extra two-point projections

classes.cpp

@@ -581,7 +581,7 @@ const modelinfo models[int(mdPolynomial)+1] = {
   {X3("band equidistant"), mf::band | mf::equidistant | mf::euc_boring},
   {X3("band equi-area"), mf::band | mf::equiarea | mf::euc_boring},
   {X3("sinusoidal"), mf::quasiband | mf::equiarea | mf::euc_boring},
-  {X3("two-point equidistant"), mf::equidistant | mf::euc_boring},
+  {X3("two-point equidistant"), mf::equidistant | mf::euc_boring | mf::twopoint},
   {X3("fisheye"), 0},
   {X3("Joukowsky transform"), mf::hyper_only | mf::conformal},
   {X3("Joukowsky+inversion"), mf::hyper_only | mf::conformal},
@@ -590,6 +590,8 @@ const modelinfo models[int(mdPolynomial)+1] = {
   {X3("native perspective"), 0},
   {X3("azimuthal equi-volume"), mf::azimuthal | mf::equivolume | mf::euc_boring},
   {X3("central inversion"), mf::azimuthal | mf::conformal},
+  {X3("two-point azimuthal"), mf::euc_boring | mf::twopoint},
+  {X3("two-point hybrid"), mf::euc_boring | mf::twopoint},
   {X3(""), 0},
   {X3(""), 0},
   {X3(""), 0},

classes.h

@@ -256,11 +256,17 @@ struct landtacinfo { eLand l; int tries, multiplier; };
 
 enum eModel {
   mdDisk, mdHalfplane, mdBand, mdPolygonal, mdFormula,
+  // 5..8.
   mdEquidistant, mdEquiarea, mdBall, mdHyperboloid, 
+  // 9..13
   mdHemisphere, mdBandEquidistant, mdBandEquiarea, mdSinusoidal, mdTwoPoint, 
+  // 14..16
   mdFisheye, mdJoukowsky, mdJoukowskyInverted,
+  // 17..19
   mdRotatedHyperboles, mdSpiral, mdPerspective,
-  mdEquivolume, mdCentralInversion,
+  // 20..22
+  mdEquivolume, mdCentralInversion, mdSimulatedPerspective, mdTwoHybrid,
+  // 24..
   mdGUARD, mdUnchanged, mdHyperboloidFlat, mdPolynomial, mdRug, mdFlatten
   };
 
@@ -278,6 +284,7 @@ namespace mf {
   static const flagtype hyper_or_torus = 256;
   static const flagtype quasiband = 512;
   static const flagtype equivolume = 1024;
+  static const flagtype twopoint = 2048;
   };
   
 struct modelinfo {

conformal.cpp

@@ -641,7 +641,7 @@ namespace conformal {
   
   bool model_has_orientation() {
     return
-      among(pmodel, mdHalfplane, mdPolynomial, mdPolygonal, mdTwoPoint, mdJoukowsky, mdJoukowskyInverted, mdSpiral) || mdBandAny();
+      among(pmodel, mdHalfplane, mdPolynomial, mdPolygonal, mdTwoPoint, mdJoukowsky, mdJoukowskyInverted, mdSpiral, mdSimulatedPerspective, mdTwoHybrid) || mdBandAny();
     }
   
   bool model_has_transition() {
@@ -752,7 +752,7 @@ namespace conformal {
       eModel m = eModel(i);
       if(m == mdFormula && ISMOBILE) continue;
       if(model_available(m)) {
-        dialog::addBoolItem(get_model_name(m), pmodel == m, "0123456789!@#$%^&*()]['" [m]);
+        dialog::addBoolItem(get_model_name(m), pmodel == m, "0123456789!@#$%^&*()][{}'" [m]);
         dialog::add_action([m] () {
           if(m == mdFormula) {
             edit_formula();
@@ -927,10 +927,10 @@ namespace conformal {
         });
       }
       
-    if(pmodel == mdTwoPoint) {
+    if(among(pmodel, mdTwoPoint, mdSimulatedPerspective, mdTwoHybrid)) {
       dialog::addSelItem(XLAT("parameter"), fts(vid.twopoint_param), 'b');
       dialog::add_action([](){
-        dialog::editNumber(vid.twopoint_param, 0, 10, .1, 1, XLAT("parameter"), 
+        dialog::editNumber(vid.twopoint_param, 1e-3, 10, .1, 1, XLAT("parameter"), 
           "This model maps the world so that the distances from two points "
           "are kept. This parameter gives the distance from the two points to "
           "the center."

hypgraph.cpp

@@ -257,6 +257,52 @@ hyperpoint mobius(hyperpoint h, ld angle, ld scale = 1) {
   return space_to_perspective(h, 1) / scale;
   }
 
+hyperpoint compute_hybrid(hyperpoint H, int rootid) {
+  auto& t = vid.twopoint_param;
+  hyperpoint Hl = xpush(+t) * H;
+  hyperpoint Hr = xpush(-t) * H;
+  ld g = (Hl[0] + 1e-7) / (Hl[1] + 1e-8);
+  ld d = hdist0(Hr);
+  
+  hyperpoint spinned = spintox(Hl) * xpush0(2*t);
+  if(Hl[0] < 0) spinned = pispin * spinned;
+
+  ld y = asin_auto(spinned[1]);
+  ld x = asin_auto_clamp(spinned[0] / cos_auto(y));
+
+  int sign = (Hl[0] > 0 ? 1 : -1) * hdist0(Hl) < x ? -1 : 1;
+  
+  switch(rootid & 3) {
+    case 1: sign = -sign; break;
+    case 2: sign = 1; break;
+    case 3: sign = -1; break;
+    }
+
+  // (x + t) / g = y
+  // yy + (x-t)(x-t) = dd
+  // (x+t)*(x+t)/g*g + x*x + t*t - 2*x*t = dd
+  
+  // x*x*(1+1/g*g) + t*t*(1+1/g*g) + 2xt (1/gg-1) = dd
+  // xx + 2xt (1/gg-1) / (1+1/gg) = dd / (1+1/gg) - tt
+  
+  ld b = t*(1/g/g - 1) / (1+1/g/g);
+  ld c = d*d / (1+1/g/g) - t*t;
+  
+  // xx + 2bx = c
+  // xx + 2bx + bb = c + bb
+  // (x+b)^2 = c+bb
+  // x = +/- sqrt(c+bb) - b
+  
+  ld a = c+b*b;
+  
+  hyperpoint ret;
+  ret[0] = (a > 0 ? sign * sqrt(a) : 0) - b;
+  ret[1] = (ret[0] + t) / g;
+  ret[2] = 0;
+  
+  return ret;
+  }
+
 void applymodel(hyperpoint H, hyperpoint& ret) {
 
   using namespace hyperpoint_vec;
@@ -436,6 +482,43 @@ void applymodel(hyperpoint H, hyperpoint& ret) {
       break;
       }
     
+    case mdSimulatedPerspective: {
+      conformal::apply_orientation_yz(H[1], H[2]);
+      conformal::apply_orientation(H[0], H[1]);
+      auto yz = move_z_to_y(H);
+      hyperpoint Hl = xpush(-vid.twopoint_param) * H;
+      hyperpoint Hr = xpush(+vid.twopoint_param) * H;
+      ld lyx = (Hl[1] + 1e-7) / (Hl[0] + 1e-8);
+      ld ryx = (Hr[1] + 1e-7) / (Hr[0] + 1e-8);
+      // (r.x + t) * lyx = (r.x - t) * ryx = r.y
+      // r.x * lyx + t * lyx = r.x * ryx - t * ryx
+      // r.x * (lyx-ryx) = - t * (ryx + lyx)
+      // r.x = -t * (ryx+lyx) / (lyx-ryx)
+      // r.x = - 2 * t * lyx * ryx / lyx / ryx
+      
+      ret[0] = -vid.twopoint_param * (ryx + lyx) / (lyx - ryx);
+      ret[1] = (ret[0] + vid.twopoint_param) * lyx;
+      ret[2] = 0;
+
+      move_y_to_z(ret, yz);      
+      conformal::apply_orientation(ret[0], ret[1]);
+      conformal::apply_orientation_yz(ret[2], ret[1]);
+      break;
+      }
+    
+    case mdTwoHybrid: {
+      conformal::apply_orientation_yz(H[1], H[2]);
+      conformal::apply_orientation(H[0], H[1]);
+      auto yz = move_z_to_y(H);
+      
+      ret = compute_hybrid(H, whateveri[0]); 
+      
+      move_y_to_z(ret, yz);      
+      conformal::apply_orientation(ret[0], ret[1]);
+      conformal::apply_orientation_yz(ret[2], ret[1]);
+      break;
+      }
+    
     case mdJoukowsky: 
     case mdJoukowskyInverted: {
       conformal::apply_orientation_yz(H[1], H[2]);
@@ -1394,8 +1477,33 @@ void draw_model_elements() {
       queuechr(current_display->xcenter, current_display->ycenter + current_display->radius * vid.alpha, 0, vid.fsize, 'X', ringcolor, 1, 8);
       return;
       }
+    
+    case mdTwoHybrid: {
+      queuereset(mdUnchanged, PPR::CIRCLE);
+      
+      for(int mode=0; mode<4; mode++) {
+        for(int s=-199; s<=199; s += 2) {
+          ld p = s / 200.;
+          ld a = vid.twopoint_param * (1+p);
+          ld b = vid.twopoint_param * (1-p);
+          ld h = ((mode & 2) ? -1 : 1) * sqrt(asin_auto(tan_auto(a) * tan_auto(b)));
+          
+          hyperpoint H = xpush(p * vid.twopoint_param) * ypush0(h);
+          
+          hyperpoint res = compute_hybrid(H, 2 | mode);
+          conformal::apply_orientation(res[0], res[1]);
+          conformal::apply_orientation_yz(res[2], res[1]);
+          using namespace hyperpoint_vec;
+          curvepoint(res * current_display->radius);
+          }
+        queuecurve(ringcolor, 0, PPR::CIRCLE);
+        }
 
-    case mdTwoPoint: {
+      queuereset(pmodel, PPR::CIRCLE);
+      /* fallthrough */
+      }
+
+    case mdTwoPoint: case mdSimulatedPerspective: {
       ld a = -conformal::model_orientation * degree;
       queuechr(xspinpush0(a, +vid.twopoint_param), vid.xres / 100, 'X', ringcolor >> 8);
       queuechr(xspinpush0(a, -vid.twopoint_param), vid.xres / 100, 'X', ringcolor >> 8);