fake geometry in 2D

fake.cpp

@@ -74,19 +74,16 @@ EX namespace fake {
       
       if(WDIM == 2) {
       
-        hyperpoint a1, a2, b1, b2;
+        ld dist;
-
+        in_underlying([c, d, &dist] {
-        in_underlying([c, d, &a1, &a2, &b1, &b2] {
+          dist = currentmap->spacedist(c, d);
-          a1 = get_corner_position(c, d);
-          a2 = get_corner_position(c, (d+1) % c->type);
-          
-          auto c1 = c->move(d);
-          auto d1 = c->c.spin(d);
-          b1 = get_corner_position(c1, d1);
-          b2 = get_corner_position(c1, (d1+1) % c1->type);
           });
         
-        cgi.adjcheck = hdist0(mid(befake(a1), befake(a2))) + hdist0(mid(befake(b1), befake(b2)));
+        auto& u = *underlying_cgip;
+        if(dist == u.tessf) cgi.adjcheck = cgi.tessf;
+        else if(dist == u.crossf) cgi.adjcheck = cgi.crossf;
+        else if(dist == u.hexhexdist) cgi.adjcheck = cgi.hexhexdist;
+        else cgi.adjcheck = dist * scale;        
         }
       
       return S1 * xpush(cgi.adjcheck) * S2;
@@ -159,7 +156,7 @@ EX namespace fake {
       
       // for(int i=0; i<S6; i++) queuepoly(ggmatrix(cwt.at), shWall3D[i], 0xFF0000FF);
       
-      if(pmodel == mdDisk && WDIM == 2) {
+      if(pmodel == mdDisk && WDIM == 2 && false) {
         draw_recursive(centerover, cview(), -1, -1, nullptr, 0);
         return;
         }
@@ -181,7 +178,7 @@ EX namespace fake {
         drawcell(c, V);
         if(in_wallopt() && isWall3(c) && isize(dq::drawqueue_c) > 1000) continue;
     
-        for(int i=0; i<S7; i++) if(c->move(i)) {
+        for(int i=0; i<c->type; i++) if(c->move(i)) {
           enqueue(c->move(i), V * adj(c, i));
           }
         }
@@ -290,6 +287,8 @@ EX ld around;
 
 /** @brief the value of 'around' which makes the tiling Euclidean */
 EX ld compute_euclidean() {
+  if(WDIM == 2) return 4 / (S7-2.) + 2;
+
   int middle = get_middle();
     
   return M_PI / asin(cos(M_PI/middle) / sin(M_PI/underlying_cgip->face));
@@ -303,10 +302,11 @@ EX void compute_scale() {
   
   if(abs(good - around) < 1e-6) good = around;
   
+  int s3 = WDIM == 2 ? S3 : underlying_cgip->loop;
+
   multiple = false;
-  for(int k=1; k<10; k++)
+  int mcount = int(around / s3 + .5);
-    if(abs(around - underlying_cgip->loop) < 1e-6)
+  multiple = abs(around - mcount * s3) < 1e-6;
-      multiple = true;
 
   if(around == good) {  
     ginf[gFake].g = WDIM == 3 ? giEuclid3 : giEuclid2;
@@ -322,7 +322,11 @@ EX void compute_scale() {
 
   ld around_ideal = 1/(1/2. - 1./get_middle());
   
-  if(euclid) scale = 1;
+  if(WDIM == 2) {
+    ginf[gFake].tiling_name = lalign(0, "{", S7, ",", around, "}");
+    return;
+    }
+  else if(euclid) scale = 1;
   else if(abs(around_ideal - around) < 1e-6) {
     hyperpoint h0 = underlying_cgip->cellshape[0];
     auto s = kleinize(h0);
@@ -385,13 +389,17 @@ EX void change_around() {
   ld range = sightranges[geometry];
   
   if(!fake::in()) {
-    if(around == cgi.loop) return; /* do nothing */
+    if(around == (WDIM == 2 ? S3 : cgi.loop)) return; /* do nothing */
     set_gfake(around);
     }
   
   else {    
     compute_scale();
     ray::reset_raycaster();
+
+    /* to compute scale */
+    if(WDIM == 2)
+      cgi.prepare_basics();
     }
 
   println(hlog, "scale = ", t, " -> ", scale, " range = ", range);

geometry.cpp

@@ -481,6 +481,8 @@ void geometry_information::prepare_basics() {
   
   ld fmin, fmax;  
   
+  ld s3, beta;
+
   if(arcm::in() && !prod) 
     ginf[gArchimedean].cclass = gcHyperbolic;
 
@@ -508,11 +510,16 @@ void geometry_information::prepare_basics() {
     goto finish;
     }
   
-  tessf = euclid ? 1 : edge_of_triangle_with_angles(S3 >= OINF ? 0 : 2*M_PI/S3, M_PI/S7, M_PI/S7);
+  s3 = S3;
+  if(fake::in()) s3 = fake::around;
   
-  if(elliptic && S7 == 4) tessf = M_PI/2;
+  beta = (S3 >= OINF && !fake::in()) ? 0 : 2*M_PI/s3;
 
-  hcrossf = euclid ? (S3 == 3 ? sqrt(3)/3 : sqrt(2)/2) : edge_of_triangle_with_angles(M_PI/2, M_PI/S7, M_PI/S3);
+  tessf = euclid ? 1 : edge_of_triangle_with_angles(beta, M_PI/S7, M_PI/S7);
+  
+  if(elliptic && S7 == 4 && !fake::in()) tessf = M_PI/2;
+  
+  hcrossf = euclid ? tessf / 2 / sin(M_PI/s3) : edge_of_triangle_with_angles(M_PI/2, M_PI/S7, beta/2);
 
   crossf = BITRUNCATED ? hcrossf : tessf;
   
@@ -523,6 +530,22 @@ void geometry_information::prepare_basics() {
     hyperpoint H1 = spin(2*M_PI/S7) * H;
     hyperpoint H2 = xpush0(tessf-f);
     ld v1 = intval(H, H1), v2 = intval(H, H2);
+
+    if(fake::in() && WDIM == 2) {
+      hexvdist = hdist(xpush0(f), xspinpush0(ALPHA/2, hcrossf));
+      v2 = hdist(
+        spin(M_PI/2/S3) * xpush0(hexvdist),
+        spin(-M_PI/2/S3) * xpush0(hexvdist)
+        );
+      
+      v1 = hdist(
+        spin(M_PI/S7) * xpush0(f),
+        spin(-M_PI/S7) * xpush0(f)
+        );
+      
+      println(hlog, f, " : ", tie(v1, v2));
+      }
+
     if(v1 < v2) fmin = f; else fmax = f;
     }
   hexf = fmin;
@@ -546,10 +569,12 @@ void geometry_information::prepare_basics() {
 
   for(int d=0; d<S7; d++) invhexmove[d] = inverse(hexmove[d]);
 
-  hexhexdist = hdist(xpush0(crossf), xspinpush0(M_PI*2/S7, crossf));
-  
   hexvdist = hdist(xpush0(hexf), xspinpush0(ALPHA/2, hcrossf));
 
+  hexhexdist = fake::in() ?
+    2 * hdist0(mid(xspinpush0(M_PI/S6, hexvdist), xspinpush0(-M_PI/S6, hexvdist)))
+    : hdist(xpush0(crossf), xspinpush0(M_PI*2/S7, crossf));
+  
   DEBB(DF_GEOM | DF_POLY,
     (format("S7=%d S6=%d hexf = " LDF" hcross = " LDF" tessf = " LDF" hexshift = " LDF " hexhex = " LDF " hexv = " LDF "\n", S7, S6, hexf, hcrossf, tessf, hexshift, 
     hexhexdist, hexvdist)));  
@@ -588,7 +613,18 @@ void geometry_information::prepare_basics() {
   scalefactor = crossf / hcrossf7;
   orbsize = crossf;
 
-  if(fake::in()) {
+  if(fake::in() && WDIM == 2) {
+    auto& u = *fake::underlying_cgip;
+    geometry = fake::underlying;
+    ld orig = xpush0(u.hcrossf)[0] / xpush0(u.hcrossf)[WDIM];
+    geometry = gFake;
+    ld our = xpush0(hcrossf)[0] / xpush0(hcrossf)[WDIM];
+    fake::scale = our / orig;
+    // if(debugflags & DF_GEOM) 
+    println(hlog, "scale set to ", fake::scale);
+    }
+
+  if(fake::in() && WDIM == 3) {
     auto& u = fake::underlying_cgip;
     crossf = u->crossf * fake::scale;
     scalefactor = u->scalefactor * fake::scale;
@@ -596,6 +632,7 @@ void geometry_information::prepare_basics() {
     hexf = u->hexf * fake::scale;
     rhexf = u->rhexf * fake::scale;
     hexvdist = u->hexvdist * fake::scale;
+    hcrossf = u->hcrossf * fake::scale;
     }
   
   if(arb::in()) {
@@ -960,9 +997,9 @@ EX string cgi_string() {
   V("VAR", its(int(variation)));
   
   if(fake::in()) {
-    if(hyperbolic) V("H", fts(fake::scale));
+    if(hyperbolic) V("H", fts(fake::around));
-    if(euclid) V("E", fts(fake::scale));
+    if(euclid) V("E", fts(fake::around));
-    if(sphere) V("S", fts(fake::scale));
+    if(sphere) V("S", fts(fake::around));
     V("G", FPIU(cgi_string()));
     return s;
     }

pattern2.cpp

@@ -839,7 +839,7 @@ EX namespace patterns {
     if(IRREGULAR || arcm::in() || bt::in() || arb::in() || WDIM == 3) si.symmetries = 1;
     else if(a46) val46(c, si, sub, pat);
     else if(a38) val38(c, si, sub, pat);
-    else if(sphere && S3 == 3) valSibling(c, si, sub, pat);
+    else if(S7 < 6 && S3 == 3) valSibling(c, si, sub, pat);
     else if(euc::in(2,4)) valEuclid4(c, si, sub);
     else if(euc::in(2,6)) valEuclid6(c, si, sub);
     else if(a4) val457(c, si, sub);