3, -2 };
static const int spec_edge_shape_gamma[] = { +2 };
static const int spec_edge_shape_delta[] = { +2, +3, +2, -3, +2 };
static const int spec_edge_shape_epsilon[] = { +3 };
static const int spec_edge_shape_zeta[] = { -2 };
/* In expansion to Spectres, a theta edge corresponds to just one
* Spectre edge, so its turns array would be completely empty! */
static const int *const spec_edge_shapes[] = {
spec_edge_shape_eta,
spec_edge_shape_alpha,
spec_edge_shape_beta,
spec_edge_shape_gamma,
spec_edge_shape_delta,
spec_edge_shape_epsilon,
spec_edge_shape_zeta,
NULL, /* theta has no turns */
};
static const size_t spec_edge_lengths[] = {
lenof(spec_edge_shape_eta) + 1,
lenof(spec_edge_shape_alpha) + 1,
lenof(spec_edge_shape_beta) + 1,
lenof(spec_edge_shape_gamma) + 1,
lenof(spec_edge_shape_delta) + 1,
lenof(spec_edge_shape_epsilon) + 1,
lenof(spec_edge_shape_zeta) + 1,
1, /* theta is only one edge long */
};
/*
* Each edge type corresponds to a fixed number of edges of the
* hexagon layout in the expansion of each hex, and also to a fixed
* number of edges of the Spectre(s) that each hex expands to in the
* final step.
*/
static const int edgelen_hex[] = {
5, /* edge_eta */
3, /* edge_alpha */
2, /* edge_beta */
5, /* edge_gamma */
5, /* edge_delta */
4, /* edge_epsilon */
3, /* edge_zeta */
6, /* edge_theta */
};
static const int edgelen_spectre[] = {
2, /* edge_eta */
3, /* edge_alpha */
3, /* edge_beta */
2, /* edge_gamma */
6, /* edge_delta */
2, /* edge_epsilon */
2, /* edge_zeta */
1, /* edge_theta */
};

534
auxiliary/spectre-test.c Normal file
View File

@ -0,0 +1,534 @@
/*
* Standalone test program for spectre.c.
*/
#include <assert.h>
#ifdef NO_TGMATH_H
# include <math.h>
#else
# include <tgmath.h>
#endif
#include <stdarg.h>
#include <stdio.h>
#include <string.h>
#include "puzzles.h"
#include "spectre-internal.h"
#include "spectre-tables-manual.h"
#include "spectre-tables-auto.h"
#include "spectre-help.h"
static void step_tests(void)
{
SpectreContext ctx[1];
random_state *rs;
SpectreCoords *sc;
unsigned outedge;
rs = random_new("12345", 5);
spectrectx_init_random(ctx, rs);
/* Simplest possible transition: between the two Spectres making
* up a G hex. */
sc = spectre_coords_new();
spectre_coords_make_space(sc, 1);
sc->index = 0;
sc->nc = 1;
sc->c[0].type = HEX_G;
sc->c[0].index = -1;
spectrectx_step(ctx, sc, 12, &outedge);
assert(outedge == 5);
assert(sc->index == 1);
assert(sc->nc == 1);
assert(sc->c[0].type == HEX_G);
assert(sc->c[0].index == -1);
spectre_coords_free(sc);
/* Test the double Spectre transition. Here, within a F superhex,
* we attempt to step from the G subhex to the S one, in such a
* way that the place where we enter the Spectre corresponding to
* the S hex is on its spur of detached edge, causing us to
* immediately transition back out of the other side of that spur
* and end up in the D subhex instead. */
sc = spectre_coords_new();
spectre_coords_make_space(sc, 2);
sc->index = 1;
sc->nc = 2;
sc->c[0].type = HEX_G;
sc->c[0].index = 2;
sc->c[1].type = HEX_F;
sc->c[1].index = -1;
spectrectx_step(ctx, sc, 1, &outedge);
assert(outedge == 6);
assert(sc->index == 0);
assert(sc->nc == 2);
assert(sc->c[0].type == HEX_D);
assert(sc->c[0].index == 5);
assert(sc->c[1].type == HEX_F);
assert(sc->c[1].index == -1);
spectre_coords_free(sc);
/* However, _this_ transition leaves the same G subhex by the same
* edge of the hexagon, but further along it, so that we land in
* the S Spectre and stay there, without needing a double
* transition. */
sc = spectre_coords_new();
spectre_coords_make_space(sc, 2);
sc->index = 1;
sc->nc = 2;
sc->c[0].type = HEX_G;
sc->c[0].index = 2;
sc->c[1].type = HEX_F;
sc->c[1].index = -1;
spectrectx_step(ctx, sc, 13, &outedge);
assert(outedge == 4);
assert(sc->index == 0);
assert(sc->nc == 2);
assert(sc->c[0].type == HEX_S);
assert(sc->c[0].index == 3);
assert(sc->c[1].type == HEX_F);
assert(sc->c[1].index == -1);
spectre_coords_free(sc);
/* A couple of randomly generated transition tests that go a long
* way up the stack. */
sc = spectre_coords_new();
spectre_coords_make_space(sc, 7);
sc->index = 0;
sc->nc = 7;
sc->c[0].type = HEX_S;
sc->c[0].index = 3;
sc->c[1].type = HEX_Y;
sc->c[1].index = 7;
sc->c[2].type = HEX_Y;
sc->c[2].index = 4;
sc->c[3].type = HEX_Y;
sc->c[3].index = 4;
sc->c[4].type = HEX_F;
sc->c[4].index = 0;
sc->c[5].type = HEX_X;
sc->c[5].index = 1;
sc->c[6].type = HEX_G;
sc->c[6].index = -1;
spectrectx_step(ctx, sc, 13, &outedge);
assert(outedge == 12);
assert(sc->index == 0);
assert(sc->nc == 7);
assert(sc->c[0].type == HEX_Y);
assert(sc->c[0].index == 1);
assert(sc->c[1].type == HEX_P);
assert(sc->c[1].index == 1);
assert(sc->c[2].type == HEX_D);
assert(sc->c[2].index == 5);
assert(sc->c[3].type == HEX_Y);
assert(sc->c[3].index == 4);
assert(sc->c[4].type == HEX_X);
assert(sc->c[4].index == 7);
assert(sc->c[5].type == HEX_S);
assert(sc->c[5].index == 3);
assert(sc->c[6].type == HEX_G);
assert(sc->c[6].index == -1);
spectre_coords_free(sc);
sc = spectre_coords_new();
spectre_coords_make_space(sc, 7);
sc->index = 0;
sc->nc = 7;
sc->c[0].type = HEX_Y;
sc->c[0].index = 7;
sc->c[1].type = HEX_F;
sc->c[1].index = 6;
sc->c[2].type = HEX_Y;
sc->c[2].index = 4;
sc->c[3].type = HEX_X;
sc->c[3].index = 7;
sc->c[4].type = HEX_L;
sc->c[4].index = 0;
sc->c[5].type = HEX_S;
sc->c[5].index = 3;
sc->c[6].type = HEX_F;
sc->c[6].index = -1;
spectrectx_step(ctx, sc, 0, &outedge);
assert(outedge == 1);
assert(sc->index == 0);
assert(sc->nc == 7);
assert(sc->c[0].type == HEX_P);
assert(sc->c[0].index == 1);
assert(sc->c[1].type == HEX_F);
assert(sc->c[1].index == 0);
assert(sc->c[2].type == HEX_Y);
assert(sc->c[2].index == 7);
assert(sc->c[3].type == HEX_F);
assert(sc->c[3].index == 0);
assert(sc->c[4].type == HEX_G);
assert(sc->c[4].index == 2);
assert(sc->c[5].type == HEX_D);
assert(sc->c[5].index == 5);
assert(sc->c[6].type == HEX_F);
assert(sc->c[6].index == -1);
spectre_coords_free(sc);
spectrectx_cleanup(ctx);
random_free(rs);
}
struct genctx {
Graphics *gr;
FILE *fp; /* for non-graphical output modes */
random_state *rs;
Coord xmin, xmax, ymin, ymax;
};
static void gctx_set_size(
struct genctx *gctx, int width, int height, double scale,
int *xmin, int *xmax, int *ymin, int *ymax)
{
*xmax = ceil(width/(2*scale));
*xmin = -*xmax;
*ymax = ceil(height/(2*scale));
*ymin = -*ymax;
/* point_x() and point_y() double their output to avoid having
* to use fractions, so double the bounds we'll compare their
* results against */
gctx->xmin.c1 = *xmin * 2; gctx->xmin.cr3 = 0;
gctx->xmax.c1 = *xmax * 2; gctx->xmax.cr3 = 0;
gctx->ymin.c1 = *ymin * 2; gctx->ymin.cr3 = 0;
gctx->ymax.c1 = *ymax * 2; gctx->ymax.cr3 = 0;
}
static bool callback(void *vctx, const Spectre *spec)
{
struct genctx *gctx = (struct genctx *)vctx;
size_t i;
for (i = 0; i < 14; i++) {
Point p = spec->vertices[i];
Coord x = point_x(p), y = point_y(p);
if (coord_cmp(x, gctx->xmin) >= 0 && coord_cmp(x, gctx->xmax) <= 0 &&
coord_cmp(y, gctx->ymin) >= 0 && coord_cmp(y, gctx->ymax) <= 0)
goto ok;
}
return false;
ok:
gr_draw_spectre_from_coords(gctx->gr, spec->sc, spec->vertices);
if (gctx->fp) {
/*
* Emit calls to a made-up Python 'spectre()' function which
* takes the following parameters:
*
* - lowest-level hexagon type (one-character string)
* - index of Spectre within hexagon (0 or rarely 1)
* - array of 14 point coordinates. Each is a 2-tuple
* containing x and y. Each of those in turn is a 2-tuple
* containing coordinates of 1 and sqrt(3).
*/
fprintf(gctx->fp, "spectre('%s', %d, [",
hex_names[spec->sc->c[0].type], spec->sc->index);
for (i = 0; i < 14; i++) {
Point p = spec->vertices[i];
Coord x = point_x(p), y = point_y(p);
fprintf(gctx->fp, "%s((%d,%d),(%d,%d))", i ? ", " : "",
x.c1, x.cr3, y.c1, y.cr3);
}
fprintf(gctx->fp, "])\n");
}
return true;
}
static void generate(struct genctx *gctx)
{
SpectreContext ctx[1];
spectrectx_init_random(ctx, gctx->rs);
ctx->prototype->hex_colour = random_upto(gctx->rs, 3);
ctx->prototype->prev_hex_colour = (ctx->prototype->hex_colour + 1 +
random_upto(gctx->rs, 2)) % 3;
ctx->prototype->incoming_hex_edge = random_upto(gctx->rs, 2);
spectrectx_generate(ctx, callback, gctx);
spectrectx_cleanup(ctx);
}
static inline Point reflected(Point p)
{
/*
* This reflection operation is used as a conjugation, so it
* doesn't matter _what_ reflection it is, only that it reverses
* sense.
*/
Point r;
size_t i;
for (i = 0; i < 4; i++)
r.coeffs[i] = p.coeffs[3-i];
return r;
}
static void reflect_spectre(Spectre *spec)
{
size_t i;
for (i = 0; i < 14; i++)
spec->vertices[i] = reflected(spec->vertices[i]);
}
static void periodic_cheat(struct genctx *gctx)
{
Spectre start, sh, sv;
size_t i;
start.sc = NULL;
{
Point u = {{ 0, 0, 0, 0 }};
Point v = {{ 1, 0, 0, 1 }};
v = point_mul(v, point_rot(1));
spectre_place(&start, u, v, 0);
}
sh = start;
while (callback(gctx, &sh)) {
sv = sh;
i = 0;
do {
if (i) {
spectre_place(&sv, sv.vertices[6], sv.vertices[7], 0);
} else {
spectre_place(&sv, reflected(sv.vertices[6]),
reflected(sv.vertices[7]), 0);
reflect_spectre(&sv);
}
i ^= 1;
} while (callback(gctx, &sv));
sv = sh;
i = 0;
do {
if (i) {
spectre_place(&sv, sv.vertices[0], sv.vertices[1], 6);
} else {
spectre_place(&sv, reflected(sv.vertices[0]),
reflected(sv.vertices[1]), 6);
reflect_spectre(&sv);
}
i ^= 1;
} while (callback(gctx, &sv));
spectre_place(&sh, sh.vertices[12], sh.vertices[11], 4);
}
sh = start;
do {
spectre_place(&sh, sh.vertices[5], sh.vertices[4], 11);
sv = sh;
i = 0;
do {
if (i) {
spectre_place(&sv, sv.vertices[6], sv.vertices[7], 0);
} else {
spectre_place(&sv, reflected(sv.vertices[6]),
reflected(sv.vertices[7]), 0);
reflect_spectre(&sv);
}
i ^= 1;
} while (callback(gctx, &sv));
sv = sh;
i = 0;
do {
if (i) {
spectre_place(&sv, sv.vertices[0], sv.vertices[1], 6);
} else {
spectre_place(&sv, reflected(sv.vertices[0]),
reflected(sv.vertices[1]), 6);
reflect_spectre(&sv);
}
i ^= 1;
} while (callback(gctx, &sv));
} while (callback(gctx, &sh));
}
static void generate_hexes(struct genctx *gctx)
{
SpectreContext ctx[1];
spectrectx_init_random(ctx, gctx->rs);
SpectreCoords *sc;
unsigned orient, outedge, inedge;
bool printed_any = false;
size_t r = 1, ri = 0, rj = 0;
Point centre = {{ 0, 0, 0, 0 }};
const Point six = {{ 6, 0, 0, 0 }};
sc = spectre_coords_copy(ctx->prototype);
orient = random_upto(gctx->rs, 6);
while (true) {
Point top = {{ -2, 0, 4, 0 }};
Point vertices[6];
bool print_this = false;
size_t i;
for (i = 0; i < 6; i++) {
vertices[i] = point_add(centre, point_mul(
top, point_rot(2 * (orient + i))));
Coord x = point_x(vertices[i]), y = point_y(vertices[i]);
if (coord_cmp(x, gctx->xmin) >= 0 &&
coord_cmp(x, gctx->xmax) <= 0 &&
coord_cmp(y, gctx->ymin) >= 0 &&
coord_cmp(y, gctx->ymax) <= 0)
print_this = true;
}
if (print_this) {
printed_any = true;
gr_draw_hex(gctx->gr, -1, sc->c[0].type, vertices);
}
/*
* Decide which way to step next. We spiral outwards from a
* central hexagon.
*/
outedge = (ri == 0 && rj == 0) ? 5 : ri;
if (++rj >= r) {
rj = 0;
if (++ri >= 6) {
ri = 0;
if (!printed_any)
break;
printed_any = false;
++r;
}
}
spectrectx_step_hex(ctx, sc, 0, (outedge + 6 - orient) % 6, &inedge);
orient = (outedge + 9 - inedge) % 6;
centre = point_add(centre, point_mul(six, point_rot(4 + 2 * outedge)));
}
spectre_coords_free(sc);
spectrectx_cleanup(ctx);
}
int main(int argc, char **argv)
{
const char *random_seed = "12345";
const char *outfile = "-";
bool four_colour = false;
enum { TESTS, TILING, CHEAT, HEXES } mode = TILING;
enum { SVG, PYTHON } outmode = SVG;
double scale = 10, linewidth = 1.5;
int width = 1024, height = 768;
bool arcs = false;
while (--argc > 0) {
const char *arg = *++argv;
if (!strcmp(arg, "--help")) {
printf(" usage: spectre-test [FIXME]\n"
" also: spectre-test --test\n");
return 0;
} else if (!strcmp(arg, "--test")) {
mode = TESTS;
} else if (!strcmp(arg, "--hex")) {
mode = HEXES;
} else if (!strcmp(arg, "--cheat")) {
mode = CHEAT;
} else if (!strcmp(arg, "--python")) {
outmode = PYTHON;
} else if (!strcmp(arg, "--arcs")) {
arcs = true;
} else if (!strncmp(arg, "--seed=", 7)) {
random_seed = arg+7;
} else if (!strcmp(arg, "--fourcolour")) {
four_colour = true;
} else if (!strncmp(arg, "--scale=", 8)) {
scale = atof(arg+8);
} else if (!strncmp(arg, "--width=", 8)) {
width = atof(arg+8);
} else if (!strncmp(arg, "--height=", 9)) {
height = atof(arg+9);
} else if (!strncmp(arg, "--linewidth=", 12)) {
linewidth = atof(arg+12);
} else if (!strcmp(arg, "-o")) {
if (--argc <= 0) {
fprintf(stderr, "expected argument to '%s'\n", arg);
return 1;
}
outfile = *++argv;
} else {
fprintf(stderr, "unexpected extra argument '%s'\n", arg);
return 1;
}
}
switch (mode) {
case TESTS: {
step_tests();
break;
}
case TILING:
case CHEAT: {
struct genctx gctx[1];
bool close_output = false;
int xmin, xmax, ymin, ymax;
gctx_set_size(gctx, width, height, scale, &xmin, &xmax, &ymin, &ymax);
switch (outmode) {
case SVG:
gctx->gr = gr_new(outfile, xmin, xmax, ymin, ymax, scale);
gctx->gr->number_cells = false;
gctx->gr->four_colour = four_colour;
gctx->gr->linewidth = linewidth;
gctx->gr->arcs = arcs;
gctx->fp = NULL;
break;
case PYTHON:
gctx->gr = NULL;
if (!strcmp(outfile, "-")) {
gctx->fp = stdout;
} else {
gctx->fp = fopen(outfile, "w");
close_output = true;
}
break;
}
gctx->rs = random_new(random_seed, strlen(random_seed));
switch (mode) {
case TILING:
generate(gctx);
break;
case CHEAT:
periodic_cheat(gctx);
break;
default: /* shouldn't happen */
break;
}
random_free(gctx->rs);
gr_free(gctx->gr);
if (close_output)
fclose(gctx->fp);
break;
}
case HEXES: {
struct genctx gctx[1];
int xmin, xmax, ymin, ymax;
gctx_set_size(gctx, width, height, scale, &xmin, &xmax, &ymin, &ymax);
gctx->gr = gr_new(outfile, xmin, xmax, ymin, ymax, scale);
gctx->gr->jigsaw_mode = true;
gctx->gr->number_edges = false;
gctx->gr->linewidth = linewidth;
gctx->rs = random_new(random_seed, strlen(random_seed));
generate_hexes(gctx); /* FIXME: bounds */
random_free(gctx->rs);
gr_free(gctx->gr);
break;
}
}
}

315
grid.c
View File

@ -24,6 +24,7 @@
#include "grid.h"
#include "penrose.h"
#include "hat.h"
#include "spectre.h"
/* Debugging options */
@ -3562,6 +3563,316 @@ static grid *grid_new_hats(int width, int height, const char *desc)
return ctx->g;
}
#define SPECTRE_TILESIZE 32
#define SPECTRE_SQUARELEN 7
#define SPECTRE_UNIT 8
static const char *grid_validate_params_spectres(
int width, int height)
{
int l = SPECTRE_UNIT * SPECTRE_SQUARELEN;
if (width > INT_MAX / l || /* xextent */
height > INT_MAX / l || /* yextent */
width > (INT_MAX / SPECTRE_SQUARELEN /
SPECTRE_SQUARELEN / height)) /* max_faces */
return "Grid must not be unreasonably large";
return NULL;
}
static void grid_size_spectres(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
*tilesize = SPECTRE_TILESIZE;
*xextent = width * SPECTRE_UNIT * SPECTRE_SQUARELEN;
*yextent = height * SPECTRE_UNIT * SPECTRE_SQUARELEN;
}
static char *grid_new_desc_spectres(
grid_type type, int width, int height, random_state *rs)
{
char *buf;
size_t i;
struct SpectrePatchParams sp;
spectre_tiling_randomise(&sp, width * SPECTRE_SQUARELEN,
height * SPECTRE_SQUARELEN, rs);
buf = snewn(sp.ncoords + 3, char);
buf[0] = (sp.orientation < 10 ? '0' + sp.orientation :
'A' + sp.orientation - 10);
for (i = 0; i < sp.ncoords; i++) {
assert(sp.coords[i] < 10); /* all indices are 1 digit */
buf[i+1] = '0' + sp.coords[i];
}
buf[sp.ncoords+1] = sp.final_hex;
buf[sp.ncoords+2] = '\0';
sfree(sp.coords);
return buf;
}
/* Shared code between validating and reading grid descs.
* Always allocates sp->coords, whether or not it returns an error. */
static const char *grid_desc_to_spectre_params(
const char *desc, struct SpectrePatchParams *sp)
{
size_t i;
if (!*desc)
return "empty grid description";
sp->ncoords = strlen(desc) - 2;
sp->coords = snewn(sp->ncoords, unsigned char);
{
char c = desc[0];
if (isdigit((unsigned char)c))
sp->orientation = c - '0';
else if (c == 'A' || c == 'B')
sp->orientation = 10 + c - 'A';
else
return "expected digit or A,B at start of grid description";
}
for (i = 0; i < sp->ncoords; i++) {
char c = desc[i+1];
if (!isdigit((unsigned char)c))
return "expected digit in grid description";
sp->coords[i] = c - '0';
}
sp->final_hex = desc[sp->ncoords+1];
return NULL;
}
static const char *grid_validate_desc_spectres(
grid_type type, int width, int height, const char *desc)
{
struct SpectrePatchParams sp;
const char *error = NULL;
if (!desc)
return "Missing grid description string.";
error = grid_desc_to_spectre_params(desc, &sp);
if (!error)
error = spectre_tiling_params_invalid(&sp);
sfree(sp.coords);
return error;
}
struct spectrecontext {
grid *g;
tree234 *points;
};
/*
* Calculate the nearest integer to n*sqrt(3), via a bitwise algorithm
* that avoids floating point.
*
* (It would probably be OK in practice to use floating point, but I
* felt like overengineering it for fun. With FP, there's at least a
* theoretical risk of rounding the wrong way, due to the three
* successive roundings involved - rounding sqrt(3), rounding its
* product with n, and then rounding to the nearest integer. This
* approach avoids that: it's exact.)
*/
static int mul_root3(int n_signed)
{
unsigned x, r, m;
int sign = n_signed < 0 ? -1 : +1;
unsigned n = n_signed * sign;
unsigned bitpos;
/*
* Method:
*
* We transform m gradually from zero into n, by multiplying it by
* 2 in each step and optionally adding 1, so that it's always
* floor(n/2^something).
*
* At the start of each step, x is the largest integer less than
* or equal to m*sqrt(3). We transform m to 2m+bit, and therefore
* we must transform x to 2x+something to match. The 'something'
* we add to 2x is at most 3. (Worst case is if m sqrt(3) was
* equal to x + 1-eps for some tiny eps, and then the incoming bit
* of m is 1, so that (2m+1)sqrt(3) = 2x+2+2eps+sqrt(3), i.e.
* about 2x + 3.732...)
*
* To compute this, we also track the residual value r such that
* x^2+r = 3m^2.
*
* The algorithm below is very similar to the usual approach for
* taking the square root of an integer in binary. The wrinkle is
* that we have an integer multiplier, i.e. we're computing
* P*sqrt(Q) (with P=n and Q=3 in this case) rather than just
* sqrt(Q). Of course in principle we could just take sqrt(P^2Q),
* but we'd need an integer twice the width to hold P^2. Pulling
* out P and treating it specially makes overflow less likely.
*/
x = r = m = 0;
for (bitpos = UINT_MAX & ~(UINT_MAX >> 1); bitpos; bitpos >>= 1) {
unsigned a, b = (n & bitpos) ? 1 : 0;
/*
* Check invariants. We expect that x^2 + r = 3m^2 (i.e. our
* residual term is correct), and also that r < 2x+1 (because
* if not, then we could replace x with x+1 and still get a
* value that made r non-negative, i.e. x would not be the
* _largest_ integer less than m sqrt(3)).
*/
assert(x*x + r == 3*m*m);
assert(r < 2*x+1);
/*
* We're going to replace m with 2m+b, and x with 2x+a for
* some a we haven't decided on yet.
*
* The new value of the residual will therefore be
*
* 3 (2m+b)^2 - (2x+a)^2
* = (12m^2 + 12mb + 3b^2) - (4x^2 + 4xa + a^2)
* = 4 (3m^2 - x^2) + 12mb + 3b^2 - 4xa - a^2
* = 4r + 12mb + 3b^2 - 4xa - a^2 (because r = 3m^2 - x^2)
* = 4r + (12m + 3)b - 4xa - a^2 (b is 0 or 1, so b = b^2)
*/
for (a = 0; a < 4; a++) {
/* If we made this routine handle square roots of numbers
* other than 3 then it would be sensible to make this a
* binary search. Here, it hardly seems important. */
unsigned pos = 4*r + b*(12*m + 3);
unsigned neg = 4*a*x + a*a;
if (pos < neg)
break; /* this value of a is too big */
}
/* The above loop will have terminated with a one too big,
* whether that's because we hit the break statement or fell
* off the end with a=4. So now decrementing a will give us
* the right value to add. */
a--;
r = 4*r + b*(12*m + 3) - (4*a*x + a*a);
m = 2*m+b;
x = 2*x+a;
}
/*
* Finally, round to the nearest integer. At present, x is the
* largest integer that is _at most_ m sqrt(3). But we want the
* _nearest_ integer, whether that's rounded up or down. So check
* whether (x + 1/2) is still less than m sqrt(3), i.e. whether
* (x + 1/2)^2 < 3m^2; if it is, then we increment x.
*
* We have 3m^2 - (x + 1/2)^2 = 3m^2 - x^2 - x - 1/4
* = r - x - 1/4
*
* and since r and x are integers, this is greater than 0 if and
* only if r > x.
*
* (There's no need to worry about tie-breaking exact halfway
* rounding cases. sqrt(3) is irrational, so none such exist.)
*/
if (r > x)
x++;
/*
* Put the sign back on, and convert back from unsigned to int.
*/
if (sign == +1) {
return x;
} else {
/* Be a little careful to avoid compilers deciding I've just
* perpetrated signed-integer overflow. This should optimise
* down to no actual code. */
return INT_MIN + (int)(-x - (unsigned)INT_MIN);
}
}
static void grid_spectres_callback(void *vctx, const int *coords)
{
struct spectrecontext *ctx = (struct spectrecontext *)vctx;
size_t i;
grid_face_add_new(ctx->g, SPECTRE_NVERTICES);
for (i = 0; i < SPECTRE_NVERTICES; i++) {
grid_dot *d = grid_get_dot(
ctx->g, ctx->points,
(coords[4*i+0] * SPECTRE_UNIT +
mul_root3(coords[4*i+1] * SPECTRE_UNIT)),
(coords[4*i+2] * SPECTRE_UNIT +
mul_root3(coords[4*i+3] * SPECTRE_UNIT)));
grid_face_set_dot(ctx->g, d, i);
}
}
static grid *grid_new_spectres(int width, int height, const char *desc)
{
struct SpectrePatchParams sp;
const char *error = NULL;
int width2 = width * SPECTRE_SQUARELEN;
int height2 = height * SPECTRE_SQUARELEN;
error = grid_desc_to_spectre_params(desc, &sp);
assert(error == NULL && "grid_validate_desc_spectres should have failed");
/*
* Bound on the number of faces: the area of a single face in the
* output coordinates is 24 + 24 rt3, which is between 65 and 66.
* Every face fits strictly inside the target rectangle, so the
* number of faces times a lower bound on their area can't exceed
* the area of the rectangle we give to spectre_tiling_generate.
*/
int max_faces = width2 * height2 / 65;
/*
* Bound on number of dots: 14*faces is certainly enough, but
* quite wasteful given that _most_ dots are shared between at
* least two faces. But to get a better estimate we'd have to
* figure out a bound for the number of dots on the perimeter,
* which is the number by which the count exceeds 14*faces/2.
*/
int max_dots = 14 * max_faces;
struct spectrecontext ctx[1];
ctx->g = grid_empty();
ctx->g->tilesize = SPECTRE_TILESIZE;
ctx->g->faces = snewn(max_faces, grid_face);
ctx->g->dots = snewn(max_dots, grid_dot);
ctx->points = newtree234(grid_point_cmp_fn);
spectre_tiling_generate(&sp, width2, height2, grid_spectres_callback, ctx);
freetree234(ctx->points);
sfree(sp.coords);
grid_trim_vigorously(ctx->g);
grid_make_consistent(ctx->g);
/*
* As with the Penrose tiling, we're likely to have different
* sized margins due to the lack of a neat grid that this tiling
* fits on. So now we know what tiles we're left with, recentre
* them.
*/
{
int w = width2 * SPECTRE_UNIT, h = height2 * SPECTRE_UNIT;
ctx->g->lowest_x -= (w - (ctx->g->highest_x - ctx->g->lowest_x))/2;
ctx->g->lowest_y -= (h - (ctx->g->highest_y - ctx->g->lowest_y))/2;
ctx->g->highest_x = ctx->g->lowest_x + w;
ctx->g->highest_y = ctx->g->lowest_y + h;
}
return ctx->g;
}
/* ----------- End of grid generators ------------- */
#define FNVAL(upper,lower) &grid_validate_params_ ## lower,
@ -3588,6 +3899,8 @@ char *grid_new_desc(grid_type type, int width, int height, random_state *rs)
return grid_new_desc_penrose(type, width, height, rs);
} else if (type == GRID_HATS) {
return grid_new_desc_hats(type, width, height, rs);
} else if (type == GRID_SPECTRES) {
return grid_new_desc_spectres(type, width, height, rs);
} else if (type == GRID_TRIANGULAR) {
return dupstr("0"); /* up-to-date version of triangular grid */
} else {
@ -3602,6 +3915,8 @@ const char *grid_validate_desc(grid_type type, int width, int height,
return grid_validate_desc_penrose(type, width, height, desc);
} else if (type == GRID_HATS) {
return grid_validate_desc_hats(type, width, height, desc);
} else if (type == GRID_SPECTRES) {
return grid_validate_desc_spectres(type, width, height, desc);
} else if (type == GRID_TRIANGULAR) {
return grid_validate_desc_triangular(type, width, height, desc);
} else {

1
grid.h
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@ -111,6 +111,7 @@ typedef struct grid {
A(PENROSE_P2,penrose_p2_kite) \
A(PENROSE_P3,penrose_p3_thick) \
A(HATS,hats) \
A(SPECTRES,spectres) \
/* end of list */
#define ENUM(upper,lower) GRID_ ## upper,

4
loopy.c
View File

@ -285,6 +285,7 @@ static void check_caches(const solver_state* sstate);
A("Kagome",KAGOME,3,3) \
A("Compass-Dodecagonal",COMPASSDODECAGONAL,2,2) \
A("Hats",HATS,6,6) \
A("Spectres",SPECTRES,6,6) \
/* end of list */
#define GRID_NAME(title,type,amin,omin) title,
@ -557,6 +558,8 @@ static const game_params loopy_presets_more[] = {
{ 3, 3, DIFF_HARD, LOOPY_GRID_GREATDODECAGONAL },
{ 3, 2, DIFF_HARD, LOOPY_GRID_GREATGREATDODECAGONAL },
{ 3, 3, DIFF_HARD, LOOPY_GRID_COMPASSDODECAGONAL },
{ 6, 6, DIFF_HARD, LOOPY_GRID_HATS },
{ 6, 6, DIFF_HARD, LOOPY_GRID_SPECTRES },
#else
{ 10, 10, DIFF_HARD, LOOPY_GRID_HONEYCOMB },
{ 5, 4, DIFF_HARD, LOOPY_GRID_GREATHEXAGONAL },
@ -568,6 +571,7 @@ static const game_params loopy_presets_more[] = {
{ 5, 3, DIFF_HARD, LOOPY_GRID_GREATGREATDODECAGONAL },
{ 5, 4, DIFF_HARD, LOOPY_GRID_COMPASSDODECAGONAL },
{ 10, 10, DIFF_HARD, LOOPY_GRID_HATS },
{ 10, 10, DIFF_HARD, LOOPY_GRID_SPECTRES },
#endif
};

277
spectre-internal.h Normal file
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@ -0,0 +1,277 @@
#include "spectre.h"
/*
* List macro of the names for hexagon types, which will be reused all
* over the place.
*
* (I have to call the parameter to this list macro something other
* than X, because here, X is also one of the macro arguments!)
*/
#define HEX_LETTERS(Z) Z(G) Z(D) Z(J) Z(L) Z(X) Z(P) Z(S) Z(F) Z(Y)
typedef enum Hex {
#define HEX_ENUM_DECL(x) HEX_##x,
HEX_LETTERS(HEX_ENUM_DECL)
#undef HEX_ENUM_DECL
} Hex;
static inline unsigned num_subhexes(Hex h)
{
return h == HEX_G ? 7 : 8;
}
static inline unsigned num_spectres(Hex h)
{
return h == HEX_G ? 2 : 1;
}
/*
* Data types used in the lookup tables.
*/
struct MapEntry {
bool internal;
unsigned char hi, lo;
};
struct MapEdge {
unsigned char startindex, len;
};
struct Possibility {
unsigned char hi, lo;
unsigned long prob;
};
/*
* Coordinate system for tracking Spectres and their hexagonal
* metatiles.
*
* SpectreCoords will store the index of a single Spectre within a
* smallest-size hexagon, plus an array of HexCoord each indexing a
* hexagon within the expansion of a larger hexagon.
*
* The last coordinate stored, sc->c[sc->nc-1], will have a hex type
* but no index (represented by index==-1). This means "we haven't
* decided yet what this level of metatile needs to be". If we need to
* refer to this level during the hatctx_step algorithm, we make it up
* at random, based on a table of what metatiles each type can
* possibly be part of, at what index.
*/
typedef struct HexCoord {
int index; /* index within that tile, or -1 if not yet known */
Hex type; /* type of this hexagon */
} HexCoord;
typedef struct SpectreCoords {
int index; /* index of Spectre within the order-0 hexagon */
HexCoord *c;
size_t nc, csize;
/* Used by spectre-test to four-colour output tilings, and
* maintained unconditionally because it's easier than making it
* conditional */
unsigned char hex_colour, prev_hex_colour, incoming_hex_edge;
} SpectreCoords;
SpectreCoords *spectre_coords_new(void);
void spectre_coords_free(SpectreCoords *hc);
void spectre_coords_make_space(SpectreCoords *hc, size_t size);
SpectreCoords *spectre_coords_copy(SpectreCoords *hc_in);
/*
* Coordinate system for locating Spectres in the plane.
*
* The 'Point' structure represents a single point by means of an
* integer linear combination of {1, d, d^2, d^3}, where d is the
* complex number exp(i pi/6) representing 1/12 of a turn about the
* origin.
*
* The 'Spectre' structure represents an entire Spectre in a tiling,
* giving both the locations of all of its vertices and its
* combinatorial coordinates. It also contains a linked-list pointer,
* used during breadth-first search to generate all the Spectres in an
* area.
*/
typedef struct Point {
int coeffs[4];
} Point;
typedef struct Spectre Spectre;
struct Spectre {
Point vertices[14];
SpectreCoords *sc;
Spectre *next; /* used in breadth-first search */
};
/* Fill in all the coordinates of a Spectre starting from any single edge */
void spectre_place(Spectre *spec, Point u, Point v, int index_of_u);
/*
* A Point is really a complex number, so we can add, subtract and
* multiply them.
*/
static inline Point point_add(Point a, Point b)
{
Point r;
size_t i;
for (i = 0; i < 4; i++)
r.coeffs[i] = a.coeffs[i] + b.coeffs[i];
return r;
}
static inline Point point_sub(Point a, Point b)
{
Point r;
size_t i;
for (i = 0; i < 4; i++)
r.coeffs[i] = a.coeffs[i] - b.coeffs[i];
return r;
}
static inline Point point_mul_by_d(Point x)
{
Point r;
/* Multiply by d by using the identity d^4 - d^2 + 1 = 0, so d^4 = d^2+1 */
r.coeffs[0] = -x.coeffs[3];
r.coeffs[1] = x.coeffs[0];
r.coeffs[2] = x.coeffs[1] + x.coeffs[3];
r.coeffs[3] = x.coeffs[2];
return r;
}
static inline Point point_mul(Point a, Point b)
{
size_t i, j;
Point r;
/* Initialise r to be a, scaled by b's d^3 term */
for (j = 0; j < 4; j++)
r.coeffs[j] = a.coeffs[j] * b.coeffs[3];
/* Now iterate r = d*r + (next coefficient down), by Horner's rule */
for (i = 3; i-- > 0 ;) {
r = point_mul_by_d(r);
for (j = 0; j < 4; j++)
r.coeffs[j] += a.coeffs[j] * b.coeffs[i];
}
return r;
}
static inline bool point_equal(Point a, Point b)
{
size_t i;
for (i = 0; i < 4; i++)
if (a.coeffs[i] != b.coeffs[i])
return false;
return true;
}
/*
* Return the Point corresponding to a rotation of s steps around the
* origin, i.e. a rotation by 30*s degrees or s*pi/6 radians.
*/
static inline Point point_rot(int s)
{
Point r = {{ 1, 0, 0, 0 }};
Point dpower = {{ 0, 1, 0, 0 }};
/* Reduce to a sensible range */
s = s % 12;
if (s < 0)
s += 12;
while (true) {
if (s & 1)
r = point_mul(r, dpower);
s >>= 1;
if (!s)
break;
dpower = point_mul(dpower, dpower);
}
return r;
}
/*
* SpectreContext is the shared context of a whole run of the
* algorithm. Its 'prototype' SpectreCoords object represents the
* coordinates of the starting Spectre, and is extended as necessary;
* any other SpectreCoord that needs extending will copy the
* higher-order values from ctx->prototype as needed, so that once
* each choice has been made, it remains consistent.
*
* When we're inventing a random piece of tiling in the first place,
* we append to ctx->prototype by choosing a random (but legal)
* higher-level metatile for the current topmost one to turn out to be
* part of. When we're replaying a generation whose parameters are
* already stored, we don't have a random_state, and we make fixed
* decisions if not enough coordinates were provided, as in the
* corresponding hat.c system.
*
* For a normal (non-testing) caller, spectrectx_generate() is the
* main useful function. It breadth-first searches a whole area to
* generate all the Spectres in it, starting from a (typically
* central) one with the coordinates of ctx->prototype. The callback
* function processes each Spectre as it's generated, and returns true
* or false to indicate whether that Spectre is within the bounds of
* the target area (and therefore the search should continue exploring
* its neighbours).
*/
typedef struct SpectreContext {
random_state *rs;
bool must_free_rs;
Point start_vertices[2]; /* vertices 0,1 of the starting Spectre */
int orientation; /* orientation to put in SpectrePatchParams */
SpectreCoords *prototype;
} SpectreContext;
void spectrectx_init_random(SpectreContext *ctx, random_state *rs);
void spectrectx_init_from_params(
SpectreContext *ctx, const struct SpectrePatchParams *ps);
void spectrectx_cleanup(SpectreContext *ctx);
SpectreCoords *spectrectx_initial_coords(SpectreContext *ctx);
void spectrectx_extend_coords(SpectreContext *ctx, SpectreCoords *hc,
size_t n);
void spectrectx_step(SpectreContext *ctx, SpectreCoords *sc,
unsigned edge, unsigned *outedge);
void spectrectx_generate(SpectreContext *ctx,
bool (*callback)(void *cbctx, const Spectre *spec),
void *cbctx);
/* For spectre-test to directly generate a tiling of hexes */
void spectrectx_step_hex(SpectreContext *ctx, SpectreCoords *sc,
size_t depth, unsigned edge, unsigned *outedge);
/* For extracting the point coordinates */
typedef struct Coord {
int c1, cr3; /* coefficients of 1 and sqrt(3) respectively */
} Coord;
static inline Coord point_x(Point p)
{
Coord x = { 2 * p.coeffs[0] + p.coeffs[2], p.coeffs[1] };
return x;
}
static inline Coord point_y(Point p)
{
Coord y = { 2 * p.coeffs[3] + p.coeffs[1], p.coeffs[2] };
return y;
}
static inline int coord_sign(Coord x)
{
if (x.c1 == 0 && x.cr3 == 0)
return 0;
if (x.c1 >= 0 && x.cr3 >= 0)
return +1;
if (x.c1 <= 0 && x.cr3 <= 0)
return -1;
if (x.c1 * x.c1 > 3 * x.cr3 * x.cr3)
return x.c1 < 0 ? -1 : +1;
else
return x.cr3 < 0 ? -1 : +1;
}
static inline int coord_cmp(Coord a, Coord b)
{
Coord diff;
diff.c1 = a.c1 - b.c1;
diff.cr3 = a.cr3 - b.cr3;
return coord_sign(diff);
}

1220
spectre-tables-auto.h Normal file
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File diff suppressed because it is too large Load Diff

160
spectre-tables-manual.h Normal file
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@ -0,0 +1,160 @@
/*
* Handwritten data tables for the Spectre tiling.
*
* This file is used by both the final tiling generator in spectre.c,
* and by spectre-gen.c which auto-generates further tables to go with
* these.
*/
/*
* We generate the Spectre tiling based on the substitution system of
* 9 types of marked hexagon shown in the paper.
*
* The substitution expands each hexagon into 8 others, except for the
* G hex which expands to only seven. The layout, numbered with the
* indices we use in the arrays here, is as follows:
*
* 0 1
* 2 3
* 4 5 6
* 7
*
* That is: the hexes are oriented with a pair of vertical edges.
* Hexes 0 and 1 are horizontally adjacent; 2 and 3 are adjacent on
* the next row, with 3 nestling between 0 and 1; 4,5,6 are on the
* third row with 5 between 2 and 3; and 7 is by itself on a fourth
* row, between 5 and 6. In the expansion of the G hex, #7 is the
* missing one, so its indices are still consecutive from 0.
*
* These arrays list the type of each child hex. The hexes also have
* orientations, but those aren't listed here, because only
* spectre-gen needs to know them - by the time it's finished
* autogenerating transition tables, the orientations are baked into
* those and don't need to be consulted separately.
*/
static const Hex subhexes_G[] = {
HEX_F,
HEX_X,
HEX_G,
HEX_S,
HEX_P,
HEX_D,
HEX_J,
/* hex #7 is not present for this tile */
};
static const Hex subhexes_D[] = {
HEX_F,
HEX_P,
HEX_G,
HEX_S,
HEX_X,
HEX_D,
HEX_F,
HEX_X,
};
static const Hex subhexes_J[] = {
HEX_F,
HEX_P,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_P,
};
static const Hex subhexes_L[] = {
HEX_F,
HEX_P,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_X,
};
static const Hex subhexes_X[] = {
HEX_F,
HEX_Y,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_P,
};
static const Hex subhexes_P[] = {
HEX_F,
HEX_Y,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_X,
};
static const Hex subhexes_S[] = {
HEX_L,
HEX_P,
HEX_G,
HEX_S,
HEX_X,
HEX_D,
HEX_F,
HEX_X,
};
static const Hex subhexes_F[] = {
HEX_F,
HEX_P,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_Y,
};
static const Hex subhexes_Y[] = {
HEX_F,
HEX_Y,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_Y,
};
/*
* Shape of the Spectre itself.
*
* Vertex 0 is taken to be at the top of the Spectre's "head"; vertex
* 1 is the adjacent vertex, in the direction of the shorter edge of
* its "cloak".
*
* This array indicates how far to turn at each vertex, in 1/12 turns.
* All edges are the same length (counting the double-edge as two
* edges, which we do).
*/
static const int spectre_angles[14] = {
-3, -2, 3, -2, -3, 2, -3, 2, -3, -2, 0, -2, 3, -2,
};
/*
* The relative probabilities of the nine hex types, in the limit, as
* the expansion process is iterated more and more times. Used to
* choose the initial hex coordinates as if the segment of tiling came
* from the limiting distribution across the whole plane.
*
* This is obtained by finding the matrix that says how many hexes of
* each type are expanded from each starting hex, and taking the
* eigenvector that goes with its limiting eigenvalue.
*/
#define PROB_G 10000000 /* 1 */
#define PROB_D 10000000 /* 1 */
#define PROB_J 1270167 /* 4 - sqrt(15) */
#define PROB_L 1270167 /* 4 - sqrt(15) */
#define PROB_X 7459667 /* 2 sqrt(15) - 7 */
#define PROB_P 7459667 /* 2 sqrt(15) - 7 */
#define PROB_S 10000000 /* 1 */
#define PROB_F 17459667 /* 2 sqrt(15) - 6 */
#define PROB_Y 13810500 /* 13 - 3 sqrt(15) */

594
spectre.c Normal file
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@ -0,0 +1,594 @@
/*
* Code to generate patches of the aperiodic 'spectre' tiling
* discovered in 2023.
*/
#include <assert.h>
#include <string.h>
#include "puzzles.h"
#include "tree234.h"
#include "spectre-internal.h"
#include "spectre-tables-manual.h"
#include "spectre-tables-auto.h"
static const char *const letters =
#define STRINGIFY(x) #x
HEX_LETTERS(STRINGIFY)
#undef STRINGIFY
;
bool spectre_valid_hex_letter(char letter)
{
return strchr(letters, letter) != NULL;
}
static Hex hex_from_letter(char letter)
{
char buf[2];
buf[0] = letter;
buf[1] = '\0';
return strcspn(letters, buf);
}
static Hex hex_to_letter(unsigned char letter)
{
return letters[letter];
}
struct HexData {
const struct MapEntry *hexmap, *hexin, *specmap, *specin;
const struct MapEdge *hexedges, *specedges;
const Hex *subhexes;
const struct Possibility *poss;
size_t nposs;
};
static const struct HexData hexdata[] = {
#define HEXDATA_ENTRY(x) { hexmap_##x, hexin_##x, specmap_##x, \
specin_##x, hexedges_##x, specedges_##x, subhexes_##x, \
poss_##x, lenof(poss_##x) },
HEX_LETTERS(HEXDATA_ENTRY)
#undef HEXDATA_ENTRY
};
static const struct Possibility *choose_poss(
random_state *rs, const struct Possibility *poss, size_t nposs)
{
/*
* If we needed to do this _efficiently_, we'd rewrite all those
* tables above as cumulative frequency tables and use binary
* search. But this happens about log n times in a grid of area n,
* so it hardly matters, and it's easier to keep the tables
* legible.
*/
unsigned long limit = 0, value;
size_t i;
for (i = 0; i < nposs; i++)
limit += poss[i].prob;
value = random_upto(rs, limit);
for (i = 0; i+1 < nposs; i++) {
if (value < poss[i].prob)
return &poss[i];
value -= poss[i].prob;
}
assert(i == nposs - 1);
assert(value < poss[i].prob);
return &poss[i];
}
SpectreCoords *spectre_coords_new(void)
{
SpectreCoords *sc = snew(SpectreCoords);
sc->nc = sc->csize = 0;
sc->c = NULL;
return sc;
}
void spectre_coords_free(SpectreCoords *sc)
{
if (sc) {
sfree(sc->c);
sfree(sc);
}
}
void spectre_coords_make_space(SpectreCoords *sc, size_t size)
{
if (sc->csize < size) {
sc->csize = sc->csize * 5 / 4 + 16;
if (sc->csize < size)
sc->csize = size;
sc->c = sresize(sc->c, sc->csize, HexCoord);
}
}
SpectreCoords *spectre_coords_copy(SpectreCoords *sc_in)
{
SpectreCoords *sc_out = spectre_coords_new();
spectre_coords_make_space(sc_out, sc_in->nc);
memcpy(sc_out->c, sc_in->c, sc_in->nc * sizeof(*sc_out->c));
sc_out->nc = sc_in->nc;
sc_out->index = sc_in->index;
sc_out->hex_colour = sc_in->hex_colour;
sc_out->prev_hex_colour = sc_in->prev_hex_colour;
sc_out->incoming_hex_edge = sc_in->incoming_hex_edge;
return sc_out;
}
void spectre_place(Spectre *spec, Point u, Point v, int index_of_u)
{
size_t i;
Point disp;
/* Vector from u to v */
disp = point_sub(v, u);
for (i = 0; i < 14; i++) {
spec->vertices[(i + index_of_u) % 14] = u;
u = point_add(u, disp);
disp = point_mul(disp, point_rot(
spectre_angles[(i + 1 + index_of_u) % 14]));
}
}
static Spectre *spectre_initial(Point u, Point v, int index_of_u,
SpectreCoords *sc)
{
Spectre *spec = snew(Spectre);
spectre_place(spec, u, v, index_of_u);
spec->sc = spectre_coords_copy(sc);
return spec;
}
static Spectre *spectre_adjacent(
SpectreContext *ctx, const Spectre *src_spec, unsigned src_edge)
{
unsigned dst_edge;
Spectre *dst_spec = snew(Spectre);
dst_spec->sc = spectre_coords_copy(src_spec->sc);
spectrectx_step(ctx, dst_spec->sc, src_edge, &dst_edge);
spectre_place(dst_spec, src_spec->vertices[(src_edge+1) % 14],
src_spec->vertices[src_edge], dst_edge);
return dst_spec;
}
static int spectre_cmp(void *av, void *bv)
{
Spectre *a = (Spectre *)av, *b = (Spectre *)bv;
size_t i, j;
/* We should only ever need to compare the first two vertices of
* any Spectre, because those force the rest */
for (i = 0; i < 2; i++) {
for (j = 0; j < 4; j++) {
int ac = a->vertices[i].coeffs[j], bc = b->vertices[i].coeffs[j];
if (ac < bc)
return -1;
if (ac > bc)
return +1;
}
}
return 0;
}
static void spectre_free(Spectre *spec)
{
spectre_coords_free(spec->sc);
sfree(spec);
}
static void spectrectx_start_vertices(SpectreContext *ctx, int orientation)
{
Point minus_sqrt3 = point_add(point_rot(5), point_rot(-5));
Point basicedge = point_mul(point_add(point_rot(0), point_rot(-3)),
point_rot(orientation));
Point diagonal = point_add(basicedge, point_mul(basicedge, point_rot(-3)));
ctx->start_vertices[0] = point_mul(diagonal, minus_sqrt3);
ctx->start_vertices[1] = point_add(ctx->start_vertices[0], basicedge);
ctx->orientation = orientation;
}
void spectrectx_init_random(SpectreContext *ctx, random_state *rs)
{
const struct Possibility *poss;
ctx->rs = rs;
ctx->must_free_rs = false;
ctx->prototype = spectre_coords_new();
spectre_coords_make_space(ctx->prototype, 1);
poss = choose_poss(rs, poss_spectre, lenof(poss_spectre));
ctx->prototype->index = poss->lo;
ctx->prototype->c[0].type = poss->hi;
ctx->prototype->c[0].index = -1;
ctx->prototype->nc = 1;
/*
* Choose a random orientation for the starting Spectre.
*
* The obvious thing is to choose the orientation out of all 12
* possibilities. But we do it a more complicated way.
*
* The Spectres in a tiling can be partitioned into two
* equivalence classes under the relation 'orientation differs by
* a multiple of 1/6 turn'. One class is much more common than the
* other class: the 'odd'-orientation Spectres occur rarely (very
* like the rare reflected hats in the hats tiling).
*
* I think it's nicer to arrange that there's a consistent
* orientation for the _common_ class of Spectres, so that there
* will always be plenty of them in the 'canonical' orientation
* with the head upwards. So if the starting Spectre is in the
* even class, we pick an even orientation for it, and if it's in
* the odd class, we pick an odd orientation.
*
* An odd-class Spectre is easy to identify from SpectreCoords.
* They're precisely the ones expanded from a G hex with index 1,
* which means they're the ones that have index 1 _at all_.
*/
spectrectx_start_vertices(ctx, random_upto(rs, 6) * 2 +
ctx->prototype->index);
/* Initialiise the colouring fields deterministically but unhelpfully.
* spectre-test will set these up properly if it wants to */
ctx->prototype->hex_colour = 0;
ctx->prototype->prev_hex_colour = 0;
ctx->prototype->incoming_hex_edge = 0;
}
void spectrectx_init_from_params(
SpectreContext *ctx, const struct SpectrePatchParams *ps)
{
size_t i;
ctx->rs = NULL;
ctx->must_free_rs = false;
ctx->prototype = spectre_coords_new();
spectre_coords_make_space(ctx->prototype, ps->ncoords);
ctx->prototype->index = ps->coords[0];
for (i = 1; i < ps->ncoords; i++)
ctx->prototype->c[i-1].index = ps->coords[i];
ctx->prototype->c[ps->ncoords-1].index = -1;
ctx->prototype->nc = ps->ncoords;
ctx->prototype->c[ps->ncoords-1].type = hex_from_letter(ps->final_hex);
for (i = ps->ncoords - 1; i-- > 0 ;) {
const struct HexData *h = &hexdata[ctx->prototype->c[i+1].type];
ctx->prototype->c[i].type = h->subhexes[ctx->prototype->c[i].index];
}
spectrectx_start_vertices(ctx, ps->orientation);
ctx->prototype->hex_colour = 0;
ctx->prototype->prev_hex_colour = 0;
ctx->prototype->incoming_hex_edge = 0;
}
void spectrectx_cleanup(SpectreContext *ctx)
{
if (ctx->must_free_rs)
random_free(ctx->rs);
spectre_coords_free(ctx->prototype);
}
SpectreCoords *spectrectx_initial_coords(SpectreContext *ctx)
{
return spectre_coords_copy(ctx->prototype);
}
/*
* Extend sc until it has at least n coordinates in, by copying from
* ctx->prototype if needed, and extending ctx->prototype if needed in
* order to do that.
*/
void spectrectx_extend_coords(SpectreContext *ctx, SpectreCoords *sc, size_t n)
{
if (ctx->prototype->nc < n) {
spectre_coords_make_space(ctx->prototype, n);
while (ctx->prototype->nc < n) {
const struct HexData *h = &hexdata[
ctx->prototype->c[ctx->prototype->nc-1].type];
const struct Possibility *poss;
if (!ctx->rs) {
/*
* If there's no random_state available, it must be
* because we were given an explicit coordinate string
* and ran off the end of it.
*
* The obvious thing to do here would be to make up an
* answer non-randomly. But in fact there's a danger
* that this leads to endless recursion within a
* single coordinate step, if the hex edge we were
* trying to traverse turns into another copy of
* itself at the higher level. That happened in early
* testing before I put the random_state in at all.
*
* To avoid that risk, in this situation - which
* _shouldn't_ come up at all in sensibly play - we
* make up a random_state, and free it when the
* context goes away.
*/
ctx->rs = random_new("dummy", 5);
ctx->must_free_rs = true;
}
poss = choose_poss(ctx->rs, h->poss, h->nposs);
ctx->prototype->c[ctx->prototype->nc-1].index = poss->lo;
ctx->prototype->c[ctx->prototype->nc].type = poss->hi;
ctx->prototype->c[ctx->prototype->nc].index = -1;
ctx->prototype->nc++;
}
}
spectre_coords_make_space(sc, n);
while (sc->nc < n) {
assert(sc->c[sc->nc - 1].index == -1);
assert(sc->c[sc->nc - 1].type == ctx->prototype->c[sc->nc - 1].type);
sc->c[sc->nc - 1].index = ctx->prototype->c[sc->nc - 1].index;
sc->c[sc->nc].index = -1;
sc->c[sc->nc].type = ctx->prototype->c[sc->nc].type;
sc->nc++;
}
}
void spectrectx_step_hex(SpectreContext *ctx, SpectreCoords *sc,
size_t depth, unsigned edge, unsigned *outedge)
{
const struct HexData *h;
const struct MapEntry *m;
spectrectx_extend_coords(ctx, sc, depth+2);
assert(0 <= sc->c[depth].index);
assert(sc->c[depth].index < num_subhexes(sc->c[depth].type));
assert(0 <= edge);
assert(edge < 6);
h = &hexdata[sc->c[depth+1].type];
m = &h->hexmap[6 * sc->c[depth].index + edge];
if (!m->internal) {
unsigned recedge;
const struct MapEdge *me;
spectrectx_step_hex(ctx, sc, depth+1, m->hi, &recedge);
assert(recedge < 6);
h = &hexdata[sc->c[depth+1].type];
me = &h->hexedges[recedge];
assert(m->lo < me->len);
m = &h->hexin[me->startindex + me->len - 1 - m->lo];
assert(m->internal);
}
sc->c[depth].index = m->hi;
sc->c[depth].type = h->subhexes[sc->c[depth].index];
*outedge = m->lo;
if (depth == 0) {
/*
* Update the colouring fields to track the colour of the new
* hexagon.
*/
unsigned char new_hex_colour;
if (!((edge ^ sc->incoming_hex_edge) & 1)) {
/* We're going out via the same parity of edge we came in
* on, so the new hex colour is the same as the previous
* one. */
new_hex_colour = sc->prev_hex_colour;
} else {
/* We're going out via the opposite parity of edge, so the
* new colour is the one of {0,1,2} that is neither this
* _nor_ the previous colour. */
new_hex_colour = 0+1+2 - sc->hex_colour - sc->prev_hex_colour;
}
sc->prev_hex_colour = sc->hex_colour;
sc->hex_colour = new_hex_colour;
sc->incoming_hex_edge = m->lo;
}
}
void spectrectx_step(SpectreContext *ctx, SpectreCoords *sc,
unsigned edge, unsigned *outedge)
{
const struct HexData *h;
const struct MapEntry *m;
assert(0 <= sc->index);
assert(sc->index < num_spectres(sc->c[0].type));
assert(0 <= edge);
assert(edge < 14);
h = &hexdata[sc->c[0].type];
m = &h->specmap[14 * sc->index + edge];
while (!m->internal) {
unsigned recedge;
const struct MapEdge *me;
spectrectx_step_hex(ctx, sc, 0, m->hi, &recedge);
assert(recedge < 6);
h = &hexdata[sc->c[0].type];
me = &h->specedges[recedge];
assert(m->lo < me->len);
m = &h->specin[me->startindex + me->len - 1 - m->lo];
}
sc->index = m->hi;
*outedge = m->lo;
}
void spectrectx_generate(SpectreContext *ctx,
bool (*callback)(void *cbctx, const Spectre *spec),
void *cbctx)
{
tree234 *placed = newtree234(spectre_cmp);
Spectre *qhead = NULL, *qtail = NULL;
{
SpectreCoords *sc = spectrectx_initial_coords(ctx);
Spectre *spec = spectre_initial(ctx->start_vertices[0],
ctx->start_vertices[1], 0, sc);
spectre_coords_free(sc);
add234(placed, spec);
spec->next = NULL;
if (callback(cbctx, spec))
qhead = qtail = spec;
}
while (qhead) {
unsigned edge;
Spectre *spec = qhead;
for (edge = 0; edge < 14; edge++) {
Spectre *new_spec;
new_spec = spectre_adjacent(ctx, spec, edge);
if (find234(placed, new_spec, NULL)) {
spectre_free(new_spec);
continue;
}
if (!callback(cbctx, new_spec)) {
spectre_free(new_spec);
continue;
}
add234(placed, new_spec);
qtail->next = new_spec;
qtail = new_spec;
new_spec->next = NULL;
}
qhead = qhead->next;
}
{
Spectre *spec;
while ((spec = delpos234(placed, 0)) != NULL)
spectre_free(spec);
freetree234(placed);
}
}
const char *spectre_tiling_params_invalid(
const struct SpectrePatchParams *params)
{
size_t i;
Hex h;
if (params->ncoords == 0)
return "expected at least one numeric coordinate";
if (!spectre_valid_hex_letter(params->final_hex))
return "invalid final hexagon type";
h = hex_from_letter(params->final_hex);
for (i = params->ncoords; i-- > 0 ;) {
unsigned limit = (i == 0) ? num_spectres(h) : num_subhexes(h);
if (params->coords[i] >= limit)
return "coordinate out of range";
if (i > 0)
h = hexdata[h].subhexes[params->coords[i]];
}
return NULL;
}
struct SpectreCallbackContext {
int xoff, yoff;
Coord xmin, xmax, ymin, ymax;
spectre_tile_callback_fn external_cb;
void *external_cbctx;
};
static bool spectre_internal_callback(void *vctx, const Spectre *spec)
{
struct SpectreCallbackContext *ctx = (struct SpectreCallbackContext *)vctx;
size_t i;
int output_coords[4*14];
for (i = 0; i < 14; i++) {
Point p = spec->vertices[i];
Coord x = point_x(p), y = point_y(p);
if (coord_cmp(x, ctx->xmin) < 0 || coord_cmp(x, ctx->xmax) > 0 ||
coord_cmp(y, ctx->ymin) < 0 || coord_cmp(y, ctx->ymax) > 0)
return false;
output_coords[4*i + 0] = ctx->xoff + x.c1;
output_coords[4*i + 1] = x.cr3;
output_coords[4*i + 2] = ctx->yoff - y.c1;
output_coords[4*i + 3] = -y.cr3;
}
if (ctx->external_cb)
ctx->external_cb(ctx->external_cbctx, output_coords);
return true;
}
static void spectre_set_bounds(struct SpectreCallbackContext *cbctx,
int w, int h)
{
cbctx->xoff = w/2;
cbctx->yoff = h/2;
cbctx->xmin.c1 = -cbctx->xoff;
cbctx->xmax.c1 = -cbctx->xoff + w;
cbctx->ymin.c1 = cbctx->yoff - h;
cbctx->ymax.c1 = cbctx->yoff;
cbctx->xmin.cr3 = 0;
cbctx->xmax.cr3 = 0;
cbctx->ymin.cr3 = 0;
cbctx->ymax.cr3 = 0;
}
void spectre_tiling_randomise(struct SpectrePatchParams *ps, int w, int h,
random_state *rs)
{
SpectreContext ctx[1];
struct SpectreCallbackContext cbctx[1];
size_t i;
spectre_set_bounds(cbctx, w, h);
cbctx->external_cb = NULL;
cbctx->external_cbctx = NULL;
spectrectx_init_random(ctx, rs);
spectrectx_generate(ctx, spectre_internal_callback, cbctx);
ps->orientation = ctx->orientation;
ps->ncoords = ctx->prototype->nc;
ps->coords = snewn(ps->ncoords, unsigned char);
ps->coords[0] = ctx->prototype->index;
for (i = 1; i < ps->ncoords; i++)
ps->coords[i] = ctx->prototype->c[i-1].index;
ps->final_hex = hex_to_letter(ctx->prototype->c[ps->ncoords-1].type);
spectrectx_cleanup(ctx);
}
void spectre_tiling_generate(
const struct SpectrePatchParams *params, int w, int h,
spectre_tile_callback_fn external_cb, void *external_cbctx)
{
SpectreContext ctx[1];
struct SpectreCallbackContext cbctx[1];
spectre_set_bounds(cbctx, w, h);
cbctx->external_cb = external_cb;
cbctx->external_cbctx = external_cbctx;
spectrectx_init_from_params(ctx, params);
spectrectx_generate(ctx, spectre_internal_callback, cbctx);
spectrectx_cleanup(ctx);
}

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#ifndef PUZZLES_SPECTRE_H
#define PUZZLES_SPECTRE_H
struct SpectrePatchParams {
/*
* A patch of Spectre tiling is identified by giving
*
* - the coordinates of the central Spectre, using a
* combinatorial coordinate system similar to the Hat tiling in
* hat.h
*
* - the orientation of that Spectre, as a number from 0 to 11 (a
* multiple of 30 degrees), with 0 representing the 'head' of
* the Spectre facing upwards, and numbers counting
* anticlockwise.
*
* Coordinates are a sequence of small non-negative integers. The
* valid range for each coordinate depends on the next coordinate,
* or on final_hex if it's the last one in the list. The largest
* valid range is {0,...,7}.
*
* 'final_hex' is one of the letters GDJLXPSFY.
* spectre_valid_hex_letter() will check that.
*/
int orientation;
size_t ncoords;
unsigned char *coords;
char final_hex;
};
bool spectre_valid_hex_letter(char c);
/*
* Fill in SpectrePatchParams with a randomly selected set of
* coordinates, in enough detail to generate a patch of tiling filling
* a w x h area. The unit of measurement is 1/(2*sqrt(2)) of a Spectre
* edge, i.e. such that a single Spectre edge at 45 degrees would
* correspond to the vector (2,2).
*
* The 'coords' field of the structure will be filled in with a new
* dynamically allocated array. Any previous pointer in that field
* will be overwritten.
*/
void spectre_tiling_randomise(struct SpectrePatchParams *params, int w, int h,
random_state *rs);
/*
* Validate a SpectrePatchParams to ensure it contains no illegal
* coordinates. Returns NULL if it's acceptable, or an error string if
* not.
*/
const char *spectre_tiling_params_invalid(
const struct SpectrePatchParams *params);
/*
* Generate the actual set of Spectre tiles from a SpectrePatchParams,
* passing each one to a callback. The callback receives the vertices
* of each point, in the form of an array of 4*14 integers. Each
* vertex is represented by four consecutive integers in this array,
* with the first two giving the x coordinate and the last two the y
* coordinate. Each pair of integers a,b represent a single coordinate
* whose value is a + b*sqrt(3). The unit of measurement is as above.
*/
typedef void (*spectre_tile_callback_fn)(void *ctx, const int *coords);
#define SPECTRE_NVERTICES 14
void spectre_tiling_generate(
const struct SpectrePatchParams *params, int w, int h,
spectre_tile_callback_fn cb, void *cbctx);
#endif