conformal:: new models: formula and rotated hyperboles

config.cpp

@@ -295,6 +295,9 @@ void initConfig() {
   addsaver(vid.cells_drawn_limit, "limit on cells drawn", 10000);
   
   addsaver(vid.skiprope, "mobius", 0);
+  
+  addsaver(conformal::formula, "formula");
+  addsaverenum(conformal::basic_model, "basic model");
 
 #if CAP_SHMUP  
   shmup::initConfig();

conformal.cpp

@@ -258,6 +258,9 @@ bool isbad(ld z) { return !isfinite(z) || fabs(z) > 1e6; }
 
 namespace conformal {
 
+  string formula = "z^2";
+  eModel basic_model;
+
   void handleKeyC(int sym, int uni);
   
   int lastprogress;
@@ -578,11 +581,11 @@ namespace conformal {
 #endif
 
   const char *modelnames[MODELCOUNT] = {
-    "disk", "half-plane", "band", "polygonal", "polynomial",
+    "disk", "half-plane", "band", "polygonal", "formula",
     "azimuthal equidistant", "azimuthal equi-area", 
     "ball model", "Minkowski hyperboloid", "hemisphere",
     "band equidistant", "band equi-area", "sinusoidal", "two-point equidistant",
-    "fisheye", "Joukowsky transform", "Joukowsky+inversion"
+    "fisheye", "Joukowsky transform", "Joukowsky+inversion", "rotated hyperboles"
     };
   
   string get_model_name(eModel pm) {
@@ -610,14 +613,34 @@ namespace conformal {
     return among(pmodel, mdJoukowsky, mdJoukowskyInverted, mdBand);
     }
   
+  int editpos = 0;
+
   void model_menu() {
     cmode = sm::SIDE | sm::MAYDARK | sm::CENTER;
     gamescreen(0);
     dialog::init(XLAT("models of hyperbolic geometry"));
     for(int i=0; i<mdGUARD; i++) {
       eModel m = eModel(i);
-      if(model_available(m))
+      if(model_available(m)) {
         dialog::addBoolItem(get_model_name(m), pmodel == m, "0123456789!@#$%^&*()" [m]);
+        dialog::add_action([m] () {
+          if(m == mdFormula) {
+            if(pmodel != m) basic_model = pmodel;
+            dialog::edit_string(formula, "formula", "");
+            dialog::reaction_final = [] () {
+              pmodel = mdFormula;
+              };
+            return;
+            }
+          pmodel = m;
+          polygonal::solve();
+          vid.alpha = 1; vid.scale = 1;
+          if(pmodel == mdBand && sphere)
+            vid.scale = .3;
+          if(pmodel == mdDisk && sphere)
+            vid.scale = .4;
+          });
+        }
       }
     
     dialog::addBreak(100);
@@ -701,32 +724,7 @@ namespace conformal {
     keyhandler = [] (int sym, int uni) {
       dialog::handleNavigation(sym, uni);
       
-      if(uni >= '0' && uni <= '9') {
-        pmodel = eModel(uni - '0');
-        polygonal::solve();
-        vid.alpha = 1; vid.scale = 1;
-        if(pmodel == mdBand && sphere)
-          vid.scale = .3;
-        if(pmodel == mdDisk && sphere)
-          vid.scale = .4;
-        }
-      else if(uni == '!') 
-        pmodel = eModel(10);
-      else if(uni == '@') 
-        pmodel = eModel(11);
-      else if(uni == '#') 
-        pmodel = eModel(12);
-      else if(uni == '$') 
-        pmodel = eModel(13);
-      else if(uni == '%') 
-        pmodel = eModel(14);
-      else if(uni == '^') 
-        pmodel = eModel(15);
-      else if(uni == '&') 
-        pmodel = eModel(16);
-      else if(uni == '6')
-        vid.alpha = 1, vid.scale = 1;
-      else if(uni == 'z')
+      if(uni == 'z')
         editScale();
       else if(uni == 'p')
         projectionDialog();

hyper.h

@@ -472,7 +472,9 @@ template<class T> struct walker {
     return at == x.at && spin == x.spin && mirrored == x.mirrored;
     }
 
-
+  bool operator < (const walker<T>& cw2) const {
+    return tie(at, spin, mirrored) < tie(cw2.at, cw2.spin, cw2.mirrored);
+    }
 
   walker<T>& operator ++ (int) { return (*this) += 1; }
   walker<T>& operator -- (int) { return (*this) -= 1; }
@@ -1269,11 +1271,13 @@ extern ld ruggo;
 #define HASLINEVIEW
 
 enum eModel {
-  mdDisk, mdHalfplane, mdBand, mdPolygonal, mdPolynomial,
+  mdDisk, mdHalfplane, mdBand, mdPolygonal, mdFormula,
   mdEquidistant, mdEquiarea, mdBall, mdHyperboloid, 
   mdHemisphere, mdBandEquidistant, mdBandEquiarea, mdSinusoidal, mdTwoPoint, 
   mdFisheye, mdJoukowsky, mdJoukowskyInverted,
-  mdGUARD, mdUnchanged, mdHyperboloidFlat };
+  mdRotatedHyperboles,
+  mdGUARD, mdUnchanged, mdHyperboloidFlat, mdPolynomial
+  };
 
 namespace conformal {
   extern bool on;
@@ -1325,6 +1329,9 @@ namespace conformal {
   void progress_screen();
   void progress(string str);
   bool model_has_orientation();
+
+  extern string formula;
+  extern eModel basic_model;
   }
   
 namespace polygonal {

hypgraph.cpp

@@ -516,6 +516,43 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
       break;
       }
     
+    case mdRotatedHyperboles: {
+      // ld zlev =  <- not implemented
+      find_zlev(H); // + geom3::depth;
+      conformal::apply_orientation(H[0], H[1]);
+      
+      ld y = asin_auto(H[1]);
+      ld x = asin_auto_clamp(H[0] / cos_auto(y));
+      // ld z = zlev == 1 ? 0 : geom3::factor_to_lev(zlev);
+      
+      ld factor = geom3::lev_to_factor(y + geom3::depth);
+      
+      ret[0] = sinh(x) * factor;
+      ret[1] = cosh(x) * factor;
+      ret[2] = 0;
+      
+      ret[0] = atan(ret[0]);
+      ret[1] = atan(ret[1]);
+
+      break;
+      }
+    
+    case mdFormula: {
+      dynamicval<eModel> m(pmodel, conformal::basic_model);
+      applymodel(H, ret);
+      exp_parser ep;
+      ep.extra_params["z"] = cld(ret[0], ret[1]);
+      ep.extra_params["cx"] = ret[0];
+      ep.extra_params["cy"] = ret[1];
+      ep.extra_params["cz"] = ret[2];
+      ep.s = conformal::formula;
+      cld res = ep.parse();
+      ret[0] = real(res);
+      ret[1] = imag(res);
+      ret[2] = 0;
+      break;
+      }
+    
     case mdGUARD: break;
     }
 

polygons.cpp

@@ -191,6 +191,7 @@ bool two_sided_model() {
   // if(pmodel == mdHemisphere) return true;
   if(pmodel == mdDisk) return sphere;
   if(pmodel == mdHemisphere) return true;
+  if(pmodel == mdRotatedHyperboles) return true;
   return false;
   }
 
@@ -201,6 +202,8 @@ int get_side(const hyperpoint& H) {
     return (H[2] <= -horizon) ? -1 : 1;
     ;
     }
+  if(pmodel == mdRotatedHyperboles)
+    return H[1] > 0 ? -1 : 1;
   if(pmodel == mdHyperboloid && hyperbolic)
     return (conformal::sin_ball * H[2] > -conformal::cos_ball * H[1]) ? -1 : 1;
   if(pmodel == mdHyperboloid && sphere)