mirror of
git://git.tartarus.org/simon/puzzles.git
synced 2025-04-21 16:05:44 -07:00
Files
1558 lines
56 KiB
C
1558 lines
56 KiB
C
/*
|
|
* (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 "puzzles.h"
|
|
#include "tree234.h"
|
|
#include "grid.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_new(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 DEBUG_GRID
|
|
/* Show the basic grid information, before doing grid_make_consistent */
|
|
static void grid_print_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. */
|
|
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");
|
|
}
|
|
}
|
|
/* Show the derived grid information, computed by grid_make_consistent */
|
|
static void grid_print_derived(grid *g)
|
|
{
|
|
/* 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 /* DEBUG_GRID */
|
|
|
|
/* 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;
|
|
}
|
|
|
|
/* 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 */
|
|
|
|
#ifdef DEBUG_GRID
|
|
grid_print_basic(g);
|
|
#endif
|
|
|
|
/* ====== 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);
|
|
}
|
|
}
|
|
|
|
#ifdef DEBUG_GRID
|
|
grid_print_derived(g);
|
|
#endif
|
|
}
|
|
|
|
/* 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;
|
|
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;
|
|
}
|
|
|
|
/* ------ 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!
|
|
*/
|
|
|
|
grid *grid_new_square(int width, int height)
|
|
{
|
|
int x, y;
|
|
/* Side length */
|
|
int a = 20;
|
|
|
|
/* 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_new();
|
|
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;
|
|
}
|
|
|
|
grid *grid_new_honeycomb(int width, int height)
|
|
{
|
|
int x, y;
|
|
/* Vector for side of hexagon - ratio is close to sqrt(3) */
|
|
int a = 15;
|
|
int b = 26;
|
|
|
|
/* 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_new();
|
|
g->tilesize = 3 * a;
|
|
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;
|
|
}
|
|
|
|
/* 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" */
|
|
grid *grid_new_triangular(int width, int height)
|
|
{
|
|
int x,y;
|
|
|
|
/* Vector for side of triangle - ratio is close to sqrt(3) */
|
|
int vec_x = 15;
|
|
int vec_y = 26;
|
|
|
|
int index;
|
|
|
|
/* convenient alias */
|
|
int w = width + 1;
|
|
|
|
grid *g = grid_new();
|
|
g->tilesize = 18; /* adjust to your taste */
|
|
|
|
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*);
|
|
f2->edges = NULL;
|
|
f2->order = 3;
|
|
f2->dots = snewn(f2->order, grid_dot*);
|
|
|
|
/* 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;
|
|
}
|
|
}
|
|
|
|
grid_make_consistent(g);
|
|
return g;
|
|
}
|
|
|
|
grid *grid_new_snubsquare(int width, int height)
|
|
{
|
|
int x, y;
|
|
/* Vector for side of triangle - ratio is close to sqrt(3) */
|
|
int a = 15;
|
|
int b = 26;
|
|
|
|
/* 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_new();
|
|
g->tilesize = 18;
|
|
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;
|
|
}
|
|
|
|
grid *grid_new_cairo(int width, int height)
|
|
{
|
|
int x, y;
|
|
/* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */
|
|
int a = 14;
|
|
int b = 31;
|
|
|
|
/* 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_new();
|
|
g->tilesize = 40;
|
|
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;
|
|
}
|
|
|
|
grid *grid_new_greathexagonal(int width, int height)
|
|
{
|
|
int x, y;
|
|
/* Vector for side of triangle - ratio is close to sqrt(3) */
|
|
int a = 15;
|
|
int b = 26;
|
|
|
|
/* 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_new();
|
|
g->tilesize = 18;
|
|
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;
|
|
}
|
|
|
|
grid *grid_new_octagonal(int width, int height)
|
|
{
|
|
int x, y;
|
|
/* b/a approx sqrt(2) */
|
|
int a = 29;
|
|
int b = 41;
|
|
|
|
/* 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_new();
|
|
g->tilesize = 40;
|
|
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;
|
|
}
|
|
|
|
grid *grid_new_kites(int width, int height)
|
|
{
|
|
int x, y;
|
|
/* b/a approx sqrt(3) */
|
|
int a = 15;
|
|
int b = 26;
|
|
|
|
/* 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_new();
|
|
g->tilesize = 40;
|
|
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;
|
|
}
|
|
|
|
grid *grid_new_floret(int width, int height)
|
|
{
|
|
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 = 75, py = -26; /* |( 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_new();
|
|
g->tilesize = 2 * px;
|
|
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;
|
|
}
|
|
|
|
grid *grid_new_dodecagonal(int width, int height)
|
|
{
|
|
int x, y;
|
|
/* Vector for side of triangle - ratio is close to sqrt(3) */
|
|
int a = 15;
|
|
int b = 26;
|
|
|
|
/* 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_new();
|
|
g->tilesize = b;
|
|
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;
|
|
}
|
|
|
|
grid *grid_new_greatdodecagonal(int width, int height)
|
|
{
|
|
int x, y;
|
|
/* Vector for side of triangle - ratio is close to sqrt(3) */
|
|
int a = 15;
|
|
int b = 26;
|
|
|
|
/* 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_new();
|
|
g->tilesize = b;
|
|
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;
|
|
}
|
|
|
|
/* ----------- End of grid generators ------------- */
|