static int isea_ptdi(ref isea_dgg g, int tri, isea_pt pt, out isea_pt di)
{
isea_pt v = pt;
int quad = isea_ptdd(tri, ref v);
quad = isea_dddi(ref g, quad, v, out di);
return(quad);
}
// fuller's at 5.2454 west, 2.3009 N, adjacent at 7.46658 deg
static void isea_grid_init(ref isea_dgg g)
{
g.polyhedron = isea_poly.ISEA_ICOSAHEDRON;
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 = isea_topology.ISEA_HEXAGON;
}
static isea_pt isea_forward(isea_dgg g, isea_geo @in)
{
isea_pt @out, coord;
int tri = isea_transform(ref g, @in, out @out);
if (g.output == isea_address_form.ISEA_PLANE)
{
isea_tri_plane(tri, ref @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_address_form.ISEA_PROJTRI:
// nothing to do, already in projected triangle
break;
case isea_address_form.ISEA_VERTEX2DD:
g.quad = isea_ptdd(tri, ref @out);
break;
case isea_address_form.ISEA_Q2DD:
// Same as above, we just don't print as much
g.quad = isea_ptdd(tri, ref @out);
break;
case isea_address_form.ISEA_Q2DI:
g.quad = isea_ptdi(ref g, tri, @out, out coord);
return(coord);
case isea_address_form.ISEA_SEQNUM:
isea_ptdi(ref g, tri, @out, out coord);
// disn will set g->serial
isea_disn(ref g, g.quad, coord);
return(coord);
case isea_address_form.ISEA_HEX:
isea_hex(ref g, tri, @out, out coord);
return(coord);
}
return(@out);
}
static int isea_transform(ref isea_dgg g, isea_geo @in, out isea_pt @out)
{
isea_geo pole;
pole.lat = g.o_lat;
pole.lon = g.o_lon;
isea_geo i = isea_ctran(ref pole, @in, g.o_az);
int tri = isea_snyder_forward(i, out @out);
@out.x *= g.radius;
@out.y *= g.radius;
g.triangle = tri;
return(tri);
}
// q2di to seqnum
static int isea_disn(ref isea_dgg g, int quad, isea_pt di)
{
if (quad == 0)
{
g.serial = 1;
return(1);
}
// hexes in a quad
int hexes = (int)(Math.Pow(g.aperture, g.resolution) + 0.5);
if (quad == 11)
{
g.serial = (ulong)(1 + 10 * hexes + 1);
return((int)g.serial);
}
int sn;
if (g.aperture == 3 && g.resolution % 2 == 1)
{
int height = (int)(Math.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
{
int sidelength = (int)(Math.Pow(g.aperture, g.resolution / 2.0) + 0.5);
sn = (int)((quad - 1) * hexes + sidelength * di.x + di.y + 2);
}
g.serial = (ulong)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
static int isea_hex(ref isea_dgg g, int tri, isea_pt pt, out isea_pt hex)
{
isea_pt v;
int quad=isea_ptdi(ref g, tri, pt, out v);
hex.x=((int)v.x<<4)+quad;
hex.y=v.y;
return 1;
// silence the compiler
#if false
double d=v.x;
double i=v.y;
// Aperture 3 odd resolutions
if(g.aperture==3&&g.resolution%2!=0)
{
int offset=(int)(Math.Pow(3.0, g.resolution-1)+0.5);
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;
}
double x=(2*d-i)/3;
double 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
double sidelength=(int)(Math.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;
#endif
}
// fuller's at 5.2454 west, 2.3009 N, adjacent at 7.46658 deg
static void isea_grid_init(ref isea_dgg g)
{
g.polyhedron=isea_poly.ISEA_ICOSAHEDRON;
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=isea_topology.ISEA_HEXAGON;
}
static isea_pt isea_forward(isea_dgg g, isea_geo @in)
{
isea_pt @out, coord;
int tri=isea_transform(ref g, @in, out @out);
if(g.output==isea_address_form.ISEA_PLANE)
{
isea_tri_plane(tri, ref @out, g.radius);
return @out;
}
// convert to isea standard triangle size
@[email protected]/g.radius*ISEA_SCALE;
@[email protected]/g.radius*ISEA_SCALE;
@out.x+=0.5;
@out.y+=2.0*.14433756729740644112;
switch(g.output)
{
case isea_address_form.ISEA_PROJTRI:
// nothing to do, already in projected triangle
break;
case isea_address_form.ISEA_VERTEX2DD:
g.quad=isea_ptdd(tri, ref @out);
break;
case isea_address_form.ISEA_Q2DD:
// Same as above, we just don't print as much
g.quad=isea_ptdd(tri, ref @out);
break;
case isea_address_form.ISEA_Q2DI:
g.quad=isea_ptdi(ref g, tri, @out, out coord);
return coord;
case isea_address_form.ISEA_SEQNUM:
isea_ptdi(ref g, tri, @out, out coord);
// disn will set g->serial
isea_disn(ref g, g.quad, coord);
return coord;
case isea_address_form.ISEA_HEX:
isea_hex(ref g, tri, @out, out coord);
return coord;
}
return @out;
}
// q2di to seqnum
static int isea_disn(ref isea_dgg g, int quad, isea_pt di)
{
if(quad==0)
{
g.serial=1;
return 1;
}
// hexes in a quad
int hexes=(int)(Math.Pow(g.aperture, g.resolution)+0.5);
if(quad==11)
{
g.serial=(ulong)(1+10*hexes+1);
return (int)g.serial;
}
int sn;
if(g.aperture==3&&g.resolution%2==1)
{
int height=(int)(Math.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
{
int sidelength=(int)(Math.Pow(g.aperture, g.resolution/2.0)+0.5);
sn=(int)((quad-1)*hexes+sidelength*di.x+di.y+2);
}
g.serial=(ulong)sn;
return sn;
}
static int isea_dddi_ap3odd(ref isea_dgg g, int quad, isea_pt pt, out isea_pt di)
{
// This is the number of hexes from apex to base of a triangle
double sidelength=(Math.Pow(2.0, g.resolution)+1.0)/2.0; // in hexes
// apex to base is cos(30deg)
double hexwidth=Math.Cos(Math.PI/6.0)/sidelength;
// TODO I think sidelength is always x.5, so
// (int)sidelength * 2 + 1 might be just as good
int maxcoord=(int)(sidelength*2.0+0.5);
isea_pt v=pt;
hex h;
h.z=0;
hexbin2(hexwidth, v.x, v.y, out h.x, out h.y);
h.iso=false;
hex_iso(ref h);
int d=h.x-h.z;
int 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;
}
static int isea_ptdi(ref isea_dgg g, int tri, isea_pt pt, out isea_pt di)
{
isea_pt v=pt;
int quad=isea_ptdd(tri, ref v);
quad=isea_dddi(ref g, quad, v, out di);
return quad;
}
static int isea_dddi(ref isea_dgg g, int quad, isea_pt pt, out isea_pt di)
{
if (g.aperture == 3 && g.resolution % 2 != 0)
{
return(isea_dddi_ap3odd(ref g, quad, pt, out di));
}
// todo might want to do this as an iterated loop
int sidelength; // in hexes
if (g.aperture > 0)
{
sidelength = (int)(Math.Pow(g.aperture, g.resolution / 2.0) + 0.5);
}
else
{
sidelength = g.resolution;
}
double hexwidth = 1.0 / sidelength;
isea_pt v = pt;
hex h;
h.z = 0;
isea_rotate(ref v, -30.0);
hexbin2(hexwidth, v.x, v.y, out h.x, out h.y);
h.iso = false;
hex_iso(ref 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);
}
static int isea_dddi_ap3odd(ref isea_dgg g, int quad, isea_pt pt, out isea_pt di)
{
// This is the number of hexes from apex to base of a triangle
double sidelength = (Math.Pow(2.0, g.resolution) + 1.0) / 2.0; // in hexes
// apex to base is cos(30deg)
double hexwidth = Math.Cos(Math.PI / 6.0) / sidelength;
// TODO I think sidelength is always x.5, so
// (int)sidelength * 2 + 1 might be just as good
int maxcoord = (int)(sidelength * 2.0 + 0.5);
isea_pt v = pt;
hex h;
h.z = 0;
hexbin2(hexwidth, v.x, v.y, out h.x, out h.y);
h.iso = false;
hex_iso(ref h);
int d = h.x - h.z;
int 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);
}
static void isea_orient_pole(ref isea_dgg g)
{
g.o_lat = Math.PI / 2.0;
g.o_lon = 0.0;
g.o_az = 0;
}
static void isea_orient_isea(ref isea_dgg g)
{
g.o_lat = ISEA_STD_LAT;
g.o_lon = ISEA_STD_LON;
g.o_az = 0.0;
}
static void isea_orient_isea(ref isea_dgg g)
{
g.o_lat=ISEA_STD_LAT;
g.o_lon=ISEA_STD_LON;
g.o_az=0.0;
}
static void isea_orient_pole(ref isea_dgg g)
{
g.o_lat=Math.PI/2.0;
g.o_lon=0.0;
g.o_az=0;
}
static int isea_dddi(ref isea_dgg g, int quad, isea_pt pt, out isea_pt di)
{
if(g.aperture==3&&g.resolution%2!=0)
return isea_dddi_ap3odd(ref g, quad, pt, out di);
// todo might want to do this as an iterated loop
int sidelength; // in hexes
if(g.aperture>0) sidelength=(int)(Math.Pow(g.aperture, g.resolution/2.0)+0.5);
else sidelength=g.resolution;
double hexwidth=1.0/sidelength;
isea_pt v=pt;
hex h;
h.z=0;
isea_rotate(ref v, -30.0);
hexbin2(hexwidth, v.x, v.y, out h.x, out h.y);
h.iso=false;
hex_iso(ref 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;
}
static int isea_transform(ref isea_dgg g, isea_geo @in, out isea_pt @out)
{
isea_geo pole;
pole.lat=g.o_lat;
pole.lon=g.o_lon;
isea_geo i=isea_ctran(ref pole, @in, g.o_az);
int tri=isea_snyder_forward(i, out @out);
@out.x*=g.radius;
@out.y*=g.radius;
g.triangle=tri;
return tri;
}
// 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
static int isea_hex(ref isea_dgg g, int tri, isea_pt pt, out isea_pt hex)
{
isea_pt v;
int quad = isea_ptdi(ref g, tri, pt, out v);
hex.x = ((int)v.x << 4) + quad;
hex.y = v.y;
return(1);
// silence the compiler
#if false
double d = v.x;
double i = v.y;
// Aperture 3 odd resolutions
if (g.aperture == 3 && g.resolution % 2 != 0)
{
int offset = (int)(Math.Pow(3.0, g.resolution - 1) + 0.5);
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;
}
double x = (2 * d - i) / 3;
double 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
double sidelength = (int)(Math.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);
#endif
}
