Five new projections: Poor Man (hyperbolic only), Panini, retroazimuthal: Craig, Hammer, Littrow (retro-Hammer buggy on sphere)

classes.cpp

@@ -980,6 +980,8 @@ enum eModel : int {
   // 32..38
   mdWerner, mdAitoff, mdHammer, mdLoximuthal, mdMiller, mdGallStereographic, mdWinkelTripel,
   // 39..
+  mdPoorMan, mdPanini, mdRetroCraig, mdRetroLittrow, mdRetroHammer,
+  // 44..
   mdGUARD, mdPixel, mdHyperboloidFlat, mdPolynomial, mdManual
   };
 #endif
@@ -1031,6 +1033,11 @@ EX vector<modelinfo> mdinf = {
   {X3("Miller projection"), mf::euc_boring | mf::band, DEFAULTS}, // scale latitude 4/5 -> Mercator -> 5/4
   {X3("Gall stereographic"), mf::euc_boring | mf::band, DEFAULTS}, // like central cylindrical but stereographic
   {X3("Winkel tripel"), mf::euc_boring | mf::broken, DEFAULTS}, // mean of equirec and Aitoff
+  {X3("Poor man's square"), mf::euc_boring, DEFAULTS}, // 
+  {X3("Panini projection"), mf::euc_boring, DEFAULTS}, // 
+  {X3("Craig retroazimuthal"), mf::euc_boring | mf::broken, DEFAULTS}, // retroazimuthal cylindrical
+  {X3("Littrow retroazimuthal"), mf::euc_boring | mf::broken, DEFAULTS}, // retroazimuthal conformal
+  {X3("Hammer retroazimuthal"), mf::euc_boring, DEFAULTS}, // retroazimuthal equidistant
   {X3("guard"), 0, DEFAULTS},
   {X3("polynomial"), mf::conformal, DEFAULTS},
   };

drawing.cpp

@@ -293,6 +293,8 @@ EX bool two_sided_model() {
   if(pmodel == mdHyperboloid) return !euclid;
   // if(pmodel == mdHemisphere) return true;
   if(pmodel == mdDisk) return sphere;
+  if(pmodel == mdRetroLittrow) return sphere;
+  if(pmodel == mdRetroHammer) return sphere;
   if(pmodel == mdHemisphere) return true;
   if(pmodel == mdRotatedHyperboles) return true;
   if(pmodel == mdSpiral && pconf.spiral_cone < 360) return true;
@@ -305,6 +307,12 @@ EX int get_side(const hyperpoint& H) {
     double horizon = curnorm / pconf.alpha;
     return (H[2] <= -horizon) ? -1 : 1;
     }
+  if(pmodel == mdRetroLittrow && sphere) {
+    return H[2] >= 0 ? 1 : -1;
+    }
+  if(pmodel == mdRetroHammer && sphere) {
+    return H[2] >= 0 ? 1 : -1;
+    }
   if(pmodel == mdRotatedHyperboles)
     return H[1] > 0 ? -1 : 1;
   if(pmodel == mdHyperboloid && hyperbolic)

geom-exp.cpp

@@ -384,7 +384,9 @@ void ge_select_tiling() {
 
 EX string current_proj_name() {
   bool h = hyperbolic || sn::in();
-  if(vpconf.model != mdDisk)
+  if(vpconf.model == mdPanini && vpconf.alpha == 1)
+    return XLAT("stereographic Panini");
+  else if(vpconf.model != mdDisk)
     return models::get_model_name(vpconf.model);
   else if(h && vpconf.alpha == 1)
     return XLAT("Poincaré model");

hypgraph.cpp

@@ -1074,6 +1074,76 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         }
       }
     
+    case mdRetroCraig: {
+      makeband(H_orig, ret, [] (ld& x, ld& y) { 
+        if(x)
+          y = x / sin_auto(x) * (sin_auto(y) * cos_auto(x) - tan_auto(pconf.loximuthal_parameter) * cos_auto(y));
+        else
+          y = sin_auto(y) - tan_auto(pconf.loximuthal_parameter) * cos_auto(y);
+        });
+      break;
+      }
+
+    case mdRetroLittrow: {
+      makeband(H_orig, ret, [] (ld& x, ld& y) { 
+        tie(x, y) = make_pair(
+          sin_auto(x) / cos_auto(y),
+          cos_auto(x) * tan_auto(y)
+          );
+        });
+      break;
+      }
+    
+    case mdRetroHammer: {
+      ld d = hdist(H, ypush0(pconf.loximuthal_parameter));
+      makeband(H_orig, ret, [d,H] (ld& x, ld& y) { 
+        if(x == 0 && y == 0) return;
+
+        if(x)
+          y = x / sin_auto(x) * (sin_auto(y) * cos_auto(x) - tan_auto(pconf.loximuthal_parameter) * cos_auto(y));
+        else
+          y = sin_auto(y) - tan_auto(pconf.loximuthal_parameter) * cos_auto(y);
+          
+        ld scale = d / hypot(x, y);
+        if(H[2] < 0) scale = -scale;
+        x *= scale;
+        y *= scale;
+        });
+      break;
+      }
+    
+    case mdPanini: {
+      ld proh = sqrt(H[2]*H[2] + curvature() * H[0] * H[0]);
+      H /= proh;
+      H /= (H[2] + pconf.alpha);
+      ret = H;
+      ret[2] = 0; ret[3] = 1;
+      break;
+      }
+    
+    case mdPoorMan: {
+      find_zlev(H);
+      H = space_to_perspective(H);
+      
+      models::apply_orientation_yz(H[1], H[2]);
+      models::apply_orientation(H[0], H[1]);
+      
+      ld u = H[0], v = H[1];
+      if(abs(u) > 1e-3 && abs(v) > 1e-3) {
+        ld r2 = u*u+v*v;
+        ld scale = sqrt((-r2+sqrt(r2*(r2+4*u*u*v*v*(r2-2))))/(2*(r2-2))) / u / v;
+        if(u*v<0) scale = -scale;
+        H = scale * H;
+        }
+      ret = H;
+      ret[2] = 0;
+      ret[3] = 1;
+  
+      models::apply_orientation(ret[1], ret[0]);
+      models::apply_orientation_yz(ret[2], ret[1]);
+      break;
+      }
+    
     case mdGUARD: case mdManual: break;
     }
 

models.cpp

@@ -200,6 +200,8 @@ EX namespace models {
     if(GDIM == 2 && pm == mdEquivolume) return false;
     if(GDIM == 3 && among(pm, mdBall, mdHyperboloid, mdFormula, mdPolygonal, mdRotatedHyperboles, mdSpiral, mdHemisphere)) return false;
     if(pm == mdCentralInversion && !euclid) return false;
+    if(pm == mdPoorMan) return hyperbolic;
+    if(pm == mdRetroHammer) return hyperbolic;
     return true;
     }    
   
@@ -442,7 +444,7 @@ EX namespace models {
       dialog::addBreak(50);
       }
     
-    if(among(vpmodel, mdDisk, mdBall, mdHyperboloid, mdRotatedHyperboles)) {
+    if(among(vpmodel, mdDisk, mdBall, mdHyperboloid, mdRotatedHyperboles, mdPanini)) {
       dialog::addSelItem(XLAT("projection distance"), fts(vpconf.alpha) + " (" + current_proj_name() + ")", 'p');
       dialog::add_action(projectionDialog);
       }
@@ -636,13 +638,17 @@ EX namespace models {
         });
       }
     
-    if(vpmodel == mdLoximuthal) {
+    if(among(vpmodel, mdLoximuthal, mdRetroHammer, mdRetroCraig)) {
       dialog::addSelItem(XLAT("parameter"), fts(vpconf.loximuthal_parameter), 'b');
-      dialog::add_action([](){
+      dialog::add_action([vpmodel](){
         dialog::editNumber(vpconf.loximuthal_parameter, -M_PI/2, M_PI/2, .1, 0, XLAT("parameter"), 
+          (vpmodel == mdLoximuthal ?
           "This model is similar to azimuthal equidistant, but based on loxodromes (lines of constant geographic direction) rather than geodesics. "
           "The loximuthal projection maps (the shortest) loxodromes to straight lines of the same length, going through the starting point. "
-          "This setting changes the latitude of the starting point." 
+          "This setting changes the latitude of the starting point." :
+          "In retroazimuthal projections, a point is drawn at such a point that the azimuth *from* that point to the chosen central point is correct. "
+          "For example, if you should move east, the point is drawn to the right. This parameter is the latitude of the central point.")
+          + string(hyperbolic ? "\n\n(In hyperbolic geometry directions are assigned according to the Lobachevsky coordinates.)" : "")
           );
         });
       }
@@ -827,7 +833,7 @@ EX namespace models {
       PHASEFROM(2); 
       if(pmodel == mdCollignon) shift_arg_formula(vpconf.collignon_parameter);
       else if(pmodel == mdMiller) shift_arg_formula(vpconf.miller_parameter);
-      else if(pmodel == mdLoximuthal) shift_arg_formula(vpconf.loximuthal_parameter);
+      else if(among(pmodel, mdLoximuthal, mdRetroCraig, mdRetroHammer)) shift_arg_formula(vpconf.loximuthal_parameter);
       else if(among(pmodel, mdAitoff, mdHammer, mdWinkelTripel)) shift_arg_formula(vpconf.aitoff_parameter);
       if(pmodel == mdWinkelTripel) shift_arg_formula(vpconf.winkel_parameter);
       }