--- /dev/null
+#include "hexagon.h"
+
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <limits.h>
+
+/* constructor function */
+struct HL_hex HL_hex_xy(int x, int y) {
+ struct HL_hex h;
+ h.x = x;
+ h.y = y;
+ return h;
+}
+
+int HL_hex_cmp(struct HL_hex const *a, struct HL_hex const *b) {
+ if (a->x != b->x) {
+ return a->x > b->x ? 1 : -1;
+ }
+ if (a->y != b->y) {
+ return a->y > b->y ? 1 : -1;
+ }
+ return 0;
+}
+
+int HL_hex_eq(struct HL_hex const *a, struct HL_hex const *b) {
+ return a->x == b->x && a->y == b->y;
+}
+
+/*
+ * This file is written by Nathan Wagner and dedicated to the public
+ * domain
+ */
+
+double HL_vertexv[12] = {
+ .577350269189625764509148780502, 0.0,
+ .288675134594812882254574390251, 0.5,
+ -.288675134594812882254574390251, 0.5,
+ -.577350269189625764509148780502, 0.0,
+ -.288675134594812882254574390251, -0.5,
+ .288675134594812882254574390251, -0.5};
+
+double HL_fand[16] = {
+ 0.0, 0.0,
+ .577350269189625764509148780502, 0.0,
+ .288675134594812882254574390251, 0.5,
+ -.288675134594812882254574390251, 0.5,
+ -.577350269189625764509148780502, 0.0,
+ -.288675134594812882254574390251, -0.5,
+ .288675134594812882254574390251, -0.5,
+ .577350269189625764509148780502, 0.0
+};
+
+double HL_hfand[16] = {
+ 0.0, 0.0,
+ 0.0, .577350269189625764509148780502,
+ 0.5, .288675134594812882254574390251,
+ 0.5, -.288675134594812882254574390251,
+ 0.0, -.577350269189625764509148780502,
+ -0.5, -.288675134594812882254574390251,
+ -0.5, .288675134594812882254574390251,
+ 0.0, .577350269189625764509148780502
+};
+
+float HL_fanf[16] = {
+ 0.0f, 0.0f,
+ .577350269189625764509148780502f, 0.0f,
+ .288675134594812882254574390251f, 0.5f,
+ -.288675134594812882254574390251f, 0.5f,
+ -.577350269189625764509148780502f, 0.0f,
+ -.288675134594812882254574390251f, -0.5f,
+ .288675134594812882254574390251f, -0.5f,
+ .577350269189625764509148780502f, 0.0f
+};
+
+float HL_hfanf[16] = {
+ 0.0f, 0.0f,
+ 0.0f, .577350269189625764509148780502f,
+ 0.5f, .288675134594812882254574390251f,
+ 0.5f, -.288675134594812882254574390251f,
+ 0.0f, -.577350269189625764509148780502f,
+ -0.5f, -.288675134594812882254574390251f,
+ -0.5f, .288675134594812882254574390251f,
+ 0.0f, .577350269189625764509148780502f
+};
+
+/* size of a square that will exactly fit in a hexagon */
+/* 2.0/(1+sqrt(3.0)) */
+double HL_square = .73205080756887729352;
+
+/* 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
+
+#define RD (180.0 / M_PI)
+/* angle ranges from 0-6 */
+/* distance is 0 at origin, 1.0 at the hex side */
+
+#if 0
+ double sqrt3;
+
+ sqrt3 = sqrt(3.0);
+
+ 1
+ /---\
+ 2/ \0
+ / \
+ \ /
+ 3\ /5
+ \---/
+ 4
+
+ /\
+ 0/ \5
+ / \
+ | |
+ 1| |4
+ | |
+ \ /
+ 2\ /3
+ \/
+
+#endif
+
+/* return the polar distance */
+struct HL_point HL_polar(double angle, double distance, double *d) {
+ double A, B, C, b;
+ struct HL_point pt;
+
+#if 0
+ C
+ /\
+ b / \ a
+ / \
+ / \
+ A -------- B
+ c
+
+ c = 1 ; fixed, will scale later
+ B = 60 ; exterior angle of hextant
+ C = 180-B-A = 120-A ; sum of angles of a triangle
+ A = function argument ; the polar coordinate we are calculating
+ b = c * sin(B) / sin(C) ; law of sines
+
+#endif
+ /* convert angle to radians */
+ angle = angle * M_PI / 3.0;
+
+ /* calculate the distance along the ray to the hex side */
+
+ A = fmod(angle, M_PI/3.0); /* constrain to within an equilateral */
+ B = M_PI / 3.0;
+ C = M_PI - B - A;
+
+ b = sin(B) / sin(C);
+
+ /* scale for hex one unit from side to side, rather than
+ * one unit from center to vertex
+ */
+/* b = b * sqrt(3.0) / 2.0 / 2.0; */
+ b = b / sqrt(3);
+
+ pt.x = distance * b * cos(angle);
+ pt.y = distance * b * sin(angle);
+
+ if (d) {
+ *d = distance * b;
+ }
+
+ return pt;
+}
+
+void HL_vertices(struct HL_hex hex, double *vc) {
+ int i;
+ double xc, yc;
+ struct HL_point center;
+
+ center = HL_hexcenter(hex);
+ xc = center.x;
+ yc = center.y;
+
+ 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;
+}
+
+#if 0
+void HL_trianglefan(int cantor, double *vc) {
+ HL_hexcenter(cantor, vc, vc+1);
+ HL_vertices(cantor, vc+2);
+}
+#endif
+
+struct HL_point HL_hexcenter(struct HL_hex hex) {
+ int x, y;
+ struct HL_point center;
+ double yc;
+
+ double stride = 1.5/sqrt(3.0);
+
+ x = hex.x;
+ y = hex.y;
+
+ center.x = x * stride;
+
+ if (x >= 0) yc = y + ((x + 1) % 2) / 2.0 - 0.5;
+ if (x < 0) yc = y + ((-x + 1) % 2) / 2.0 - 0.5;
+
+ center.y = yc;
+
+ return center;
+}
+
+/*
+ * 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.
+ */
+struct HL_hex HL_bin(double x, double y) {
+ return HL_hexbin(1.0, x, y);
+}
+
+struct HL_isohex HL_xy2ijk(struct HL_hex hex) {
+ int pi, pj, pk;
+ int x, y;
+ struct HL_isohex iso;
+
+ x = hex.x;
+ y = hex.y;
+
+ pi = x;
+ pj = -y;
+
+ if (x < 0) {
+ pj = pj + (-x + 1) / 2;
+ } else {
+ pj = pj - x/2;
+ }
+ pk = -pi - pj;
+
+ iso.i = pi;
+ iso.j = pj;
+ iso.k = pk;
+
+ return iso;
+}
+
+#if 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);
+}
+
+#endif
+
+struct HL_hex HL_ijk2xy(struct HL_isohex iso) {
+ int px, py;
+ struct HL_hex xy;
+ int i,j;
+
+ i = iso.i;
+ j = iso.j;
+
+ px = i;
+
+ /* py = -j - i/2; */
+ py = -j;
+
+ if (i < 0) {
+ py += (-i + 1)/2;
+ } else {
+ py -= i/2;
+ }
+
+ xy.x = px;
+ xy.y = py;
+
+ return xy;
+}
+
+
+static void xy2ijkp(struct HL_hex h, int *ijk) {
+ struct HL_isohex iso;
+
+ iso = HL_xy2ijk(h);
+ ijk[0] = iso.i;
+ ijk[1] = iso.j;
+ ijk[2] = iso.k;
+}
+
+int HL_distance(struct HL_hex from, struct HL_hex to) {
+ int dist = 0, i;;
+ int fc[3], tc[3];
+
+ xy2ijkp(from, fc);
+ xy2ijkp(to, tc);
+
+ for (i=0;i<=2;i++) {
+ dist += abs(fc[i] - tc[i]);
+ }
+
+ return dist / 2;
+}
+
+int HL_hexes_within_range(struct HL_hex hex, int range, struct HL_hex *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(struct HL_hex hex, int range, struct HL_hex *list, int size) {
+ int q; /* p and q are count/loop vars */
+ struct HL_isohex iso;
+
+
+ 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;
+
+ iso = HL_xy2ijk(hex);
+
+ iso.i += range;
+ iso.k = -iso.i - iso.j;
+
+ hex = HL_ijk2xy(iso);
+
+ for(q=0; q<size && q < range * 6; q++) {
+ list[q] = hex;
+ hex = HL_adjhex(hex, q/range+2);
+ }
+
+ return range * 6;
+}
+
+/* direction 0 is positive X , counter clockwise from there */
+struct HL_hex HL_adjhex(struct HL_hex hex, int dir) {
+ int c[3];
+ struct HL_isohex iso;
+
+ iso = HL_xy2ijk(hex);
+ c[0] = iso.i;
+ c[1] = iso.j;
+ c[2] = iso.k;
+
+ 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;
+ }
+
+ iso.i = c[0];
+ iso.j = c[1];
+ iso.k = c[2];
+
+ return HL_ijk2xy(iso);
+}
+
+int HL_adjhexp(struct HL_hex hex, int dir, struct HL_hex *adj) {
+ if (adj) {
+ *adj = HL_adjhex(hex, dir);
+ }
+ return dir;
+}
+
+/* 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;
+}
+
+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
+
+#define COS30 (.866025403784438646763723170752)
+
+struct HL_hex HL_hexbin(double width, double x, double y) {
+ double z, rx, ry, rz;
+ double abs_dx, abs_dy, abs_dz;
+ int ix, iy, iz, s;
+ struct hex h;
+ struct HL_hex hex;
+
+ /*x = x / cos(30 * M_PI / 180.0); */ /* rotated X coord */
+ x = x / COS30;
+ 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);
+
+ hex.x = h.x;
+ hex.y = h.y;
+
+ return hex;
+}
projects / hexagon / blobdiff