From d1a30c3920bb2aec82a1fd96ba524df3c726d2c1 Mon Sep 17 00:00:00 2001
From: Zeno Rogue <zeno@attnam.com>
Date: Mon, 24 Feb 2025 09:33:39 +0100
Subject: [PATCH] rogueviz::fundamental:: more general corner / connection
 renderer

---
 rogueviz/fundamental.cpp | 271 ++++++++++++++++++++++-----------------
 1 file changed, 150 insertions(+), 121 deletions(-)

diff --git a/rogueviz/fundamental.cpp b/rogueviz/fundamental.cpp
index a0f38ef2..288473a2 100644
--- a/rogueviz/fundamental.cpp
+++ b/rogueviz/fundamental.cpp
@@ -45,26 +45,11 @@ void be_connected(cellwalker cw) {
 
 int funmode = 0;
 
-shiftpoint corner(cellwalker cw) {
-  shiftmatrix T = gm[cw.at];
+bool single_edges = false;
+bool fill_faces = true;
 
-  if(funmode == 3) switch(geometry) {
-    case gKleinQuartic: {
-      ld a = edge_of_triangle_with_angles(90._deg, M_PI/14, M_PI*2/14);
-      shiftpoint at = gm[cw.at] * get_corner_position(cw.at, cw.spin+(cw.mirrored?0:1), 3);
-      shiftpoint best = at; ld bestdist = 999;
-      for(int i=0; i<14; i++) {
-        shiftmatrix sm = gm[starter];
-        if(variation == eVariation::untruncated)
-          sm = sm * rgpushxto0(get_corner_position(starter, 0, 3));
-        auto s = sm * xspinpush0(i * M_PI/7, a);
-        ld d = hdist(at, s);
-        if(d < bestdist) bestdist = d, best = s;
-        }
-      return best;
-      }
-    default: /* no special */;
-    }
+shiftpoint cwcorner(cellwalker cw) {
+  shiftmatrix T = gm[cw.at];
 
   if(funmode == 2 && BITRUNCATED) {
     while(cw.at->type != S7) { 
@@ -74,9 +59,108 @@ shiftpoint corner(cellwalker cw) {
       }
     return T * C0;
     }
+
   return gm[cw.at] * get_corner_position(cw.at, cw.spin+(cw.mirrored?0:1), 3);
   }
 
+int group_count(cellwalker cw);
+
+void auto_corners() {
+  cellwalker cw;
+
+  corners = 0;
+
+  for(int k=0; k<isize(cells); k++) {
+    cell *c = cells[k];
+    for(int i=0; i<c->type; i++) {
+      cellwalker cw0(c, i);
+      if(single_edges) {
+        if(!is_connected(cw0)) corners++, cw = cw0;
+        }
+      else {
+        if(group_count(cw0) >= 3) corners++, cw = cw0;
+        }
+      }
+    }
+
+  if(!corners) return;
+
+  cornerlist.clear();
+  corner_id.clear();
+
+  for(int ci=0; ci<corners; ci++) {
+    corner_id[cw] = cornerlist.size();
+    cornerlist.push_back(cw);
+
+    while(true) {
+      cw++;
+      while(is_connected(cw)) {
+        cw += wstep;
+        cw++;
+        }
+      if(single_edges || group_count(cw) >= 3) break;
+      }
+    }
+  auto corners0 = corners;
+  corners = isize(cornerlist);
+  cornerlist.push_back(cw);
+
+  if(corners0 != corners) println(hlog, "corners=", tie(corners0, corners));
+
+  abs_cornerpos.clear();
+  for(auto c: cornerlist) {
+    auto co = cwcorner(c);
+    abs_cornerpos.push_back(inverse_shift(gm[starter], co));
+    }
+  }
+
+void find_corners() {
+
+  abs_cornerpos.clear();
+
+  auto build = [&] (int sides, ld a, ld a1, ld shift) {
+    transmatrix T = Id;
+    if(variation == eVariation::untruncated)
+      T = T * rgpushxto0(get_corner_position(starter, 0, 3));
+    for(int i=0; i<=sides; i++) {
+      abs_cornerpos.push_back(T * xspinpush0(-i * TAU/sides + shift, (i&1) ? a : a1));
+      }
+    corners = sides;
+    };
+
+  if(funmode == 3) switch(geometry) {
+    case gKleinQuartic: {
+      ld a = edge_of_triangle_with_angles(90._deg, M_PI/14, M_PI*2/14);
+      return build(14, a, a, 0);
+      }
+    case gSchmutzM2: {
+      ld a = edge_of_triangle_with_angles(90._deg, M_PI/12, M_PI/6);
+      ld a1 = edge_of_triangle_with_angles(45._deg, M_PI/12, 60._deg);
+      return build(24, a1, a, 0);
+      }
+    case gSchmutzM3: {
+      ld a = edge_of_triangle_with_angles(60._deg, M_PI/12, M_PI/12);
+      ld a1 = edge_of_triangle_with_angles(M_PI/12, 60._deg, M_PI/12);
+      return build(24, a, a1, 0);
+      }
+    case gBolza: {
+      ld a = edge_of_triangle_with_angles(90._deg, M_PI/8, M_PI/8);
+      return build(8, a, a, 22.5_deg);
+      }
+    case gBolza2: {
+      ld a = edge_of_triangle_with_angles(90._deg, M_PI/8, M_PI/8);
+      hyperpoint h1 = xspinpush0(0, a);
+      hyperpoint h2 = xspinpush0(45._deg, a);
+      hyperpoint hm = mid(h1, h2);
+      ld a1 = hdist0(hm) * 2;
+      return build(16, a, a1, 0);
+      }
+    default: break;
+    }
+
+  return auto_corners();
+  }
+
 transmatrix rel(cellwalker cw) {
   return currentmap->adj(cw.at, cw.spin);
   }
@@ -94,9 +178,6 @@ shiftmatrix labelpos(shiftpoint h1, shiftpoint h2) {
 ld widthfactor = 5;
 ld label_scale = 1;
 
-bool single_edges = false;
-bool fill_faces = true;
-
 int group_count(cellwalker cw) {
   if(is_connected(cw)) return 0;
   auto cw1 = cw;
@@ -176,55 +257,7 @@ void compute_shape() {
     if(f == face_edges) break;
     }
 
-  cellwalker cw;
-  
-  corners = 0;
-
-  for(int k=0; k<isize(cells); k++) {
-    cell *c = cells[k];
-    for(int i=0; i<c->type; i++) {
-      cellwalker cw0(c, i);
-      if(single_edges) {
-        if(!is_connected(cw0)) corners++, cw = cw0;
-        }
-      else {
-        if(group_count(cw0) >= 3) corners++, cw = cw0;
-        }
-      }
-    }
-
-  if(!corners) return;
-  
-  cornerlist.clear();
-  corner_id.clear();
-    
-  for(int ci=0; ci<corners; ci++) {
-    corner_id[cw] = cornerlist.size();
-    cornerlist.push_back(cw);
-        
-    while(true) {
-      cw++;
-      while(is_connected(cw)) {
-        cw += wstep;
-        cw++;
-        }
-      if(single_edges || group_count(cw) >= 3) break;
-      }
-    }
-  auto corners0 = corners;
-  corners = isize(cornerlist);
-  cornerlist.push_back(cw);
-
-  if(corners0 != corners) println(hlog, "corners=", tie(corners0, corners));
-
-  vid.linewidth *= widthfactor;
-
-  abs_cornerpos.clear();
-  for(auto c: cornerlist) {
-    auto co = corner(c);
-    abs_cornerpos.push_back(inverse_shift(gm[starter], co));
-    }
-
+  find_corners();
   }
 
 void fundamental_marker() {
@@ -240,6 +273,18 @@ void fundamental_marker() {
 
   auto pos = current_position * last_view * inverse(View);
 
+  vector<int> connections(corners, -1);
+  vector<bool> mirrored(corners, false);
+  map<unsigned, int> midedge_id;
+  auto T = ggmatrix(starter);
+  unsigned central_bucket = bucketer(unshift(T*C0));
+  for(int i=0; i<corners; i++)
+    midedge_id[bucketer(unshift(T*mid(abs_cornerpos[i], abs_cornerpos[i+1])))] = i;
+
+  int next_connection_id = 0;
+
+  dynamicval<ld> lw(vid.linewidth, vid.linewidth * widthfactor);
+
   for(auto c: cells)
   for(const shiftmatrix& V : hr::span_at(current_display->all_drawn_copies, c)) {
     auto V1 = V * inverse_shift(gm[c], gm[starter]);
@@ -254,47 +299,38 @@ void fundamental_marker() {
 
     if(c == cwt.at && alpha && !current_domain) current_domain = &bucket_color[bu];
     queuecurve_reuse(V1, color1, alpha ? bucket_color[bu] : 0, PPR::LINE);
-    }
 
-  queuecurve(gm[starter], color2, 0, PPR::LINE);
-
-  set<cellwalker> visited;
-  
-  int id = 0;
-
-  auto T = ggmatrix(starter);
-  
-  for(int ci=0; ci<corners; ci++) {
-    
-    auto cw = cornerlist[ci];
-    cellwalker cw1 = (cw+1+wstep);
-    bool mirrored = false;
-    while(is_connected(cw1)) cw1 = cw1 + 1 + wstep;
-    if(!corner_id.count(cw1)) cw1 = cw1 + wmirror - 1, mirrored = true;
-    if(!corner_id.count(cw1)) println(hlog, "still bad");
-    auto ci1 = corner_id[cw1];
-
-    auto pcw  = T * abs_cornerpos[ci];
-    auto pnx  = T * abs_cornerpos[ci+1];
-    auto pcw1 = T * abs_cornerpos[ci1];
-    auto pnx1 = T * abs_cornerpos[ci1+1];
-    auto pv1  = T * abs_cornerpos[(ci1+corners-1) % corners];
-
-    if(ci+1 < (mirrored ? ci1+1 : ci1)) {
-    
-      int mc = (mirrored ? color1 : color2) >> 8;
-      if(hdist(pcw, pnx) > 1e-3) {
-        queuestr(labelpos(pcw, pnx), label_scale/cgi.scalefactor, its(id), mc);
-        if(mirrored)
-          queuestr(labelpos(pcw1, pnx1), label_scale/cgi.scalefactor, its(id), mc);
-        else
-          queuestr(labelpos(pv1, pcw1), label_scale/cgi.scalefactor, its(id), mc);
-        id++;
-        }      
+    if(bu != central_bucket) {
+      for(int i=0; i<corners; i++) {
+        unsigned val = bucketer(unshift(V1*mid(abs_cornerpos[i], abs_cornerpos[i+1])));
+        auto p = at_or_null(midedge_id, val);
+        if(p && connections[*p] == -1) {
+          connections[*p] = connections[i] = next_connection_id++;
+          mirrored[*p] = mirrored[i] = det(V1.T) * det(T.T) < 0;
+          }
+        }
       }
     }
+  
+  queuecurve(T, color2, 0, PPR::LINE);
 
-  vid.linewidth /= widthfactor;
+  for(int ci=0; ci<corners; ci++) {
+    int mc = (mirrored[ci] ? color1 : color2) >> 8;
+    int id = connections[ci];
+    if(id == -1) continue;
+    queuestr(labelpos(T * abs_cornerpos[ci], T * abs_cornerpos[ci+1]), label_scale/cgi.scalefactor, its(id), mc);
+    }
+  }
+
+void clear_data() {
+  same.clear();
+  gm.clear();
+  bucket_color.clear();
+  current_starter = nullptr;
+  cornerlist.clear();
+  corner_id.clear();
+  abs_cornerpos.clear();
+  cells.clear();
   }
 
 void showMenu() {
@@ -303,7 +339,7 @@ void showMenu() {
   dialog::init(XLAT("display fundamental domains"), 0xFFFFFFFF, 150, 0);
   vector<string> mode_names = {"no display", "corners", "centers", "special"};
   dialog::addSelItem("mode", mode_names[funmode], 'm');
-  dialog::add_action([] { funmode = (1 + funmode) % 4; });
+  dialog::add_action([] { funmode = (1 + funmode) % 4; clear_data(); });
   dialog::addSelItem("label distance", fts(label_dist), 'd');
   dialog::add_action([] {
     dialog::editNumber(label_dist, 0, 10, .1, 0.5, "label fistance", "label distance");
@@ -330,8 +366,10 @@ void showMenu() {
   dialog::add_action([] () {
     starter = cwt.at;
     });
-  dialog::addBoolItem_action("remove internal lines", fill_faces, 'r');
-  dialog::addBoolItem_action("all edges be single", single_edges, 'z');
+  dialog::addBoolItem("remove internal lines", fill_faces, 'r');
+  dialog::add_action([] { fill_faces = !fill_faces; clear_data(); });
+  dialog::addBoolItem("all edges be single", single_edges, 'z');
+  dialog::add_action([] { single_edges = !single_edges; clear_data(); });
   dialog::addSelItem("line quality", its(lq), 'w');
   dialog::add_action([] {
     dialog::editNumber(lq, 0, 5, 1, 3, "line quality", "line quality");
@@ -359,16 +397,7 @@ void showMenu() {
 void enable_fundamental() {
   start_game(); starter = cwt.at;
   rogueviz::rv_hook(hooks_frame, 100, fundamental_marker);
-  rogueviz::rv_hook(hooks_clearmemory, 100, [] {
-    same.clear();
-    gm.clear();
-    bucket_color.clear();
-    current_starter = nullptr;
-    cornerlist.clear();
-    corner_id.clear();
-    abs_cornerpos.clear();
-    cells.clear();
-    });
+  rogueviz::rv_hook(hooks_clearmemory, 100, clear_data);
   rogueviz::rv_hook(hooks_o_key, 80, [] (o_funcs& v) { v.push_back(named_dialog("fundamental", showMenu)); });
 
   current_position = Id; last_view = View;