rogueviz:: add extra-projections

rogueviz/extra-projections.cpp

@@ -0,0 +1,167 @@
+#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 / 6. / M_PI);
+    y = sy * sqrt(2*M_PI/3) * (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+M_PI/2) * 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*degree) {
+      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 - M_PI/2;
+      }
+    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));
+    });      
+  }
+
+int ar = addHook(hooks_initialize, 100, add_extra_projections);
+
+}
+}