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puzzles/grid.c
Simon Tatham 7f64f4a50e Sort out abs/fabs confusion. 
My Mac has just upgraded itself to include a version of clang which
warns if you use abs() on a floating-point value, or fabs() on an
integer. Fixed the two occurrences that came up in this build (and
which were actual build failures, because of -Werror), one in each
direction.

I think both were benign. The potentially dangerous one was using abs
in place of fabs in grid_find_incentre(), because that could actually
lose precision, but I think that function had plenty of precision to
spare (grid point separation being of the order of tens of pixels) so
nothing should have gone seriously wrong with the old code.
2015-04-10 07:58:26 +01:00

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/*
* (c) Lambros Lambrou 2008
*
* Code for working with general grids, which can be any planar graph
* with faces, edges and vertices (dots). Includes generators for a few
* types of grid, including square, hexagonal, triangular and others.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <ctype.h>
#include <math.h>
#include <float.h>
#include "puzzles.h"
#include "tree234.h"
#include "grid.h"
#include "penrose.h"
/* Debugging options */
/*
#define DEBUG_GRID
*/
/* ----------------------------------------------------------------------
* Deallocate or dereference a grid
*/
void grid_free(grid *g)
{
assert(g->refcount);
g->refcount--;
if (g->refcount == 0) {
int i;
for (i = 0; i < g->num_faces; i++) {
sfree(g->faces[i].dots);
sfree(g->faces[i].edges);
}
for (i = 0; i < g->num_dots; i++) {
sfree(g->dots[i].faces);
sfree(g->dots[i].edges);
}
sfree(g->faces);
sfree(g->edges);
sfree(g->dots);
sfree(g);
}
}
/* Used by the other grid generators. Create a brand new grid with nothing
* initialised (all lists are NULL) */
static grid *grid_empty(void)
{
grid *g = snew(grid);
g->faces = NULL;
g->edges = NULL;
g->dots = NULL;
g->num_faces = g->num_edges = g->num_dots = 0;
g->refcount = 1;
g->lowest_x = g->lowest_y = g->highest_x = g->highest_y = 0;
return g;
}
/* Helper function to calculate perpendicular distance from
* a point P to a line AB. A and B mustn't be equal here.
*
* Well-known formula for area A of a triangle:
* / 1 1 1 \
* 2A = determinant of matrix | px ax bx |
* \ py ay by /
*
* Also well-known: 2A = base * height
* = perpendicular distance * line-length.
*
* Combining gives: distance = determinant / line-length(a,b)
*/
static double point_line_distance(long px, long py,
long ax, long ay,
long bx, long by)
{
long det = ax*by - bx*ay + bx*py - px*by + px*ay - ax*py;
double len;
det = max(det, -det);
len = sqrt(SQ(ax - bx) + SQ(ay - by));
return det / len;
}
/* Determine nearest edge to where the user clicked.
* (x, y) is the clicked location, converted to grid coordinates.
* Returns the nearest edge, or NULL if no edge is reasonably
* near the position.
*
* Just judging edges by perpendicular distance is not quite right -
* the edge might be "off to one side". So we insist that the triangle
* with (x,y) has acute angles at the edge's dots.
*
* edge1
* *---------*------
* |
* | *(x,y)
* edge2 |
* | edge2 is OK, but edge1 is not, even though
* | edge1 is perpendicularly closer to (x,y)
* *
*
*/
grid_edge *grid_nearest_edge(grid *g, int x, int y)
{
grid_edge *best_edge;
double best_distance = 0;
int i;
best_edge = NULL;
for (i = 0; i < g->num_edges; i++) {
grid_edge *e = &g->edges[i];
long e2; /* squared length of edge */
long a2, b2; /* squared lengths of other sides */
double dist;
/* See if edge e is eligible - the triangle must have acute angles
* at the edge's dots.
* Pythagoras formula h^2 = a^2 + b^2 detects right-angles,
* so detect acute angles by testing for h^2 < a^2 + b^2 */
e2 = SQ((long)e->dot1->x - (long)e->dot2->x) + SQ((long)e->dot1->y - (long)e->dot2->y);
a2 = SQ((long)e->dot1->x - (long)x) + SQ((long)e->dot1->y - (long)y);
b2 = SQ((long)e->dot2->x - (long)x) + SQ((long)e->dot2->y - (long)y);
if (a2 >= e2 + b2) continue;
if (b2 >= e2 + a2) continue;
/* e is eligible so far. Now check the edge is reasonably close
* to where the user clicked. Don't want to toggle an edge if the
* click was way off the grid.
* There is room for experimentation here. We could check the
* perpendicular distance is within a certain fraction of the length
* of the edge. That amounts to testing a rectangular region around
* the edge.
* Alternatively, we could check that the angle at the point is obtuse.
* That would amount to testing a circular region with the edge as
* diameter. */
dist = point_line_distance((long)x, (long)y,
(long)e->dot1->x, (long)e->dot1->y,
(long)e->dot2->x, (long)e->dot2->y);
/* Is dist more than half edge length ? */
if (4 * SQ(dist) > e2)
continue;
if (best_edge == NULL || dist < best_distance) {
best_edge = e;
best_distance = dist;
}
}
return best_edge;
}
/* ----------------------------------------------------------------------
* Grid generation
*/
#ifdef SVG_GRID
#define SVG_DOTS 1
#define SVG_EDGES 2
#define SVG_FACES 4
#define FACE_COLOUR "red"
#define EDGE_COLOUR "blue"
#define DOT_COLOUR "black"
static void grid_output_svg(FILE *fp, grid *g, int which)
{
int i, j;
fprintf(fp,"\
<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n\
<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 20010904//EN\"\n\
\"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd\">\n\
\n\
<svg xmlns=\"http://www.w3.org/2000/svg\"\n\
xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n\n");
if (which & SVG_FACES) {
fprintf(fp, "<g>\n");
for (i = 0; i < g->num_faces; i++) {
grid_face *f = g->faces + i;
fprintf(fp, "<polygon points=\"");
for (j = 0; j < f->order; j++) {
grid_dot *d = f->dots[j];
fprintf(fp, "%s%d,%d", (j == 0) ? "" : " ",
d->x, d->y);
}
fprintf(fp, "\" style=\"fill: %s; fill-opacity: 0.2; stroke: %s\" />\n",
FACE_COLOUR, FACE_COLOUR);
}
fprintf(fp, "</g>\n");
}
if (which & SVG_EDGES) {
fprintf(fp, "<g>\n");
for (i = 0; i < g->num_edges; i++) {
grid_edge *e = g->edges + i;
grid_dot *d1 = e->dot1, *d2 = e->dot2;
fprintf(fp, "<line x1=\"%d\" y1=\"%d\" x2=\"%d\" y2=\"%d\" "
"style=\"stroke: %s\" />\n",
d1->x, d1->y, d2->x, d2->y, EDGE_COLOUR);
}
fprintf(fp, "</g>\n");
}
if (which & SVG_DOTS) {
fprintf(fp, "<g>\n");
for (i = 0; i < g->num_dots; i++) {
grid_dot *d = g->dots + i;
fprintf(fp, "<ellipse cx=\"%d\" cy=\"%d\" rx=\"%d\" ry=\"%d\" fill=\"%s\" />",
d->x, d->y, g->tilesize/20, g->tilesize/20, DOT_COLOUR);
}
fprintf(fp, "</g>\n");
}
fprintf(fp, "</svg>\n");
}
#endif
#ifdef SVG_GRID
#include <errno.h>
static void grid_try_svg(grid *g, int which)
{
char *svg = getenv("PUZZLES_SVG_GRID");
if (svg) {
FILE *svgf = fopen(svg, "w");
if (svgf) {
grid_output_svg(svgf, g, which);
fclose(svgf);
} else {
fprintf(stderr, "Unable to open file `%s': %s", svg, strerror(errno));
}
}
}
#endif
/* Show the basic grid information, before doing grid_make_consistent */
static void grid_debug_basic(grid *g)
{
/* TODO: Maybe we should generate an SVG image of the dots and lines
* of the grid here, before grid_make_consistent.
* Would help with debugging grid generation. */
#ifdef DEBUG_GRID
int i;
printf("--- Basic Grid Data ---\n");
for (i = 0; i < g->num_faces; i++) {
grid_face *f = g->faces + i;
printf("Face %d: dots[", i);
int j;
for (j = 0; j < f->order; j++) {
grid_dot *d = f->dots[j];
printf("%s%d", j ? "," : "", (int)(d - g->dots));
}
printf("]\n");
}
#endif
#ifdef SVG_GRID
grid_try_svg(g, SVG_FACES);
#endif
}
/* Show the derived grid information, computed by grid_make_consistent */
static void grid_debug_derived(grid *g)
{
#ifdef DEBUG_GRID
/* edges */
int i;
printf("--- Derived Grid Data ---\n");
for (i = 0; i < g->num_edges; i++) {
grid_edge *e = g->edges + i;
printf("Edge %d: dots[%d,%d] faces[%d,%d]\n",
i, (int)(e->dot1 - g->dots), (int)(e->dot2 - g->dots),
e->face1 ? (int)(e->face1 - g->faces) : -1,
e->face2 ? (int)(e->face2 - g->faces) : -1);
}
/* faces */
for (i = 0; i < g->num_faces; i++) {
grid_face *f = g->faces + i;
int j;
printf("Face %d: faces[", i);
for (j = 0; j < f->order; j++) {
grid_edge *e = f->edges[j];
grid_face *f2 = (e->face1 == f) ? e->face2 : e->face1;
printf("%s%d", j ? "," : "", f2 ? (int)(f2 - g->faces) : -1);
}
printf("]\n");
}
/* dots */
for (i = 0; i < g->num_dots; i++) {
grid_dot *d = g->dots + i;
int j;
printf("Dot %d: dots[", i);
for (j = 0; j < d->order; j++) {
grid_edge *e = d->edges[j];
grid_dot *d2 = (e->dot1 == d) ? e->dot2 : e->dot1;
printf("%s%d", j ? "," : "", (int)(d2 - g->dots));
}
printf("] faces[");
for (j = 0; j < d->order; j++) {
grid_face *f = d->faces[j];
printf("%s%d", j ? "," : "", f ? (int)(f - g->faces) : -1);
}
printf("]\n");
}
#endif
#ifdef SVG_GRID
grid_try_svg(g, SVG_DOTS | SVG_EDGES | SVG_FACES);
#endif
}
/* Helper function for building incomplete-edges list in
* grid_make_consistent() */
static int grid_edge_bydots_cmpfn(void *v1, void *v2)
{
grid_edge *a = v1;
grid_edge *b = v2;
grid_dot *da, *db;
/* Pointer subtraction is valid here, because all dots point into the
* same dot-list (g->dots).
* Edges are not "normalised" - the 2 dots could be stored in any order,
* so we need to take this into account when comparing edges. */
/* Compare first dots */
da = (a->dot1 < a->dot2) ? a->dot1 : a->dot2;
db = (b->dot1 < b->dot2) ? b->dot1 : b->dot2;
if (da != db)
return db - da;
/* Compare last dots */
da = (a->dot1 < a->dot2) ? a->dot2 : a->dot1;
db = (b->dot1 < b->dot2) ? b->dot2 : b->dot1;
if (da != db)
return db - da;
return 0;
}
/*
* 'Vigorously trim' a grid, by which I mean deleting any isolated or
* uninteresting faces. By which, in turn, I mean: ensure that the
* grid is composed solely of faces adjacent to at least one
* 'landlocked' dot (i.e. one not in contact with the infinite
* exterior face), and that all those dots are in a single connected
* component.
*
* This function operates on, and returns, a grid satisfying the
* preconditions to grid_make_consistent() rather than the
* postconditions. (So call it first.)
*/
static void grid_trim_vigorously(grid *g)
{
int *dotpairs, *faces, *dots;
int *dsf;
int i, j, k, size, newfaces, newdots;
/*
* First construct a matrix in which each ordered pair of dots is
* mapped to the index of the face in which those dots occur in
* that order.
*/
dotpairs = snewn(g->num_dots * g->num_dots, int);
for (i = 0; i < g->num_dots; i++)
for (j = 0; j < g->num_dots; j++)
dotpairs[i*g->num_dots+j] = -1;
for (i = 0; i < g->num_faces; i++) {
grid_face *f = g->faces + i;
int dot0 = f->dots[f->order-1] - g->dots;
for (j = 0; j < f->order; j++) {
int dot1 = f->dots[j] - g->dots;
dotpairs[dot0 * g->num_dots + dot1] = i;
dot0 = dot1;
}
}
/*
* Now we can identify landlocked dots: they're the ones all of
* whose edges have a mirror-image counterpart in this matrix.
*/
dots = snewn(g->num_dots, int);
for (i = 0; i < g->num_dots; i++) {
dots[i] = TRUE;
for (j = 0; j < g->num_dots; j++) {
if ((dotpairs[i*g->num_dots+j] >= 0) ^
(dotpairs[j*g->num_dots+i] >= 0))
dots[i] = FALSE; /* non-duplicated edge: coastal dot */
}
}
/*
* Now identify connected pairs of landlocked dots, and form a dsf
* unifying them.
*/
dsf = snew_dsf(g->num_dots);
for (i = 0; i < g->num_dots; i++)
for (j = 0; j < i; j++)
if (dots[i] && dots[j] &&
dotpairs[i*g->num_dots+j] >= 0 &&
dotpairs[j*g->num_dots+i] >= 0)
dsf_merge(dsf, i, j);
/*
* Now look for the largest component.
*/
size = 0;
j = -1;
for (i = 0; i < g->num_dots; i++) {
int newsize;
if (dots[i] && dsf_canonify(dsf, i) == i &&
(newsize = dsf_size(dsf, i)) > size) {
j = i;
size = newsize;
}
}
/*
* Work out which faces we're going to keep (precisely those with
* at least one dot in the same connected component as j) and
* which dots (those required by any face we're keeping).
*
* At this point we reuse the 'dots' array to indicate the dots
* we're keeping, rather than the ones that are landlocked.
*/
faces = snewn(g->num_faces, int);
for (i = 0; i < g->num_faces; i++)
faces[i] = 0;
for (i = 0; i < g->num_dots; i++)
dots[i] = 0;
for (i = 0; i < g->num_faces; i++) {
grid_face *f = g->faces + i;
int keep = FALSE;
for (k = 0; k < f->order; k++)
if (dsf_canonify(dsf, f->dots[k] - g->dots) == j)
keep = TRUE;
if (keep) {
faces[i] = TRUE;
for (k = 0; k < f->order; k++)
dots[f->dots[k]-g->dots] = TRUE;
}
}
/*
* Work out the new indices of those faces and dots, when we
* compact the arrays containing them.
*/
for (i = newfaces = 0; i < g->num_faces; i++)
faces[i] = (faces[i] ? newfaces++ : -1);
for (i = newdots = 0; i < g->num_dots; i++)
dots[i] = (dots[i] ? newdots++ : -1);
/*
* Free the dynamically allocated 'dots' pointer lists in faces
* we're going to discard.
*/
for (i = 0; i < g->num_faces; i++)
if (faces[i] < 0)
sfree(g->faces[i].dots);
/*
* Go through and compact the arrays.
*/
for (i = 0; i < g->num_dots; i++)
if (dots[i] >= 0) {
grid_dot *dnew = g->dots + dots[i], *dold = g->dots + i;
*dnew = *dold; /* structure copy */
}
for (i = 0; i < g->num_faces; i++)
if (faces[i] >= 0) {
grid_face *fnew = g->faces + faces[i], *fold = g->faces + i;
*fnew = *fold; /* structure copy */
for (j = 0; j < fnew->order; j++) {
/*
* Reindex the dots in this face.
*/
k = fnew->dots[j] - g->dots;
fnew->dots[j] = g->dots + dots[k];
}
}
g->num_faces = newfaces;
g->num_dots = newdots;
sfree(dotpairs);
sfree(dsf);
sfree(dots);
sfree(faces);
}
/* Input: grid has its dots and faces initialised:
* - dots have (optionally) x and y coordinates, but no edges or faces
* (pointers are NULL).
* - edges not initialised at all
* - faces initialised and know which dots they have (but no edges yet). The
* dots around each face are assumed to be clockwise.
*
* Output: grid is complete and valid with all relationships defined.
*/
static void grid_make_consistent(grid *g)
{
int i;
tree234 *incomplete_edges;
grid_edge *next_new_edge; /* Where new edge will go into g->edges */
grid_debug_basic(g);
/* ====== Stage 1 ======
* Generate edges
*/
/* We know how many dots and faces there are, so we can find the exact
* number of edges from Euler's polyhedral formula: F + V = E + 2 .
* We use "-1", not "-2" here, because Euler's formula includes the
* infinite face, which we don't count. */
g->num_edges = g->num_faces + g->num_dots - 1;
g->edges = snewn(g->num_edges, grid_edge);
next_new_edge = g->edges;
/* Iterate over faces, and over each face's dots, generating edges as we
* go. As we find each new edge, we can immediately fill in the edge's
* dots, but only one of the edge's faces. Later on in the iteration, we
* will find the same edge again (unless it's on the border), but we will
* know the other face.
* For efficiency, maintain a list of the incomplete edges, sorted by
* their dots. */
incomplete_edges = newtree234(grid_edge_bydots_cmpfn);
for (i = 0; i < g->num_faces; i++) {
grid_face *f = g->faces + i;
int j;
for (j = 0; j < f->order; j++) {
grid_edge e; /* fake edge for searching */
grid_edge *edge_found;
int j2 = j + 1;
if (j2 == f->order)
j2 = 0;
e.dot1 = f->dots[j];
e.dot2 = f->dots[j2];
/* Use del234 instead of find234, because we always want to
* remove the edge if found */
edge_found = del234(incomplete_edges, &e);
if (edge_found) {
/* This edge already added, so fill out missing face.
* Edge is already removed from incomplete_edges. */
edge_found->face2 = f;
} else {
assert(next_new_edge - g->edges < g->num_edges);
next_new_edge->dot1 = e.dot1;
next_new_edge->dot2 = e.dot2;
next_new_edge->face1 = f;
next_new_edge->face2 = NULL; /* potentially infinite face */
add234(incomplete_edges, next_new_edge);
++next_new_edge;
}
}
}
freetree234(incomplete_edges);
/* ====== Stage 2 ======
* For each face, build its edge list.
*/
/* Allocate space for each edge list. Can do this, because each face's
* edge-list is the same size as its dot-list. */
for (i = 0; i < g->num_faces; i++) {
grid_face *f = g->faces + i;
int j;
f->edges = snewn(f->order, grid_edge*);
/* Preload with NULLs, to help detect potential bugs. */
for (j = 0; j < f->order; j++)
f->edges[j] = NULL;
}
/* Iterate over each edge, and over both its faces. Add this edge to
* the face's edge-list, after finding where it should go in the
* sequence. */
for (i = 0; i < g->num_edges; i++) {
grid_edge *e = g->edges + i;
int j;
for (j = 0; j < 2; j++) {
grid_face *f = j ? e->face2 : e->face1;
int k, k2;
if (f == NULL) continue;
/* Find one of the dots around the face */
for (k = 0; k < f->order; k++) {
if (f->dots[k] == e->dot1)
break; /* found dot1 */
}
assert(k != f->order); /* Must find the dot around this face */
/* Labelling scheme: as we walk clockwise around the face,
* starting at dot0 (f->dots[0]), we hit:
* (dot0), edge0, dot1, edge1, dot2,...
*
* 0
* 0-----1
* |
* |1
* |
* 3-----2
* 2
*
* Therefore, edgeK joins dotK and dot{K+1}
*/
/* Around this face, either the next dot or the previous dot
* must be e->dot2. Otherwise the edge is wrong. */
k2 = k + 1;
if (k2 == f->order)
k2 = 0;
if (f->dots[k2] == e->dot2) {
/* dot1(k) and dot2(k2) go clockwise around this face, so add
* this edge at position k (see diagram). */
assert(f->edges[k] == NULL);
f->edges[k] = e;
continue;
}
/* Try previous dot */
k2 = k - 1;
if (k2 == -1)
k2 = f->order - 1;
if (f->dots[k2] == e->dot2) {
/* dot1(k) and dot2(k2) go anticlockwise around this face. */
assert(f->edges[k2] == NULL);
f->edges[k2] = e;
continue;
}
assert(!"Grid broken: bad edge-face relationship");
}
}
/* ====== Stage 3 ======
* For each dot, build its edge-list and face-list.
*/
/* We don't know how many edges/faces go around each dot, so we can't
* allocate the right space for these lists. Pre-compute the sizes by
* iterating over each edge and recording a tally against each dot. */
for (i = 0; i < g->num_dots; i++) {
g->dots[i].order = 0;
}
for (i = 0; i < g->num_edges; i++) {
grid_edge *e = g->edges + i;
++(e->dot1->order);
++(e->dot2->order);
}
/* Now we have the sizes, pre-allocate the edge and face lists. */
for (i = 0; i < g->num_dots; i++) {
grid_dot *d = g->dots + i;
int j;
assert(d->order >= 2); /* sanity check */
d->edges = snewn(d->order, grid_edge*);
d->faces = snewn(d->order, grid_face*);
for (j = 0; j < d->order; j++) {
d->edges[j] = NULL;
d->faces[j] = NULL;
}
}
/* For each dot, need to find a face that touches it, so we can seed
* the edge-face-edge-face process around each dot. */
for (i = 0; i < g->num_faces; i++) {
grid_face *f = g->faces + i;
int j;
for (j = 0; j < f->order; j++) {
grid_dot *d = f->dots[j];
d->faces[0] = f;
}
}
/* Each dot now has a face in its first slot. Generate the remaining
* faces and edges around the dot, by searching both clockwise and
* anticlockwise from the first face. Need to do both directions,
* because of the possibility of hitting the infinite face, which
* blocks progress. But there's only one such face, so we will
* succeed in finding every edge and face this way. */
for (i = 0; i < g->num_dots; i++) {
grid_dot *d = g->dots + i;
int current_face1 = 0; /* ascends clockwise */
int current_face2 = 0; /* descends anticlockwise */
/* Labelling scheme: as we walk clockwise around the dot, starting
* at face0 (d->faces[0]), we hit:
* (face0), edge0, face1, edge1, face2,...
*
* 0
* |
* 0 | 1
* |
* -----d-----1
* |
* | 2
* |
* 2
*
* So, for example, face1 should be joined to edge0 and edge1,
* and those edges should appear in an anticlockwise sense around
* that face (see diagram). */
/* clockwise search */
while (TRUE) {
grid_face *f = d->faces[current_face1];
grid_edge *e;
int j;
assert(f != NULL);
/* find dot around this face */
for (j = 0; j < f->order; j++) {
if (f->dots[j] == d)
break;
}
assert(j != f->order); /* must find dot */
/* Around f, required edge is anticlockwise from the dot. See
* the other labelling scheme higher up, for why we subtract 1
* from j. */
j--;
if (j == -1)
j = f->order - 1;
e = f->edges[j];
d->edges[current_face1] = e; /* set edge */
current_face1++;
if (current_face1 == d->order)
break;
else {
/* set face */
d->faces[current_face1] =
(e->face1 == f) ? e->face2 : e->face1;
if (d->faces[current_face1] == NULL)
break; /* cannot progress beyond infinite face */
}
}
/* If the clockwise search made it all the way round, don't need to
* bother with the anticlockwise search. */
if (current_face1 == d->order)
continue; /* this dot is complete, move on to next dot */
/* anticlockwise search */
while (TRUE) {
grid_face *f = d->faces[current_face2];
grid_edge *e;
int j;
assert(f != NULL);
/* find dot around this face */
for (j = 0; j < f->order; j++) {
if (f->dots[j] == d)
break;
}
assert(j != f->order); /* must find dot */
/* Around f, required edge is clockwise from the dot. */
e = f->edges[j];
current_face2--;
if (current_face2 == -1)
current_face2 = d->order - 1;
d->edges[current_face2] = e; /* set edge */
/* set face */
if (current_face2 == current_face1)
break;
d->faces[current_face2] =
(e->face1 == f) ? e->face2 : e->face1;
/* There's only 1 infinite face, so we must get all the way
* to current_face1 before we hit it. */
assert(d->faces[current_face2]);
}
}
/* ====== Stage 4 ======
* Compute other grid settings
*/
/* Bounding rectangle */
for (i = 0; i < g->num_dots; i++) {
grid_dot *d = g->dots + i;
if (i == 0) {
g->lowest_x = g->highest_x = d->x;
g->lowest_y = g->highest_y = d->y;
} else {
g->lowest_x = min(g->lowest_x, d->x);
g->highest_x = max(g->highest_x, d->x);
g->lowest_y = min(g->lowest_y, d->y);
g->highest_y = max(g->highest_y, d->y);
}
}
grid_debug_derived(g);
}
/* Helpers for making grid-generation easier. These functions are only
* intended for use during grid generation. */
/* Comparison function for the (tree234) sorted dot list */
static int grid_point_cmp_fn(void *v1, void *v2)
{
grid_dot *p1 = v1;
grid_dot *p2 = v2;
if (p1->y != p2->y)
return p2->y - p1->y;
else
return p2->x - p1->x;
}
/* Add a new face to the grid, with its dot list allocated.
* Assumes there's enough space allocated for the new face in grid->faces */
static void grid_face_add_new(grid *g, int face_size)
{
int i;
grid_face *new_face = g->faces + g->num_faces;
new_face->order = face_size;
new_face->dots = snewn(face_size, grid_dot*);
for (i = 0; i < face_size; i++)
new_face->dots[i] = NULL;
new_face->edges = NULL;
new_face->has_incentre = FALSE;
g->num_faces++;
}
/* Assumes dot list has enough space */
static grid_dot *grid_dot_add_new(grid *g, int x, int y)
{
grid_dot *new_dot = g->dots + g->num_dots;
new_dot->order = 0;
new_dot->edges = NULL;
new_dot->faces = NULL;
new_dot->x = x;
new_dot->y = y;
g->num_dots++;
return new_dot;
}
/* Retrieve a dot with these (x,y) coordinates. Either return an existing dot
* in the dot_list, or add a new dot to the grid (and the dot_list) and
* return that.
* Assumes g->dots has enough capacity allocated */
static grid_dot *grid_get_dot(grid *g, tree234 *dot_list, int x, int y)
{
grid_dot test, *ret;
test.order = 0;
test.edges = NULL;
test.faces = NULL;
test.x = x;
test.y = y;
ret = find234(dot_list, &test, NULL);
if (ret)
return ret;
ret = grid_dot_add_new(g, x, y);
add234(dot_list, ret);
return ret;
}
/* Sets the last face of the grid to include this dot, at this position
* around the face. Assumes num_faces is at least 1 (a new face has
* previously been added, with the required number of dots allocated) */
static void grid_face_set_dot(grid *g, grid_dot *d, int position)
{
grid_face *last_face = g->faces + g->num_faces - 1;
last_face->dots[position] = d;
}
/*
* Helper routines for grid_find_incentre.
*/
static int solve_2x2_matrix(double mx[4], double vin[2], double vout[2])
{
double inv[4];
double det;
det = (mx[0]*mx[3] - mx[1]*mx[2]);
if (det == 0)
return FALSE;
inv[0] = mx[3] / det;
inv[1] = -mx[1] / det;
inv[2] = -mx[2] / det;
inv[3] = mx[0] / det;
vout[0] = inv[0]*vin[0] + inv[1]*vin[1];
vout[1] = inv[2]*vin[0] + inv[3]*vin[1];
return TRUE;
}
static int solve_3x3_matrix(double mx[9], double vin[3], double vout[3])
{
double inv[9];
double det;
det = (mx[0]*mx[4]*mx[8] + mx[1]*mx[5]*mx[6] + mx[2]*mx[3]*mx[7] -
mx[0]*mx[5]*mx[7] - mx[1]*mx[3]*mx[8] - mx[2]*mx[4]*mx[6]);
if (det == 0)
return FALSE;
inv[0] = (mx[4]*mx[8] - mx[5]*mx[7]) / det;
inv[1] = (mx[2]*mx[7] - mx[1]*mx[8]) / det;
inv[2] = (mx[1]*mx[5] - mx[2]*mx[4]) / det;
inv[3] = (mx[5]*mx[6] - mx[3]*mx[8]) / det;
inv[4] = (mx[0]*mx[8] - mx[2]*mx[6]) / det;
inv[5] = (mx[2]*mx[3] - mx[0]*mx[5]) / det;
inv[6] = (mx[3]*mx[7] - mx[4]*mx[6]) / det;
inv[7] = (mx[1]*mx[6] - mx[0]*mx[7]) / det;
inv[8] = (mx[0]*mx[4] - mx[1]*mx[3]) / det;
vout[0] = inv[0]*vin[0] + inv[1]*vin[1] + inv[2]*vin[2];
vout[1] = inv[3]*vin[0] + inv[4]*vin[1] + inv[5]*vin[2];
vout[2] = inv[6]*vin[0] + inv[7]*vin[1] + inv[8]*vin[2];
return TRUE;
}
void grid_find_incentre(grid_face *f)
{
double xbest, ybest, bestdist;
int i, j, k, m;
grid_dot *edgedot1[3], *edgedot2[3];
grid_dot *dots[3];
int nedges, ndots;
if (f->has_incentre)
return;
/*
* Find the point in the polygon with the maximum distance to any
* edge or corner.
*
* Such a point must exist which is in contact with at least three
* edges and/or vertices. (Proof: if it's only in contact with two
* edges and/or vertices, it can't even be at a _local_ maximum -
* any such circle can always be expanded in some direction.) So
* we iterate through all 3-subsets of the combined set of edges
* and vertices; for each subset we generate one or two candidate
* points that might be the incentre, and then we vet each one to
* see if it's inside the polygon and what its maximum radius is.
*
* (There's one case which this algorithm will get noticeably
* wrong, and that's when a continuum of equally good answers
* exists due to parallel edges. Consider a long thin rectangle,
* for instance, or a parallelogram. This algorithm will pick a
* point near one end, and choose the end arbitrarily; obviously a
* nicer point to choose would be in the centre. To fix this I
* would have to introduce a special-case system which detected
* parallel edges in advance, set aside all candidate points
* generated using both edges in a parallel pair, and generated
* some additional candidate points half way between them. Also,
* of course, I'd have to cope with rounding error making such a
* point look worse than one of its endpoints. So I haven't done
* this for the moment, and will cross it if necessary when I come
* to it.)
*
* We don't actually iterate literally over _edges_, in the sense
* of grid_edge structures. Instead, we fill in edgedot1[] and
* edgedot2[] with a pair of dots adjacent in the face's list of
* vertices. This ensures that we get the edges in consistent
* orientation, which we could not do from the grid structure
* alone. (A moment's consideration of an order-3 vertex should
* make it clear that if a notional arrow was written on each
* edge, _at least one_ of the three faces bordering that vertex
* would have to have the two arrows tip-to-tip or tail-to-tail
* rather than tip-to-tail.)
*/
nedges = ndots = 0;
bestdist = 0;
xbest = ybest = 0;
for (i = 0; i+2 < 2*f->order; i++) {
if (i < f->order) {
edgedot1[nedges] = f->dots[i];
edgedot2[nedges++] = f->dots[(i+1)%f->order];
} else
dots[ndots++] = f->dots[i - f->order];
for (j = i+1; j+1 < 2*f->order; j++) {
if (j < f->order) {
edgedot1[nedges] = f->dots[j];
edgedot2[nedges++] = f->dots[(j+1)%f->order];
} else
dots[ndots++] = f->dots[j - f->order];
for (k = j+1; k < 2*f->order; k++) {
double cx[2], cy[2]; /* candidate positions */
int cn = 0; /* number of candidates */
if (k < f->order) {
edgedot1[nedges] = f->dots[k];
edgedot2[nedges++] = f->dots[(k+1)%f->order];
} else
dots[ndots++] = f->dots[k - f->order];
/*
* Find a point, or pair of points, equidistant from
* all the specified edges and/or vertices.
*/
if (nedges == 3) {
/*
* Three edges. This is a linear matrix equation:
* each row of the matrix represents the fact that
* the point (x,y) we seek is at distance r from
* that edge, and we solve three of those
* simultaneously to obtain x,y,r. (We ignore r.)
*/
double matrix[9], vector[3], vector2[3];
int m;
for (m = 0; m < 3; m++) {
int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x;
int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y;
int dx = x2-x1, dy = y2-y1;
/*
* ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)|
*
* => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx)
*/
matrix[3*m+0] = dy;
matrix[3*m+1] = -dx;
matrix[3*m+2] = -sqrt((double)dx*dx+(double)dy*dy);
vector[m] = (double)x1*dy - (double)y1*dx;
}
if (solve_3x3_matrix(matrix, vector, vector2)) {
cx[cn] = vector2[0];
cy[cn] = vector2[1];
cn++;
}
} else if (nedges == 2) {
/*
* Two edges and a dot. This will end up in a
* quadratic equation.
*
* First, look at the two edges. Having our point
* be some distance r from both of them gives rise
* to a pair of linear equations in x,y,r of the
* form
*
* (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2)
*
* We eliminate r between those equations to give
* us a single linear equation in x,y describing
* the locus of points equidistant from both lines
* - i.e. the angle bisector.
*
* We then choose one of x,y to be a parameter t,
* and derive linear formulae for x,y,r in terms
* of t. This enables us to write down the
* circular equation (x-xd)^2+(y-yd)^2=r^2 as a
* quadratic in t; solving that and substituting
* in for x,y gives us two candidate points.
*/
double eqs[2][4]; /* a,b,c,d : ax+by+cr=d */
double eq[3]; /* a,b,c: ax+by=c */
double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */
double q[3]; /* a,b,c: at^2+bt+c=0 */
double disc;
/* Find equations of the two input lines. */
for (m = 0; m < 2; m++) {
int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x;
int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y;
int dx = x2-x1, dy = y2-y1;
eqs[m][0] = dy;
eqs[m][1] = -dx;
eqs[m][2] = -sqrt(dx*dx+dy*dy);
eqs[m][3] = x1*dy - y1*dx;
}
/* Derive the angle bisector by eliminating r. */
eq[0] = eqs[0][0]*eqs[1][2] - eqs[1][0]*eqs[0][2];
eq[1] = eqs[0][1]*eqs[1][2] - eqs[1][1]*eqs[0][2];
eq[2] = eqs[0][3]*eqs[1][2] - eqs[1][3]*eqs[0][2];
/* Parametrise x and y in terms of some t. */
if (fabs(eq[0]) < fabs(eq[1])) {
/* Parameter is x. */
xt[0] = 1; xt[1] = 0;
yt[0] = -eq[0]/eq[1]; yt[1] = eq[2]/eq[1];
} else {
/* Parameter is y. */
yt[0] = 1; yt[1] = 0;
xt[0] = -eq[1]/eq[0]; xt[1] = eq[2]/eq[0];
}
/* Find a linear representation of r using eqs[0]. */
rt[0] = -(eqs[0][0]*xt[0] + eqs[0][1]*yt[0])/eqs[0][2];
rt[1] = (eqs[0][3] - eqs[0][0]*xt[1] -
eqs[0][1]*yt[1])/eqs[0][2];
/* Construct the quadratic equation. */
q[0] = -rt[0]*rt[0];
q[1] = -2*rt[0]*rt[1];
q[2] = -rt[1]*rt[1];
q[0] += xt[0]*xt[0];
q[1] += 2*xt[0]*(xt[1]-dots[0]->x);
q[2] += (xt[1]-dots[0]->x)*(xt[1]-dots[0]->x);
q[0] += yt[0]*yt[0];
q[1] += 2*yt[0]*(yt[1]-dots[0]->y);
q[2] += (yt[1]-dots[0]->y)*(yt[1]-dots[0]->y);
/* And solve it. */
disc = q[1]*q[1] - 4*q[0]*q[2];
if (disc >= 0) {
double t;
disc = sqrt(disc);
t = (-q[1] + disc) / (2*q[0]);
cx[cn] = xt[0]*t + xt[1];
cy[cn] = yt[0]*t + yt[1];
cn++;
t = (-q[1] - disc) / (2*q[0]);
cx[cn] = xt[0]*t + xt[1];
cy[cn] = yt[0]*t + yt[1];
cn++;
}
} else if (nedges == 1) {
/*
* Two dots and an edge. This one's another
* quadratic equation.
*
* The point we want must lie on the perpendicular
* bisector of the two dots; that much is obvious.
* So we can construct a parametrisation of that
* bisecting line, giving linear formulae for x,y
* in terms of t. We can also express the distance
* from the edge as such a linear formula.
*
* Then we set that equal to the radius of the
* circle passing through the two points, which is
* a Pythagoras exercise; that gives rise to a
* quadratic in t, which we solve.
*/
double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */
double q[3]; /* a,b,c: at^2+bt+c=0 */
double disc;
double halfsep;
/* Find parametric formulae for x,y. */
{
int x1 = dots[0]->x, x2 = dots[1]->x;
int y1 = dots[0]->y, y2 = dots[1]->y;
int dx = x2-x1, dy = y2-y1;
double d = sqrt((double)dx*dx + (double)dy*dy);
xt[1] = (x1+x2)/2.0;
yt[1] = (y1+y2)/2.0;
/* It's convenient if we have t at standard scale. */
xt[0] = -dy/d;
yt[0] = dx/d;
/* Also note down half the separation between
* the dots, for use in computing the circle radius. */
halfsep = 0.5*d;
}
/* Find a parametric formula for r. */
{
int x1 = edgedot1[0]->x, x2 = edgedot2[0]->x;
int y1 = edgedot1[0]->y, y2 = edgedot2[0]->y;
int dx = x2-x1, dy = y2-y1;
double d = sqrt((double)dx*dx + (double)dy*dy);
rt[0] = (xt[0]*dy - yt[0]*dx) / d;
rt[1] = ((xt[1]-x1)*dy - (yt[1]-y1)*dx) / d;
}
/* Construct the quadratic equation. */
q[0] = rt[0]*rt[0];
q[1] = 2*rt[0]*rt[1];
q[2] = rt[1]*rt[1];
q[0] -= 1;
q[2] -= halfsep*halfsep;
/* And solve it. */
disc = q[1]*q[1] - 4*q[0]*q[2];
if (disc >= 0) {
double t;
disc = sqrt(disc);
t = (-q[1] + disc) / (2*q[0]);
cx[cn] = xt[0]*t + xt[1];
cy[cn] = yt[0]*t + yt[1];
cn++;
t = (-q[1] - disc) / (2*q[0]);
cx[cn] = xt[0]*t + xt[1];
cy[cn] = yt[0]*t + yt[1];
cn++;
}
} else if (nedges == 0) {
/*
* Three dots. This is another linear matrix
* equation, this time with each row of the matrix
* representing the perpendicular bisector between
* two of the points. Of course we only need two
* such lines to find their intersection, so we
* need only solve a 2x2 matrix equation.
*/
double matrix[4], vector[2], vector2[2];
int m;
for (m = 0; m < 2; m++) {
int x1 = dots[m]->x, x2 = dots[m+1]->x;
int y1 = dots[m]->y, y2 = dots[m+1]->y;
int dx = x2-x1, dy = y2-y1;
/*
* ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2
*
* => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy)
*/
matrix[2*m+0] = 2*dx;
matrix[2*m+1] = 2*dy;
vector[m] = ((double)dx*dx + (double)dy*dy +
2.0*x1*dx + 2.0*y1*dy);
}
if (solve_2x2_matrix(matrix, vector, vector2)) {
cx[cn] = vector2[0];
cy[cn] = vector2[1];
cn++;
}
}
/*
* Now go through our candidate points and see if any
* of them are better than what we've got so far.
*/
for (m = 0; m < cn; m++) {
double x = cx[m], y = cy[m];
/*
* First, disqualify the point if it's not inside
* the polygon, which we work out by counting the
* edges to the right of the point. (For
* tiebreaking purposes when edges start or end on
* our y-coordinate or go right through it, we
* consider our point to be offset by a small
* _positive_ epsilon in both the x- and
* y-direction.)
*/
int e, in = 0;
for (e = 0; e < f->order; e++) {
int xs = f->edges[e]->dot1->x;
int xe = f->edges[e]->dot2->x;
int ys = f->edges[e]->dot1->y;
int ye = f->edges[e]->dot2->y;
if ((y >= ys && y < ye) || (y >= ye && y < ys)) {
/*
* The line goes past our y-position. Now we need
* to know if its x-coordinate when it does so is
* to our right.
*
* The x-coordinate in question is mathematically
* (y - ys) * (xe - xs) / (ye - ys), and we want
* to know whether (x - xs) >= that. Of course we
* avoid the division, so we can work in integers;
* to do this we must multiply both sides of the
* inequality by ye - ys, which means we must
* first check that's not negative.
*/
int num = xe - xs, denom = ye - ys;
if (denom < 0) {
num = -num;
denom = -denom;
}
if ((x - xs) * denom >= (y - ys) * num)
in ^= 1;
}
}
if (in) {
#ifdef HUGE_VAL
double mindist = HUGE_VAL;
#else
#ifdef DBL_MAX
double mindist = DBL_MAX;
#else
#error No way to get maximum floating-point number.
#endif
#endif
int e, d;
/*
* This point is inside the polygon, so now we check
* its minimum distance to every edge and corner.
* First the corners ...
*/
for (d = 0; d < f->order; d++) {
int xp = f->dots[d]->x;
int yp = f->dots[d]->y;
double dx = x - xp, dy = y - yp;
double dist = dx*dx + dy*dy;
if (mindist > dist)
mindist = dist;
}
/*
* ... and now also check the perpendicular distance
* to every edge, if the perpendicular lies between
* the edge's endpoints.
*/
for (e = 0; e < f->order; e++) {
int xs = f->edges[e]->dot1->x;
int xe = f->edges[e]->dot2->x;
int ys = f->edges[e]->dot1->y;
int ye = f->edges[e]->dot2->y;
/*
* If s and e are our endpoints, and p our
* candidate circle centre, the foot of a
* perpendicular from p to the line se lies
* between s and e if and only if (p-s).(e-s) lies
* strictly between 0 and (e-s).(e-s).
*/
int edx = xe - xs, edy = ye - ys;
double pdx = x - xs, pdy = y - ys;
double pde = pdx * edx + pdy * edy;
long ede = (long)edx * edx + (long)edy * edy;
if (0 < pde && pde < ede) {
/*
* Yes, the nearest point on this edge is
* closer than either endpoint, so we must
* take it into account by measuring the
* perpendicular distance to the edge and
* checking its square against mindist.
*/
double pdre = pdx * edy - pdy * edx;
double sqlen = pdre * pdre / ede;
if (mindist > sqlen)
mindist = sqlen;
}
}
/*
* Right. Now we know the biggest circle around this
* point, so we can check it against bestdist.
*/
if (bestdist < mindist) {
bestdist = mindist;
xbest = x;
ybest = y;
}
}
}
if (k < f->order)
nedges--;
else
ndots--;
}
if (j < f->order)
nedges--;
else
ndots--;
}
if (i < f->order)
nedges--;
else
ndots--;
}
assert(bestdist > 0);
f->has_incentre = TRUE;
f->ix = xbest + 0.5; /* round to nearest */
f->iy = ybest + 0.5;
}
/* ------ Generate various types of grid ------ */
/* General method is to generate faces, by calculating their dot coordinates.
* As new faces are added, we keep track of all the dots so we can tell when
* a new face reuses an existing dot. For example, two squares touching at an
* edge would generate six unique dots: four dots from the first face, then
* two additional dots for the second face, because we detect the other two
* dots have already been taken up. This list is stored in a tree234
* called "points". No extra memory-allocation needed here - we store the
* actual grid_dot* pointers, which all point into the g->dots list.
* For this reason, we have to calculate coordinates in such a way as to
* eliminate any rounding errors, so we can detect when a dot on one
* face precisely lands on a dot of a different face. No floating-point
* arithmetic here!
*/
#define SQUARE_TILESIZE 20
static void grid_size_square(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int a = SQUARE_TILESIZE;
*tilesize = a;
*xextent = width * a;
*yextent = height * a;
}
static grid *grid_new_square(int width, int height, const char *desc)
{
int x, y;
/* Side length */
int a = SQUARE_TILESIZE;
/* Upper bounds - don't have to be exact */
int max_faces = width * height;
int max_dots = (width + 1) * (height + 1);
tree234 *points;
grid *g = grid_empty();
g->tilesize = a;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
/* generate square faces */
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* face position */
int px = a * x;
int py = a * y;
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a, py);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + a, py + a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px, py + a);
grid_face_set_dot(g, d, 3);
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
#define HONEY_TILESIZE 45
/* Vector for side of hexagon - ratio is close to sqrt(3) */
#define HONEY_A 15
#define HONEY_B 26
static void grid_size_honeycomb(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int a = HONEY_A;
int b = HONEY_B;
*tilesize = HONEY_TILESIZE;
*xextent = (3 * a * (width-1)) + 4*a;
*yextent = (2 * b * (height-1)) + 3*b;
}
static grid *grid_new_honeycomb(int width, int height, const char *desc)
{
int x, y;
int a = HONEY_A;
int b = HONEY_B;
/* Upper bounds - don't have to be exact */
int max_faces = width * height;
int max_dots = 2 * (width + 1) * (height + 1);
tree234 *points;
grid *g = grid_empty();
g->tilesize = HONEY_TILESIZE;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
/* generate hexagonal faces */
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* face centre */
int cx = 3 * a * x;
int cy = 2 * b * y;
if (x % 2)
cy += b;
grid_face_add_new(g, 6);
d = grid_get_dot(g, points, cx - a, cy - b);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, cx + a, cy - b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, cx + 2*a, cy);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, cx + a, cy + b);
grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, cx - a, cy + b);
grid_face_set_dot(g, d, 4);
d = grid_get_dot(g, points, cx - 2*a, cy);
grid_face_set_dot(g, d, 5);
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
#define TRIANGLE_TILESIZE 18
/* Vector for side of triangle - ratio is close to sqrt(3) */
#define TRIANGLE_VEC_X 15
#define TRIANGLE_VEC_Y 26
static void grid_size_triangular(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int vec_x = TRIANGLE_VEC_X;
int vec_y = TRIANGLE_VEC_Y;
*tilesize = TRIANGLE_TILESIZE;
*xextent = (width+1) * 2 * vec_x;
*yextent = height * vec_y;
}
static char *grid_validate_desc_triangular(grid_type type, int width,
int height, const char *desc)
{
/*
* Triangular grids: an absent description is valid (indicating
* the old-style approach which had 'ears', i.e. triangles
* connected to only one other face, at some grid corners), and so
* is a description reading just "0" (indicating the new-style
* approach in which those ears are trimmed off). Anything else is
* illegal.
*/
if (!desc || !strcmp(desc, "0"))
return NULL;
return "Unrecognised grid description.";
}
/* Doesn't use the previous method of generation, it pre-dates it!
* A triangular grid is just about simple enough to do by "brute force" */
static grid *grid_new_triangular(int width, int height, const char *desc)
{
int x,y;
int version = (desc == NULL ? -1 : atoi(desc));
/* Vector for side of triangle - ratio is close to sqrt(3) */
int vec_x = TRIANGLE_VEC_X;
int vec_y = TRIANGLE_VEC_Y;
int index;
/* convenient alias */
int w = width + 1;
grid *g = grid_empty();
g->tilesize = TRIANGLE_TILESIZE;
if (version == -1) {
/*
* Old-style triangular grid generation, preserved as-is for
* backwards compatibility with old game ids, in which it's
* just a little asymmetric and there are 'ears' (faces linked
* to only one other face) at two grid corners.
*
* Example old-style game ids, which should still work, and in
* which you should see the ears in the TL/BR corners on the
* first one and in the TL/BL corners on the second:
*
* 5x5t1:2c2a1a2a201a1a1a1112a1a2b1211f0b21a2a2a0a
* 5x6t1:a022a212h1a1d1a12c2b11a012b1a20d1a0a12e
*/
g->num_faces = width * height * 2;
g->num_dots = (width + 1) * (height + 1);
g->faces = snewn(g->num_faces, grid_face);
g->dots = snewn(g->num_dots, grid_dot);
/* generate dots */
index = 0;
for (y = 0; y <= height; y++) {
for (x = 0; x <= width; x++) {
grid_dot *d = g->dots + index;
/* odd rows are offset to the right */
d->order = 0;
d->edges = NULL;
d->faces = NULL;
d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0);
d->y = y * vec_y;
index++;
}
}
/* generate faces */
index = 0;
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
/* initialise two faces for this (x,y) */
grid_face *f1 = g->faces + index;
grid_face *f2 = f1 + 1;
f1->edges = NULL;
f1->order = 3;
f1->dots = snewn(f1->order, grid_dot*);
f1->has_incentre = FALSE;
f2->edges = NULL;
f2->order = 3;
f2->dots = snewn(f2->order, grid_dot*);
f2->has_incentre = FALSE;
/* face descriptions depend on whether the row-number is
* odd or even */
if (y % 2) {
f1->dots[0] = g->dots + y * w + x;
f1->dots[1] = g->dots + (y + 1) * w + x + 1;
f1->dots[2] = g->dots + (y + 1) * w + x;
f2->dots[0] = g->dots + y * w + x;
f2->dots[1] = g->dots + y * w + x + 1;
f2->dots[2] = g->dots + (y + 1) * w + x + 1;
} else {
f1->dots[0] = g->dots + y * w + x;
f1->dots[1] = g->dots + y * w + x + 1;
f1->dots[2] = g->dots + (y + 1) * w + x;
f2->dots[0] = g->dots + y * w + x + 1;
f2->dots[1] = g->dots + (y + 1) * w + x + 1;
f2->dots[2] = g->dots + (y + 1) * w + x;
}
index += 2;
}
}
} else {
/*
* New-style approach, in which there are never any 'ears',
* and if height is even then the grid is nicely 4-way
* symmetric.
*
* Example new-style grids:
*
* 5x5t1:0_21120b11a1a01a1a00c1a0b211021c1h1a2a1a0a
* 5x6t1:0_a1212c22c2a02a2f22a0c12a110d0e1c0c0a101121a1
*/
tree234 *points = newtree234(grid_point_cmp_fn);
/* Upper bounds - don't have to be exact */
int max_faces = height * (2*width+1);
int max_dots = (height+1) * (width+1) * 4;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
for (y = 0; y < height; y++) {
/*
* Each row contains (width+1) triangles one way up, and
* (width) triangles the other way up. Which way up is
* which varies with parity of y. Also, the dots around
* each face will flip direction with parity of y, so we
* set up n1 and n2 to cope with that easily.
*/
int y0, y1, n1, n2;
y0 = y1 = y * vec_y;
if (y % 2) {
y1 += vec_y;
n1 = 2; n2 = 1;
} else {
y0 += vec_y;
n1 = 1; n2 = 2;
}
for (x = 0; x <= width; x++) {
int x0 = 2*x * vec_x, x1 = x0 + vec_x, x2 = x1 + vec_x;
/*
* If the grid has odd height, then we skip the first
* and last triangles on this row, otherwise they'll
* end up as ears.
*/
if (height % 2 == 1 && y == height-1 && (x == 0 || x == width))
continue;
grid_face_add_new(g, 3);
grid_face_set_dot(g, grid_get_dot(g, points, x0, y0), 0);
grid_face_set_dot(g, grid_get_dot(g, points, x1, y1), n1);
grid_face_set_dot(g, grid_get_dot(g, points, x2, y0), n2);
}
for (x = 0; x < width; x++) {
int x0 = (2*x+1) * vec_x, x1 = x0 + vec_x, x2 = x1 + vec_x;
grid_face_add_new(g, 3);
grid_face_set_dot(g, grid_get_dot(g, points, x0, y1), 0);
grid_face_set_dot(g, grid_get_dot(g, points, x1, y0), n2);
grid_face_set_dot(g, grid_get_dot(g, points, x2, y1), n1);
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
}
grid_make_consistent(g);
return g;
}
#define SNUBSQUARE_TILESIZE 18
/* Vector for side of triangle - ratio is close to sqrt(3) */
#define SNUBSQUARE_A 15
#define SNUBSQUARE_B 26
static void grid_size_snubsquare(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int a = SNUBSQUARE_A;
int b = SNUBSQUARE_B;
*tilesize = SNUBSQUARE_TILESIZE;
*xextent = (a+b) * (width-1) + a + b;
*yextent = (a+b) * (height-1) + a + b;
}
static grid *grid_new_snubsquare(int width, int height, const char *desc)
{
int x, y;
int a = SNUBSQUARE_A;
int b = SNUBSQUARE_B;
/* Upper bounds - don't have to be exact */
int max_faces = 3 * width * height;
int max_dots = 2 * (width + 1) * (height + 1);
tree234 *points;
grid *g = grid_empty();
g->tilesize = SNUBSQUARE_TILESIZE;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* face position */
int px = (a + b) * x;
int py = (a + b) * y;
/* generate square faces */
grid_face_add_new(g, 4);
if ((x + y) % 2) {
d = grid_get_dot(g, points, px + a, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a + b, py + a);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + b, py + a + b);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px, py + b);
grid_face_set_dot(g, d, 3);
} else {
d = grid_get_dot(g, points, px + b, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a + b, py + b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + a, py + a + b);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px, py + a);
grid_face_set_dot(g, d, 3);
}
/* generate up/down triangles */
if (x > 0) {
grid_face_add_new(g, 3);
if ((x + y) % 2) {
d = grid_get_dot(g, points, px + a, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px, py + b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px - a, py);
grid_face_set_dot(g, d, 2);
} else {
d = grid_get_dot(g, points, px, py + a);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a, py + a + b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px - a, py + a + b);
grid_face_set_dot(g, d, 2);
}
}
/* generate left/right triangles */
if (y > 0) {
grid_face_add_new(g, 3);
if ((x + y) % 2) {
d = grid_get_dot(g, points, px + a, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a + b, py - a);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + a + b, py + a);
grid_face_set_dot(g, d, 2);
} else {
d = grid_get_dot(g, points, px, py - a);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + b, py);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px, py + a);
grid_face_set_dot(g, d, 2);
}
}
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
#define CAIRO_TILESIZE 40
/* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */
#define CAIRO_A 14
#define CAIRO_B 31
static void grid_size_cairo(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int b = CAIRO_B; /* a unused in determining grid size. */
*tilesize = CAIRO_TILESIZE;
*xextent = 2*b*(width-1) + 2*b;
*yextent = 2*b*(height-1) + 2*b;
}
static grid *grid_new_cairo(int width, int height, const char *desc)
{
int x, y;
int a = CAIRO_A;
int b = CAIRO_B;
/* Upper bounds - don't have to be exact */
int max_faces = 2 * width * height;
int max_dots = 3 * (width + 1) * (height + 1);
tree234 *points;
grid *g = grid_empty();
g->tilesize = CAIRO_TILESIZE;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* cell position */
int px = 2 * b * x;
int py = 2 * b * y;
/* horizontal pentagons */
if (y > 0) {
grid_face_add_new(g, 5);
if ((x + y) % 2) {
d = grid_get_dot(g, points, px + a, py - b);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + 2*b - a, py - b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + 2*b, py);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + b, py + a);
grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 4);
} else {
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + b, py - a);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + 2*b, py);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + 2*b - a, py + b);
grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px + a, py + b);
grid_face_set_dot(g, d, 4);
}
}
/* vertical pentagons */
if (x > 0) {
grid_face_add_new(g, 5);
if ((x + y) % 2) {
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + b, py + a);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + b, py + 2*b - a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px, py + 2*b);
grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px - a, py + b);
grid_face_set_dot(g, d, 4);
} else {
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a, py + b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px, py + 2*b);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px - b, py + 2*b - a);
grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px - b, py + a);
grid_face_set_dot(g, d, 4);
}
}
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
#define GREATHEX_TILESIZE 18
/* Vector for side of triangle - ratio is close to sqrt(3) */
#define GREATHEX_A 15
#define GREATHEX_B 26
static void grid_size_greathexagonal(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int a = GREATHEX_A;
int b = GREATHEX_B;
*tilesize = GREATHEX_TILESIZE;
*xextent = (3*a + b) * (width-1) + 4*a;
*yextent = (2*a + 2*b) * (height-1) + 3*b + a;
}
static grid *grid_new_greathexagonal(int width, int height, const char *desc)
{
int x, y;
int a = GREATHEX_A;
int b = GREATHEX_B;
/* Upper bounds - don't have to be exact */
int max_faces = 6 * (width + 1) * (height + 1);
int max_dots = 6 * width * height;
tree234 *points;
grid *g = grid_empty();
g->tilesize = GREATHEX_TILESIZE;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* centre of hexagon */
int px = (3*a + b) * x;
int py = (2*a + 2*b) * y;
if (x % 2)
py += a + b;
/* hexagon */
grid_face_add_new(g, 6);
d = grid_get_dot(g, points, px - a, py - b);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a, py - b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + 2*a, py);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + a, py + b);
grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px - a, py + b);
grid_face_set_dot(g, d, 4);
d = grid_get_dot(g, points, px - 2*a, py);
grid_face_set_dot(g, d, 5);
/* square below hexagon */
if (y < height - 1) {
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px - a, py + b);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a, py + b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + a, py + 2*a + b);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px - a, py + 2*a + b);
grid_face_set_dot(g, d, 3);
}
/* square below right */
if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) {
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px + 2*a, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + 2*a + b, py + a);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + a + b, py + a + b);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + a, py + b);
grid_face_set_dot(g, d, 3);
}
/* square below left */
if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) {
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px - 2*a, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px - a, py + b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px - a - b, py + a + b);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px - 2*a - b, py + a);
grid_face_set_dot(g, d, 3);
}
/* Triangle below right */
if ((x < width - 1) && (y < height - 1)) {
grid_face_add_new(g, 3);
d = grid_get_dot(g, points, px + a, py + b);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a + b, py + a + b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + a, py + 2*a + b);
grid_face_set_dot(g, d, 2);
}
/* Triangle below left */
if ((x > 0) && (y < height - 1)) {
grid_face_add_new(g, 3);
d = grid_get_dot(g, points, px - a, py + b);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px - a, py + 2*a + b);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px - a - b, py + a + b);
grid_face_set_dot(g, d, 2);
}
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
#define OCTAGONAL_TILESIZE 40
/* b/a approx sqrt(2) */
#define OCTAGONAL_A 29
#define OCTAGONAL_B 41
static void grid_size_octagonal(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int a = OCTAGONAL_A;
int b = OCTAGONAL_B;
*tilesize = OCTAGONAL_TILESIZE;
*xextent = (2*a + b) * width;
*yextent = (2*a + b) * height;
}
static grid *grid_new_octagonal(int width, int height, const char *desc)
{
int x, y;
int a = OCTAGONAL_A;
int b = OCTAGONAL_B;
/* Upper bounds - don't have to be exact */
int max_faces = 2 * width * height;
int max_dots = 4 * (width + 1) * (height + 1);
tree234 *points;
grid *g = grid_empty();
g->tilesize = OCTAGONAL_TILESIZE;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* cell position */
int px = (2*a + b) * x;
int py = (2*a + b) * y;
/* octagon */
grid_face_add_new(g, 8);
d = grid_get_dot(g, points, px + a, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a + b, py);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + 2*a + b, py + a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + 2*a + b, py + a + b);
grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px + a + b, py + 2*a + b);
grid_face_set_dot(g, d, 4);
d = grid_get_dot(g, points, px + a, py + 2*a + b);
grid_face_set_dot(g, d, 5);
d = grid_get_dot(g, points, px, py + a + b);
grid_face_set_dot(g, d, 6);
d = grid_get_dot(g, points, px, py + a);
grid_face_set_dot(g, d, 7);
/* diamond */
if ((x > 0) && (y > 0)) {
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px, py - a);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + a, py);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px, py + a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px - a, py);
grid_face_set_dot(g, d, 3);
}
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
#define KITE_TILESIZE 40
/* b/a approx sqrt(3) */
#define KITE_A 15
#define KITE_B 26
static void grid_size_kites(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int a = KITE_A;
int b = KITE_B;
*tilesize = KITE_TILESIZE;
*xextent = 4*b * width + 2*b;
*yextent = 6*a * (height-1) + 8*a;
}
static grid *grid_new_kites(int width, int height, const char *desc)
{
int x, y;
int a = KITE_A;
int b = KITE_B;
/* Upper bounds - don't have to be exact */
int max_faces = 6 * width * height;
int max_dots = 6 * (width + 1) * (height + 1);
tree234 *points;
grid *g = grid_empty();
g->tilesize = KITE_TILESIZE;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* position of order-6 dot */
int px = 4*b * x;
int py = 6*a * y;
if (y % 2)
px += 2*b;
/* kite pointing up-left */
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + 2*b, py);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + 2*b, py + 2*a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + b, py + 3*a);
grid_face_set_dot(g, d, 3);
/* kite pointing up */
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + b, py + 3*a);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px, py + 4*a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px - b, py + 3*a);
grid_face_set_dot(g, d, 3);
/* kite pointing up-right */
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px - b, py + 3*a);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px - 2*b, py + 2*a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px - 2*b, py);
grid_face_set_dot(g, d, 3);
/* kite pointing down-right */
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px - 2*b, py);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px - 2*b, py - 2*a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px - b, py - 3*a);
grid_face_set_dot(g, d, 3);
/* kite pointing down */
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px - b, py - 3*a);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px, py - 4*a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + b, py - 3*a);
grid_face_set_dot(g, d, 3);
/* kite pointing down-left */
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px, py);
grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + b, py - 3*a);
grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + 2*b, py - 2*a);
grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + 2*b, py);
grid_face_set_dot(g, d, 3);
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
#define FLORET_TILESIZE 150
/* -py/px is close to tan(30 - atan(sqrt(3)/9))
* using py=26 makes everything lean to the left, rather than right
*/
#define FLORET_PX 75
#define FLORET_PY -26
static void grid_size_floret(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int px = FLORET_PX, py = FLORET_PY; /* |( 75, -26)| = 79.43 */
int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */
int ry = qy-py;
/* rx unused in determining grid size. */
*tilesize = FLORET_TILESIZE;
*xextent = (6*px+3*qx)/2 * (width-1) + 4*qx + 2*px;
*yextent = (5*qy-4*py) * (height-1) + 4*qy + 2*ry;
}
static grid *grid_new_floret(int width, int height, const char *desc)
{
int x, y;
/* Vectors for sides; weird numbers needed to keep puzzle aligned with window
* -py/px is close to tan(30 - atan(sqrt(3)/9))
* using py=26 makes everything lean to the left, rather than right
*/
int px = FLORET_PX, py = FLORET_PY; /* |( 75, -26)| = 79.43 */
int qx = 4*px/5, qy = -py*2; /* |( 60, 52)| = 79.40 */
int rx = qx-px, ry = qy-py; /* |(-15, 78)| = 79.38 */
/* Upper bounds - don't have to be exact */
int max_faces = 6 * width * height;
int max_dots = 9 * (width + 1) * (height + 1);
tree234 *points;
grid *g = grid_empty();
g->tilesize = FLORET_TILESIZE;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
/* generate pentagonal faces */
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* face centre */
int cx = (6*px+3*qx)/2 * x;
int cy = (4*py-5*qy) * y;
if (x % 2)
cy -= (4*py-5*qy)/2;
else if (y && y == height-1)
continue; /* make better looking grids? try 3x3 for instance */
grid_face_add_new(g, 5);
d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, cx+2*rx+qx, cy+2*ry+qy); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, cx+2*qx+rx, cy+2*qy+ry); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 4);
grid_face_add_new(g, 5);
d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, cx+2*qx , cy+2*qy ); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, cx+2*qx+px, cy+2*qy+py); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, cx+2*px+qx, cy+2*py+qy); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 4);
grid_face_add_new(g, 5);
d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, cx+2*px , cy+2*py ); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, cx+2*px-rx, cy+2*py-ry); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, cx-2*rx+px, cy-2*ry+py); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 4);
grid_face_add_new(g, 5);
d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, cx-2*rx , cy-2*ry ); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, cx-2*rx-qx, cy-2*ry-qy); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, cx-2*qx-rx, cy-2*qy-ry); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 4);
grid_face_add_new(g, 5);
d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, cx-2*qx , cy-2*qy ); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, cx-2*qx-px, cy-2*qy-py); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, cx-2*px-qx, cy-2*py-qy); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 4);
grid_face_add_new(g, 5);
d = grid_get_dot(g, points, cx , cy ); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, cx-2*px , cy-2*py ); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, cx-2*px+rx, cy-2*py+ry); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, cx+2*rx-px, cy+2*ry-py); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, cx+2*rx , cy+2*ry ); grid_face_set_dot(g, d, 4);
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
/* DODEC_* are used for dodecagonal and great-dodecagonal grids. */
#define DODEC_TILESIZE 26
/* Vector for side of triangle - ratio is close to sqrt(3) */
#define DODEC_A 15
#define DODEC_B 26
static void grid_size_dodecagonal(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int a = DODEC_A;
int b = DODEC_B;
*tilesize = DODEC_TILESIZE;
*xextent = (4*a + 2*b) * (width-1) + 3*(2*a + b);
*yextent = (3*a + 2*b) * (height-1) + 2*(2*a + b);
}
static grid *grid_new_dodecagonal(int width, int height, const char *desc)
{
int x, y;
int a = DODEC_A;
int b = DODEC_B;
/* Upper bounds - don't have to be exact */
int max_faces = 3 * width * height;
int max_dots = 14 * width * height;
tree234 *points;
grid *g = grid_empty();
g->tilesize = DODEC_TILESIZE;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* centre of dodecagon */
int px = (4*a + 2*b) * x;
int py = (3*a + 2*b) * y;
if (y % 2)
px += 2*a + b;
/* dodecagon */
grid_face_add_new(g, 12);
d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4);
d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5);
d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6);
d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7);
d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8);
d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9);
d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10);
d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11);
/* triangle below dodecagon */
if ((y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) {
grid_face_add_new(g, 3);
d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px , py + (2*a + 2*b)); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 2);
}
/* triangle above dodecagon */
if ((y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) {
grid_face_add_new(g, 3);
d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px , py - (2*a + 2*b)); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 2);
}
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
static void grid_size_greatdodecagonal(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int a = DODEC_A;
int b = DODEC_B;
*tilesize = DODEC_TILESIZE;
*xextent = (6*a + 2*b) * (width-1) + 2*(2*a + b) + 3*a + b;
*yextent = (3*a + 3*b) * (height-1) + 2*(2*a + b);
}
static grid *grid_new_greatdodecagonal(int width, int height, const char *desc)
{
int x, y;
/* Vector for side of triangle - ratio is close to sqrt(3) */
int a = DODEC_A;
int b = DODEC_B;
/* Upper bounds - don't have to be exact */
int max_faces = 30 * width * height;
int max_dots = 200 * width * height;
tree234 *points;
grid *g = grid_empty();
g->tilesize = DODEC_TILESIZE;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
for (y = 0; y < height; y++) {
for (x = 0; x < width; x++) {
grid_dot *d;
/* centre of dodecagon */
int px = (6*a + 2*b) * x;
int py = (3*a + 3*b) * y;
if (y % 2)
px += 3*a + b;
/* dodecagon */
grid_face_add_new(g, 12);
d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + (2*a + b), py - ( a )); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + (2*a + b), py + ( a )); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px + ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 4);
d = grid_get_dot(g, points, px + ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 5);
d = grid_get_dot(g, points, px - ( a ), py + (2*a + b)); grid_face_set_dot(g, d, 6);
d = grid_get_dot(g, points, px - ( a + b), py + ( a + b)); grid_face_set_dot(g, d, 7);
d = grid_get_dot(g, points, px - (2*a + b), py + ( a )); grid_face_set_dot(g, d, 8);
d = grid_get_dot(g, points, px - (2*a + b), py - ( a )); grid_face_set_dot(g, d, 9);
d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 10);
d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 11);
/* hexagon below dodecagon */
if (y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) {
grid_face_add_new(g, 6);
d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px - a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px - 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 4);
d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 5);
}
/* hexagon above dodecagon */
if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) {
grid_face_add_new(g, 6);
d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px - 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px - a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 3);
d = grid_get_dot(g, points, px + 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 4);
d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 5);
}
/* square on right of dodecagon */
if (x < width - 1) {
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px + 2*a + b, py - a); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + 4*a + b, py - a); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + 4*a + b, py + a); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + 2*a + b, py + a); grid_face_set_dot(g, d, 3);
}
/* square on top right of dodecagon */
if (y && (x < width - 1 || !(y % 2))) {
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px + ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px + (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px + (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px + ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 3);
}
/* square on top left of dodecagon */
if (y && (x || (y % 2))) {
grid_face_add_new(g, 4);
d = grid_get_dot(g, points, px - ( a + b), py - ( a + b)); grid_face_set_dot(g, d, 0);
d = grid_get_dot(g, points, px - (2*a + b), py - ( a + 2*b)); grid_face_set_dot(g, d, 1);
d = grid_get_dot(g, points, px - (2*a ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 2);
d = grid_get_dot(g, points, px - ( a ), py - (2*a + b)); grid_face_set_dot(g, d, 3);
}
}
}
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
grid_make_consistent(g);
return g;
}
typedef struct setface_ctx
{
int xmin, xmax, ymin, ymax;
grid *g;
tree234 *points;
} setface_ctx;
static double round_int_nearest_away(double r)
{
return (r > 0.0) ? floor(r + 0.5) : ceil(r - 0.5);
}
static int set_faces(penrose_state *state, vector *vs, int n, int depth)
{
setface_ctx *sf_ctx = (setface_ctx *)state->ctx;
int i;
int xs[4], ys[4];
if (depth < state->max_depth) return 0;
#ifdef DEBUG_PENROSE
if (n != 4) return 0; /* triangles are sent as debugging. */
#endif
for (i = 0; i < n; i++) {
double tx = v_x(vs, i), ty = v_y(vs, i);
xs[i] = (int)round_int_nearest_away(tx);
ys[i] = (int)round_int_nearest_away(ty);
if (xs[i] < sf_ctx->xmin || xs[i] > sf_ctx->xmax) return 0;
if (ys[i] < sf_ctx->ymin || ys[i] > sf_ctx->ymax) return 0;
}
grid_face_add_new(sf_ctx->g, n);
debug(("penrose: new face l=%f gen=%d...",
penrose_side_length(state->start_size, depth), depth));
for (i = 0; i < n; i++) {
grid_dot *d = grid_get_dot(sf_ctx->g, sf_ctx->points,
xs[i], ys[i]);
grid_face_set_dot(sf_ctx->g, d, i);
debug((" ... dot 0x%x (%d,%d) (was %2.2f,%2.2f)",
d, d->x, d->y, v_x(vs, i), v_y(vs, i)));
}
return 0;
}
#define PENROSE_TILESIZE 100
static void grid_size_penrose(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
int l = PENROSE_TILESIZE;
*tilesize = l;
*xextent = l * width;
*yextent = l * height;
}
static grid *grid_new_penrose(int width, int height, int which, const char *desc); /* forward reference */
static char *grid_new_desc_penrose(grid_type type, int width, int height, random_state *rs)
{
int tilesize = PENROSE_TILESIZE, startsz, depth, xoff, yoff, aoff;
double outer_radius;
int inner_radius;
char gd[255];
int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3);
grid *g;
while (1) {
/* We want to produce a random bit of penrose tiling, so we
* calculate a random offset (within the patch that penrose.c
* calculates for us) and an angle (multiple of 36) to rotate
* the patch. */
penrose_calculate_size(which, tilesize, width, height,
&outer_radius, &startsz, &depth);
/* Calculate radius of (circumcircle of) patch, subtract from
* radius calculated. */
inner_radius = (int)(outer_radius - sqrt(width*width + height*height));
/* Pick a random offset (the easy way: choose within outer
* square, discarding while it's outside the circle) */
do {
xoff = random_upto(rs, 2*inner_radius) - inner_radius;
yoff = random_upto(rs, 2*inner_radius) - inner_radius;
} while (sqrt(xoff*xoff+yoff*yoff) > inner_radius);
aoff = random_upto(rs, 360/36) * 36;
debug(("grid_desc: ts %d, %dx%d patch, orad %2.2f irad %d",
tilesize, width, height, outer_radius, inner_radius));
debug((" -> xoff %d yoff %d aoff %d", xoff, yoff, aoff));
sprintf(gd, "G%d,%d,%d", xoff, yoff, aoff);
/*
* Now test-generate our grid, to make sure it actually
* produces something.
*/
g = grid_new_penrose(width, height, which, gd);
if (g) {
grid_free(g);
break;
}
/* If not, go back to the top of this while loop and try again
* with a different random offset. */
}
return dupstr(gd);
}
static char *grid_validate_desc_penrose(grid_type type, int width, int height,
const char *desc)
{
int tilesize = PENROSE_TILESIZE, startsz, depth, xoff, yoff, aoff, inner_radius;
double outer_radius;
int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3);
grid *g;
if (!desc)
return "Missing grid description string.";
penrose_calculate_size(which, tilesize, width, height,
&outer_radius, &startsz, &depth);
inner_radius = (int)(outer_radius - sqrt(width*width + height*height));
if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &aoff) != 3)
return "Invalid format grid description string.";
if (sqrt(xoff*xoff + yoff*yoff) > inner_radius)
return "Patch offset out of bounds.";
if ((aoff % 36) != 0 || aoff < 0 || aoff >= 360)
return "Angle offset out of bounds.";
/*
* Test-generate to ensure these parameters don't end us up with
* no grid at all.
*/
g = grid_new_penrose(width, height, which, desc);
if (!g)
return "Patch coordinates do not identify a usable grid fragment";
grid_free(g);
return NULL;
}
/*
* We're asked for a grid of a particular size, and we generate enough
* of the tiling so we can be sure to have enough random grid from which
* to pick.
*/
static grid *grid_new_penrose(int width, int height, int which, const char *desc)
{
int max_faces, max_dots, tilesize = PENROSE_TILESIZE;
int xsz, ysz, xoff, yoff, aoff;
double rradius;
tree234 *points;
grid *g;
penrose_state ps;
setface_ctx sf_ctx;
penrose_calculate_size(which, tilesize, width, height,
&rradius, &ps.start_size, &ps.max_depth);
debug(("penrose: w%d h%d, tile size %d, start size %d, depth %d",
width, height, tilesize, ps.start_size, ps.max_depth));
ps.new_tile = set_faces;
ps.ctx = &sf_ctx;
max_faces = (width*3) * (height*3); /* somewhat paranoid... */
max_dots = max_faces * 4; /* ditto... */
g = grid_empty();
g->tilesize = tilesize;
g->faces = snewn(max_faces, grid_face);
g->dots = snewn(max_dots, grid_dot);
points = newtree234(grid_point_cmp_fn);
memset(&sf_ctx, 0, sizeof(sf_ctx));
sf_ctx.g = g;
sf_ctx.points = points;
if (desc != NULL) {
if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &aoff) != 3)
assert(!"Invalid grid description.");
} else {
xoff = yoff = aoff = 0;
}
xsz = width * tilesize;
ysz = height * tilesize;
sf_ctx.xmin = xoff - xsz/2;
sf_ctx.xmax = xoff + xsz/2;
sf_ctx.ymin = yoff - ysz/2;
sf_ctx.ymax = yoff + ysz/2;
debug(("penrose: centre (%f, %f) xsz %f ysz %f",
0.0, 0.0, xsz, ysz));
debug(("penrose: x range (%f --> %f), y range (%f --> %f)",
sf_ctx.xmin, sf_ctx.xmax, sf_ctx.ymin, sf_ctx.ymax));
penrose(&ps, which, aoff);
freetree234(points);
assert(g->num_faces <= max_faces);
assert(g->num_dots <= max_dots);
debug(("penrose: %d faces total (equivalent to %d wide by %d high)",
g->num_faces, g->num_faces/height, g->num_faces/width));
/*
* Return NULL if we ended up with an empty grid, either because
* the initial generation was over too small a rectangle to
* encompass any face or because grid_trim_vigorously ended up
* removing absolutely everything.
*/
if (g->num_faces == 0 || g->num_dots == 0) {
grid_free(g);
return NULL;
}
grid_trim_vigorously(g);
if (g->num_faces == 0 || g->num_dots == 0) {
grid_free(g);
return NULL;
}
grid_make_consistent(g);
/*
* Centre the grid in its originally promised rectangle.
*/
g->lowest_x -= ((sf_ctx.xmax - sf_ctx.xmin) -
(g->highest_x - g->lowest_x)) / 2;
g->highest_x = g->lowest_x + (sf_ctx.xmax - sf_ctx.xmin);
g->lowest_y -= ((sf_ctx.ymax - sf_ctx.ymin) -
(g->highest_y - g->lowest_y)) / 2;
g->highest_y = g->lowest_y + (sf_ctx.ymax - sf_ctx.ymin);
return g;
}
static void grid_size_penrose_p2_kite(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
grid_size_penrose(width, height, tilesize, xextent, yextent);
}
static void grid_size_penrose_p3_thick(int width, int height,
int *tilesize, int *xextent, int *yextent)
{
grid_size_penrose(width, height, tilesize, xextent, yextent);
}
static grid *grid_new_penrose_p2_kite(int width, int height, const char *desc)
{
return grid_new_penrose(width, height, PENROSE_P2, desc);
}
static grid *grid_new_penrose_p3_thick(int width, int height, const char *desc)
{
return grid_new_penrose(width, height, PENROSE_P3, desc);
}
/* ----------- End of grid generators ------------- */
#define FNNEW(upper,lower) &grid_new_ ## lower,
#define FNSZ(upper,lower) &grid_size_ ## lower,
static grid *(*(grid_news[]))(int, int, const char*) = { GRIDGEN_LIST(FNNEW) };
static void(*(grid_sizes[]))(int, int, int*, int*, int*) = { GRIDGEN_LIST(FNSZ) };
char *grid_new_desc(grid_type type, int width, int height, random_state *rs)
{
if (type == GRID_PENROSE_P2 || type == GRID_PENROSE_P3) {
return grid_new_desc_penrose(type, width, height, rs);
} else if (type == GRID_TRIANGULAR) {
return dupstr("0"); /* up-to-date version of triangular grid */
} else {
return NULL;
}
}
char *grid_validate_desc(grid_type type, int width, int height,
const char *desc)
{
if (type == GRID_PENROSE_P2 || type == GRID_PENROSE_P3) {
return grid_validate_desc_penrose(type, width, height, desc);
} else if (type == GRID_TRIANGULAR) {
return grid_validate_desc_triangular(type, width, height, desc);
} else {
if (desc != NULL)
return "Grid description strings not used with this grid type";
return NULL;
}
}
grid *grid_new(grid_type type, int width, int height, const char *desc)
{
char *err = grid_validate_desc(type, width, height, desc);
if (err) assert(!"Invalid grid description.");
return grid_news[type](width, height, desc);
}
void grid_compute_size(grid_type type, int width, int height,
int *tilesize, int *xextent, int *yextent)
{
grid_sizes[type](width, height, tilesize, xextent, yextent);
}
/* ----------- End of grid helpers ------------- */
/* vim: set shiftwidth=4 tabstop=8: */
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