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);
}
// convert projected triangle coords to quad xy coords, return quad number
static int isea_ptdd(int tri, ref isea_pt pt)
{
bool downtri = (((tri - 1) / 5) % 2 == 1);
int quad = ((tri - 1) % 5) + ((tri - 1) / 10) * 5 + 1;
isea_rotate(ref pt, downtri?240.0:60.0);
if (downtri)
{
pt.x += 0.5;
// pt->y += cos(30.0 * Math.PI / 180.0);
pt.y += 0.86602540378443864672;
}
return(quad);
}
static int isea_tri_plane(int tri, ref isea_pt pt, double radius)
{
isea_pt tc; // center of triangle
if (((tri - 1) / 5) % 2 == 1)
{
isea_rotate(ref pt, 180.0);
}
tc = isea_triangle_xy(tri);
tc.x *= radius;
tc.y *= radius;
pt.x += tc.x;
pt.y += tc.y;
return(tri);
}
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);
}
// Proj 4 integration code follows
// spheroid
XY s_forward(LP lp)
{
XY xy;
xy.x = xy.y = 0;
isea_geo @in;
@in.lon = lp.lam;
@in.lat = lp.phi;
isea_pt @out = isea_forward(dgg, @in);
xy.x = @out.x;
xy.y = @out.y;
return(xy);
}
static void isea_rotate(ref isea_pt pt, double degrees)
{
double rad = -degrees * Math.PI / 180.0;
while (rad >= 2.0 * Math.PI)
{
rad -= 2.0 * Math.PI;
}
while (rad <= -2.0 * Math.PI)
{
rad += 2.0 * Math.PI;
}
double x = pt.x * Math.Cos(rad) + pt.y * Math.Sin(rad);
double y = -pt.x * Math.Sin(rad) + pt.y * Math.Cos(rad);
pt.x = x;
pt.y = y;
}
// 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);
}
// coord needs to be in radians
static int isea_snyder_forward(isea_geo ll, out isea_pt @out)
{
// TODO by locality of reference, start by trying the same triangle
// as last time
// TODO put these constants in as radians to begin with
snyder_constants c=constants[(int)snyder_polyhedron.SNYDER_POLY_ICOSAHEDRON];
// plane angle between radius vector to center and adjacent edge of
// plane polygon
double theta=c.theta*DEG2RAD;
// spherical distance from center of polygon face to any of its
// vertexes on the globe
double g=c.g*DEG2RAD;
// spherical angle between radius vector to center and adjacent edge
// of spherical polygon on the globe
double G=c.G*DEG2RAD;
for(int i=1; i<=20; i++)
{
double z;
isea_geo center;
center=icostriangles[i];
// step 1
z=Math.Acos(Math.Sin(center.lat)*Math.Sin(ll.lat)+Math.Cos(center.lat)*Math.Cos(ll.lat)*Math.Cos(ll.lon-center.lon));
// not on this triangle
if(z>g+0.000005) continue; // TODO DBL_EPSILON
double Az=sph_azimuth(center.lon, center.lat, ll.lon, ll.lat);
// step 2
// This calculates "some" vertex coordinate
double 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*Math.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
int Az_adjust_multiples=0; // how many multiples of 60 degrees we adjust the azimuth
while(Az<0.0)
{
Az+=DEG120;
Az_adjust_multiples--;
}
while(Az>DEG120+double.Epsilon)
{
Az-=DEG120;
Az_adjust_multiples++;
}
// step 3
double cot_theta=1.0/Math.Tan(theta);
double tan_g=Math.Tan(g); // TODO this is a constant
// Calculate q from eq 9.
// TODO cot_theta is cot(30)
double q=Math.Atan2(tan_g, Math.Cos(Az)+Math.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
double Rprime=0.91038328153090290025;
// eq 6
double H=Math.Acos(Math.Sin(Az)*Math.Sin(G)*Math.Cos(g)-Math.Cos(Az)*Math.Cos(G));
// eq 7
// Ag = (Az + G + H - DEG180) * M_PI * R * R / DEG180;
double Ag=Az+G+H-DEG180;
// eq 8
double Azprime=Math.Atan2(2.0*Ag, Rprime*Rprime*tan_g*tan_g-2.0*Ag*cot_theta);
// eq 10
// cot(theta) = 1.73205080756887729355
double dprime=Rprime*tan_g/(Math.Cos(Azprime)+Math.Sin(Azprime)*cot_theta);
// eq 11
double f=dprime/(2.0*Rprime*Math.Sin(q/2.0));
// eq 12
double rho=2.0*Rprime*f*Math.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
double x=rho*Math.Sin(Azprime);
double y=rho*Math.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);
throw new Exception();
}
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 void isea_rotate(ref isea_pt pt, double degrees)
{
double rad=-degrees*Math.PI/180.0;
while(rad>=2.0*Math.PI) rad-=2.0*Math.PI;
while(rad<=-2.0*Math.PI) rad+=2.0*Math.PI;
double x=pt.x*Math.Cos(rad)+pt.y*Math.Sin(rad);
double y=-pt.x*Math.Sin(rad)+pt.y*Math.Cos(rad);
pt.x=x;
pt.y=y;
}
// 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
}
// convert projected triangle coords to quad xy coords, return quad number
static int isea_ptdd(int tri, ref isea_pt pt)
{
bool downtri=(((tri-1)/5)%2==1);
int quad=((tri-1)%5)+((tri-1)/10)*5+1;
isea_rotate(ref pt, downtri?240.0:60.0);
if(downtri)
{
pt.x+=0.5;
// pt->y += cos(30.0 * Math.PI / 180.0);
pt.y+=0.86602540378443864672;
}
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;
}
// 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(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;
}
// coord needs to be in radians
static int isea_snyder_forward(isea_geo ll, out isea_pt @out)
{
// TODO by locality of reference, start by trying the same triangle
// as last time
// TODO put these constants in as radians to begin with
snyder_constants c = constants[(int)snyder_polyhedron.SNYDER_POLY_ICOSAHEDRON];
// plane angle between radius vector to center and adjacent edge of
// plane polygon
double theta = c.theta * DEG2RAD;
// spherical distance from center of polygon face to any of its
// vertexes on the globe
double g = c.g * DEG2RAD;
// spherical angle between radius vector to center and adjacent edge
// of spherical polygon on the globe
double G = c.G * DEG2RAD;
for (int i = 1; i <= 20; i++)
{
double z;
isea_geo center;
center = icostriangles[i];
// step 1
z = Math.Acos(Math.Sin(center.lat) * Math.Sin(ll.lat) + Math.Cos(center.lat) * Math.Cos(ll.lat) * Math.Cos(ll.lon - center.lon));
// not on this triangle
if (z > g + 0.000005)
{
continue; // TODO DBL_EPSILON
}
double Az = sph_azimuth(center.lon, center.lat, ll.lon, ll.lat);
// step 2
// This calculates "some" vertex coordinate
double 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 * Math.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
int Az_adjust_multiples = 0; // how many multiples of 60 degrees we adjust the azimuth
while (Az < 0.0)
{
Az += DEG120;
Az_adjust_multiples--;
}
while (Az > DEG120 + double.Epsilon)
{
Az -= DEG120;
Az_adjust_multiples++;
}
// step 3
double cot_theta = 1.0 / Math.Tan(theta);
double tan_g = Math.Tan(g); // TODO this is a constant
// Calculate q from eq 9.
// TODO cot_theta is cot(30)
double q = Math.Atan2(tan_g, Math.Cos(Az) + Math.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
double Rprime = 0.91038328153090290025;
// eq 6
double H = Math.Acos(Math.Sin(Az) * Math.Sin(G) * Math.Cos(g) - Math.Cos(Az) * Math.Cos(G));
// eq 7
// Ag = (Az + G + H - DEG180) * M_PI * R * R / DEG180;
double Ag = Az + G + H - DEG180;
// eq 8
double Azprime = Math.Atan2(2.0 * Ag, Rprime * Rprime * tan_g * tan_g - 2.0 * Ag * cot_theta);
// eq 10
// cot(theta) = 1.73205080756887729355
double dprime = Rprime * tan_g / (Math.Cos(Azprime) + Math.Sin(Azprime) * cot_theta);
// eq 11
double f = dprime / (2.0 * Rprime * Math.Sin(q / 2.0));
// eq 12
double rho = 2.0 * Rprime * f * Math.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
double x = rho * Math.Sin(Azprime);
double y = rho * Math.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);
throw new Exception();
}
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;
}
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 int isea_tri_plane(int tri, ref isea_pt pt, double radius)
{
isea_pt tc; // center of triangle
if(((tri-1)/5)%2==1) isea_rotate(ref pt, 180.0);
tc=isea_triangle_xy(tri);
tc.x*=radius;
tc.y*=radius;
pt.x+=tc.x;
pt.y+=tc.y;
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
}
