puzzles/hat-internal.h

/*
 * Internal definitions for the hat.c tiling generator, shared between
 * hat.c itself and hat-test.c.
 */

#include "puzzles.h"

/*
 * Coordinate system:
 *
 * The output of this code lives on the tiling known to grid.c as
 * 'Kites', which can be viewed as a tiling of hexagons each of which
 * is subdivided into six kites sharing their pointy vertex, or
 * (equivalently) a tiling of equilateral triangles each subdivided
 * into three kits sharing their blunt vertex.
 *
 * We express coordinates in this system relative to the basis (1, r)
 * where r = (1 + sqrt(3)i) / 2 is a primitive 6th root of unity. This
 * gives us a system in which two integer coordinates can address any
 * grid point, provided we scale up so that the side length of the
 * equilateral triangles in the tiling is 6.
 */

typedef struct Point {
    int x, y;                          /* represents x + yr */
} Point;

static inline Point pointscale(int scale, Point a)
{
    Point r = { scale * a.x, scale * a.y };
    return r;
}

static inline Point pointadd(Point a, Point b)
{
    Point r = { a.x + b.x, a.y + b.y };
    return r;
}

/*
 * We identify a single kite by the coordinates of its four vertices.
 * This allows us to construct the coordinates of an adjacent kite by
 * taking affine transformations of the original kite's vertices.
 *
 * This is a useful way to do it because it means that if you reflect
 * the kite (by swapping its left and right vertices) then these
 * transformations also perform in a reflected way. This will be
 * useful in the code below that outputs the coordinates of each hat,
 * because this way it can work by walking around its 8 kites using a
 * fixed set of steps, and if the hat is reflected, then we just
 * reflect the starting kite before doing that, and everything still
 * works.
 */

typedef struct Kite {
    Point centre, left, right, outer;
} Kite;

static inline Kite kite_left(Kite k)
{
    Kite r;
    r.centre = k.centre;
    r.right = k.left;
    r.outer = pointadd(pointscale(2, k.left), pointscale(-1, k.outer));
    r.left = pointadd(pointadd(k.centre, k.left), pointscale(-1, k.right));
    return r;
}

static inline Kite kite_right(Kite k)
{
    Kite r;
    r.centre = k.centre;
    r.left = k.right;
    r.outer = pointadd(pointscale(2, k.right), pointscale(-1, k.outer));
    r.right = pointadd(pointadd(k.centre, k.right), pointscale(-1, k.left));
    return r;
}

static inline Kite kite_forward_left(Kite k)
{
    Kite r;
    r.outer = k.outer;
    r.right = k.left;
    r.centre = pointadd(pointscale(2, k.left), pointscale(-1, k.centre));
    r.left = pointadd(pointadd(k.right, k.left), pointscale(-1, k.centre));
    return r;
}

static inline Kite kite_forward_right(Kite k)
{
    Kite r;
    r.outer = k.outer;
    r.left = k.right;
    r.centre = pointadd(pointscale(2, k.right), pointscale(-1, k.centre));
    r.right = pointadd(pointadd(k.left, k.right), pointscale(-1, k.centre));
    return r;
}

typedef enum KiteStep { KS_LEFT, KS_RIGHT, KS_F_LEFT, KS_F_RIGHT } KiteStep;

static inline Kite kite_step(Kite k, KiteStep step)
{
    switch (step) {
      case KS_LEFT: return kite_left(k);
      case KS_RIGHT: return kite_right(k);
      case KS_F_LEFT: return kite_forward_left(k);
      default /* case KS_F_RIGHT */: return kite_forward_right(k);
    }
}

/*
 * Functiond to enumerate the kites in a rectangular region, in a
 * serpentine-raster fashion so that every kite delivered shares an
 * edge with a recent previous one.
 */
#define KE_NKEEP 3
typedef struct KiteEnum {
    /* Fields private to the enumerator */
    int state;
    int x, y, w, h;
    unsigned curr_index;

    /* Fields the client can legitimately read out */
    Kite *curr;
    Kite recent[KE_NKEEP];
    unsigned last_index;
    KiteStep last_step; /* step that got curr from recent[last_index] */
} KiteEnum;
void hat_kiteenum_first(KiteEnum *s, int w, int h);
bool hat_kiteenum_next(KiteEnum *s);

/*
 * Assorted useful definitions.
 */
typedef enum TileType { TT_H, TT_T, TT_P, TT_F, TT_KITE, TT_HAT } TileType;
static const char tilechars[] = "HTPF";

#define HAT_KITES 8     /* number of kites in a hat */
#define MT_MAXEXPAND 13 /* largest number of metatiles in any expansion */

/*
 * Definitions for the autogenerated hat-tables.h header file that
 * defines all the lookup tables.
 */
typedef struct KitemapEntry {
    int kite, hat, meta;               /* all -1 if impossible */
} KitemapEntry;

typedef struct MetamapEntry {
    int meta, meta2;
} MetamapEntry;

static inline size_t kitemap_index(KiteStep step, unsigned kite,
                                   unsigned hat, unsigned meta)
{
    return step + 4 * (kite + 8 * (hat + 4 * meta));
}

static inline size_t metamap_index(unsigned meta, unsigned meta2)
{
    return meta2 * MT_MAXEXPAND + meta;
}

/*
 * Coordinate system for tracking kites within a randomly selected
 * part of the recursively expanded hat tiling.
 *
 * HatCoords will store an array of HatCoord, in little-endian
 * arrangement. So hc->c[0] will always have type TT_KITE and index a
 * single kite within a hat; hc->c[1] will have type TT_HAT and index
 * a hat within a first-order metatile; hc->c[2] will be the smallest
 * metatile containing this hat, and hc->c[3, 4, 5, ...] will be
 * higher-order metatiles as needed.
 *
 * The last coordinate stored, hc->c[hc->nc-1], will have a tile 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 HatCoord {
    int index; /* index within that tile, or -1 if not yet known */
    TileType type;  /* type of this tile */
} HatCoord;

typedef struct HatCoords {
    HatCoord *c;
    size_t nc, csize;
} HatCoords;

HatCoords *hat_coords_new(void);
void hat_coords_free(HatCoords *hc);
void hat_coords_make_space(HatCoords *hc, size_t size);
HatCoords *hat_coords_copy(HatCoords *hc_in);

#ifdef HAT_COORDS_DEBUG
static inline void hat_coords_debug(const char *prefix, HatCoords *hc,
                                    const char *suffix)
{
    const char *sep = "";
    static const char *const types[] = {"H","T","P","F","kite","hat"};

    fputs(prefix, stderr);
    for (size_t i = 0; i < hc->nc; i++) {
        fprintf(stderr, "%s %s ", sep, types[hc->c[i].type]);
        sep = " .";
        if (hc->c[i].index == -1)
            fputs("?", stderr);
        else
            fprintf(stderr, "%d", hc->c[i].index);
    }
    fputs(suffix, stderr);
}
#else
#define hat_coords_debug(p,c,s) ((void)0)
#endif

/*
 * HatContext is the shared context of a whole run of the algorithm.
 * Its 'prototype' HatCoords object represents the coordinates of the
 * starting kite, and is extended as necessary; any other HatCoord
 * 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.
 *
 * (Of course another approach would be to reject grid descriptions
 * that didn't define enough coordinates! But that would involve a
 * whole extra iteration over the whole grid region just for
 * validation, and that seems like more timewasting than really
 * needed. So we tolerate short descriptions, and do something
 * deterministic with them.)
 */

typedef struct HatContext {
    random_state *rs;
    HatCoords *prototype;
} HatContext;

void hatctx_init_random(HatContext *ctx, random_state *rs);
void hatctx_cleanup(HatContext *ctx);
HatCoords *hatctx_initial_coords(HatContext *ctx);
void hatctx_extend_coords(HatContext *ctx, HatCoords *hc, size_t n);
HatCoords *hatctx_step(HatContext *ctx, HatCoords *hc_in, KiteStep step);

/*
 * Subroutine of hat_tiling_generate, called for each kite in the grid
 * as we iterate over it, to decide whether to generate an output hat
 * and pass it to the client. Exposed in this header file so that
 * hat-test can reuse it.
 *
 * We do this by starting from kite #0 of each hat, and tracing round
 * the boundary. If the whole boundary is within the caller's bounding
 * region, we return it; if it goes off the edge, we don't.
 *
 * (Of course, every hat we _do_ want to return will have all its
 * kites inside the rectangle, so its kite #0 will certainly be caught
 * by this iteration.)
 */

typedef void (*internal_hat_callback_fn)(void *ctx, Kite kite0, HatCoords *hc,
                                         int *coords);
void maybe_report_hat(int w, int h, Kite kite, HatCoords *hc,
                      internal_hat_callback_fn cb, void *cbctx);