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a33d9fad02
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.
595 lines
18 KiB
C
595 lines
18 KiB
C
/*
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* Code to generate patches of the aperiodic 'spectre' tiling
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* discovered in 2023.
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*/
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#include <assert.h>
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#include <string.h>
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#include "puzzles.h"
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#include "tree234.h"
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#include "spectre-internal.h"
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#include "spectre-tables-manual.h"
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#include "spectre-tables-auto.h"
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static const char *const letters =
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#define STRINGIFY(x) #x
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HEX_LETTERS(STRINGIFY)
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#undef STRINGIFY
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;
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bool spectre_valid_hex_letter(char letter)
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{
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return strchr(letters, letter) != NULL;
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}
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static Hex hex_from_letter(char letter)
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{
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char buf[2];
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buf[0] = letter;
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buf[1] = '\0';
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return strcspn(letters, buf);
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}
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static Hex hex_to_letter(unsigned char letter)
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{
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return letters[letter];
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}
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struct HexData {
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const struct MapEntry *hexmap, *hexin, *specmap, *specin;
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const struct MapEdge *hexedges, *specedges;
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const Hex *subhexes;
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const struct Possibility *poss;
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size_t nposs;
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};
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static const struct HexData hexdata[] = {
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#define HEXDATA_ENTRY(x) { hexmap_##x, hexin_##x, specmap_##x, \
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specin_##x, hexedges_##x, specedges_##x, subhexes_##x, \
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poss_##x, lenof(poss_##x) },
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HEX_LETTERS(HEXDATA_ENTRY)
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#undef HEXDATA_ENTRY
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};
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static const struct Possibility *choose_poss(
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random_state *rs, const struct Possibility *poss, size_t nposs)
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{
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/*
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* If we needed to do this _efficiently_, we'd rewrite all those
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* tables above as cumulative frequency tables and use binary
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* search. But this happens about log n times in a grid of area n,
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* so it hardly matters, and it's easier to keep the tables
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* legible.
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*/
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unsigned long limit = 0, value;
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size_t i;
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for (i = 0; i < nposs; i++)
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limit += poss[i].prob;
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value = random_upto(rs, limit);
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for (i = 0; i+1 < nposs; i++) {
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if (value < poss[i].prob)
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return &poss[i];
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value -= poss[i].prob;
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}
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assert(i == nposs - 1);
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assert(value < poss[i].prob);
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return &poss[i];
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}
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SpectreCoords *spectre_coords_new(void)
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{
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SpectreCoords *sc = snew(SpectreCoords);
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sc->nc = sc->csize = 0;
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sc->c = NULL;
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return sc;
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}
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void spectre_coords_free(SpectreCoords *sc)
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{
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if (sc) {
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sfree(sc->c);
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sfree(sc);
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}
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}
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void spectre_coords_make_space(SpectreCoords *sc, size_t size)
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{
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if (sc->csize < size) {
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sc->csize = sc->csize * 5 / 4 + 16;
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if (sc->csize < size)
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sc->csize = size;
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sc->c = sresize(sc->c, sc->csize, HexCoord);
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}
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}
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SpectreCoords *spectre_coords_copy(SpectreCoords *sc_in)
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{
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SpectreCoords *sc_out = spectre_coords_new();
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spectre_coords_make_space(sc_out, sc_in->nc);
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memcpy(sc_out->c, sc_in->c, sc_in->nc * sizeof(*sc_out->c));
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sc_out->nc = sc_in->nc;
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sc_out->index = sc_in->index;
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sc_out->hex_colour = sc_in->hex_colour;
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sc_out->prev_hex_colour = sc_in->prev_hex_colour;
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sc_out->incoming_hex_edge = sc_in->incoming_hex_edge;
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return sc_out;
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}
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void spectre_place(Spectre *spec, Point u, Point v, int index_of_u)
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{
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size_t i;
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Point disp;
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/* Vector from u to v */
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disp = point_sub(v, u);
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for (i = 0; i < 14; i++) {
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spec->vertices[(i + index_of_u) % 14] = u;
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u = point_add(u, disp);
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disp = point_mul(disp, point_rot(
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spectre_angles[(i + 1 + index_of_u) % 14]));
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}
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}
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static Spectre *spectre_initial(Point u, Point v, int index_of_u,
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SpectreCoords *sc)
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{
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Spectre *spec = snew(Spectre);
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spectre_place(spec, u, v, index_of_u);
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spec->sc = spectre_coords_copy(sc);
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return spec;
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}
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static Spectre *spectre_adjacent(
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SpectreContext *ctx, const Spectre *src_spec, unsigned src_edge)
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{
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unsigned dst_edge;
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Spectre *dst_spec = snew(Spectre);
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dst_spec->sc = spectre_coords_copy(src_spec->sc);
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spectrectx_step(ctx, dst_spec->sc, src_edge, &dst_edge);
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spectre_place(dst_spec, src_spec->vertices[(src_edge+1) % 14],
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src_spec->vertices[src_edge], dst_edge);
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return dst_spec;
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}
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static int spectre_cmp(void *av, void *bv)
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{
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Spectre *a = (Spectre *)av, *b = (Spectre *)bv;
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size_t i, j;
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/* We should only ever need to compare the first two vertices of
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* any Spectre, because those force the rest */
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for (i = 0; i < 2; i++) {
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for (j = 0; j < 4; j++) {
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int ac = a->vertices[i].coeffs[j], bc = b->vertices[i].coeffs[j];
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if (ac < bc)
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return -1;
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if (ac > bc)
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return +1;
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}
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}
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return 0;
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}
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static void spectre_free(Spectre *spec)
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{
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spectre_coords_free(spec->sc);
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sfree(spec);
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}
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static void spectrectx_start_vertices(SpectreContext *ctx, int orientation)
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{
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Point minus_sqrt3 = point_add(point_rot(5), point_rot(-5));
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Point basicedge = point_mul(point_add(point_rot(0), point_rot(-3)),
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point_rot(orientation));
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Point diagonal = point_add(basicedge, point_mul(basicedge, point_rot(-3)));
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ctx->start_vertices[0] = point_mul(diagonal, minus_sqrt3);
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ctx->start_vertices[1] = point_add(ctx->start_vertices[0], basicedge);
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ctx->orientation = orientation;
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}
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void spectrectx_init_random(SpectreContext *ctx, random_state *rs)
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{
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const struct Possibility *poss;
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ctx->rs = rs;
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ctx->must_free_rs = false;
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ctx->prototype = spectre_coords_new();
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spectre_coords_make_space(ctx->prototype, 1);
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poss = choose_poss(rs, poss_spectre, lenof(poss_spectre));
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ctx->prototype->index = poss->lo;
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ctx->prototype->c[0].type = poss->hi;
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ctx->prototype->c[0].index = -1;
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ctx->prototype->nc = 1;
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/*
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* Choose a random orientation for the starting Spectre.
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*
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* The obvious thing is to choose the orientation out of all 12
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* possibilities. But we do it a more complicated way.
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*
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* The Spectres in a tiling can be partitioned into two
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* equivalence classes under the relation 'orientation differs by
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* a multiple of 1/6 turn'. One class is much more common than the
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* other class: the 'odd'-orientation Spectres occur rarely (very
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* like the rare reflected hats in the hats tiling).
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*
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* I think it's nicer to arrange that there's a consistent
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* orientation for the _common_ class of Spectres, so that there
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* will always be plenty of them in the 'canonical' orientation
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* with the head upwards. So if the starting Spectre is in the
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* even class, we pick an even orientation for it, and if it's in
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* the odd class, we pick an odd orientation.
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*
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* An odd-class Spectre is easy to identify from SpectreCoords.
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* They're precisely the ones expanded from a G hex with index 1,
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* which means they're the ones that have index 1 _at all_.
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*/
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spectrectx_start_vertices(ctx, random_upto(rs, 6) * 2 +
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ctx->prototype->index);
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/* Initialiise the colouring fields deterministically but unhelpfully.
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* spectre-test will set these up properly if it wants to */
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ctx->prototype->hex_colour = 0;
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ctx->prototype->prev_hex_colour = 0;
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ctx->prototype->incoming_hex_edge = 0;
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}
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void spectrectx_init_from_params(
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SpectreContext *ctx, const struct SpectrePatchParams *ps)
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{
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size_t i;
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ctx->rs = NULL;
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ctx->must_free_rs = false;
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ctx->prototype = spectre_coords_new();
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spectre_coords_make_space(ctx->prototype, ps->ncoords);
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ctx->prototype->index = ps->coords[0];
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for (i = 1; i < ps->ncoords; i++)
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ctx->prototype->c[i-1].index = ps->coords[i];
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ctx->prototype->c[ps->ncoords-1].index = -1;
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ctx->prototype->nc = ps->ncoords;
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ctx->prototype->c[ps->ncoords-1].type = hex_from_letter(ps->final_hex);
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for (i = ps->ncoords - 1; i-- > 0 ;) {
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const struct HexData *h = &hexdata[ctx->prototype->c[i+1].type];
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ctx->prototype->c[i].type = h->subhexes[ctx->prototype->c[i].index];
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}
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spectrectx_start_vertices(ctx, ps->orientation);
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ctx->prototype->hex_colour = 0;
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ctx->prototype->prev_hex_colour = 0;
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ctx->prototype->incoming_hex_edge = 0;
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}
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void spectrectx_cleanup(SpectreContext *ctx)
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{
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if (ctx->must_free_rs)
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random_free(ctx->rs);
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spectre_coords_free(ctx->prototype);
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}
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SpectreCoords *spectrectx_initial_coords(SpectreContext *ctx)
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{
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return spectre_coords_copy(ctx->prototype);
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}
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/*
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* Extend sc until it has at least n coordinates in, by copying from
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* ctx->prototype if needed, and extending ctx->prototype if needed in
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* order to do that.
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*/
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void spectrectx_extend_coords(SpectreContext *ctx, SpectreCoords *sc, size_t n)
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{
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if (ctx->prototype->nc < n) {
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spectre_coords_make_space(ctx->prototype, n);
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while (ctx->prototype->nc < n) {
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const struct HexData *h = &hexdata[
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ctx->prototype->c[ctx->prototype->nc-1].type];
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const struct Possibility *poss;
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if (!ctx->rs) {
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/*
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* If there's no random_state available, it must be
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* because we were given an explicit coordinate string
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* and ran off the end of it.
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*
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* The obvious thing to do here would be to make up an
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* answer non-randomly. But in fact there's a danger
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* that this leads to endless recursion within a
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* single coordinate step, if the hex edge we were
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* trying to traverse turns into another copy of
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* itself at the higher level. That happened in early
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* testing before I put the random_state in at all.
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*
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* To avoid that risk, in this situation - which
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* _shouldn't_ come up at all in sensibly play - we
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* make up a random_state, and free it when the
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* context goes away.
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*/
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ctx->rs = random_new("dummy", 5);
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ctx->must_free_rs = true;
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}
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poss = choose_poss(ctx->rs, h->poss, h->nposs);
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ctx->prototype->c[ctx->prototype->nc-1].index = poss->lo;
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ctx->prototype->c[ctx->prototype->nc].type = poss->hi;
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ctx->prototype->c[ctx->prototype->nc].index = -1;
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ctx->prototype->nc++;
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}
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}
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spectre_coords_make_space(sc, n);
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while (sc->nc < n) {
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assert(sc->c[sc->nc - 1].index == -1);
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assert(sc->c[sc->nc - 1].type == ctx->prototype->c[sc->nc - 1].type);
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sc->c[sc->nc - 1].index = ctx->prototype->c[sc->nc - 1].index;
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sc->c[sc->nc].index = -1;
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sc->c[sc->nc].type = ctx->prototype->c[sc->nc].type;
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sc->nc++;
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}
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}
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void spectrectx_step_hex(SpectreContext *ctx, SpectreCoords *sc,
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size_t depth, unsigned edge, unsigned *outedge)
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{
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const struct HexData *h;
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const struct MapEntry *m;
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spectrectx_extend_coords(ctx, sc, depth+2);
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assert(0 <= sc->c[depth].index);
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assert(sc->c[depth].index < num_subhexes(sc->c[depth].type));
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assert(0 <= edge);
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assert(edge < 6);
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h = &hexdata[sc->c[depth+1].type];
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m = &h->hexmap[6 * sc->c[depth].index + edge];
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if (!m->internal) {
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unsigned recedge;
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const struct MapEdge *me;
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spectrectx_step_hex(ctx, sc, depth+1, m->hi, &recedge);
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assert(recedge < 6);
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h = &hexdata[sc->c[depth+1].type];
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me = &h->hexedges[recedge];
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assert(m->lo < me->len);
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m = &h->hexin[me->startindex + me->len - 1 - m->lo];
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assert(m->internal);
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}
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sc->c[depth].index = m->hi;
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sc->c[depth].type = h->subhexes[sc->c[depth].index];
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*outedge = m->lo;
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if (depth == 0) {
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/*
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* Update the colouring fields to track the colour of the new
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* hexagon.
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*/
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unsigned char new_hex_colour;
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if (!((edge ^ sc->incoming_hex_edge) & 1)) {
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/* We're going out via the same parity of edge we came in
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* on, so the new hex colour is the same as the previous
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* one. */
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new_hex_colour = sc->prev_hex_colour;
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} else {
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/* We're going out via the opposite parity of edge, so the
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* new colour is the one of {0,1,2} that is neither this
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* _nor_ the previous colour. */
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new_hex_colour = 0+1+2 - sc->hex_colour - sc->prev_hex_colour;
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}
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sc->prev_hex_colour = sc->hex_colour;
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sc->hex_colour = new_hex_colour;
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sc->incoming_hex_edge = m->lo;
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}
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}
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void spectrectx_step(SpectreContext *ctx, SpectreCoords *sc,
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unsigned edge, unsigned *outedge)
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{
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const struct HexData *h;
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const struct MapEntry *m;
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assert(0 <= sc->index);
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assert(sc->index < num_spectres(sc->c[0].type));
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assert(0 <= edge);
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assert(edge < 14);
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h = &hexdata[sc->c[0].type];
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m = &h->specmap[14 * sc->index + edge];
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while (!m->internal) {
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unsigned recedge;
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const struct MapEdge *me;
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spectrectx_step_hex(ctx, sc, 0, m->hi, &recedge);
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assert(recedge < 6);
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h = &hexdata[sc->c[0].type];
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me = &h->specedges[recedge];
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assert(m->lo < me->len);
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m = &h->specin[me->startindex + me->len - 1 - m->lo];
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}
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sc->index = m->hi;
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*outedge = m->lo;
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}
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void spectrectx_generate(SpectreContext *ctx,
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bool (*callback)(void *cbctx, const Spectre *spec),
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void *cbctx)
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{
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tree234 *placed = newtree234(spectre_cmp);
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Spectre *qhead = NULL, *qtail = NULL;
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{
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SpectreCoords *sc = spectrectx_initial_coords(ctx);
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Spectre *spec = spectre_initial(ctx->start_vertices[0],
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ctx->start_vertices[1], 0, sc);
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spectre_coords_free(sc);
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add234(placed, spec);
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spec->next = NULL;
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if (callback(cbctx, spec))
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qhead = qtail = spec;
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}
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while (qhead) {
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unsigned edge;
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Spectre *spec = qhead;
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for (edge = 0; edge < 14; edge++) {
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Spectre *new_spec;
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new_spec = spectre_adjacent(ctx, spec, edge);
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if (find234(placed, new_spec, NULL)) {
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spectre_free(new_spec);
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continue;
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}
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if (!callback(cbctx, new_spec)) {
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spectre_free(new_spec);
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continue;
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}
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add234(placed, new_spec);
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qtail->next = new_spec;
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qtail = new_spec;
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new_spec->next = NULL;
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}
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qhead = qhead->next;
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}
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{
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Spectre *spec;
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while ((spec = delpos234(placed, 0)) != NULL)
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spectre_free(spec);
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freetree234(placed);
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}
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}
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const char *spectre_tiling_params_invalid(
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const struct SpectrePatchParams *params)
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{
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size_t i;
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Hex h;
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if (params->ncoords == 0)
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return "expected at least one numeric coordinate";
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if (!spectre_valid_hex_letter(params->final_hex))
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return "invalid final hexagon type";
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h = hex_from_letter(params->final_hex);
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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);
|
|
}
|