conical spirals and bands

conformal.cpp

@@ -391,6 +391,10 @@ namespace conformal {
   int spiral_id = 7;
   
   cld spiral_multiplier;
+  ld right_spiral_multiplier = 1;
+  ld spiral_cone = 360;
+  ld spiral_cone_rad;
+  bool ring_not_spiral;
 
   void configure() {
     ld ball = -vid.ballangle * degree;
@@ -404,7 +408,15 @@ namespace conformal {
       ld b = spiral_angle * degree;
       ld cos_spiral = cos(b);
       ld sin_spiral = sin(b);
-      spiral_multiplier = cld(cos_spiral, sin_spiral) * M_PI * cos_spiral;
+      spiral_cone_rad = spiral_cone * degree;
+      ring_not_spiral = abs(cos_spiral) < 1e-3;
+      if(ring_not_spiral) {
+        cos_spiral = 0;
+        sin_spiral = 1;
+        spiral_multiplier = cld(0, right_spiral_multiplier * spiral_cone_rad / 2);
+        }
+      else
+        spiral_multiplier = cld(cos_spiral, sin_spiral) * cld(spiral_cone_rad * cos_spiral / 2., 0);
       }
     if(euclid) {
       hyperpoint h = tC0(eumove(spiral_x, spiral_y));
@@ -756,7 +768,7 @@ namespace conformal {
         });
       }
     
-    if(pmodel == mdBall || pmodel == mdHyperboloid || pmodel == mdHemisphere) {
+    if(pmodel == mdBall || pmodel == mdHyperboloid || pmodel == mdHemisphere || (pmodel == mdSpiral && spiral_cone != 360)) {
       dialog::addSelItem(XLAT("camera rotation in 3D models"), fts3(vid.ballangle), 'b');
       dialog::add_action(config_camera_rotation);
       }
@@ -811,6 +823,18 @@ namespace conformal {
       dialog::add_action([](){
         dialog::editNumber(spiral_angle, 0, 360, 15, 0, XLAT("spiral angle"), "");
         });
+
+      if(ring_not_spiral) {
+        dialog::addSelItem(XLAT("spiral multiplier"), fts(right_spiral_multiplier), 'M');
+        dialog::add_action([](){
+          dialog::editNumber(right_spiral_multiplier, 0, 10, -.1, 1, XLAT("spiral multiplier"), "");
+          });
+        }
+
+      dialog::addSelItem(XLAT("spiral cone"), fts(spiral_cone), 'C');
+      dialog::add_action([](){
+        dialog::editNumber(spiral_cone, 0, 360, -45, 360, XLAT("spiral cone"), "");
+        });
       }
 
     if(pmodel == mdSpiral && euclid) {
@@ -1097,6 +1121,13 @@ namespace conformal {
     else if(argis("-sang")) { 
       PHASEFROM(2); 
       shift_arg_formula(conformal::spiral_angle);
+      if(conformal::spiral_angle == 90) {
+        shift_arg_formula(conformal::right_spiral_multiplier);
+        }        
+      }
+    else if(argis("-scone")) { 
+      PHASEFROM(2); 
+      shift_arg_formula(conformal::spiral_cone);
       }
     else if(argis("-sxy")) { 
       PHASEFROM(2); 

hyper.h

@@ -1331,6 +1331,7 @@ namespace conformal {
   extern ld model_transition;
   extern ld top_z;
   extern ld spiral_angle, spiral_x, spiral_y;
+  extern ld spiral_cone;
   
   // screen coordinates to logical coordinates: apply_orientation(x,y)
   // logical coordinates back to screen coordinates: apply_orientation(y,x)
@@ -4620,6 +4621,8 @@ void show_color_dialog();
 
 extern ld band_shift;
 
+int cone_side(const hyperpoint H);
+
 void fix_the_band(transmatrix& T);
 
 struct bandfixer {

hypgraph.cpp

@@ -569,6 +569,19 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
       if(hyperbolic) makeband(H, ret, band_conformal);
       else ret = H;
       z = cld(ret[0], ret[1]) * conformal::spiral_multiplier;
+      
+      if(conformal::spiral_cone < 360) {
+        ld alpha = imag(z) * 360 / conformal::spiral_cone;
+        ld r = real(z);
+        r = exp(r);
+        
+        ret[0] = -sin(alpha) * r;
+        ret[1] = cos(alpha) * r;
+        ret[2] = (r-1) * sqrt( pow(360/conformal::spiral_cone, 2) - 1);
+        
+        conformal::apply_ball(ret[2], ret[1]);
+        }
+      else {      
         z = exp(z);
         ret[0] = real(z);
         ret[1] = imag(z);
@@ -576,6 +589,7 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
         if(vid.skiprope) 
           ret = mobius(ret, vid.skiprope, 1);
         }
+      }
     
     case mdGUARD: break;
     }
@@ -1502,6 +1516,14 @@ bool do_draw(cell *c, const transmatrix& T) {
     ld iz = imag(z) + 1.14279e-2; // make it never fall exactly on PI
     if(iz < -M_PI || iz >= M_PI) return false;
     }
+  if(hyperbolic && pmodel == mdSpiral && conformal::ring_not_spiral) {
+    cld z;
+    hyperpoint H = tC0(T);
+    hyperpoint ret;
+    makeband(H, ret, band_conformal);
+    z = cld(ret[0], ret[1]) * conformal::spiral_multiplier;
+    if(imag(z) < -conformal::spiral_cone_rad/2-1e-5 || imag(z) >= conformal::spiral_cone_rad/2-1e-5) return false;
+    }
   if(cells_drawn > vid.cells_drawn_limit) return false;
   bool usr = vid.use_smart_range || quotient || euwrap;
   if(usr && cells_drawn >= 50 && !in_smart_range(T)) return false;
@@ -1509,4 +1531,32 @@ bool do_draw(cell *c, const transmatrix& T) {
   return true; 
   }
 
+int cone_side(const hyperpoint H) {
+  hyperpoint ret;
+  if(hyperbolic) makeband(H, ret, band_conformal);
+  else ret = H;
+  cld z = cld(ret[0], ret[1]) * conformal::spiral_multiplier;
+  
+  auto zth = [&] (cld z) {
+    ld alpha = imag(z) * 360 / conformal::spiral_cone;
+    ld r = real(z);
+    r = exp(r);
+    
+    hyperpoint ret;
+      
+    ret[0] = -sin(alpha) * r;
+    ret[1] = cos(alpha) * r;
+    ret[2] = (r-1) * sqrt( pow(360/conformal::spiral_cone, 2) - 1);
+    
+    conformal::apply_ball(ret[2], ret[1]);
+    return ret;
+    };
+  
+  hyperpoint ret0 = zth(z);
+  hyperpoint ret1 = zth(z + cld(1e-3, 0));
+  hyperpoint ret2 = zth(z + cld(0, 1e-3));
+
+  return (ret1[1] - ret0[1]) * (ret2[0] - ret0[0]) < (ret2[1] - ret0[1]) * (ret1[0] - ret0[0]) ? 1 : -1;
+  }
+
 }

polygons.cpp

@@ -198,6 +198,7 @@ bool two_sided_model() {
   if(pmodel == mdDisk) return sphere;
   if(pmodel == mdHemisphere) return true;
   if(pmodel == mdRotatedHyperboles) return true;
+  if(pmodel == mdSpiral && conformal::spiral_cone < 360) return true;
   return false;
   }
 
@@ -219,6 +220,9 @@ int get_side(const hyperpoint& H) {
     applymodel(H, res);
     return res[2] < 0 ? -1 : 1;
     }
+  if(pmodel == mdSpiral && conformal::spiral_cone < 360) {    
+    return cone_side(H);
+    }
   return 0;
   }