mirror of
https://github.com/zenorogue/hyperrogue.git
synced 2024-11-24 13:27:17 +00:00
224 lines
7.0 KiB
C++
224 lines
7.0 KiB
C++
#include "rogueviz.h"
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namespace hr {
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namespace extra {
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template<class T> void makeband_complex(shiftpoint H, hyperpoint& ret, const T& f) {
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makeband_f(H, ret, [&] (ld& x, ld& y) {
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if(euclid) return;
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if(isnan(x)) return;
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// auto orx = x, ory = y;
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cld i = hyperbolic ? cld(0,1) : cld(1, 0);
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cld cx = x*i;
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cld cy = y*i;
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f(cx, cy);
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x = real(cx/i) + (anyshiftclick ? 1 : 0) * imag(cx/i);
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y = real(cy/i) + (anyshiftclick ? 1 : 0) * imag(cy/i);
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});
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}
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template<class T> void add_complex(const char *name, flagtype flag, const T& f) {
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int q = isize(mdinf);
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mdinf.emplace_back(modelinfo{name, name, name, mf::euc_boring | mf::broken | flag, 0, 0, 0, 0, 0, nullptr});
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while(isize(extra_projections) < q) extra_projections.emplace_back();
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extra_projections.emplace_back([f] (shiftpoint& H_orig, hyperpoint& H, hyperpoint& ret) {
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makeband_complex(H_orig, ret, f);
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});
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}
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template<class T> void add_band(const char *name, flagtype flag, const T& f) {
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int q = isize(mdinf);
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mdinf.emplace_back(modelinfo{name, name, name, mf::euc_boring | mf::broken | flag, 0, 0, 0, 0, 0, nullptr});
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while(isize(extra_projections) < q) extra_projections.emplace_back();
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extra_projections.emplace_back([f] (shiftpoint& H_orig, hyperpoint& H, hyperpoint& ret) {
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makeband_f(H_orig, ret, f);
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});
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}
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template<class T1, class T2> cld newton_inverse(const T1& f, const T2& fp, cld yf, cld x0) {
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cld x = x0;
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for(int it=0;; it++) {
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cld y = f(x);
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cld yp = fp(x);
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x = x + (yf - y) / yp;
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if(abs(y-yf) < 1e-9) return x;
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if(it == 20) {
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println(hlog, "failed for: ", yf, " x=", x, " y=", y);
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return x;
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}
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}
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}
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void add_extra_projections() {
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// does not work in H3...
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add_complex("van der Grinten", 0, [] (cld& x, cld& y) {
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if(abs(y) < 1e-4) return;
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bool ox = abs(x) < 1e-4;
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if(x == 0.) x = 1e-6;
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cld sx = real(x)+imag(x) > 0 ? 1 : -1;
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cld sy = real(y)+imag(y) > 0 ? 1 : -1;
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x /= sx;
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y /= sy;
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auto pi = M_PI;
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cld sin_theta = 2. * y / pi;
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cld cos_theta2 = 1. - sin_theta * sin_theta;
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cld A = (1/2.) * (pi / x - x / pi);
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cld G = sqrt(cos_theta2) / (sin_theta + sqrt(cos_theta2) - 1.);
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cld P = G * (2./sin_theta - 1.);
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cld Q = A*A + G;
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cld diag = A*A+P*P;
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cld s1 = A*A*(G-P*P)*(G-P*P) - diag*(G*G-P*P);
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cld s2 = (A*A+1.)*diag - Q*Q;
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if(ox) {
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x = 0;
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cld theta = asin(sin_theta);
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y = sy * M_PI * tan(theta/2.);
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}
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else {
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x = sx * M_PI * (A * (G-P*P) + sqrt(s1)) / diag;
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y = sy * M_PI * (P*Q - (hyperbolic?-1.:1.) * A*sqrt(s2)) / diag;
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}
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});
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// https://en.wikipedia.org/wiki/Eckert_II_projection
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add_band("Eckert II", mf::pseudoband | mf::equiarea, [] (ld& x, ld& y) {
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ld sy = y > 0 ? 1 : -1;
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y /= sy;
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ld z = 4. - 3. * (hyperbolic ? -sinh(y) : sin(y));
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x = 2. * x * sqrt(z / 6. / M_PI);
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y = sy * sqrt(2*M_PI/3) * (2. - sqrt(z));
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});
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// https://en.wikipedia.org/wiki/Eckert_IV_projection
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add_complex("Eckert IV", mf::pseudoband | mf::equiarea, [] (cld& x, cld& y) {
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cld theta = newton_inverse(
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[] (cld th) { return th + sin(th) * cos(th) + 2. * sin(th); },
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[] (cld th) { return 1. + cos(th) * cos(th) - sin(th) * sin(th) + 2. * cos(th); },
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(2+M_PI/2) * sin(y), y);
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static ld cox = 2 / sqrt(4*M_PI+M_PI*M_PI);
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static ld coy = 2 * sqrt(M_PI/(4+M_PI));
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x = cox * x * (1. + cos(theta));
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y = coy * sin(theta);
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});
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// does not work in H3...
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add_complex("Ortelius", 0, [] (cld& x, cld& y) {
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cld sx = (real(x)+imag(x)) > 0 ? 1 : -1;
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x /= sx;
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if(abs(real(x)) < 90*degree) {
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cld F = M_PI*M_PI / 8. / x + x / 2.;
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x = (x - F + sqrt(F*F-y*y));
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}
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else {
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x = sqrt(M_PI*M_PI/4 - y*y) + x - M_PI/2;
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}
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x *= sx;
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});
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// https://en.wikipedia.org/wiki/Equal_Earth_projection
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add_complex("Equal Earth", mf::equiarea | mf::pseudoband, [] (cld& x, cld& y) {
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static cld M = sqrt(3)/2;
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auto theta = asin(M * sin(y));
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ld A1 = 1.340624;
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ld A2 = -0.081106;
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ld A3 = 0.000893;
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ld A4 = 0.003796;
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cld pows[10];
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pows[1] = theta; for(int i=2; i<10; i++) pows[i] = pows[i-1] * theta;
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x = x*cos(theta) / M / (9*A4*pows[8] + 7*A3*pows[6] + 3*A2*pows[2] + A1);
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y = A4 * pows[9] + A3 * pows[7] + A2 * pows[3] + A1 * pows[1];
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});
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// https://en.wikipedia.org/wiki/Natural_Earth_projection
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add_complex("Natural Earth", mf::pseudoband, [] (cld& x, cld& y) {
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cld pows[13];
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pows[1] = y; for(int i=2; i<13; i++) pows[i] = pows[i-1] * y;
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cld l = 0.870700 - 0.131979 * pows[2] - 0.013791 * pows[4] + 0.003971 * pows[10] - 0.001529 * pows[12];
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y = y * (1.007226 + 0.015085 * pows[2] - 0.044475 * pows[6] + 0.028874 * pows[8] - 0.005916 * pows[10]);
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x = x * l;
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});
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// https://en.wikipedia.org/wiki/Wagner_VI_projection
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add_complex("Wagner VI", mf::equiarea | mf::pseudoband, [] (cld& x, cld& y) {
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x = x * sqrt(1. - 3. * pow(y/M_PI, 2));
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});
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/* does the Poincare model work in spherical? -- hint: it does not, as expected */
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if(0) add_complex("alt poincare", mf::equiarea | mf::pseudoband, [] (cld& x, cld& y) {
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cld i(0, 1);
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x /= i;
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y /= i;
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cld c1(1, 0);
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auto ax = cosh(y) * sinh(x);
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auto ay = sinh(y);
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auto az = cosh(x) * cosh(y);
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ax /= (az+c1);
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ay /= (az+c1);
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ay += c1;
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cld z = ax*ax + ay*ay;
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ax /= z;
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ay /= z;
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ay -= c1;
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ax *= i;
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ay *= i;
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x = ax;
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y = ay;
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});
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}
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void gen_dual() {
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int q = isize(mdinf);
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eModel p = pmodel;
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auto& mo= mdinf[p];
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mdinf.push_back(mo);
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auto& m = mdinf.back();
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m.name_hyperbolic = strdup((string("dual to ") + mo.name_spherical).c_str());
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m.name_euclidean = strdup((string("dual to ") + mo.name_euclidean).c_str());
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m.name_spherical = strdup((string("dual to ") + mo.name_hyperbolic).c_str());
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while(isize(extra_projections) < q) extra_projections.emplace_back();
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extra_projections.emplace_back([p] (shiftpoint& H_orig, hyperpoint& H, hyperpoint& ret) {
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if(hyperbolic) {
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auto Hdual = H_orig;
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auto& H1 = Hdual.h;
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H1 /= H1[2];
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H1[2] = sqrt(1 - H1[0] * H1[0] - H1[1] * H1[1]);
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dynamicval<eGeometry> g(geometry, gSphere);
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apply_other_model(Hdual, ret, p);
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}
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else if(sphere) {
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auto Hdual = H_orig;
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auto& H1 = Hdual.h;
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H1 /= H1[2];
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H1[2] = sqrt(1 + H1[0] * H1[0] + H1[1] * H1[1]);
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dynamicval<eGeometry> g(geometry, gNormal);
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apply_other_model(Hdual, ret, p);
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}
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else
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apply_other_model(H_orig, ret, p);
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});
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pmodel = eModel(q);
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}
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int ar = addHook(hooks_initialize, 100, add_extra_projections)
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+ arg::add3("-gen-dual", gen_dual);
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}
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}
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