From aa02d6808bdfb7b7f5570523bd8bf4e1283d1f31 Mon Sep 17 00:00:00 2001
From: Zeno Rogue <zeno@attnam.com>
Date: Thu, 13 Feb 2020 12:09:42 +0100
Subject: [PATCH] rogueviz:: impossible triangle viz

---
 rogueviz/triangle.cpp | 299 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 299 insertions(+)
 create mode 100644 rogueviz/triangle.cpp

diff --git a/rogueviz/triangle.cpp b/rogueviz/triangle.cpp
new file mode 100644
index 00000000..f1cb2fd4
--- /dev/null
+++ b/rogueviz/triangle.cpp
@@ -0,0 +1,299 @@
+#include "../hyper.h"
+
+// Impossible Triangle visualization
+
+// used in: https://www.youtube.com/watch?v=YmFDd49WsrY
+
+// settings:
+// ./mymake rogueviz/triangle
+// ./hyper -geo Nil -canvas x -tstep 8 -nilperiod 3 3 3
+
+// also used in: https://youtu.be/RPL4-Ydviug
+
+// ./hyper -geo Nil -nilwidth .9 -canvas x -tstep 1 -nilperiod 1 10 1 -triset 32 31 992
+
+namespace hr {
+
+// each color group (i.e., each face direction) is a different hpcshape
+hpcshape ptriangle[6];
+
+EX hyperpoint lerp(hyperpoint a0, hyperpoint a1, ld x) {
+  return a0 + (a1-a0) * x;
+  }
+
+hyperpoint operator+(hyperpoint x) { return x; }
+
+// do not change this
+int shape = 1;
+
+// how many cubes to subdivide edges to
+int how = 4;
+
+// how many cubes to draw (should be smaller than how because they are not really cubes and thus they get into each other)
+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() {
+
+  static bool done = false;
+  if(done) return;
+  done = true;
+  
+  // four main axes of the regular tetrahedron, rotated so that ds[3] points to (0,0,1)
+  
+  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.);
+  ds[3] = point3(0, 0, +1);
+  
+  hyperpoint start = point31(0, 0, 0);
+    
+  double lastz;
+  
+  double lasta;
+  
+  double ca;
+  
+  // compute how to scale this in Nil so that everything fits
+  
+  for(ld a = 1e-5;; a+=1e-5) {
+    hyperpoint at = start;
+    for(int d=0; d<3; d++) {
+      for(int i=0; i<isteps; i++) {
+        at = nisot::translate(at) * (start + ds[d] * a);
+        }
+      }
+    
+    println(hlog, "at = ", at, " for a = ", a, " sq = ", at[2] / a / a);
+    if(at[2] > 0) {
+      ld z = at[2];
+      ca = lerp(lasta, a, ilerp(lastz, z, 0));
+      break;
+      }
+    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++) {
+      at = nisot::translate(at) * (start + ds[d] * ca);
+      }
+    uds[d] = (at - start) / 2.;
+    }
+  
+  println(hlog, "uds = ", uds);
+
+  for(int a=0; a<3; a++) println(hlog, sqhypot_d(3, inverse_exp(start + ds[a] * ca, iTable, false)));
+
+  for(int a=0; a<3; a++) println(hlog, sqhypot_d(3, inverse_exp(uds[a], iTable, false)));
+  
+  // compute cube vertices
+
+  hyperpoint verts[8];
+  for(int a=0; a<8; a++) {
+    verts[a] = start;
+    for(int k=0; k<3; k++) 
+      verts[a] += (a&(1<<k)) ? uds[k] : -uds[k];
+    }
+  
+  // since Nil does not really have cubes, we need to move the vertices a bit so that it looks nicer
+  
+  // ugliness of the current vertices
+  
+  auto errf = [&] {
+    ld res = 0;
+    for(int s=0; s<8; s++)
+    for(int t=0; t<3; t++) {
+      if((s & (1<<t)) == 0) {
+        int s1 = s | (1<<t);
+        ld dix = sqhypot_d(3, inverse(nisot::translate(nisot::translate(start + 2*uds[t]) * verts[s])) * verts[s1]);
+        // println(hlog, tie(s, t), "di = ", dix);
+        res += dix * dix;
+        }
+      }
+    return res;
+    };
+  
+  // minimize the ugliness
+
+  ld curerr = errf();
+  println(hlog, "curerr = ", curerr);
+  int att = 0;
+  if(1) while(true) {
+    int id = rand() % 8;
+    int j = rand() % 3;
+    ld eps = (rand() % 100 - rand() % 100) / 100000.;
+    verts[id][j] += eps;
+    ld nerr = errf();
+    if(nerr < curerr) {
+      curerr = nerr;
+      println(hlog, "curerr = ", curerr, " # ", att);
+      att = 0;
+      }
+    else {
+      verts[id][j] -= eps;
+      }
+    att++;
+    if(att > 50000) break;
+    }
+
+    for(int s=0; s<8; s++)
+    for(int t=0; t<3; t++) {
+      if((s & (1<<t)) == 0) {
+        int s1 = s | (1<<t);
+        ld dix = sqhypot_d(3, inverse(nisot::translate(nisot::translate(start + 2*uds[t]) * verts[s])) * verts[s1]);
+        println(hlog, tie(s, t), "di = ", dix);
+        }
+      }
+  
+  scale = 1.;
+  
+  // build all the faces
+  
+  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); });
+        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); });
+        };
+  
+      auto sidewall = [&] (hyperpoint wide, hyperpoint shift) {
+        textured_square( [&] (ld ix, ld iy) {
+          hyperpoint online = path[int(ix * isteps + .1)];
+          hyperpoint shf = lerp(u, -u, ix) + lerp(-wide, wide, iy) + shift;
+          shf *= scale;
+          cgi.hpcpush(nisot::translate(online) * (start + shf));
+          });
+        };
+  
+      auto sidesquare = [&] (hyperpoint wx, hyperpoint wy, hyperpoint shift, ld p) {
+        textured_square( [&] (ld ix, ld iy) {
+          hyperpoint online = path[int(p * isteps + .1)];
+          hyperpoint shf = lerp(wx, -wx, ix) + lerp(wy, -wy, iy) + shift;
+          shf *= scale;
+          cgi.hpcpush(nisot::translate(online) * (start + shf));
+          });
+        };
+      
+      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);
+        if(si == d2*2+1) sidewall(v, -w);
+        if(si == d1*2+1) sidewall(w, -v);
+        
+        if(si == d2*2) sidesquare(u, v, w, 0);
+        if(si == d1*2) sidesquare(w, u, v, 0);
+        if(si == d1*2+1) sidesquare(u, w, -v, 0);
+        if(si == d*2+1) sidesquare(w, v, -u, 0);
+        }
+      
+      if(shape == 1) for(int a=0; 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);
+        
+        }
+      }
+  
+    cgi.last->flags |= POLY_TRIANGLES;
+    cgi.last->tinf = &floor_texture_vertices[0];
+    cgi.last->texture_offset = 0;
+    cgi.finishshape();
+    cgi.extra_vertices();
+    }
+  }
+
+// 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();
+  
+  if(c == cwt.at) {
+    for(int side=0; side<6; side++) {
+      auto &s = queuepoly(V, ptriangle[side], magiccolors[side]);
+      ensure_vertex_number(*s.tinf, s.cnt);
+      }
+    }    
+
+  return false;
+  }
+
+
+auto hchook = addHook(hooks_drawcell, 100, draw_ptriangle)
+
++ addHook(hooks_args, 100, [] {
+  using namespace arg;
+           
+  if(0) ;
+  else if(argis("-triset")) {
+    shift(); how = argi();
+    shift(); how1 = argi();
+    shift(); isteps = argi();
+    }
+  else return 1;
+  return 0;
+  });
+
+
+
+}