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four new models, Mercator improved

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Zeno Rogue
2018-03-26 19:06:47 +02:00
parent fa49fc550f
commit 7c84280b73
7 changed files with 265 additions and 78 deletions
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130
hypgraph.cpp
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@@ -203,8 +203,78 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
using namespace hyperpoint_vec;
H = H / zlev;
}
if(pmodel == mdTwoPoint || mdBandAny() || pmodel == mdSinusoidal) {
// map to plane
if(pmodel == mdTwoPoint) {
auto p = vid.twopoint_param;
ld dleft = hdist(H, xpush(-p) * C0);
ld dright = hdist(H, xpush(p) * C0);
ld x = (dright*dright-dleft*dleft) / 4 / p;
ld y = sqrt(dleft * dleft - (x-p)*(x-p) + 1e-9);
x = -x;
if(H[1] < 0) y = -y;
ret = hpxyz(x/M_PI, y/M_PI, 0);
}
else {
ld x, y;
switch(cgclass) {
case gcHyperbolic:
y = asinh(H[1]), x = asinh(H[0] / cosh(y));
break;
case gcSphere:
y = asin(H[1]), x = asin(H[0] / cos(y));
if(H[2] < 0 && x > 0) x = M_PI - x;
else if(H[2] < 0 && x <= 0) x = -M_PI - x;
break;
case gcEuclid:
y = H[1], x = H[0];
break;
}
if(pmodel == mdBand) switch(cgclass) {
case gcSphere:
y = atanh(sin(y) * zlev);
x *= 2; y *= 2;
break;
case gcHyperbolic:
y = 2 * atan(tanh(y/2) * zlev);
x *= 2; y *= 2;
break;
case gcEuclid:
y = y;
y *= 2; x *= 2;
break;
}
if(pmodel == mdBandEquiarea) switch(cgclass) {
case gcHyperbolic:
y = sinh(y);
break;
case gcSphere:
y = sin(y);
break;
default:
y = y;
break;
}
if(pmodel == mdSinusoidal) switch(cgclass) {
case gcHyperbolic:
x *= cosh(y);
break;
case gcSphere:
x *= cos(y);
break;
default:
x *= 1;
break;
}
ret = hpxyz(x / M_PI, y / M_PI, 0);
}
apply_depth(ret, -geom3::factor_to_lev(zlev));
ghcheck(ret, H);
return;
}
if(mdEqui()) {
if(mdAzimuthalEqui()) {
ld rad = sqrt(H[0] * H[0] + H[1] * H[1]);
if(rad == 0) rad = 1;
ld d = hdist0(H);
@@ -236,21 +306,21 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
return;
}
// Poincare to half-plane
ld x0, y0;
x0 = H[0] / tz;
y0 = H[1] / tz;
if(conformal::lower_halfplane) x0 = -x0, y0 = -y0;
y0 += 1;
double rad = x0*x0 + y0*y0;
y0 /= rad;
x0 /= rad;
y0 -= .5;
if(conformal::lower_halfplane) x0 = -x0, y0 = -y0;
if(pmodel == mdHalfplane) {
// Poincare to half-plane
ld x0, y0;
x0 = H[0] / tz;
y0 = H[1] / tz;
if(conformal::lower_halfplane) x0 = -x0, y0 = -y0;
y0 += 1;
double rad = x0*x0 + y0*y0;
y0 /= rad;
x0 /= rad;
y0 -= .5;
if(conformal::lower_halfplane) x0 = -x0, y0 = -y0;
ret[0] = x0;
if(wmspatial || mmspatial) {
if(conformal::lower_halfplane) y0 /= zlev;
@@ -263,36 +333,6 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
ghcheck(ret,H);
return;
}
// center
x0 *= 2; y0 *= 2;
// half-plane to band
double tau = (log((x0+1)*(x0+1) + y0*y0) - log((x0-1)*(x0-1) + y0*y0)) / 2;
double u=(1-x0*x0-y0*y0);
u = (1 - x0*x0 - y0*y0 + sqrt(u*u+4*y0*y0));
double yv = 2*y0 / u;
double sigma = 2 * atan(yv * zlev) - M_PI/2;
x0 = tau; y0 = sigma;
/* if(zlev != 1) {
double alp = (y0 * y0) / (1-y0*y0);
double gx = alp + sqrt(alp*alp-1);
double gy = y0 * (gx+1);
double yr = zlev * gy / (zlev * gx + 1);
printf("zlev = %10.5lf y0 = %20.10lf yr = %20.10lf\n", double(zlev), (double)y0, yr);
y0 = yr;
} */
ret[0] = x0/M_PI*2;
ret[1] = -y0/M_PI*2;
ret[2] = 0;
if(zlev != 1 && stereo::active())
apply_depth(ret, -geom3::factor_to_lev(zlev) / (1 + yv * yv));
ghcheck(ret,H);
}
// game-related graphics