implemented the correct wall shapes in the rotspace raytracer

graph.cpp

@@ -4395,7 +4395,7 @@ int hrmap::wall_offset(cell *c) {
     if(!cgi.wallstart.empty()) cgi.wallstart.pop_back();
     cgi.reserve_wall3d(wo + isize(ss.faces));
 
-    
+    kleinize_sides = isize(ss.faces) - 2;
     for(int i=0; i<isize(ss.faces); i++) {
       cgi.make_wall(wo, i, ss.faces[i]);
       cgi.walltester[wo + i] = ss.walltester[i];

polygons.cpp

@@ -877,9 +877,53 @@ void geometry_information::compute_cornerbonus() { }
 
 // Make a wall
 
+EX int kleinize_sides;
+
+hyperpoint ray_kleinize_rotspace(hyperpoint h, int ks, int id) {
+
+  /* todo: in Archimedean tilings it may be the case that pispin is incorrect, as shown by `angle of zero` -- need to carry it to raycaster */
+  h = pispin * h;
+
+  ld& x = h[0];
+  ld& y = h[1];
+  ld& z = h[2];
+  ld& w = h[3];
+
+  if(id < ks) h = spin(-TAU * id / ks) * h;
+
+  ld dx, dy;
+
+  if(sl2) {
+    dx = -2 * (y*z - x*w);
+    dy = -2 * (x*z + y*w);
+    }
+  else {
+    dx = +2 * (x*z + y*w);
+    dy = -2 * (y*z - x*w);
+    }
+
+  if(id >= ks) return hyperpoint(dx, dy, 0, 1);
+
+  if(sl2) {
+    ld vy = -asinh(dy)/2;
+    ld vx = asinh(dx / cosh(2*vy)) / 2;
+    hyperpoint h1 = lorentz(1, 3, -vy) * lorentz(0, 2, -vy) * lorentz(0, 3, -vx) * lorentz(2, 1, vx) * h;
+    ld vz = atan2(h1[2], h1[3]);
+    return hyperpoint(vx, vy, vz, 1);
+    }
+  else {
+    ld vy = -asin(dy)/2;
+    ld vx = asin(dx / cos(2*vy)) / 2;
+    hyperpoint h1 = cspin(0, 3, vy) * cspin(1, 2, -vy) * cspin(1, 3, -vx) * cspin(0, 2, -vx) * h;
+    ld vz = atan2(h1[2], h1[3]);
+    return hyperpoint(vx, vy, vz, 1);
+    }
+  }
+
 hyperpoint ray_kleinize(hyperpoint h, int id, ld pz) {
   if(nil && nilv::nil_structure_index == 0 && among(id, 2, 5)) h[2] = 0;
   if(nil && nilv::nil_structure_index == 2 && among(id, 6, 7)) h[2] = 0;
+  if(rotspace) return ray_kleinize_rotspace(h, kleinize_sides, id);
   #if CAP_BT
   if(hyperbolic && bt::in()) {
     // ld co = vid.binary_width / log(2) / 4;

raycaster.cpp

@@ -80,7 +80,7 @@ EX bool is_eyes() {
   }
 
 EX bool is_stepbased() {
-  return nonisotropic || stretch::in() || is_eyes();
+  return nonisotropic || stretch::in() || is_eyes() || rotspace;
   }
 
 EX bool horos() {
@@ -127,7 +127,7 @@ EX bool available() {
   #endif
   if(hyperbolic && pmodel == mdPerspective && !kite::in())
     return true;
-  if(sphere && pmodel == mdPerspective && !rotspace)
+  if(sphere && pmodel == mdPerspective)
     return true;
   if(nil && nilv::nil_structure_index == 1)
     return false;
@@ -341,7 +341,7 @@ struct raygen {
   void create();
 
   string f_xpush() { return hyperbolic ? "xpush_h3" : "xpush_s3"; }
-  string f_len() { return hyperbolic ? "len_h3" : (sphere && rotspace) ? "len_sr" : sl2 ? "len_sl2" : sphere ? "len_s3" : "len_x"; }
+  string f_len() { return hyperbolic ? "len_h3" : rotspace ? "rot_flatdist" : sphere ? "len_s3" : "len_x"; }
   string f_len_prod() { return in_h2xe() ? "len_h2" : in_s2xe() ? "len_s2" : "len_e2"; }
   void add_functions();
   };
@@ -867,11 +867,9 @@ void raygen::move_forward() {
     "      }\n";
       if(rotspace) fmain +=
     "   if(which == -1) {\n"
-    "     best = len_rotspace(nposition);\n"
+    "     mediump float z = rot_zlevel(nposition, sides-2);\n"
-    "     mediump float cand1 = len_rotspace(" + getM("walloffset+sides-2") + "*nposition);\n"
+    "     if(z > uPLevel) which = sides-1;\n"
-    "     if(cand1 < best) { best = cand1; which = sides-2; }\n"
+    "     if(z <-uPLevel) which = sides-2;\n"
-    "     mediump float cand2 = len_rotspace(" + getM("walloffset+sides-1") + "*nposition);\n"
-    "     if(cand2 < best) { best = cand2; which = sides-1; }\n"
     "     }\n";
       if(gproduct) {
         fmain +=
@@ -1409,6 +1407,50 @@ void raygen::emit_iterate(int gid1) {
     fmain += "  mediump vec4 pos = position;\n";
     if(nil && nilv::nil_structure_index == 0) fmain += "if(which == 2 || which == 5) pos.z = 0.;\n";
     if(nil && nilv::nil_structure_index == 2) fmain += "if(which == 6 || which == 7) pos.z = 0.;\n";
+    else if(rotspace) {
+      fmain += "pos = rot_coordinates(pos, sides-2, which);\n";
+      string spinner = "h = cspin(0, 1, PI) * h;\n";
+      string calc_dxy = sl2 ?
+            "dx = -2. * (h.y*h.z - h.x*h.w);\n"
+            "dy = -2. * (h.x*h.z + h.y*h.w);\n" :
+            "dx = +2. * (h.x*h.z + h.y*h.w);\n"
+            "dy = -2. * (h.y*h.z - h.x*h.w);\n";
+      string dcalc_dxy = "mediump float dx, dy;\n" + calc_dxy;
+      string calc_vxy = sl2 ?
+            "mediump float vy = -asinh(dy)/2.;\n"
+            "mediump float vx = asinh(dx / cosh(2.*vy)) / 2.;\n" :
+            "mediump float vy = -asin(dy)/2.;\n"
+            "mediump float vx = asin(dx / cos(2.*vy)) / 2.;\n";
+      string calc_h1 = sl2 ?
+            "vec4 h1 = lorentz(1, 3, -vy) * lorentz(0, 2, -vy) * lorentz(0, 3, -vx) * lorentz(2, 1, vx) * h;\n" :
+            "vec4 h1 = cspin(0, 3, vy) * cspin(1, 2, -vy) * cspin(1, 3, -vx) * cspin(0, 2, -vx) * h;\n";
+      fsh +=
+        "vec4 rot_coordinates(vec4 h, int ks, int id) {\n"
+          +spinner+
+          "if(id < ks) h = cspin(0, 1, -TAU * float(id) / float(ks)) * h;\n"
+          +dcalc_dxy +
+          "if(id >= ks) return vec4(dx, dy, 0, 1);\n"
+          + calc_vxy + calc_h1 +
+          "float vz = atan2(h1[2], h1[3]);\n"
+          "return vec4(vx, vy, vz, 1);\n"
+          "}\n\n";
+      fsh +=
+        "mediump float rot_flatdist(mediump vec4 h) {\n" + dcalc_dxy +
+           "return dx*dx+dy*dy;\n"
+           "}\n";
+      fsh +=
+        "mediump float rot_zlevel(vec4 h, int ks) {\n" + spinner + dcalc_dxy +
+          "float alpha = (floor(atan2(dy, dx) * float(ks) / TAU + 0.5)) * TAU / float(ks);\n"
+          "h = cspin(1, 0, alpha) * h;\n" + calc_dxy + calc_vxy + calc_h1 +
+          "return atan2(h1[2], h1[3]);\n"
+          "}\n\n";
+      fsh +=
+        "mediump bool rot_dark(vec4 h, int ks) {\n" + spinner + dcalc_dxy +
+          "float alpha = atan2(dy, dx) * float(ks);\n"
+          "return cos(alpha) < -0.99;\n"
+          "}\n\n";
+       }
+
     else if(hyperbolic && bt::in()) fmain +=
         "pos = deparabolici13(pos);\n"
         "pos.xyz = pos.zxy;\n";
@@ -1440,6 +1482,8 @@ void raygen::emit_iterate(int gid1) {
   if(!volumetric::on) fmain +=
     "    col.xyz = col.xyz * d + uFogColor.xyz * (1.-d);\n";
 
+  if(rotspace) fmain +=
+    "    if(rot_dark(position, sides-2)) col.xyz /= 2.;\n";
   if(nil && nilv::nil_structure_index == 0) fmain +=
     "    if(abs(abs(position.x)-abs(position.y)) < .005) col.xyz /= 2.;\n";
 
@@ -1811,16 +1855,27 @@ void raygen::add_functions() {
         "  return res;\n"
         "  }\n\n");
 
-  add_if("len_rotspace", "mediump float len_rotspace(vec4 h) { return 1. - h[3]; }\n");
-
   add_if("len_h3",  "  mediump float len_h3(mediump vec4 x) { return x[3]; }\n");
   add_if("len_sr", "  mediump float len_sr(mediump vec4 x) { return 1.+x.x*x.x+x.y*x.y-x.z*x.z-x.w*x.w; }\n");
-  add_if("len_sl2","  mediump float len_sl2(mediump vec4 x) { return 1.+x.x*x.x+x.y*x.y; }\n");
   add_if("len_s3",  "  mediump float len_s3(mediump vec4 x) { return 1.-x[3]; }\n");
   add_if("len_x",  "  mediump float len_x(mediump vec4 x) { return length(x.xyz); }\n");
   add_if("len_h2",  "  mediump float len_h2(mediump vec4 x) { return x[2]; }\n");
   add_if("len_s2",  "  mediump float len_s2(mediump vec4 x) { return 1.-x[2]; }\n");
   add_if("len_e2",  "  mediump float len_e2(mediump vec4 x) { return length(x.xy); }\n");
+
+  add_if("cspin",
+    "mediump mat4 cspin(int a, int b, mediump float x) {\n"
+    "  mat4 m = mat4(1.,0.,0.,0.,0.,1.,0.,0.,0.,0.,1.,0.,0.,0.,0.,1.);\n"
+    "  m[a][a] = m[b][b] = cos(x); m[b][a] = sin(x); m[a][b] = -m[b][a];\n"
+    "  return m;\n"
+    "  }\n");
+
+  add_if("lorentz",
+    "mediump mat4 lorentz(int a, int b, mediump float x) {\n"
+    "  mat4 m = mat4(1.,0.,0.,0.,0.,1.,0.,0.,0.,0.,1.,0.,0.,0.,0.,1.);\n"
+    "  m[a][a] = m[b][b] = cosh(x); m[a][b] = m[b][a] = sinh(x);\n"
+    "  return m;\n"
+    "  }\n");
   }
 
 void raygen::emit_raystarter() {
@@ -1989,7 +2044,7 @@ void raygen::create() {
     if((gproduct || intra::in) && vid.stereo_mode != sODS) fsh +=
       "uniform mediump mat4 uLP;\n";
 
-    if(gproduct || intra::in) fsh +=
+    if(gproduct || intra::in || rotspace) fsh +=
       "uniform mediump float uPLevel;\n";
 
     if(many_cell_types) fsh +=

shaders.cpp

@@ -956,6 +956,7 @@ EX void add_fixed_functions(string& shader) {
         "  }\n\n");
 
   add_if(shader, "PI", "#define PI 3.14159265358979324\n");
+  add_if(shader, "TAU", "#define TAU 6.28318530367958648\n");
   #ifndef GLES_ONLY
   add_if(shader, "mediump", "#define mediump\n");
   #endif