hemisphere in spherical now produces the hyperboloid model

classes.cpp

@@ -1030,7 +1030,7 @@ EX vector<modelinfo> mdinf = {
   {X3("azimuthal equi-area"), mf::azimuthal | mf::equiarea | mf::euc_boring, DEFAULTS},
   {X3("ball model"), mf::conformal | mf::azimuthal | mf::space, DEFAULTS},
   {"Minkowski hyperboloid", "plane", "sphere", mf::conformal | mf::space | mf::euc_boring, DEFAULTS},
-  {"hemisphere", "sphere", "sphere", mf::conformal | mf::space, DEFAULTS},
+  {"hemisphere", "sphere", "Minkowski hyperboloid", mf::conformal | mf::space, DEFAULTS},
   {X3("band equidistant"), mf::band | mf::equidistant | mf::euc_boring, DEFAULTS},
   {X3("band equi-area"), mf::band | mf::equiarea | mf::euc_boring, DEFAULTS},
   {X3("sinusoidal"), mf::pseudoband | mf::equiarea | mf::euc_boring, DEFAULTS},

drawing.cpp

@@ -304,7 +304,7 @@ EX bool two_sided_model() {
   #endif
   if(GDIM == 3) return false;
   if(in_vr_sphere) return true;
-  if(pmodel == mdHyperboloid) return !euclid && !in_vr;
+  if(models::is_hyperboloid(pmodel)) return !euclid && !in_vr;
   // if(pmodel == mdHemisphere) return true;
   if(pmodel == mdDisk) return sphere || (hyperbolic && pconf.alpha < 0 && pconf.alpha > -1);
   if(pmodel == mdRetroLittrow) return sphere;
@@ -348,11 +348,21 @@ EX int get_side(const hyperpoint& H) {
     return (models::sin_ball * H[2] > -models::cos_ball * H[1]) ? -1 : 1;
   if(pmodel == mdHyperboloid && sphere)
     return (models::sin_ball * H[2] > models::cos_ball * H[1]) ? -1 : 1;
-  if(pmodel == mdHemisphere) {
+  if(pmodel == mdHyperboloidFlat && sphere)
+    return H[2] >= 0 ? 1 : -1;
+  if(pmodel == mdHemisphere && hyperbolic) {
     hyperpoint res;
     applymodel(shiftless(H), res);
     return res[2] < 0 ? -1 : 1;
     }
+  if(pmodel == mdHemisphere && sphere) {
+    auto H1 = H;
+    int s = H1[2] > 0 ? 1 : -1;
+    if(hemi_side && s != hemi_side) return -spherespecial;
+    H1[0] /= H1[2]; H1[1] /= H1[2];
+    H1[2] = s * sqrt(1 + H1[0]*H1[0] + H1[1] * H1[1]);
+    return (models::sin_ball * H1[2] > models::cos_ball * H1[1]) ? 1 : -1;
+    }
   if(pmodel == mdSpiral && pconf.spiral_cone < 360) {    
     return cone_side(shiftless(H));
     }
@@ -2283,6 +2293,8 @@ EX void set_vr_sphere() {
   #endif
   }
 
+EX int hemi_side = 0;
+
 EX void draw_main() {
   DEBBI(DF_GRAPH, ("draw_main"));
   
@@ -2296,6 +2308,24 @@ EX void draw_main() {
     return;
     }
 
+  if(pmodel == mdHemisphere && sphere && hemi_side == 0 && !vrhr::rendering()) {
+    hemi_side = models::sin_ball > 0 ? 1 : -1;
+    draw_main();
+
+    if(pconf.show_hyperboloid_flat) {
+      dynamicval<eModel> dv (pmodel, mdHyperboloidFlat);
+      dynamicval<int> ds (spherespecial, 1);
+      for(auto& ptd: ptds)
+        if(!among(ptd->prio, PPR::MOBILE_ARROW, PPR::OUTCIRCLE, PPR::CIRCLE))
+          ptd->draw();
+      }
+
+    hemi_side *= -1;
+    draw_main();
+    hemi_side = 0;
+    return;
+    }
+
   set_vr_sphere();  
   
   if(sphere && GDIM == 3 && pmodel == mdPerspective && !stretch::in() && !ray::in_use) {

hypgraph.cpp

@@ -778,11 +778,23 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         
         case gcSphere: {
           if(vrhr::rendering()) { vr_sphere(ret, H, md); return; }
+          ld z = sqhypot_d(3, H);
+          int s = H[2] > 0 ? 1 : -1;
           ret = H;
+          ret /= ret[2];
+          ret[2] = sqrt(1 + ret[0]*ret[0] + ret[1]*ret[1]) * s;
+          ret *= z;
+          ld& topz = pconf.top_z;
+          if(abs(ret[2]) > topz || (hemi_side && s != hemi_side)) {
+            ld scale = sqrt(topz*topz-1) / hypot_d(2, ret);
+            ret *= scale;
+            ret[2] = topz * s;
+            }
           if(pconf.depth_scaling != 1) {
             ld v = intval(H, Hypc);
             ret *= pow(v, (dir * pconf.depth_scaling-1) / 2);
             }
+          ret /= 3;
           break;
           }
         }
@@ -823,27 +835,35 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         }
       #endif
       
+      ret = H;
+
+      if(sphere && pmodel == mdHyperboloidFlat) {
+        int s = H[2] > 0 ? 1 : -1;
+        ret /= ret[2];
+        ret[2] = sqrt(1 + ret[0]*ret[0] + ret[1]*ret[1]) * s;
+        }
+
       if(pconf.depth_scaling != 1) {
-        ld v = intval(H, Hypc);
+        ld v = intval(ret, Hypc);
-        H *= pow(v, (pconf.depth_scaling-1) / 2);
+        ret *= pow(v, (pconf.depth_scaling-1) / 2);
         }
 
       if(pmodel == mdHyperboloid) {
         ld& topz = pconf.top_z;
-        if(H[2] > topz) {
+        if(ret[2] > topz) {
-          ld scale = sqrt(topz*topz-1) / hypot_d(2, H);
+          ld scale = sqrt(topz*topz-1) / hypot_d(2, ret);
-          H *= scale;
+          ret *= scale;
-          H[2] = topz;
+          ret[2] = topz;
           }
         }
       else {
-        H = space_to_perspective(H, pconf.alpha);
+        ret = space_to_perspective(ret, pconf.alpha);
-        H[2] = 1 - pconf.alpha;
+        ret[2] = 1 - pconf.alpha;
+        if(sphere) ret[2] = -ret[2];
         }
   
-      ret[0] = H[0] / 3;
+      ret[0] = ret[0] / 3;
-      ret[1] = (1 - H[2]) / 3;
+      tie(ret[1], ret[2]) = make_pair(((sphere?0:1) - ret[2]) / 3, ret[1] / 3);
-      ret[2] = H[1] / 3;
       
       models::apply_ball(ret[2], ret[1]);
       break;
@@ -2276,7 +2296,7 @@ EX color_t modelcolor = 0;
 EX void draw_model_elements() {
 
   #if CAP_VR
-  if(vrhr::active() && pmodel == mdHyperboloid) return;
+  if(vrhr::active() && is_hyperboloid(pmodel)) return;
   #endif
 
   dynamicval<ld> lw(vid.linewidth, vid.linewidth * vid.multiplier_ring);
@@ -2339,9 +2359,10 @@ EX void draw_model_elements() {
       return;
       }
     
-    case mdHyperboloid: {
+    case mdHyperboloid:
+    case mdHemisphere: {
       if(!pconf.show_hyperboloid_flat) return;
-      if(hyperbolic) {
+      if(models::is_hyperboloid(pmodel)) {
 #if CAP_QUEUE
         curvepoint(point3(0,0,1));
         curvepoint(point3(0,0,-pconf.alpha));
@@ -2550,7 +2571,7 @@ EX void draw_boundary(int w) {
         queuecurve(shiftless(Id), lc, fc, p);
         queuereset(pmodel, p);
         }
-      if(euclid || sphere) {
+      if(euclid) {
         queuereset(mdPixel, p);  
         for(int i=0; i<=360; i++) {
           curvepoint(point3(current_display->radius * cos(i * degree), current_display->radius * sin(i * degree), 0));
@@ -2558,13 +2579,15 @@ EX void draw_boundary(int w) {
         queuecurve(shiftless(Id), lc, fc, p);
         queuereset(pmodel, p);
         }
+      if(sphere) goto as_hyperboloid;
       return;
       }
     
     case mdHyperboloid: {
       if(hyperbolic) {
+        as_hyperboloid:
         ld& tz = pconf.top_z;
-        ld mz = acosh(tz);
+        ld mz = sphere ? atan(sqrt(tz*tz-1)) : acosh(tz);
         ld cb = models::cos_ball;
         ld sb = models::sin_ball;
         
@@ -2609,6 +2632,13 @@ EX void draw_boundary(int w) {
           curvepoint(xspinpush0(t * degree, mz));
 
         queuecurve(shiftless(Id), lc, fc, p);
+
+        if(sphere) {
+          for(ld t=0; t<=360; t ++)
+            curvepoint(xspinpush0(t * degree, M_PI-mz));
+
+          queuecurve(shiftless(Id), lc, fc, p);
+          }
         }
       return;
       }

models.cpp

@@ -223,6 +223,10 @@ EX namespace models {
     return 0;
     }
 
+  EX bool is_hyperboloid(eModel m) {
+    return m == (sphere ? mdHemisphere : mdHyperboloid);
+    }
+  
   EX bool is_perspective(eModel m) {
     return among(m, mdPerspective, mdGeodesic);
     }
@@ -592,7 +596,7 @@ EX namespace models {
         });
       }
     
-    if(vpmodel == mdHyperboloid) 
+    if(is_hyperboloid(vpmodel))
       add_edit(vpconf.top_z);
     
     if(has_transition(vpmodel)) 
@@ -613,7 +617,7 @@ EX namespace models {
     if(vpmodel == mdFisheye) 
       add_edit(vpconf.fisheye_param);
 
-    if(vpmodel == mdHyperboloid) 
+    if(is_hyperboloid(vpmodel))
       add_edit(pconf.show_hyperboloid_flat);
     
     if(vpmodel == mdCollignon)