model transition for Joukowsky, inverted Joukowsky, and Band.

conformal.cpp

@@ -299,6 +299,7 @@ namespace conformal {
   ld cos_ball, sin_ball;
   bool model_straight;
   ld top_z = 5;
+  ld model_transition = 1;
 
   bool autoband = false;
   bool autobandhistory = false;
@@ -605,6 +606,10 @@ namespace conformal {
       among(pmodel, mdHalfplane, mdPolynomial, mdPolygonal, mdTwoPoint, mdJoukowsky, mdJoukowskyInverted) || mdBandAny();
     }
   
+  bool model_has_transition() {
+    return among(pmodel, mdJoukowsky, mdJoukowskyInverted, mdBand);
+    }
+  
   void model_menu() {
     cmode = sm::SIDE | sm::MAYDARK | sm::CENTER;
     gamescreen(0);
@@ -665,6 +670,9 @@ namespace conformal {
     if(pmodel == mdHyperboloid)
       dialog::addSelItem(XLAT("topz"), fts3(top_z), 'l');
     
+    if(model_has_transition())
+      dialog::addSelItem(XLAT("model transition"), fts3(model_transition), 't');
+    
     if(pmodel == mdHemisphere && euclid) {
       dialog::addSelItem(XLAT("parameter"), fts3(vid.euclid_to_sphere), 'l');
       }
@@ -719,6 +727,8 @@ namespace conformal {
         dialog::editNumber(model_orientation, 0, 360, 90, 0, XLAT("model orientation"), "");
       else if(uni == 'l' && pmodel == mdHyperboloid) 
         dialog::editNumber(top_z, 1, 20, 0.25, 4, XLAT("topz"), "");
+      else if(uni == 't')
+        dialog::editNumber(model_transition, 0, 1, 0.1, 1, XLAT("model transition"), "");
       else if(uni == 'b' && pmodel == mdHalfplane)
         dialog::editNumber(model_orientation, 0, 2, 0.25, 1, XLAT("halfplane scale"), "");
       else if(uni == 's') {

hyper.h

@@ -1281,6 +1281,7 @@ namespace conformal {
   extern ld ocos, osin;
   extern ld cos_ball, sin_ball;
   extern bool model_straight;
+  extern ld model_transition;
   extern ld top_z;
   
   // screen coordinates to logical coordinates: apply_orientation(x,y)

hypgraph.cpp

@@ -267,6 +267,39 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
     if(zlev_used) H /= zlev;
     }
   
+  if(pmodel == mdBand && conformal::model_transition != 1) {
+    ld& mt = conformal::model_transition;
+
+    ld x0, y0;  
+    x0 = H[0] / tz;
+    y0 = H[1] / tz;
+    
+    conformal::apply_orientation(x0, y0);
+
+    x0 += 1;
+    double rad = x0*x0 + y0*y0;
+    y0 /= rad;
+    x0 /= rad;
+    x0 -= .5;
+    
+    ld phi = atan2(y0, x0);
+    ld r = hypot(x0, y0);
+    
+    r = pow(r, 1 - mt);
+    phi *= (1 - mt);
+    ret[0] = r * cos(phi);
+    ret[1] = r * sin(phi);
+    ret[2] = 0;
+    
+    ret[0] -= pow(0.5, 1-mt);
+    ret[0] /= -(1-mt) * M_PI / 2;
+    ret[1] /= (1-mt) * M_PI / 2;
+    
+    conformal::apply_orientation(ret[1], ret[0]);
+    ghcheck(ret,H);
+    return;
+    }
+  
   if(pmodel == mdTwoPoint || mdBandAny() || pmodel == mdSinusoidal) {
     // map to plane
     if(false) {
@@ -411,16 +444,32 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
     ld r = hypot(x0, y0);
     ld c = x0 / r;
     ld s = y0 / r;
-    ret[0] = (r + 1/r) * c / 2;
+    ld& mt = conformal::model_transition;
-    ret[1] = (r - 1/r) * s / 2;
+    ld a = 1 - .5 * mt, b = .5 * mt;
+    swap(a, b);
+    
+    ret[0] = (a * r + b/r) * c / 2;
+    ret[1] = (a * r - b/r) * s / 2;
     ret[2] = 0;
+    
     if(pmodel == mdJoukowskyInverted) {
       ld r2 = sqhypot2(ret);
       ret[0] = ret[0] / r2;
       ret[1] = -ret[1] / r2;
       conformal::apply_orientation(ret[1], ret[0]);
+      
+      /*
+
+      ret[0] += 1;
+      ld alpha = atan2(ret[1], ret[0]);
+      ld mod = hypot(ret[0], ret[1]);
+      // ret[0] = cos(alpha/2) * sqrt(mod);
+      // ret[1] = sin(alpha/2) * sqrt(mod);
+      ret[0] = alpha;
+      ret[1] = log(mod); */
       }
     else conformal::apply_orientation(ret[0], ret[1]);
+
     ghcheck(ret,H);
     return;
     }

screenshot.cpp

@@ -422,6 +422,8 @@ vector<animatable_parameter> animatable_parameters = {
   animatable_parameter(surface::dini_b),
   animatable_parameter(surface::hyper_b),
   animatable_parameter(conformal::halfplane_scale),
+  animatable_parameter(conformal::model_transition),
+  animatable_parameter(conformal::top_z, dialog::logarithmic),
   };
 
 ld anim_param = 0;
@@ -429,6 +431,8 @@ int paramstate = 0;
 
 bool needs_highqual;
 
+bool joukowsky_anim;
+
 void reflect_view() {
   if(centerover.at) {
     transmatrix T = Id;
@@ -531,6 +535,15 @@ void apply() {
     if(need_reset_geometry) resetGeometry(), need_reset_geometry = false;
     calcparam();
     }
+  if(joukowsky_anim) {
+    ld t = ticks / period;
+    t = t - floor(t);
+    conformal::model_transition = t / 1.1;
+    vid.scale = (1 - conformal::model_transition) / 2.;
+    calcparam();
+    printf("scale = %lf tr = %lf t = %lf\n", vid.scale, conformal::model_transition, t);
+    printf("radius = %lf\n", vid.radius);
+    }
   }
 
 void rollback() {
@@ -647,6 +660,10 @@ void show() {
     dialog::addBoolItem(XLAT("parabolic"), ma == maParabolic, '3');
     dialog::add_action([] () { ma = maParabolic; });
     }
+  if(among(pmodel, mdJoukowsky, mdJoukowskyInverted)) {
+    dialog::addBoolItem(XLAT("joukowsky_anim"), joukowsky_anim, 'j');
+    dialog::add_action([] () { joukowsky_anim = !joukowsky_anim; });
+    }
   dialog::addBoolItem(XLAT("circle"), ma == maCircle, '4');
   dialog::add_action([] () { ma = maCircle; 
     rotation_center_h = viewctr;
@@ -827,6 +844,9 @@ int readArgs() {
   else if(argis("-animball")) {
     shift(); ballangle_rotation = argf();
     }
+  else if(argis("-animj")) {
+    shift(); joukowsky_anim = true;
+    }
 
   else return 1;
   return 0;