+++ /dev/null
-#include "hexmap.h"
-
-#include <math.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <limits.h>
-
-static int inversecantor(int cantor, int *x, int *y);
-
-/*
- * This file is written by Nathan Wagner and dedicated to the public
- * domain
- */
-
-double HL_vertexv[] = {
- .577350269189625764509148780502, 0.0,
- .288675134594812882254574390251, 0.5,
- -.288675134594812882254574390251, 0.5,
- -.577350269189625764509148780502, 0.0,
- -.288675134594812882254574390251, -0.5,
- .288675134594812882254574390251, -0.5};
-
-/* these all are for a hex one unit across */
-static double hexptvd[6][2] = {
- {.577350269189625764509148780502, 0.0}, /* 1.0/sqrt3 */
- {.288675134594812882254574390251, 0.5}, /* 0.5/sqrt3 */
- {-.288675134594812882254574390251, 0.5},
- {-.577350269189625764509148780502, 0.0},
- {-.288675134594812882254574390251, -0.5},
- {.288675134594812882254574390251, -0.5}
-};
-
-#if 0
-
-/* TODO how is this related? to the above? */
-static double texptvd[6][2] = {
- {1.154700538379251529018297561004, 0.5}, /* 2.0/sqrt3 */
- {.866025403784438646763723170753, 1.0}, /* 1.5/sqrt3 */
- {.288675134594812882254574390251, 1.0},
- {0.0, 0.5},
- {.288675134594812882254574390251, 0.0},
- {.866025403784438646763723170753, 0.0}
-};
-
-static double hexpthd[6][2] = {
- {0.0, .577350269189625764509148780502},
- {0.5, .288675134594812882254574390251},
- {0.5, -.288675134594812882254574390251},
- {0.0, -.577350269189625764509148780502},
- {-0.5, -.288675134594812882254574390251},
- {-0.5, .288675134594812882254574390251}
-};
-
-#endif
-
-void HL_vertices(int cantor, double *vc) {
- int i;
- double xc, yc;
-
- HL_hexcenter(cantor, &xc, &yc);
-
- for (i=0; i<6; i++) {
- *vc++ = hexptvd[i][0] + xc;
- *vc++ = hexptvd[i][1] + yc;
- }
- *vc++ = hexptvd[0][0] + xc;
- *vc++ = hexptvd[0][1] + yc;
-}
-
-void HL_trianglefan(int cantor, double *vc) {
- HL_hexcenter(cantor, vc, vc+1);
- HL_vertices(cantor, vc+2);
-}
-
-double HL_center_x(int cantor) {
- double x;
-
- HL_hexcenter(cantor, &x, 0);
- return x;
-}
-
-double HL_center_y(int cantor) {
- double y;
-
- HL_hexcenter(cantor, 0, &y);
- return y;
-}
-
-int HL_hexcenter(int cantor, double *xc, double *yc) {
- int x, y;
- double stride = 1.5/sqrt(3.0);
-
- inversecantor(cantor, &x, &y);
-
- if (xc) *xc = x * stride;
- if (yc && x >= 0) *yc = y + ((x + 1) % 2) / 2.0 - 0.5;
- if (yc && x < 0) *yc = y + ((-x + 1) % 2) / 2.0 - 0.5;
-
- return cantor;
-}
-
-/*
- * This function assumes that the hexes are one unit across, and vertically
- * oriented. If that is not the case, you will need to transform
- * your input coordinates first.
- */
-int HL_cantor_bin(double x, double y) {
- return HL_hexbin(1.0, x, y, 0, 0);
-}
-
-static int xy2ijk(int x, int y, int *i, int *j, int *k) {
- int pi, pj, pk;
-
- pi = x;
- pj = -y;
- if (x < 0) {
- pj = pj + (-x + 1) / 2;
- } else {
- pj = pj - x/2;
- }
- pk = -pi - pj;
-
- if (i) *i = pi;
- if (j) *j = pj;
- if (k) *k = pk;
-
- return HL_cantor_xy(x,y);
-}
-
-static int ijk2xy(int i, int j, int k, int *x, int *y) {
- int px, py;
-
- px = i;
-
- /* py = -j - i/2; */
- py = -j;
-
- if (i < 0) {
- py += (-i + 1)/2;
- } else {
- py -= i/2;
- }
-
- if (x) *x = px;
- if (y) *y = py;
-
- return HL_cantor_xy(px,py);
-}
-
-int HL_cantor_ijk(int i, int j, int k) {
- return ijk2xy(i,j,k,0,0);
-}
-
-int HL_distance(int from, int to) {
- int dist = 0, i;;
- int fc[3], tc[3];
-
- HL_cantor_arrays(from, 0, fc);
- HL_cantor_arrays(to, 0, tc);
-
- for (i=0;i<=2;i++) {
- dist += abs(fc[i] - tc[i]);
- }
-
- return dist / 2;
-}
-
-int HL_hexes_within_range(int hex, int range, int *list, int size) {
- int count = 0;
- int i;
-
- if (range == 0) {
- return HL_hexes_at_range(hex, 0, list, size);
- }
-
- for (i=1;i<=range;i++) {
- count += HL_hexes_at_range(hex, i, count > size ? 0 : list+count, size-count);
- }
- return count;
-}
-
-int HL_hexes_at_range(int hex, int range, int *list, int size) {
- int q; /* p and q are count/loop vars */
- int c[3]; /* ijk coord array */
-
- if (range == 0) {
- if (list) {
- list[0] = hex;
- }
- return 1;
- } else if (range < 0) {
- return 0;
- }
-
- /* TODO don't bother to collect if the list isn't big enough? */
- /* i.e. if (!list || size < range * 6) */
- if (!list || size < 1) return range * 6;
-
- HL_cantor_arrays(hex, 0, c);
- c[0] += range;
- c[2] = -c[0] - c[1];
- hex = HL_cantor_ijkp(c);
-
- for(q=0; q<size && q < range * 6; q++) {
- list[q] = hex;
- hex = HL_adjhex(hex, q/range+2);
- }
-
- return range * 6;
-}
-
-int HL_adjacent_hex(int start, int dir) {
- if (dir < 0 || dir > 5) return 0;
-
- return HL_adjhex(start, dir);
-}
-
-/* direction 0 is positive X , counter clockwise from there */
-int HL_adjhex(int start, int dir) {
- int c[3];
-
- HL_cantor_arrays(start, 0, c);
-
- switch (dir%6) {
- case 2:
- c[0]--; c[1]++; break;
- case 1:
- c[1]++; c[2]--; break;
- case 0:
- c[0]++; c[2]--; break;
- case 5:
- c[0]++; c[1]--; break;
- case 4:
- c[1]--; c[2]++; break;
- case 3:
- c[0]--; ; c[2]++; break;
- }
-
- return HL_cantor_ijkp(c);
-}
-
-int HL_cantor_xyp(int *xy) {
- return HL_cantor_xy(xy[0], xy[1]);
-}
-
-int HL_cantor_ijkp(int *ijk) {
- return HL_cantor_ijk(ijk[0], ijk[1], ijk[2]);
-}
-
-int HL_cantor_arrays(int can, int *xy, int *ijk) {
- return HL_cantor_decode(can, xy, xy ? xy+1 : 0,
- ijk, ijk ? ijk+1 : 0, ijk ? ijk+2 : 0);
-}
-
-int HL_cantor_decode(int can, int *x, int *y, int *i, int *j, int *k) {
- int px, py;
-
- inversecantor(can, &px, &py);
- if (x) *x = px;
- if (y) *y = py;
-
- xy2ijk(px, py, i, j, k);
-
- return can;
-}
-
-int HL_cantor_i(int cantor) {
- int i;
-
- HL_cantor_decode(cantor, 0,0, &i,0,0);
- return i;
-}
-
-int HL_cantor_j(int cantor) {
- int j;
-
- HL_cantor_decode(cantor, 0,0, 0,&j,0);
- return j;
-}
-
-int HL_cantor_k(int cantor) {
- int k;
-
- HL_cantor_decode(cantor, 0,0, 0,0,&k);
- return k;
-}
-
-int HL_cantor_x(int cantor) {
- int x;
- inversecantor(cantor, &x, 0);
- return x;
-}
-
-int HL_cantor_y(int cantor) {
- int y;
- inversecantor(cantor, 0, &y);
- return y;
-}
-
-/* Determine if a map with these dimensions will overflow */
-int HL_map_bounds_ok(int xdim, int ydim) {
-
- /* return (x+y) * (x + y + 1) / 2 + y+1; */
-
- if (INT_MAX - xdim - 1 < ydim) return 0;
- if (INT_MAX / (xdim+ydim) < (xdim+ydim+1)) return 0;
- if ( (xdim+ydim) * (xdim+ydim+1) / 2 > INT_MAX - ydim - 1)
- return 0;
-
- return 1;
-}
-
-int HL_map_max_dimension(void) {
- int low, high, try;
-
- low = 1; high = INT_MAX/2;
-
- while (low != high - 1) {
- try = (low + high) / 2;
- if (HL_map_bounds_ok(try,try)) {
- low = try;
- } else {
- high = try;
- }
- }
-
- return low;
-}
-
-static int inversenatcantor(int cantor, int *x, int *y) {
- int w, t, py;
-
- cantor -= 1;
-
- w = (int)floor((sqrt(8.0 * cantor + 1.0) - 1.0)/2.0);
- t = (w * w + w)/2;
-
- py = cantor - t;
-
- if (y) *y = py;
- if (x) *x = w - py;
-
- return cantor;
-}
-
-/*
- * map non negative integer pairs to their cantor pairing function
- * number, plus one. We add one so that the result is never zero,
- * leaving zero to be "invalid" or "none" or what have you.
- */
-
-static int natcantor(int x, int y) {
- return (x+y) * (x + y + 1) / 2 + y+1;
-}
-
-/* See http://en.wikipedia.org/wiki/Cantor_pairing_function */
-/* see also http://szudzik.com/ElegantPairing.pdf */
-/*
- * if either coordinate is negative, map the integers onto the
- * whole numbers, and then return the negative of the adjusted
- * cantor number. As for most grids negative coordinates will
- * be invalid, this will allow for a <= 0 test for invalid
- * or out of bounds (on the negative side anyway, you'll
- * still have to test for out of range on the positive side).
- *
- * TODO figure out what the maximum supported coordinates are
- * for given integer sizes.
- */
-int HL_cantor_xy(int x, int y) {
- if (x < 0 || y < 0) {
- x = abs(2 * x) - (x < 0);
- y = abs(2 * y) - (y < 0);
- return -natcantor(x, y);
- }
- return natcantor(x,y);
-}
-
-static int inversecantor(int cantor, int *x, int *y) {
- if (cantor < 0) {
- inversenatcantor(-cantor, x, y);
- if (x) {
- if (*x % 2) {
- *x = -(*x+1)/2;
- } else {
- *x = *x / 2;
- }
- }
- if (y) {
- if (*y % 2) {
- *y = -(*y+1)/2;
- } else {
- *y = *y/2;
- }
- }
- } else {
- inversenatcantor(cantor, x, y);
- }
-
- return cantor;
-}
-
-struct hex {
- int iso;
- int x, y, z;
-};
-
-/* y *must* be positive down as the xy /iso conversion assumes this */
-static int hex_xy(struct hex *h) {
- if (!h->iso) return 1;
- if (h->x >= 0) {
- h->y = -h->y - (h->x+1)/2;
- } else {
- /* need to round toward -inf, not toward zero, so x-1 */
- h->y = -h->y - h->x/2;
- }
- h->iso = 0;
-
- return 1;
-}
-
-#if 0
-
-static int hex_iso(struct hex *h) {
- if (h->iso) return 1;
-
- if (h->x >= 0) {
- h->y = (-h->y - (h->x+1)/2);
- } else {
- /* need to round toward -inf, not toward zero, so x-1 */
- h->y = (-h->y - (h->x)/2);
- }
-
- h->z = -h->x - h->y;
- h->iso = 1;
- return 1;
-}
-
-#endif
-
-int HL_hexbin(double width, double x, double y, int *i, int *j) {
- double z, rx, ry, rz;
- double abs_dx, abs_dy, abs_dz;
- int ix, iy, iz, s;
- struct hex h;
-
- /* TODO just hard-code this cosine */
- x = x / cos(30 * M_PI / 180.0); /* rotated X coord */
- y = y - x / 2.0; /* adjustment for rotated X */
-
- /* adjust for actual hexwidth */
- x /= width;
- y /= width;
-
- z = -x - y;
-
- ix = rx = floor(x + 0.5);
- iy = ry = floor(y + 0.5);
- iz = rz = floor(z + 0.5);
-
- s = ix + iy + iz;
-
- if (s) {
- abs_dx = fabs(rx - x);
- abs_dy = fabs(ry - y);
- abs_dz = fabs(rz - z);
-
- if (abs_dx >= abs_dy && abs_dx >= abs_dz) {
- ix -= s;
- } else if (abs_dy >= abs_dx && abs_dy >= abs_dz) {
- iy -= s;
- } else {
- iz -= s;
- }
- }
- h.x = ix;
- h.y = iy;
- h.z = iz;
- h.iso = 1;
-
- hex_xy(&h);
- if (i) *i = h.x;
- if (j) *j = h.y;
- return HL_cantor_xy(h.x, h.y);
-}
projects / hexagon / blobdiff