--- /dev/null
+#include "hexagon.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