Triangle vizualization now includes the network

2025-10-31 14:02:59 +00:00 · 2020-03-27 13:47:48 +01:00
parent f4130ec730
commit d68ff2eeda
1 changed files with 387 additions and 193 deletions
--- a/rogueviz/triangle.cpp
+++ b/rogueviz/triangle.cpp
@@ -12,10 +12,13 @@

 // ./hyper -geo Nil -nilwidth .9 -canvas x -tstep 1 -nilperiod 1 10 1 -triset 32 31 992

+// network of triangles:
+
+// ./hyper -geo Nil -canvas x -tri-net
+
 namespace hr {

-// each color group (i.e., each face direction) is a different hpcshape
-hpcshape ptriangle[6];
+bool net = false;

 EX hyperpoint lerp(hyperpoint a0, hyperpoint a1, ld x) {
  return a0 + (a1-a0) * x;
@@ -35,20 +38,32 @@ int how1 = how - 1;
 // precision: number of substeps to simulate (best if divisible by how and how1)
 int isteps = 4 * 1024;

-/* make the impossible triangle shape */
-void make_shape() {
+struct triangledata {
+  hyperpoint at;
+  bool computed;
+  int tcolor;
+  int id;
+  // each color group (i.e., each face direction) is a different hpcshape
+  triangledata(hyperpoint h) : at(h), computed(false) { tcolor = 0; id = 0; }
+  };

-  static bool done = false;
-  if(done) return;
-  done = true;
+struct trianglemaker {

-  // four main axes of the regular tetrahedron, rotated so that ds[3] points to (0,0,1)
+  map<cell*, vector<triangledata> > tds;
+
+  array<hpcshape, 6> ptriangle;
+
+  array<hpcshape, 6> pcube;
+  
+  hyperpoint ds[4], uds[4], dmoves[6];
+  
+  ld scale;
+  
+  void init() {

    ld rest = sqrt(8/9.);
    ld rex = sqrt(1 - 1/9. - pow(rest/2., 2));
  
-  hyperpoint ds[4];
-  
    ds[0] = point3(rex, -rest/2, -1/3.);
    ds[1] = point3(0, rest, -1/3.);
    ds[2] = point3(-rex, -rest/2, -1/3.);
@@ -81,13 +96,8 @@ void make_shape() {
      lastz = at[2]; lasta  =a;
      }
    
-  println(hlog, "ca = ", ca);
-  
-  ld scale = .2;
-  
    // compute the shift between the cubes
  
-  array<hyperpoint, 4> uds;
    for(int d=0; d<3; d++) {
      hyperpoint at = start;
      for(int i=0; i<isteps/how; i++) {
@@ -96,7 +106,7 @@ void make_shape() {
      uds[d] = (at - start) / 2.;
      }
    
-  println(hlog, "uds = ", uds);
+    // println(hlog, "uds = ", uds);
  
    for(int a=0; a<3; a++) println(hlog, sqhypot_d(3, inverse_exp(start + ds[a] * ca, iTable, false)));
  
@@ -161,30 +171,9 @@ void make_shape() {
        }
      }
      
-  scale = 1.;
-  
-  // build all the faces
+    scale = 1;

    for(int si=0; si<6; si++) {
-    cgi.bshape(ptriangle[si], PPR::WALL);
-    hyperpoint at = start;
-    
-    for(int d=0; d<3; d++) {
-      
-      int d1 = (d+1) % 3;
-      int d2 = (d+2) % 3;
-
-      hyperpoint path[isteps+1];
-      for(int i=0; i<isteps; i++) {
-        path[i] = at;
-        at = nisot::translate(at) * (start + ds[d] * ca);
-        }
-      path[isteps] = at;
-      
-      auto &u = uds[d];
-      auto &v = uds[d1];
-      auto &w = uds[d2];
-      
      auto textured_square = [&] (auto f) {
        texture_order([&] (ld ix, ld iy) { f(.5 + ix/2 + iy/2, .5 + ix/2 - iy/2); });
        texture_order([&] (ld ix, ld iy) { f(.5 - ix/2 - iy/2, .5 - ix/2 + iy/2); });
@@ -192,6 +181,58 @@ void make_shape() {
        texture_order([&] (ld ix, ld iy) { f(.5 - ix/2 + iy/2, .5 + ix/2 + iy/2); });
        };
  
+      auto cube_at = [&] (hyperpoint online) {
+  
+        auto sidesquare1 = [&] (hyperpoint a00, hyperpoint a01, hyperpoint a10, hyperpoint a11) {
+          textured_square( [&] (ld ix, ld iy) {
+            hyperpoint shf = lerp(lerp(a00, a01, ix), lerp(a10, a11, ix), iy);
+            if(scale) shf = shf * scale - start * (scale-1);
+            cgi.hpcpush(nisot::translate(online) * (shf));
+            });
+          };
+            
+        if(si == 0) sidesquare1(verts[0], verts[2], verts[4], verts[6]);
+        if(si == 1) sidesquare1(verts[1], verts[3], verts[5], verts[7]);
+        if(si == 2) sidesquare1(verts[0], verts[1], verts[4], verts[5]);
+        if(si == 3) sidesquare1(verts[2], verts[3], verts[6], verts[7]);
+        if(si == 4) sidesquare1(verts[0], verts[1], verts[2], verts[3]);
+        if(si == 5) sidesquare1(verts[4], verts[5], verts[6], verts[7]);
+        };
+      
+      scale = 2;
+      cgi.bshape(pcube[si], PPR::WALL);
+      cube_at(start);
+      cgi.last->flags |= POLY_TRIANGLES;
+      cgi.last->tinf = &floor_texture_vertices[0];
+      cgi.last->texture_offset = 0;
+      
+      scale = 1;
+      
+      cgi.bshape(ptriangle[si], PPR::WALL);
+      hyperpoint at = start;
+      
+      vector<hyperpoint> atx = {start};
+      
+      cube_at(start);
+  
+      for(int dx: {0, 1, 2}) {
+        int d = dx;
+        if(net) at = start;
+        else cube_at(at);
+        int d1 = (d+1) % 3;
+        int d2 = (d+2) % 3;
+  
+        hyperpoint path[isteps+1];
+        for(int i=0; i<isteps; i++) {
+          path[i] = at;
+          at = nisot::translate(at) * (start + ds[d] * ca * (dx >= 3 ? -1 : 1));
+          }
+        path[isteps] = at;
+        
+        auto &u = uds[d];
+        auto &v = uds[d1];
+        auto &w = uds[d2];
+        
        auto sidewall = [&] (hyperpoint wide, hyperpoint shift) {
          textured_square( [&] (ld ix, ld iy) {
            hyperpoint online = path[int(ix * isteps + .1)];
@@ -210,15 +251,6 @@ void make_shape() {
            });
          };
        
-      auto sidesquare1 = [&] (hyperpoint a00, hyperpoint a01, hyperpoint a10, hyperpoint a11, ld p) {
-        hyperpoint online = path[int(p * isteps + .1)];
-        textured_square( [&] (ld ix, ld iy) {
-          hyperpoint shf = lerp(lerp(a00, a01, ix), lerp(a10, a11, ix), iy);
-          shf *= scale;
-          cgi.hpcpush(nisot::translate(online) * (shf));
-          });
-        };
-      
        if(shape == 0) {
          if(si == d2*2) sidewall(v, w);
          if(si == d1*2) sidewall(w, v);
@@ -231,26 +263,13 @@ void make_shape() {
          if(si == d*2+1) sidesquare(w, v, -u, 0);
          }
        
-      if(shape == 1) for(int a=0; a<how1; a++) {
+        if(shape == 1) for(int a=1; a<how1; a++) {
          ld c = a * 1. / how1;
          
-/*
-        if(si == d*2) sidesquare(v, w, u, c);
-        if(si == d*2+1) sidesquare(w, v, -u, c);
-        if(si == d1*2) sidesquare(w, u, v, c);
-        if(si == d1*2+1) sidesquare(u, w, -v, c);
-        if(si == d2*2) sidesquare(u, v, w, c);
-        if(si == d2*2+1) sidesquare(v, u, -w, c);
-*/
-
-        if(si == 0) sidesquare1(verts[0], verts[2], verts[4], verts[6], c);
-        if(si == 1) sidesquare1(verts[1], verts[3], verts[5], verts[7], c);
-        if(si == 2) sidesquare1(verts[0], verts[1], verts[4], verts[5], c);
-        if(si == 3) sidesquare1(verts[2], verts[3], verts[6], verts[7], c);
-        if(si == 4) sidesquare1(verts[0], verts[1], verts[2], verts[3], c);
-        if(si == 5) sidesquare1(verts[4], verts[5], verts[6], verts[7], c);
-        
+          cube_at(path[int(c * isteps + .1)]);
          }
+        
+        dmoves[d] = at;        
        }
    
      cgi.last->flags |= POLY_TRIANGLES;
@@ -259,19 +278,191 @@ void make_shape() {
      cgi.finishshape();
      cgi.extra_vertices();
      }
+
+    tds[cwt.at].emplace_back(start);
+    dmoves[3] = inverse(nisot::translate(dmoves[0])) * C0;
+    dmoves[4] = inverse(nisot::translate(dmoves[1])) * C0;
+    dmoves[5] = inverse(nisot::translate(dmoves[2])) * C0;
    }

+  void compute(triangledata &td, cell *c) {
+    if(td.computed) return;
+    td.computed = true;
+    if(!net) return;
+
+    hyperpoint at;
+    
+    for(int d=0; d<6; d++) {
+      hyperpoint at = nisot::translate(td.at) * dmoves[d];
+      cell *c0 = c;
+      virtualRebase(c0, at);
+      
+      bool newat = true;
+      for(auto& td: tds[c0]) {
+        ld d = sqhypot_d(3, at - td.at);
+        if(d < .01) {      
+          if(d>1e-5) println(hlog, "d = ", d);
+          newat = false;
+          }
+        }
+      
+      if(newat) {
+        triangledata ntd = at;
+        ntd.id = td.id + 1;
+        tds[c0].push_back(ntd);
+        tds[c0].back().tcolor = (td.tcolor + (d < 3 ? 1 : 2)) % 3;
+        }
+      }
+    }
+    
+  };
+
+trianglemaker *mkr;
+
 // Magic Cube (aka Rubik Cube) colors

 color_t magiccolors[6] = { 0xFFFF00FF, 0xFFFFFFFF, 0x0000FFFF, 0x00FF00FF, 0xFF0000FF, 0xFF8000FF};

-bool draw_ptriangle(cell *c, const transmatrix& V) {
-  make_shape();
+#define CTO (isize(cnts))

-  if(c == cwt.at) {
+  vector<int> cnts;
+  vector<ld> coef;
+  int valid_from;
+  int tested_to;
+  int coefficients_known;
+
+bool verify(int id) {
+  if(id < isize(coef)) return false;
+  ld res = 0;
+  for(int t=0; t<isize(coef); t++)
+    res += coef[t] * cnts[id-t-1];
+  return abs(res - cnts[id]) < .5;
+  }
+
+
+int valid(int v, int step) {
+  if(step < 0) return 0;
+  if(step+v+v+5 >= CTO) return 0;
+  ld matrix[100][128];
+  for(int i=0; i<v; i++)
+  for(int j=0; j<v+1; j++)
+    matrix[i][j] = cnts[step+i+j];
+  
+  for(int k=0; k<v; k++) {
+    int nextrow = k;
+    while(nextrow < v && std::abs(matrix[nextrow][k]) < 1e-6)
+      nextrow++;
+    if(nextrow == v) return 1;
+    if(nextrow != k) {
+      // printf("swap %d %d\n", k, nextrow);
+      for(int l=0; l<=v; l++) swap(matrix[k][l], matrix[nextrow][l]);
+      // display();
+      }
+    ld divv = 1. / matrix[k][k];
+    for(int k1=k; k1<=v; k1++) matrix[k][k1] *= divv;
+    // printf("divide %d\n", k);
+    // display();
+    for(int k1=k+1; k1<v; k1++) if(matrix[k1][k] != 0) {
+      ld coef = -matrix[k1][k];
+      for(int k2=k; k2<=v; k2++) matrix[k1][k2] += matrix[k][k2] * coef;
+      }
+    // printf("zeros below %d\n", k);
+    // display();
+    }
+  
+  for(int k=v-1; k>=0; k--)
+  for(int l=k-1; l>=0; l--)
+    if(matrix[l][k]) matrix[l][v] -= matrix[l][k] * matrix[k][v];
+  
+  coef.resize(v);
+  for(int i=0; i<v; i++) coef[i] = matrix[v-1-i][v];
+    
+  println(hlog, "coef = ", coef);
+  for(int t=step+v; t<step+v+v+5; t++) {
+    println(hlog, "verify(", t, ") = ", verify(t));
+    if(!verify(t)) return 2;
+    }
+  println(hlog, "got here");
+  tested_to = step+v+v+5;
+  while(tested_to < CTO) {
+    if(!verify(tested_to)) return 2;
+    tested_to++;
+    }
+  
+  valid_from = step+v;
+  return 3;
+  }
+
+void find_coefficients() {
+  if(coefficients_known) return;
+  for(int v=1; v<25; v++) 
+  for(int step=0; step<1000; step++) { 
+    int val = valid(v, step);
+    if(val == 0) break;
+    println(hlog, "v=", v, "step=", step, " val=", val);
+    if(val == 3) { coefficients_known = 2; return; }
+    }
+  coefficients_known = 1;
+  }
+
+void growthrate() {
+  /*
+  for(int a=0; a<CTO; a++) {
+    int cnt = 0;
+    map<cell*, int> howmany;
+    for(auto& p: mkr->tds) cnt += (howmany[p.first] = isize(p.second));
+    for(auto& p: howmany) for(int i=0; i<p.second; i++) {
+      // println(hlog, p.first, mkr->tds[p.first][i].at, mkr->tds[p.first][i].computed);
+      mkr->compute(mkr->tds[p.first][i], p.first);
+      }
+    println(hlog, "cnt = ", cnt, " / ", cnt / pow(1+a, 4));
+    cnts[a] = cnt;
+    if(a >= 4) println(hlog, "D4 = ", cnts[a-4] - 4 * cnts[a-3] + 6 * cnts[a-2] - 4 * cnts[a-1] + cnts[a]);
+    println(hlog, "cnts = ", cnts);
+    }*/
+  
+  cnts = {1,7,31,113,299,681,1363,2501,4181,6570,9874,14256,20027,27601,37171,48815,62993,79912,100181,123868,151680,184339,222347,265733,314523,369424,431221,500952,578350,665794,763300,871250,988488,1116635,1256293,1409165,1575969,1758327,1958977,2174877};
+  find_coefficients();
+  
+  println(hlog, "coefficients_known = ", coefficients_known);
+  if(coefficients_known == 2) {
+    string fmt = "a(d+" + its(isize(coef)) + ") = ";
+    bool first = true;
+    for(int i=0; i<isize(coef); i++) if(coef[i]) {
+      if(first && coef[i] == 1) ;
+      else if(first) fmt += its(coef[i]);
+      else if(coef[i] == 1) fmt += " + ";
+      else if(coef[i] == -1) fmt += " - ";
+      else if(coef[i] > 1) fmt += " + " + its(coef[i]);
+      else if(coef[i] < -1) fmt += " - " + its(-coef[i]);
+      fmt += "a(d";
+      if(i != isize(coef) - 1)
+        fmt += "+" + its(isize(coef) - 1 - i);
+      fmt += ")";
+      first = false;
+      }
+    fmt += " (d>" + its(valid_from-1) + ")";
+    println(hlog, fmt);
+    }
+  }
+
+color_t tcolors[3] = { 0xFF0000FF, 0x00FF00FF, 0x0000FFFF };
+
+
+bool draw_ptriangle(cell *c, const transmatrix& V) {
+  
+  if(!mkr) { mkr = new trianglemaker; mkr->init(); 
+    growthrate();
+    }
+  
+  for(auto& td: mkr->tds[c]) {
+    mkr->compute(td, c);
    for(int side=0; side<6; side++) {
-      auto &s = queuepoly(V, ptriangle[side], magiccolors[side]);
+      auto &s = queuepoly(V * nisot::translate(td.at), mkr->ptriangle[side], magiccolors[side]);
      ensure_vertex_number(*s.tinf, s.cnt);
+
+      /* auto& s1 = queuepoly(V * nisot::translate(td.at), mkr->pcube[side], gradient(tcolors[td.tcolor], magiccolors[side], 0, .2, 1));
+      ensure_vertex_number(*s1.tinf, s1.cnt); */
      }
    }

@@ -290,6 +481,9 @@ auto hchook = addHook(hooks_drawcell, 100, draw_ptriangle)
    shift(); how1 = argi();
    shift(); isteps = argi();
    }
+  else if(argis("-tri-net")) {
+    net = true;
+    }
  else return 1;
  return 0;
  });