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hyperrogue/rogueviz/extra-projections.cpp

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#include "rogueviz.h"
namespace hr {
namespace extra {
template<class T> void makeband_complex(shiftpoint H, hyperpoint& ret, const T& f) {
makeband_f(H, ret, [&] (ld& x, ld& y) {
if(euclid) return;
if(isnan(x)) return;
// auto orx = x, ory = y;
cld i = hyperbolic ? cld(0,1) : cld(1, 0);
cld cx = x*i;
cld cy = y*i;
f(cx, cy);
x = real(cx/i) + (anyshiftclick ? 1 : 0) * imag(cx/i);
y = real(cy/i) + (anyshiftclick ? 1 : 0) * imag(cy/i);
});
}
template<class T> void add_complex(const char *name, flagtype flag, const T& f) {
int q = isize(mdinf);
mdinf.emplace_back(modelinfo{name, name, name, mf::euc_boring | mf::broken | flag, 0, 0, 0, 0, 0, nullptr});
while(isize(extra_projections) < q) extra_projections.emplace_back();
extra_projections.emplace_back([f] (shiftpoint& H_orig, hyperpoint& H, hyperpoint& ret) {
makeband_complex(H_orig, ret, f);
});
}
template<class T> void add_band(const char *name, flagtype flag, const T& f) {
int q = isize(mdinf);
mdinf.emplace_back(modelinfo{name, name, name, mf::euc_boring | mf::broken | flag, 0, 0, 0, 0, 0, nullptr});
while(isize(extra_projections) < q) extra_projections.emplace_back();
extra_projections.emplace_back([f] (shiftpoint& H_orig, hyperpoint& H, hyperpoint& ret) {
makeband_f(H_orig, ret, f);
});
}
template<class T1, class T2> cld newton_inverse(const T1& f, const T2& fp, cld yf, cld x0) {
cld x = x0;
for(int it=0;; it++) {
cld y = f(x);
cld yp = fp(x);
x = x + (yf - y) / yp;
if(abs(y-yf) < 1e-9) return x;
if(it == 20) {
println(hlog, "failed for: ", yf, " x=", x, " y=", y);
return x;
}
}
}
void add_extra_projections() {
// does not work in H3...
add_complex("van der Grinten", 0, [] (cld& x, cld& y) {
if(abs(y) < 1e-4) return;
bool ox = abs(x) < 1e-4;
if(x == 0.) x = 1e-6;
cld sx = real(x)+imag(x) > 0 ? 1 : -1;
cld sy = real(y)+imag(y) > 0 ? 1 : -1;
x /= sx;
y /= sy;
auto pi = M_PI;
cld sin_theta = 2. * y / pi;
cld cos_theta2 = 1. - sin_theta * sin_theta;
cld A = (1/2.) * (pi / x - x / pi);
cld G = sqrt(cos_theta2) / (sin_theta + sqrt(cos_theta2) - 1.);
cld P = G * (2./sin_theta - 1.);
cld Q = A*A + G;
cld diag = A*A+P*P;
cld s1 = A*A*(G-P*P)*(G-P*P) - diag*(G*G-P*P);
cld s2 = (A*A+1.)*diag - Q*Q;
if(ox) {
x = 0;
cld theta = asin(sin_theta);
y = sy * M_PI * tan(theta/2.);
}
else {
x = sx * M_PI * (A * (G-P*P) + sqrt(s1)) / diag;
y = sy * M_PI * (P*Q - (hyperbolic?-1.:1.) * A*sqrt(s2)) / diag;
}
});
// https://en.wikipedia.org/wiki/Eckert_II_projection
add_band("Eckert II", mf::pseudoband | mf::equiarea, [] (ld& x, ld& y) {
ld sy = y > 0 ? 1 : -1;
y /= sy;
ld z = 4. - 3. * (hyperbolic ? -sinh(y) : sin(y));
x = 2. * x * sqrt(z / 1080._deg);
y = sy * sqrt(120._deg) * (2. - sqrt(z));
});
// https://en.wikipedia.org/wiki/Eckert_IV_projection
add_complex("Eckert IV", mf::pseudoband | mf::equiarea, [] (cld& x, cld& y) {
cld theta = newton_inverse(
[] (cld th) { return th + sin(th) * cos(th) + 2. * sin(th); },
[] (cld th) { return 1. + cos(th) * cos(th) - sin(th) * sin(th) + 2. * cos(th); },
(2+90._deg) * sin(y), y);
static ld cox = 2 / sqrt(4*M_PI+M_PI*M_PI);
static ld coy = 2 * sqrt(M_PI/(4+M_PI));
x = cox * x * (1. + cos(theta));
y = coy * sin(theta);
});
// does not work in H3...
add_complex("Ortelius", 0, [] (cld& x, cld& y) {
cld sx = (real(x)+imag(x)) > 0 ? 1 : -1;
x /= sx;
if(abs(real(x)) < 90._deg) {
cld F = M_PI*M_PI / 8. / x + x / 2.;
x = (x - F + sqrt(F*F-y*y));
}
else {
x = sqrt(M_PI*M_PI/4 - y*y) + x - 90._deg;
}
x *= sx;
});
// https://en.wikipedia.org/wiki/Equal_Earth_projection
add_complex("Equal Earth", mf::equiarea | mf::pseudoband, [] (cld& x, cld& y) {
static cld M = sqrt(3)/2;
auto theta = asin(M * sin(y));
ld A1 = 1.340624;
ld A2 = -0.081106;
ld A3 = 0.000893;
ld A4 = 0.003796;
cld pows[10];
pows[1] = theta; for(int i=2; i<10; i++) pows[i] = pows[i-1] * theta;
x = x*cos(theta) / M / (9*A4*pows[8] + 7*A3*pows[6] + 3*A2*pows[2] + A1);
y = A4 * pows[9] + A3 * pows[7] + A2 * pows[3] + A1 * pows[1];
});
// https://en.wikipedia.org/wiki/Natural_Earth_projection
add_complex("Natural Earth", mf::pseudoband, [] (cld& x, cld& y) {
cld pows[13];
pows[1] = y; for(int i=2; i<13; i++) pows[i] = pows[i-1] * y;
cld l = 0.870700 - 0.131979 * pows[2] - 0.013791 * pows[4] + 0.003971 * pows[10] - 0.001529 * pows[12];
y = y * (1.007226 + 0.015085 * pows[2] - 0.044475 * pows[6] + 0.028874 * pows[8] - 0.005916 * pows[10]);
x = x * l;
});
// https://en.wikipedia.org/wiki/Wagner_VI_projection
add_complex("Wagner VI", mf::equiarea | mf::pseudoband, [] (cld& x, cld& y) {
x = x * sqrt(1. - 3. * pow(y/M_PI, 2));
});
/* does the Poincare model work in spherical? -- hint: it does not, as expected */
if(0) add_complex("alt poincare", mf::equiarea | mf::pseudoband, [] (cld& x, cld& y) {
cld i(0, 1);
x /= i;
y /= i;
cld c1(1, 0);
auto ax = cosh(y) * sinh(x);
auto ay = sinh(y);
auto az = cosh(x) * cosh(y);
ax /= (az+c1);
ay /= (az+c1);
ay += c1;
cld z = ax*ax + ay*ay;
ax /= z;
ay /= z;
ay -= c1;
ax *= i;
ay *= i;
x = ax;
y = ay;
});
}
void gen_dual() {
int q = isize(mdinf);
eModel p = pmodel;
auto& mo= mdinf[p];
mdinf.push_back(mo);
auto& m = mdinf.back();
m.name_hyperbolic = strdup((string("dual to ") + mo.name_spherical).c_str());
m.name_euclidean = strdup((string("dual to ") + mo.name_euclidean).c_str());
m.name_spherical = strdup((string("dual to ") + mo.name_hyperbolic).c_str());
while(isize(extra_projections) < q) extra_projections.emplace_back();
extra_projections.emplace_back([p] (shiftpoint& H_orig, hyperpoint& H, hyperpoint& ret) {
if(hyperbolic) {
auto Hdual = H_orig;
auto& H1 = Hdual.h;
H1 /= H1[2];
H1[2] = sqrt(1 - H1[0] * H1[0] - H1[1] * H1[1]);
dynamicval<eGeometry> g(geometry, gSphere);
apply_other_model(Hdual, ret, p);
}
else if(sphere) {
auto Hdual = H_orig;
auto& H1 = Hdual.h;
H1 /= H1[2];
H1[2] = sqrt(1 + H1[0] * H1[0] + H1[1] * H1[1]);
dynamicval<eGeometry> g(geometry, gNormal);
apply_other_model(Hdual, ret, p);
}
else
apply_other_model(H_orig, ret, p);
});
pmodel = eModel(q);
}
int ar = addHook(hooks_initialize, 100, add_extra_projections)
+ arg::add3("-gen-dual", gen_dual);
}
}
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