static isea_geo isea_ctran(ref isea_geo np, isea_geo pt, double lon0)
{
isea_geo npt;
np.lon += Math.PI;
npt = snyder_ctran(np, pt);
np.lon -= Math.PI;
npt.lon -= (Math.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 += Math.PI;
// normalize longitude
npt.lon = Math.IEEERemainder(npt.lon, 2 * Math.PI);
while (npt.lon > Math.PI)
{
npt.lon -= 2 * Math.PI;
}
while (npt.lon < -Math.PI)
{
npt.lon += 2 * Math.PI;
}
return(npt);
}
static double az_adjustment(int triangle)
{
double adj;
isea_geo v = vertex[tri_v1[triangle]];
isea_geo c = icostriangles[triangle];
// TODO looks like the adjustment is always either 0 or 180
// at least if you pick your vertex carefully
adj = Math.Atan2(Math.Cos(v.lat) * Math.Sin(v.lon - c.lon),
Math.Cos(c.lat) * Math.Sin(v.lat) - Math.Sin(c.lat) * Math.Cos(v.lat) * Math.Cos(v.lon - c.lon));
return(adj);
}
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);
}
// 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
static isea_geo snyder_ctran(isea_geo np, isea_geo pt)
{
double phi = pt.lat;
double lambda = pt.lon;
double alpha = np.lat;
double beta = np.lon;
double lambda0 = beta;
double cos_p = Math.Cos(phi);
double sin_a = Math.Sin(alpha);
// mpawm 5-7
double sin_phip = sin_a * Math.Sin(phi) - Math.Cos(alpha) * cos_p * Math.Cos(lambda - lambda0);
// mpawm 5-8b
// lambda prime minus beta
// use the two argument form so we end up in the right quadrant
double lp_b = Math.Atan2(cos_p * Math.Sin(lambda - lambda0), (sin_a * cos_p * Math.Cos(lambda - lambda0) + Math.Cos(alpha) * Math.Sin(phi)));
double lambdap = lp_b + beta;
// normalize longitude
// TODO can we just do a modulus ?
lambdap = Math.IEEERemainder(lambdap, 2 * Math.PI);
while (lambdap > Math.PI)
{
lambdap -= 2 * Math.PI;
}
while (lambdap < -Math.PI)
{
lambdap += 2 * Math.PI;
}
double phip = Math.Asin(sin_phip);
isea_geo npt;
npt.lat = phip;
npt.lon = lambdap;
return(npt);
}
// 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
static isea_geo snyder_ctran(isea_geo np, isea_geo pt)
{
double phi=pt.lat;
double lambda=pt.lon;
double alpha=np.lat;
double beta=np.lon;
double lambda0=beta;
double cos_p=Math.Cos(phi);
double sin_a=Math.Sin(alpha);
// mpawm 5-7
double sin_phip=sin_a*Math.Sin(phi)-Math.Cos(alpha)*cos_p*Math.Cos(lambda-lambda0);
// mpawm 5-8b
// lambda prime minus beta
// use the two argument form so we end up in the right quadrant
double lp_b=Math.Atan2(cos_p*Math.Sin(lambda-lambda0), (sin_a*cos_p*Math.Cos(lambda-lambda0)+Math.Cos(alpha)*Math.Sin(phi)));
double lambdap=lp_b+beta;
// normalize longitude
// TODO can we just do a modulus ?
lambdap=Math.IEEERemainder(lambdap, 2*Math.PI);
while(lambdap>Math.PI) lambdap-=2*Math.PI;
while(lambdap<-Math.PI) lambdap+=2*Math.PI;
double phip=Math.Asin(sin_phip);
isea_geo npt;
npt.lat=phip;
npt.lon=lambdap;
return npt;
}
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;
}
// 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 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;
}
static isea_geo isea_ctran(ref isea_geo np, isea_geo pt, double lon0)
{
isea_geo npt;
np.lon+=Math.PI;
npt=snyder_ctran(np, pt);
np.lon-=Math.PI;
npt.lon-=(Math.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+=Math.PI;
// normalize longitude
npt.lon=Math.IEEERemainder(npt.lon, 2*Math.PI);
while(npt.lon>Math.PI) npt.lon-=2*Math.PI;
while(npt.lon<-Math.PI) npt.lon+=2*Math.PI;
return npt;
}
// 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();
}
