ray:: horospherical hyperbolic honeycombs

binary-tiling.cpp

@@ -558,6 +558,21 @@ EX namespace binary {
     return S7-1;
     }
   
+  EX int dirs_outer() {
+    switch(geometry) {
+      case gBinary3: return 4;
+      case gHoroTris: return 4;
+      case gHoroRec: return 2;
+      case gHoroHex: return 6;
+      default: return -1;
+      }
+    }
+
+  EX int dirs_inner() {
+    if(among(geometry, gBinaryTiling, gHoroHex)) return 2;
+    return 1;
+    }
+  
   EX void build_tmatrix() {
     if(among(geometry, gBinaryTiling, gSol)) return; // unused
     use_direct = (1 << (S7-1)) - 1;

hyperpoint.cpp

@@ -586,6 +586,19 @@ EX transmatrix parabolic13(ld u, ld v) {
     }
   }
 
+EX hyperpoint parabolic10(hyperpoint h) {
+  if(euclid) { h[MDIM] = 1; return h; }
+  else if(MDIM == 4) return hyperpoint(sinh(h[0]), h[1]/exp(h[0]), h[2]/exp(h[0]), cosh(h[0]));
+  else return hyperpoint(sinh(h[0]), h[1]/exp(h[0]), cosh(h[0]), 0);
+  }
+
+EX hyperpoint deparabolic10(const hyperpoint h) {
+  if(euclid) return h;
+  ld x = -log(h[LDIM] - h[0]);
+  if(MDIM == 3) return hyperpoint(x, h[1] * exp(x), 1, 0);
+  return point31(x, h[1] * exp(x), h[2] * exp(x));
+  }
+
 EX transmatrix spintoc(const hyperpoint& H, int t, int f) {
   transmatrix T = Id;
   ld R = hypot(H[f], H[t]);

polygons.cpp

@@ -709,6 +709,11 @@ void geometry_information::compute_cornerbonus() { }
 
 hyperpoint ray_kleinize(hyperpoint h, int id, ld pz) {
   if(geometry == gNil && among(id, 2, 5)) h[2] = 0;
+  if(hyperbolic && binarytiling) {
+    // ld co = vid.binary_width / log(2) / 4;
+    // hyperpoint res = point31(h[2]*log(2)/2, h[0]*co, h[1]*co);
+    return deparabolic10(binary::parabolic3(h[0], h[1]) * xpush0(log(2)/2*h[2]));
+    }
   if(prod) {
     return point3(h[0]/h[2], h[1]/h[2], pz);
     }
@@ -918,7 +923,7 @@ void geometry_information::create_wall3d() {
     ld h = binary::horohex_scale / 2;
     hyperpoint down = point3(0,0,2*z);
 
-    for(int i=0; i<3; i++) {
+    for(int j=0; j<4; j++) for(int i=0; i<3; i++) {
       transmatrix T = cspin(0, 1, 2*M_PI*i/3);
 
       hyperpoint hcenter = point3(0,0,-z);
@@ -929,10 +934,10 @@ void geometry_information::create_wall3d() {
       hyperpoint hcn = T*point3(-h*2,0,  -z);
       hyperpoint hun = T*point3(-h*3,+r3,-z);
       hyperpoint hdn = T*point3(-h*3,-r3,-z);
-      make_wall(i, {hcenter, hu0, hu1, hd1, hd0});
+      if(j == 0) make_wall(i, {hcenter, hu0, hu1, hd1, hd0});
-      make_wall(i+3, {hcn, hun, hdn});
+      if(j == 1) make_wall(i+3, {hcn, hun, hdn});
-      make_wall(i+6, make4(hd1, hu1, hd1+down));
+      if(j == 2) make_wall(i+6, make4(hd1, hu1, hd1+down));
-      make_wall(i+9, make4(hun, hdn, hun+down));
+      if(j == 3) make_wall(i+9, make4(hun, hdn, hun+down));
       }
 
     make_wall(12, {point3(3*h,r3,z), point3(0,2*r3,z), point3(-3*h,r3,z)});

raycaster.cpp

@@ -54,7 +54,7 @@ eGeometry last_geometry;
 /** is the raycaster available? */
 EX bool available() {
   if(WDIM == 2) return false;
-  if(hyperbolic && pmodel == mdPerspective && !binarytiling)
+  if(hyperbolic && pmodel == mdPerspective && !penrose)
     return true;
   if((sol || nil) && pmodel == mdGeodesic)
     return true;
@@ -79,6 +79,7 @@ struct raycaster : glhr::GLprogram {
   GLint tConnections, tWallcolor, tTextureMap;
   GLint uBinaryWidth, uPLevel, uLP;
   GLint uLinearSightRange, uExpStart, uExpDecay;
+  GLint uBLevel;
   
   raycaster(string vsh, string fsh) : GLprogram(vsh, fsh) {
     println(hlog, "assigning");
@@ -101,6 +102,8 @@ struct raycaster : glhr::GLprogram {
     uLinearSightRange = glGetUniformLocation(_program, "uLinearSightRange");
     uExpDecay = glGetUniformLocation(_program, "uExpDecay");
     uExpStart = glGetUniformLocation(_program, "uExpStart");
+
+    uBLevel = glGetUniformLocation(_program, "uBLevel");
   
     tConnections = glGetUniformLocation(_program, "tConnections");
     tWallcolor = glGetUniformLocation(_program, "tWallcolor");
@@ -158,14 +161,24 @@ void enable_raycaster() {
       "uniform float uPLevel;\n"
       "uniform mat4 uLP;\n";
     
-    if(IN_ODS) fsh += 
+    int flat1 = 0, flat2 = S7;
+    
+    if(hyperbolic && binarytiling) {
+      fsh += "uniform float uBLevel;\n";
+      flat1 = binary::dirs_outer();
+      flat2 -= binary::dirs_inner();
+      }
+
+    if(IN_ODS || hyperbolic) fsh += 
 
     "mat4 xpush(float x) { return mat4("
          "cosh(x), 0., 0., sinh(x),\n"
          "0., 1., 0., 0.,\n"
          "0., 0., 1., 0.,\n"
          "sinh(x), 0., 0., cosh(x)"
-         ");}\n"
+         ");}\n";
+    
+    if(IN_ODS) fsh += 
 
     "mat4 xzspin(float x) { return mat4("
          "cos(x), 0., sin(x), 0.,\n"
@@ -184,6 +197,9 @@ void enable_raycaster() {
    fsh += 
      "vec2 map_texture(vec4 pos, int which) {\n";
    if(nil) fsh += "if(which == 2 || which == 5) pos.z = 0.;\n";
+   else if(hyperbolic && binarytiling) fsh += 
+       "pos = vec4(-log(pos.w-pos.x), pos.y, pos.z, 1);\n"
+       "pos.yz *= exp(pos.x);\n";
    else if(hyperbolic) fsh += 
        "pos /= pos.w;\n";
    else if(prod) fsh +=
@@ -269,7 +285,7 @@ void enable_raycaster() {
       fmain +=
         "  if(which == -1) {\n";
       
-      fmain += "for(int i=0; i<"+its(S7)+"; i++) {\n";
+      fmain += "for(int i="+its(flat1)+"; i<"+its(flat2)+"; i++) {\n";
       
       if(in_h2xe()) fmain +=
           "    float v = ((position - uM[i] * position)[2] / (uM[i] * tangent - tangent)[2]);\n"
@@ -301,6 +317,31 @@ void enable_raycaster() {
       fmain += 
           "  if(d < dist) { dist = d; which = i; }\n"
             "}\n";
+    
+      // 20: get to horosphere +uBLevel (take smaller root)
+      // 21: get to horosphere -uBLevel (take larger root)
+                          
+      if(hyperbolic && binarytiling) {
+        fmain += 
+          "for(int i=20; i<22; i++) {\n"
+            "float sgn = i == 20 ? -1. : 1.;\n"
+            "vec4 zpos = xpush(uBLevel*sgn) * position;\n"
+            "vec4 ztan = xpush(uBLevel*sgn) * tangent;\n"
+            "float Mp = zpos.w - zpos.x;\n"
+            "float Mt = ztan.w - ztan.x;\n"
+            "float a = (Mp*Mp-Mt*Mt);\n"
+            "float b = Mp/a;\n"
+            "float c = (1.+Mt*Mt) / a;\n"
+            "if(b*b < c) continue;\n"
+            "if(sgn < 0. && Mt > 0.) continue;\n"
+            "float zsgn = (Mt > 0. ? -sgn : sgn);\n"
+            "float u = sqrt(b*b-c)*zsgn + b;\n"
+            "float v = -(Mp*u-1.) / Mt;\n"
+            "float d = asinh(v);\n"
+            "if(d < 0. && abs(log(position.w*position.w-position.x*position.x)) < uBLevel) continue;\n"
+            "if(d < dist) { dist = d; which = i; }\n"
+            "}\n";
+        }
           
       if(prod) fmain += 
         "if(zspeed > 0.) { float d = (uPLevel - zpos) / zspeed; if(d < dist) { dist = d; which = "+its(S7)+"+1; }}\n"
@@ -461,10 +502,29 @@ void enable_raycaster() {
     else fmain += 
       "position = position + tangent * dist;\n";
     
+    if(hyperbolic && binarytiling) {
+      fmain += 
+        "if(which == 20) {\n"
+        "  float best = 999.;\n"
+        "  for(int i="+its(flat2)+"; i<"+its(S7)+"; i++) {\n"
+          "  float cand = len(uM[i] * position);\n"
+          "  if(cand < best) { best = cand; which = i; }\n"
+          "  }\n"
+          "}\n"
+        "if(which == 21) {\n"
+          "float best = 999.;\n"
+          "for(int i=0; i<"+its(flat1)+"; i++) {\n"
+          "  float cand = len(uM[i] * position);\n"
+          "  if(cand < best) { best = cand; which = i; }\n"
+          "  }\n"
+//          "gl_FragColor = vec4(.5 + .5 * sin((go+dist)*100.), 1, float(which)/3., 1); return;\n"
+          "}\n";
+      }
+    
     fmain += "  go = go + dist;\n";
-    
+
     fmain += "if(which == -1) continue;\n";
-    
+        
     if(prod) fmain += "position.w = -zpos;\n";
     
     // apply wall color
@@ -525,6 +585,17 @@ void enable_raycaster() {
 
     if(use_reflect) {
       if(prod) fmain += "if(reflect && which >= "+its(S7)+") { zspeed = -zspeed; continue; }\n";
+      if(hyperbolic && binarytiling) fmain +=
+        "if(reflect && (which < "+its(flat1)+" || which >= "+its(flat2)+")) {\n"
+        "  float x = -log(position.w - position.x);\n"
+        "  vec4 xtan = xpush(-x) * tangent;\n"
+        "  float diag = (position.y*position.y+position.z*position.z)/2.;\n"
+        "  vec4 normal = vec4(1.-diag, -position.y, -position.z, -diag);\n"
+        "  float mdot = dot(xtan.xyz, normal.xyz) - xtan.w * normal.w;\n"
+        "  xtan = xtan - normal * mdot * 2.;\n"
+        "  tangent = xpush(x) * xtan;\n"
+        "  continue;\n"
+        "  }\n";
       if(sol) fmain += 
         "  if(reflect) {\n"
         "    if(which == 0 || which == 4) tangent.x = -tangent.x;\n"
@@ -765,6 +836,8 @@ EX void cast() {
     glUniform1f(o->uBinaryWidth, vid.binary_width * log(2) / 2);
   if(o->uPLevel != -1)
     glUniform1f(o->uPLevel, cgi.plevel / 2);
+  if(o->uBLevel != -1)
+    glUniform1f(o->uBLevel, log(binary::expansion()) / 2);
   
   glUniform1f(o->uLinearSightRange, sightranges[geometry]);
   glUniform1f(o->uExpDecay, exp_decay_current());