+#ifndef ISEA_STATIC
+#define ISEA_STATIC
+#endif
+
+enum isea_poly { ISEA_NONE, ISEA_ICOSAHEDRON = 20 };
+enum isea_topology { ISEA_HEXAGON=6, ISEA_TRIANGLE=3, ISEA_DIAMOND=4 };
+enum isea_address_form { ISEA_GEO, ISEA_Q2DI, ISEA_SEQNUM, ISEA_INTERLEAVE,
+ ISEA_PLANE, ISEA_Q2DD, ISEA_PROJTRI, ISEA_VERTEX2DD, ISEA_HEX
+};
+
+struct isea_dgg {
+ int polyhedron; /* ignored, icosahedron */
+ double o_lat, o_lon, o_az; /* orientation, radians */
+ int pole; /* true if standard snyder */
+ int topology; /* ignored, hexagon */
+ int aperture; /* valid values depend on partitioning method */
+ int resolution;
+ double radius; /* radius of the earth in meters, ignored 1.0 */
+ int output; /* an isea_address_form */
+ int triangle; /* triangle of last transformed point */
+ int quad; /* quad of last transformed point */
+ unsigned long serial;
+};
+
+struct isea_pt {
+ double x, y;
+};
+
+struct isea_geo {
+ double lon, lat;
+};
+
+struct isea_address {
+ int type; /* enum isea_address_form */
+ int number;
+ double x,y; /* or i,j or lon,lat depending on type */
+};
+
+/* ENDINC */
+
+enum snyder_polyhedron {
+ SNYDER_POLY_HEXAGON, SNYDER_POLY_PENTAGON,
+ SNYDER_POLY_TETRAHEDRON, SNYDER_POLY_CUBE,
+ SNYDER_POLY_OCTAHEDRON, SNYDER_POLY_DODECAHEDRON,
+ SNYDER_POLY_ICOSAHEDRON
+};
+
+struct snyder_constants {
+ double g, G, theta, ea_w, ea_a, ea_b, g_w, g_a, g_b;
+};
+
+/* TODO put these in radians to avoid a later conversion */
+ISEA_STATIC
+struct snyder_constants constants[] = {
+ {23.80018260, 62.15458023, 60.0, 3.75, 1.033, 0.968, 5.09, 1.195, 1.0},
+ {20.07675127, 55.69063953, 54.0, 2.65, 1.030, 0.983, 3.59, 1.141, 1.027},
+ {0.0},
+ {0.0},
+ {0.0},
+ {0.0},
+ {37.37736814, 36.0, 30.0, 17.27, 1.163, 0.860, 13.14, 1.584, 1.0},
+};
+
+#define E 52.62263186
+#define F 10.81231696
+
+#define DEG60 1.04719755119659774614
+#define DEG120 2.09439510239319549229
+#define DEG72 1.25663706143591729537
+#define DEG90 1.57079632679489661922
+#define DEG144 2.51327412287183459075
+#define DEG36 0.62831853071795864768
+#define DEG108 1.88495559215387594306
+#define DEG180 M_PI
+/* sqrt(5)/M_PI */
+#define ISEA_SCALE 0.8301572857837594396028083
+
+/* 26.565051177 degrees */
+#define V_LAT 0.46364760899944494524
+
+#define RAD2DEG (180.0/M_PI)
+#define DEG2RAD (M_PI/180.0)
+
+ISEA_STATIC
+struct isea_geo vertex[] = {
+ {0.0, DEG90},
+ {DEG180, V_LAT},
+ {-DEG108, V_LAT},
+ {-DEG36, V_LAT},
+ {DEG36, V_LAT},
+ {DEG108, V_LAT},
+ {-DEG144, -V_LAT},
+ {-DEG72, -V_LAT},
+ {0.0, -V_LAT},
+ {DEG72, -V_LAT},
+ {DEG144, -V_LAT},
+ {0.0, -DEG90}
+};
+
+/* TODO make an isea_pt array of the vertices as well */
+
+static int tri_v1[] = {0, 0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 2, 3, 4, 5, 1, 11, 11, 11, 11, 11};
+
+/* 52.62263186 */
+#define E_RAD 0.91843818702186776133
+
+/* 10.81231696 */
+#define F_RAD 0.18871053072122403508
+
+/* triangle Centers */
+struct isea_geo icostriangles[] = {
+ {0.0, 0.0},
+ {-DEG144, E_RAD},
+ {-DEG72, E_RAD},
+ {0.0, E_RAD},
+ {DEG72, E_RAD},
+ {DEG144, E_RAD},
+ {-DEG144, F_RAD},
+ {-DEG72, F_RAD},
+ {0.0, F_RAD},
+ {DEG72, F_RAD},
+ {DEG144, F_RAD},
+ {-DEG108, -F_RAD},
+ {-DEG36, -F_RAD},
+ {DEG36, -F_RAD},
+ {DEG108, -F_RAD},
+ {DEG180, -F_RAD},
+ {-DEG108, -E_RAD},
+ {-DEG36, -E_RAD},
+ {DEG36, -E_RAD},
+ {DEG108, -E_RAD},
+ {DEG180, -E_RAD},
+};
+
+static double
+az_adjustment(int triangle)
+{
+ double adj;
+
+ struct isea_geo v;
+ struct isea_geo c;
+
+ v = vertex[tri_v1[triangle]];
+ c = icostriangles[triangle];
+
+ /* TODO looks like the adjustment is always either 0 or 180 */
+ /* at least if you pick your vertex carefully */
+ adj = atan2(cos(v.lat) * sin(v.lon - c.lon),
+ cos(c.lat) * sin(v.lat)
+ - sin(c.lat) * cos(v.lat) * cos(v.lon - c.lon));
+ return adj;
+}
+
+/* R tan(g) sin(60) */
+#define TABLE_G 0.6615845383
+
+/* H = 0.25 R tan g = */
+#define TABLE_H 0.1909830056
+
+#define RPRIME 0.91038328153090290025
+
+ISEA_STATIC
+struct isea_pt
+isea_triangle_xy(int triangle)
+{
+ struct isea_pt c;
+ double Rprime = 0.91038328153090290025;
+
+ triangle = (triangle - 1) % 20;
+
+ c.x = TABLE_G * ((triangle % 5) - 2) * 2.0;
+ if (triangle > 9) {
+ c.x += TABLE_G;
+ }
+ switch (triangle / 5) {
+ case 0:
+ c.y = 5.0 * TABLE_H;
+ break;
+ case 1:
+ c.y = TABLE_H;
+ break;
+ case 2:
+ c.y = -TABLE_H;
+ break;
+ case 3:
+ c.y = -5.0 * TABLE_H;
+ break;
+ default:
+ /* should be impossible */
+ exit(EXIT_FAILURE);
+ };
+ c.x *= Rprime;
+ c.y *= Rprime;
+
+ return c;
+}
+
+/* snyder eq 14 */
+static double
+sph_azimuth(double f_lon, double f_lat, double t_lon, double t_lat)
+{
+ double az;
+
+ az = atan2(cos(t_lat) * sin(t_lon - f_lon),
+ cos(f_lat) * sin(t_lat)
+ - sin(f_lat) * cos(t_lat) * cos(t_lon - f_lon)
+ );
+ return az;
+}
+
+/* coord needs to be in radians */
+ISEA_STATIC
+int
+isea_snyder_forward(struct isea_geo * ll, struct isea_pt * out)
+{
+ int i;
+
+ /*
+ * spherical distance from center of polygon face to any of its
+ * vertexes on the globe
+ */
+ double g;
+
+ /*
+ * spherical angle between radius vector to center and adjacent edge
+ * of spherical polygon on the globe
+ */
+ double G;
+
+ /*
+ * plane angle between radius vector to center and adjacent edge of
+ * plane polygon
+ */
+ double theta;
+
+ /* additional variables from snyder */
+ double q, Rprime, H, Ag, Azprime, Az, dprime, f, rho,
+ x, y;
+
+ /* variables used to store intermediate results */
+ double cot_theta, tan_g, az_offset;
+
+ /* how many multiples of 60 degrees we adjust the azimuth */
+ int Az_adjust_multiples;
+
+ struct snyder_constants c;
+
+ /*
+ * TODO by locality of reference, start by trying the same triangle
+ * as last time
+ */
+
+ /* TODO put these constants in as radians to begin with */
+ c = constants[SNYDER_POLY_ICOSAHEDRON];
+ theta = c.theta * DEG2RAD;
+ g = c.g * DEG2RAD;
+ G = c.G * DEG2RAD;
+
+ for (i = 1; i <= 20; i++) {
+ double z;
+ struct isea_geo center;
+
+ center = icostriangles[i];
+
+ /* step 1 */
+#if 0
+ z = sph_distance(center.lon, center.lat, ll->lon, ll->lat);
+#else
+ z = acos(sin(center.lat) * sin(ll->lat)
+ + cos(center.lat) * cos(ll->lat) * cos(ll->lon - center.lon));
+#endif
+
+ /* not on this triangle */
+ if (z > g + 0.000005) { /* TODO DBL_EPSILON */
+ continue;
+ }
+ Az = sph_azimuth(ll->lon, ll->lat, center.lon, center.lat);
+
+ Az = atan2(cos(ll->lat) * sin(ll->lon - center.lon),
+ cos(center.lat) * sin(ll->lat)
+ - sin(center.lat) * cos(ll->lat) * cos(ll->lon - center.lon)
+ );
+
+ /* step 2 */
+
+ /* This calculates "some" vertex coordinate */
+ az_offset = az_adjustment(i);
+
+ Az -= az_offset;
+
+ /* TODO I don't know why we do this. It's not in snyder */
+ /* maybe because we should have picked a better vertex */
+ if (Az < 0.0) {
+ Az += 2.0 * M_PI;
+ }
+ /*
+ * adjust Az for the point to fall within the range of 0 to
+ * 2(90 - theta) or 60 degrees for the hexagon, by
+ * and therefore 120 degrees for the triangle
+ * of the icosahedron
+ * subtracting or adding multiples of 60 degrees to Az and
+ * recording the amount of adjustment
+ */
+
+ Az_adjust_multiples = 0;
+ while (Az < 0.0) {
+ Az += DEG120;
+ Az_adjust_multiples--;
+ }
+ while (Az > DEG120 + DBL_EPSILON) {
+ Az -= DEG120;
+ Az_adjust_multiples++;
+ }
+
+ /* step 3 */
+ cot_theta = 1.0 / tan(theta);
+ tan_g = tan(g); /* TODO this is a constant */
+
+ /* Calculate q from eq 9. */
+ /* TODO cot_theta is cot(30) */
+ q = atan2(tan_g, cos(Az) + sin(Az) * cot_theta);
+
+ /* not in this triangle */
+ if (z > q + 0.000005) {
+ continue;
+ }
+ /* step 4 */
+
+ /* Apply equations 5-8 and 10-12 in order */
+
+ /* eq 5 */
+ /* Rprime = 0.9449322893 * R; */
+ /* R' in the paper is for the truncated */
+ Rprime = 0.91038328153090290025;
+
+ /* eq 6 */
+ H = acos(sin(Az) * sin(G) * cos(g) - cos(Az) * cos(G));
+
+ /* eq 7 */
+ /* Ag = (Az + G + H - DEG180) * M_PI * R * R / DEG180; */
+ Ag = Az + G + H - DEG180;
+
+ /* eq 8 */
+ Azprime = atan2(2.0 * Ag, Rprime * Rprime * tan_g * tan_g - 2.0 * Ag * cot_theta);
+
+ /* eq 10 */
+ /* cot(theta) = 1.73205080756887729355 */
+ dprime = Rprime * tan_g / (cos(Azprime) + sin(Azprime) * cot_theta);
+
+ /* eq 11 */
+ f = dprime / (2.0 * Rprime * sin(q / 2.0));
+
+ /* eq 12 */
+ rho = 2.0 * Rprime * f * sin(z / 2.0);
+
+ /*
+ * add back the same 60 degree multiple adjustment from step
+ * 2 to Azprime
+ */
+
+ Azprime += DEG120 * Az_adjust_multiples;
+
+ /* calculate rectangular coordinates */
+
+ x = rho * sin(Azprime);
+ y = rho * cos(Azprime);
+
+ /*
+ * TODO
+ * translate coordinates to the origin for the particular
+ * hexagon on the flattened polyhedral map plot
+ */
+
+ out->x = x;
+ out->y = y;
+
+ return i;
+ }
+
+ /*
+ * should be impossible, this implies that the coordinate is not on
+ * any triangle
+ */
+
+ fprintf(stderr, "impossible transform: %f %f is not on any triangle\n",
+ ll->lon * RAD2DEG, ll->lat * RAD2DEG);
+
+ exit(EXIT_FAILURE);
+
+ /* not reached */
+ return 0; /* supresses a warning */
+}
+
+/*
+ * return the new coordinates of any point in orginal coordinate system.
+ * Define a point (newNPold) in orginal coordinate system as the North Pole in
+ * new coordinate system, and the great circle connect the original and new
+ * North Pole as the lon0 longitude in new coordinate system, given any point
+ * in orginal coordinate system, this function return the new coordinates.
+ */
+
+#define PRECISION 0.0000000000005
+
+/*
+ * TODO rename to isea_coordtrans and take an struct pointer to the result
+ * struct TODO remove function entirely. we use the synder one. the only
+ * difference is a 180 degree longitude rotation
+ */
+ISEA_STATIC
+struct isea_geo
+coordtrans(struct isea_geo * newNPold, struct isea_geo * ptold, double lon0)
+{
+ double cosptnewlat, cosptnewlon;
+ struct isea_geo ptnew;
+
+ cosptnewlat = sin(newNPold->lat) * sin(ptold->lat) +
+ cos(newNPold->lat) * cos(ptold->lat) * cos(newNPold->lon - ptold->lon);
+
+ if (cosptnewlat > 1.)
+ cosptnewlat = 1.0;
+ if (cosptnewlat < -1.)
+ cosptnewlat = -1.0;
+
+ ptnew.lat = acos(cosptnewlat);
+
+ if (fabs(ptnew.lat - 0.0) < PRECISION * 100000)
+ ptnew.lon = 0.0;
+ else if (fabs(ptnew.lat - M_PI) < PRECISION * 100000)
+ ptnew.lon = 0.0;
+ else {
+ cosptnewlon = (sin(ptold->lat) * cos(newNPold->lat) - cos(ptold->lat) *
+ sin(newNPold->lat) * cos(newNPold->lon - ptold->lon)) / sin(ptnew.lat);
+ if (cosptnewlon > 1.)
+ cosptnewlon = 1.0;
+ if (cosptnewlon < -1.)
+ cosptnewlon = -1.0;
+
+ ptnew.lon = acos(cosptnewlon);
+
+ if ((ptold->lon - newNPold->lon) >= 0 && (ptold->lon - newNPold->lon) < 180)
+ ptnew.lon = -ptnew.lon + lon0;
+
+ else
+ ptnew.lon = ptnew.lon + lon0;
+
+ if (ptnew.lon > M_PI)
+ ptnew.lon -= 2 * M_PI;
+ if (ptnew.lon < -M_PI)
+ ptnew.lon += 2 * M_PI;
+ }
+ ptnew.lat = M_PI / 2 - ptnew.lat;
+ return ptnew;
+}
+
+/* formula from Snyder, Map Projections: A working manual, p31 */
+/*
+ * old north pole at np in new coordinates
+ * could be simplified a bit with fewer intermediates
+ *
+ * TODO take a result pointer
+ */
+ISEA_STATIC
+struct isea_geo
+snyder_ctran(struct isea_geo * np, struct isea_geo * pt)
+{
+ struct isea_geo npt;
+ double alpha, phi, lambda, lambda0, beta, lambdap, phip;
+ double sin_phip;
+ double lp_b; /* lambda prime minus beta */
+ double cos_p, sin_a;
+
+ phi = pt->lat;
+ lambda = pt->lon;
+ alpha = np->lat;
+ beta = np->lon;
+ lambda0 = beta;
+
+ cos_p = cos(phi);
+ sin_a = sin(alpha);
+
+ /* mpawm 5-7 */
+ sin_phip = sin_a * sin(phi) - cos(alpha) * cos_p * cos(lambda - lambda0);
+
+ /* mpawm 5-8b */
+
+ /* use the two argument form so we end up in the right quadrant */
+ lp_b = atan2(cos_p * sin(lambda - lambda0),
+ (sin_a * cos_p * cos(lambda - lambda0) + cos(alpha) * sin(phi)));
+
+ lambdap = lp_b + beta;
+
+ /* normalize longitude */
+ /* TODO can we just do a modulus ? */
+ lambdap = fmod(lambdap, 2 * M_PI);
+ while (lambdap > M_PI)
+ lambdap -= 2 * M_PI;
+ while (lambdap < -M_PI)
+ lambdap += 2 * M_PI;
+
+ phip = asin(sin_phip);
+
+ npt.lat = phip;
+ npt.lon = lambdap;
+
+ return npt;
+}
+
+ISEA_STATIC
+struct isea_geo
+isea_ctran(struct isea_geo * np, struct isea_geo * pt, double lon0)
+{
+ struct isea_geo npt;
+
+ np->lon += M_PI;
+ npt = snyder_ctran(np, pt);
+ np->lon -= M_PI;
+
+ npt.lon -= (M_PI - lon0 + np->lon);
+
+ /*
+ * snyder is down tri 3, isea is along side of tri1 from vertex 0 to
+ * vertex 1 these are 180 degrees apart
+ */
+ npt.lon += M_PI;
+ /* normalize longitude */
+ npt.lon = fmod(npt.lon, 2 * M_PI);
+ while (npt.lon > M_PI)
+ npt.lon -= 2 * M_PI;
+ while (npt.lon < -M_PI)
+ npt.lon += 2 * M_PI;
+
+ return npt;
+}
+
+/* in radians */
+#define ISEA_STD_LAT 1.01722196792335072101
+#define ISEA_STD_LON .19634954084936207740
+
+ISEA_STATIC
+struct isea_dgg isea_standard_dgg = {
+ 20, 58.28252559, 11.25, 0.0,
+ 6, 4, 0, 6, 1.0
+};
+
+/* fuller's at 5.2454 west, 2.3009 N, adjacent at 7.46658 deg */
+
+ISEA_STATIC
+int
+isea_grid_init(struct isea_dgg * g)
+{
+ if (!g)
+ return 0;
+
+ g->polyhedron = 20;
+ g->o_lat = ISEA_STD_LAT;
+ g->o_lon = ISEA_STD_LON;
+ g->o_az = 0.0;
+ g->aperture = 4;
+ g->resolution = 6;
+ g->radius = 1.0;
+ g->topology = 6;
+
+ return 1;
+}
+
+ISEA_STATIC
+int
+isea_orient_isea(struct isea_dgg * g)
+{
+ if (!g)
+ return 0;
+ g->o_lat = ISEA_STD_LAT;
+ g->o_lon = ISEA_STD_LON;
+ g->o_az = 0.0;
+ return 1;
+}
+
+ISEA_STATIC
+int
+isea_orient_pole(struct isea_dgg * g)
+{
+ if (!g)
+ return 0;
+ g->o_lat = M_PI / 2.0;
+ g->o_lon = 0.0;
+ g->o_az = 0;
+ return 1;
+}
+
+ISEA_STATIC
+int
+isea_orient_dymax(struct isea_dgg * g)
+{
+ if (!g)
+ return 0;
+ g->o_lat = 2.300882 * M_PI / 180.0;
+ g->o_lon = -5.24539 * M_PI / 180.0;
+ g->o_az = 7.46658 * M_PI / 180.0;
+ return 1;
+}
+
+ISEA_STATIC
+int
+isea_transform(struct isea_dgg * g, struct isea_geo * in,
+ struct isea_pt * out)
+{
+ struct isea_geo i, pole;
+ int tri;
+
+ pole.lat = g->o_lat;
+ pole.lon = g->o_lon;
+
+ i = isea_ctran(&pole, in, g->o_az);
+
+ tri = isea_snyder_forward(&i, out);
+ out->x *= g->radius;
+ out->y *= g->radius;
+ g->triangle = tri;
+
+ return tri;
+}
+
+#define DOWNTRI(tri) (((tri - 1) / 5) % 2 == 1)
+
+/* get which triangle a point is in, assumes radius = 1.0 */
+ISEA_STATIC
+int isea_xy_triangle(struct isea_pt *p, double radius) {
+ double dist, test;
+ int tri, closest;
+ struct isea_pt tc, pt;
+ pt.x = p->x / radius;
+ pt.y = p->y / radius;
+
+ tc = isea_triangle_xy(1);
+ dist = (pt.x - tc.x) * (pt.x - tc.x) + (pt.y - tc.y) * (pt.y - tc.y);
+ closest = 1;
+
+ /* TODO just calculate it directly, no need to actually do all this
+ * work
+ */
+ for (tri = 2; tri <= 20; tri++) {
+ tc = isea_triangle_xy(tri);
+ test = (pt.x - tc.x) * (pt.x - tc.x) + (pt.y - tc.y) * (pt.y - tc.y);
+ if (test < dist) {
+ dist = test;
+ closest = tri;
+ }
+ }
+ return closest;
+}
+
+ISEA_STATIC
+int isea_projtri(struct isea_pt *xy, double radius) {
+ int tri;
+
+ tri = isea_xy_triangle(xy, radius);
+
+ xy->x /= radius;
+ xy->y /= radius;
+ xy->x += 0.5;
+ xy->y += 2.0 * .14433756729740644112;
+
+ return tri;
+}
+
+ISEA_STATIC
+void
+isea_rotate(struct isea_pt * pt, double degrees)
+{
+ double rad;
+
+ double x, y;
+
+ rad = -degrees * M_PI / 180.0;
+ while (rad >= 2.0 * M_PI) rad -= 2.0 * M_PI;
+ while (rad <= -2.0 * M_PI) rad += 2.0 * M_PI;
+
+ x = pt->x * cos(rad) + pt->y * sin(rad);
+ y = -pt->x * sin(rad) + pt->y * cos(rad);
+
+ pt->x = x;
+ pt->y = y;
+}
+
+ISEA_STATIC
+int isea_tri_plane(int tri, struct isea_pt *pt, double radius) {
+ struct isea_pt tc; /* center of triangle */
+
+ if (DOWNTRI(tri)) {
+ isea_rotate(pt, 180.0);
+ }
+ tc = isea_triangle_xy(tri);
+ tc.x *= radius;
+ tc.y *= radius;
+ pt->x += tc.x;
+ pt->y += tc.y;
+
+ return tri;
+}
+
+ISEA_STATIC
+int isea_projection(struct isea_dgg *g, double xin, double yin, double *xout,
+ double *yout) {
+ return 1;
+}
+
+/* convert projected triangle coords to quad xy coords, return quad number */
+ISEA_STATIC
+int
+isea_ptdd(int tri, struct isea_pt *pt) {
+ int downtri, quad;
+
+ downtri = (((tri - 1) / 5) % 2 == 1);
+ quad = ((tri - 1) % 5) + ((tri - 1) / 10) * 5 + 1;
+
+ isea_rotate(pt, downtri ? 240.0 : 60.0);
+ if (downtri) {
+ pt->x += 0.5;
+ /* pt->y += cos(30.0 * M_PI / 180.0); */
+ pt->y += .86602540378443864672;
+ }
+ return quad;
+}
+
+ISEA_STATIC
+int
+isea_dddi_ap3odd(struct isea_dgg *g, int quad, struct isea_pt *pt, struct isea_pt *di)
+{
+ struct isea_pt v;
+ double hexwidth;
+ double sidelength; /* in hexes */
+ int d, i;
+ int maxcoord;
+ struct hex h;
+
+ /* This is the number of hexes from apex to base of a triangle */
+ sidelength = (pow(2.0, g->resolution) + 1.0) / 2.0;
+
+ /* apex to base is cos(30deg) */
+ hexwidth = cos(M_PI / 6.0) / sidelength;
+
+ /* TODO I think sidelength is always x.5, so
+ * (int)sidelength * 2 + 1 might be just as good
+ */
+ maxcoord = (int) (sidelength * 2.0 + 0.5);
+
+ v = *pt;
+ hexbin2(0, hexwidth, v.x, v.y, &h.x, &h.y);
+ h.iso = 0;
+ hex_iso(&h);
+
+ d = h.x - h.z;
+ i = h.x + h.y + h.y;
+
+ /*
+ * you want to test for max coords for the next quad in the same
+ * "row" first to get the case where both are max
+ */
+ if (quad <= 5) {
+ if (d == 0 && i == maxcoord) {
+ /* north pole */
+ quad = 0;
+ d = 0;
+ i = 0;
+ } else if (i == maxcoord) {
+ /* upper right in next quad */
+ quad += 1;
+ if (quad == 6)
+ quad = 1;
+ i = maxcoord - d;
+ d = 0;
+ } else if (d == maxcoord) {
+ /* lower right in quad to lower right */
+ quad += 5;
+ d = 0;
+ }
+ } else if (quad >= 6) {
+ if (i == 0 && d == maxcoord) {
+ /* south pole */
+ quad = 11;
+ d = 0;
+ i = 0;
+ } else if (d == maxcoord) {
+ /* lower right in next quad */
+ quad += 1;
+ if (quad == 11)
+ quad = 6;
+ d = maxcoord - i;
+ i = 0;
+ } else if (i == maxcoord) {
+ /* upper right in quad to upper right */
+ quad = (quad - 4) % 5;
+ i = 0;
+ }
+ }
+
+ di->x = d;
+ di->y = i;
+
+ g->quad = quad;
+ return quad;
+}
+
+ISEA_STATIC
+int
+isea_dddi(struct isea_dgg *g, int quad, struct isea_pt *pt, struct isea_pt *di) {
+ struct isea_pt v;
+ double hexwidth;
+ int sidelength; /* in hexes */
+ struct hex h;
+
+ if (g->aperture == 3 && g->resolution % 2 != 0) {
+ return isea_dddi_ap3odd(g, quad, pt, di);
+ }
+ /* todo might want to do this as an iterated loop */
+ if (g->aperture >0) {
+ sidelength = (int) (pow(g->aperture, g->resolution / 2.0) + 0.5);
+ } else {
+ sidelength = g->resolution;
+ }
+
+ hexwidth = 1.0 / sidelength;
+
+ v = *pt;
+ isea_rotate(&v, -30.0);
+ hexbin2(0, hexwidth, v.x, v.y, &h.x, &h.y);
+ h.iso = 0;
+ hex_iso(&h);
+
+ /* we may actually be on another quad */
+ if (quad <= 5) {
+ if (h.x == 0 && h.z == -sidelength) {
+ /* north pole */
+ quad = 0;
+ h.z = 0;
+ h.y = 0;
+ h.x = 0;
+ } else if (h.z == -sidelength) {
+ quad = quad + 1;
+ if (quad == 6)
+ quad = 1;
+ h.y = sidelength - h.x;
+ h.z = h.x - sidelength;
+ h.x = 0;
+ } else if (h.x == sidelength) {
+ quad += 5;
+ h.y = -h.z;
+ h.x = 0;
+ }
+ } else if (quad >= 6) {
+ if (h.z == 0 && h.x == sidelength) {
+ /* south pole */
+ quad = 11;
+ h.x = 0;
+ h.y = 0;
+ h.z = 0;
+ } else if (h.x == sidelength) {
+ quad = quad + 1;
+ if (quad == 11)
+ quad = 6;
+ h.x = h.y + sidelength;
+ h.y = 0;
+ h.z = -h.x;
+ } else if (h.y == -sidelength) {
+ quad -= 4;
+ h.y = 0;
+ h.z = -h.x;
+ }
+ }
+ di->x = h.x;
+ di->y = -h.z;
+
+ g->quad = quad;
+ return quad;
+}
+
+ISEA_STATIC
+int isea_ptdi(struct isea_dgg *g, int tri, struct isea_pt *pt,
+ struct isea_pt *di) {
+ struct isea_pt v;
+ int quad;
+
+ v = *pt;
+ quad = isea_ptdd(tri, &v);
+ quad = isea_dddi(g, quad, &v, di);
+ return quad;
+}
+
+/* q2di to seqnum */
+ISEA_STATIC
+int isea_disn(struct isea_dgg *g, int quad, struct isea_pt *di) {
+ int sidelength;
+ int sn, height;
+ int hexes;
+
+ if (quad == 0) {
+ g->serial = 1;
+ return g->serial;
+ }
+ /* hexes in a quad */
+ hexes = (int) (pow(g->aperture, g->resolution) + 0.5);
+ if (quad == 11) {
+ g->serial = 1 + 10 * hexes + 1;
+ return g->serial;
+ }
+ if (g->aperture == 3 && g->resolution % 2 == 1) {
+ height = (int) (pow(g->aperture, (g->resolution - 1) / 2.0));
+ sn = ((int) di->x) * height;
+ sn += ((int) di->y) / height;
+ sn += (quad - 1) * hexes;
+ sn += 2;
+ } else {
+ sidelength = (int) (pow(g->aperture, g->resolution / 2.0) + 0.5);
+ sn = (quad - 1) * hexes + sidelength * di->x + di->y + 2;
+ }
+
+ g->serial = sn;
+ return sn;
+}
+
+/* TODO just encode the quad in the d or i coordinate
+ * quad is 0-11, which can be four bits.
+ * d' = d << 4 + q, d = d' >> 4, q = d' & 0xf
+ */
+/* convert a q2di to global hex coord */
+ISEA_STATIC
+int isea_hex(struct isea_dgg *g, int tri,
+ struct isea_pt *pt, struct isea_pt *hex) {
+ struct isea_pt v;
+ int sidelength;
+ int d, i, x, y, quad;
+ double oddsl;
+
+ quad = isea_ptdi(g, tri, pt, &v);
+
+ hex->x = ((int)v.x << 4) + quad;
+ hex->y = v.y;
+
+ return 1;
+
+ d = v.x;
+ i = v.y;
+
+ /* Aperture 3 odd resolutions */
+ if (g->aperture == 3 && g->resolution % 2 != 0) {
+ int offset = (int)(pow(3.0, g->resolution - 1) + 0.5);
+
+ oddsl = (pow(2.0, g->resolution) + 1.0) / 2.0;
+
+ d += offset * ((g->quad-1) % 5);
+ i += offset * ((g->quad-1) % 5);
+
+ if (quad == 0) {
+ d = 0;
+ i = offset;
+ } else if (quad == 11) {
+ d = 2 * offset;
+ i = 0;
+ } else if (quad > 5) {
+ d += offset;
+ }
+
+ x = (2*d - i) /3;
+ y = (2*i - d) /3;
+
+ hex->x = x + offset / 3;
+ hex->y = y + 2 * offset / 3;
+ return 1;
+ }
+
+ /* aperture 3 even resolutions and aperture 4 */
+ sidelength = (int) (pow(g->aperture, g->resolution / 2.0) + 0.5);
+ if (g->quad == 0) {
+ hex->x = 0;
+ hex->y = sidelength;
+ } else if (g->quad == 11) {
+ hex->x = sidelength * 2;
+ hex->y = 0;
+ } else {
+ hex->x = d + sidelength * ((g->quad-1) % 5);
+ if (g->quad > 5) hex->x += sidelength;
+ hex->y = i + sidelength * ((g->quad-1) % 5);
+ }
+
+ return 1;
+}
+
+ISEA_STATIC
+struct isea_pt
+isea_forward(struct isea_dgg *g, struct isea_geo *in)
+{
+ int tri, downtri, quad;
+ struct isea_pt out, coord;
+
+ tri = isea_transform(g, in, &out);
+
+ downtri = (((tri - 1) / 5) % 2 == 1);
+ quad = ((tri - 1) % 5) + ((tri - 1) / 10) * 5 + 1;
+
+ if (g->output == ISEA_PLANE) {
+ isea_tri_plane(tri, &out, g->radius);
+ return out;
+ }
+
+ /* convert to isea standard triangle size */
+ out.x = out.x / g->radius * ISEA_SCALE;
+ out.y = out.y / g->radius * ISEA_SCALE;
+ out.x += 0.5;
+ out.y += 2.0 * .14433756729740644112;
+
+ switch (g->output) {
+ case ISEA_PROJTRI:
+ /* nothing to do, already in projected triangle */
+ break;
+ case ISEA_VERTEX2DD:
+ g->quad = isea_ptdd(tri, &out);
+ break;
+ case ISEA_Q2DD:
+ /* Same as above, we just don't print as much */
+ g->quad = isea_ptdd(tri, &out);
+ break;
+ case ISEA_Q2DI:
+ g->quad = isea_ptdi(g, tri, &out, &coord);
+ return coord;
+ break;
+ case ISEA_SEQNUM:
+ isea_ptdi(g, tri, &out, &coord);
+ /* disn will set g->serial */
+ isea_disn(g, g->quad, &coord);
+ return coord;
+ break;
+ case ISEA_HEX:
+ isea_hex(g, tri, &out, &coord);
+ return coord;
+ break;
+ }
+
+ return out;
+}