hyperrogue/binary-tiling.cpp

namespace hr {

namespace binary {
#if CAP_BT

  enum bindir {
    bd_right = 0,
    bd_up_right = 1,
    bd_up = 2,
    bd_up_left = 3,
    bd_left = 4,
    bd_down = 5, /* for cells of degree 6 */
    bd_down_left = 5, /* for cells of degree 7 */
    bd_down_right = 6 /* for cells of degree 7 */
    };
  
  int type_of(heptagon *h) {
    return h->c7->type;
    }

  // 0 - central, -1 - left, +1 - right
  int mapside(heptagon *h) {
    return h->zebraval;
    }
  
  #if DEBUG_BINARY_TILING
  map<heptagon*, long long> xcode;
  map<long long, heptagon*> rxcode;

  long long expected_xcode(heptagon *h, int d) {
    auto r =xcode[h];
    if(d == 0) return r + 1;
    if(d == 1) return 2*r + 1;
    if(d == 2) return 2*r;
    if(d == 3) return 2*r - 1;
    if(d == 4) return r-1;
    if(d == 5 && type_of(h) == 6) return r / 2;
    if(d == 5 && type_of(h) == 7) return (r-1) / 2;
    if(d == 6 && type_of(h) == 7) return (r+1) / 2;
    breakhere();
    }
  #endif
  
  void breakhere() {
    exit(1);
    }
  
  heptagon *path(heptagon *h, int d, int d1, std::initializer_list<int> p) {
    static int rec = 0;
    rec++; if(rec>100) exit(1);
    // printf("{generating path from %p (%d/%d) dir %d:", h, type_of(h), mapside(h), d);
    heptagon *h1 = h;
    for(int d0: p) {
      // printf(" [%d]", d0);
      h1 = hr::createStep(h1, d0);
      // printf(" %p", h1);
      }

    #if DEBUG_BINARY_TILING    
    if(xcode[h1] != expected_xcode(h, d)) {
      printf("expected_xcode mismatch\n");
      breakhere();
      }
    #endif
    // printf("}\n");
    if(h->move(d) && h->move(d) != h1) {
      printf("already connected to something else (1)\n");
      breakhere();
      }
    if(h1->move(d1) && h1->move(d1) != h) {
      printf("already connected to something else (2)\n");
      breakhere();
      }
    h->c.connect(d, h1, d1, false);
    rec--;
    return h1;
    }
  
  heptagon *build(heptagon *parent, int d, int d1, int t, int side, int delta) {
    auto h = buildHeptagon1(tailored_alloc<heptagon> (t), parent, d, hsOrigin, d1);
    h->distance = parent->distance + delta;
    h->c7 = NULL;
    if(parent->c7) h->c7 = newCell(t, h);
    h->cdata = NULL;
    h->zebraval = side;
    #if DEBUG_BINARY_TILING
    xcode[h] = expected_xcode(parent, d);
    if(rxcode.count(xcode[h])) {
      printf("xcode clash\n");
      breakhere();
      }
    rxcode[xcode[h]] = h;
    #endif
    return h;
    }

  #if MAXMDIM==4
  heptagon *build3(heptagon *parent, int d, int d1, int delta) {
    int side = 0;
    if(d < 4) side = (parent->zebraval * 2 + d) % 5;
    if(d == 8) side = ((parent->zebraval-d1) * 3) % 5;
    return build(parent, d, d1, 9, side, delta);
    }
  #endif
  
  heptagon *createStep(heptagon *parent, int d) {
    auto h = parent;
    switch(d) {
      case bd_right: {
        if(mapside(h) > 0 && type_of(h) == 7) 
          return path(h, d, bd_left, {bd_left, bd_down, bd_right, bd_up});
        else if(mapside(h) >= 0) 
          return build(parent, bd_right, bd_left, type_of(parent) ^ 1, 1, 0);
        else if(type_of(h) == 6)
          return path(h, d, bd_left, {bd_down, bd_right, bd_up, bd_left});
        else
          return path(h, d, bd_left, {bd_down_right, bd_up});
        }
      case bd_left: {
        if(mapside(h) < 0 && type_of(h) == 7) 
          return path(h, d, bd_right, {bd_right, bd_down, bd_left, bd_up});
        else if(mapside(h) <= 0) 
          return build(parent, bd_left, bd_right, type_of(parent) ^ 1, -1, 0);
        else if(type_of(h) == 6)
          return path(h, d, bd_right, {bd_down, bd_left, bd_up, bd_right});
        else
          return path(h, d, bd_right, {bd_down_left, bd_up});
        }
      case bd_up_right: {
        return path(h, d, bd_down_left, {bd_up, bd_right});
        }
      case bd_up_left: {
        return path(h, d, bd_down_right, {bd_up, bd_left});
        }
      case bd_up: 
        return build(parent, bd_up, bd_down, 6, mapside(parent), 1);
      default:
        /* bd_down */
        if(type_of(h) == 6) {
          if(mapside(h) == 0)
            return build(parent, bd_down, bd_up, 6, 0, -1);
          else if(mapside(h) == 1)
            return path(h, d, bd_up, {bd_left, bd_left, bd_down, bd_right});
          else if(mapside(h) == -1)
            return path(h, d, bd_up, {bd_right, bd_right, bd_down, bd_left});
          }
        /* bd_down_left */
        else if(d == bd_down_left) {
          return path(h, d, bd_up_right, {bd_left, bd_down});
          }
        else if(d == bd_down_right) {
          return path(h, d, bd_up_left, {bd_right, bd_down});
          }
        }
    printf("error: case not handled in binary tiling\n");
    breakhere();
    return NULL;
    }

  #if MAXMDIM==4
  heptagon *createStep3(heptagon *parent, int d) {
    auto h = parent;
    switch(d) {
      case 0: case 1:
      case 2: case 3:
        return build3(parent, d, 8, 1);
      case 8:
        return build3(parent, 8, hrand(4), -1);
      case 4:
        parent->cmove(8);
        if(parent->c.spin(8) & 1)
          return path(h, 4, 5, {8, parent->c.spin(8) ^ 1});
        else
          return path(h, 4, 5, {8, 4, parent->c.spin(8) ^ 1});
      case 5:
        parent->cmove(8);
        if(!(parent->c.spin(8) & 1))
          return path(h, 5, 4, {8, parent->c.spin(8) ^ 1});
        else
          return path(h, 5, 4, {8, 5, parent->c.spin(8) ^ 1});
      case 6:
        parent->cmove(8);
        if(parent->c.spin(8) & 2)
          return path(h, 6, 7, {8, parent->c.spin(8) ^ 2});
        else
          return path(h, 6, 7, {8, 6, parent->c.spin(8) ^ 2});
      case 7:
        parent->cmove(8);
        if(!(parent->c.spin(8) & 2))
          return path(h, 7, 6, {8, parent->c.spin(8) ^ 2});
        else
          return path(h, 7, 6, {8, 7, parent->c.spin(8) ^ 2});
      }
    printf("error: case not handled in binary tiling\n");
    breakhere();
    return NULL;
    }
  #endif
  
  transmatrix direct_tmatrix[8];
  transmatrix inverse_tmatrix[8];
  
  void build_tmatrix() {
    direct_tmatrix[0] = xpush(-log(2)) * parabolic3(-1, -1);
    direct_tmatrix[1] = xpush(-log(2)) * parabolic3(1, -1);
    direct_tmatrix[2] = xpush(-log(2)) * parabolic3(-1, 1);
    direct_tmatrix[3] = xpush(-log(2)) * parabolic3(1, 1);
    direct_tmatrix[4] = parabolic3(-2, 0);
    direct_tmatrix[5] = parabolic3(+2, 0);
    direct_tmatrix[6] = parabolic3(0, -2);
    direct_tmatrix[7] = parabolic3(0, +2);
    for(int i=0; i<8; i++)
      inverse_tmatrix[i] = inverse(direct_tmatrix[i]);
    }
  
  const transmatrix& tmatrix(heptagon *h, int dir) {
    if(dir == 8) {
      h->cmove(8);
      return inverse_tmatrix[h->c.spin(8)];
      }
    else
      return direct_tmatrix[dir];
    }

  const transmatrix& itmatrix(heptagon *h, int dir) {
    if(dir == 8) {
      h->cmove(8);
      return h->cmove(8), direct_tmatrix[h->c.spin(8)];
      }
    else
      return inverse_tmatrix[dir];
    }
  
  #if MAXMDIM == 4

  void queuecube(const transmatrix& V, ld size, color_t linecolor, color_t facecolor) {
    ld yy = log(2) / 2;
    const int STEP=3;
    const ld MUL = 1. / STEP;
    auto at = [&] (ld x, ld y, ld z) { curvepoint(V * parabolic3(size*x, size*y) * xpush0(size*yy*z)); };
    for(int a:{-1,1}) {
      for(ld t=-STEP; t<STEP; t++) at(a, 1,t*MUL);
      for(ld t=-STEP; t<STEP; t++) at(a, -t*MUL,1);
      for(ld t=-STEP; t<STEP; t++) at(a, -1,-t*MUL);
      for(ld t=-STEP; t<STEP; t++) at(a, t*MUL,-1);
      at(a, 1,-1);
      queuecurve(linecolor, facecolor, PPR::LINE);

      for(ld t=-STEP; t<STEP; t++) at(1,t*MUL,a);
      for(ld t=-STEP; t<STEP; t++) at(-t*MUL,1,a);
      for(ld t=-STEP; t<STEP; t++) at(-1,-t*MUL,a);
      for(ld t=-STEP; t<STEP; t++) at(t*MUL,-1,a);
      at(1,-1,a);
      queuecurve(linecolor, facecolor, PPR::LINE);

      for(ld t=-STEP; t<STEP; t++) at(1,a,t*MUL);
      for(ld t=-STEP; t<STEP; t++) at(-t*MUL,a,1);
      for(ld t=-STEP; t<STEP; t++) at(-1,a,-t*MUL);
      for(ld t=-STEP; t<STEP; t++) at(t*MUL,a,-1);
      at(1,a,-1);
      queuecurve(linecolor, facecolor, PPR::LINE);
      }
    /*for(int a:{-1,1}) for(int b:{-1,1}) for(int c:{-1,1}) {
      at(0,0,0); at(a,b,c);  queuecurve(linecolor, facecolor, PPR::LINE);
      }*/
    }
  #endif

  transmatrix parabolic(ld u) {
    return parabolic1(u * vid.binary_width / log(2) / 2);
    }

  transmatrix parabolic3(ld y, ld z) {
    ld co = vid.binary_width / log(2) / 4;
    return hr::parabolic13(y * co, z * co);
    }
  
  hyperpoint deparabolic3(hyperpoint h) {
    using namespace hyperpoint_vec;
    h /= (1 + h[3]);
    hyperpoint one = point3(1,0,0);
    h -= one;
    h /= sqhypot_d(3, h);
    h[0] += .5;
    ld co = vid.binary_width / log(2) / 8;
    return point3(log(2) + log(-h[0]), h[1] / co, h[2] / co);
    }
  
  void draw() {
    dq::visited.clear();
    dq::enqueue(viewctr.at, cview());
    
    while(!dq::drawqueue.empty()) {
      auto& p = dq::drawqueue.front();
      heptagon *h = get<0>(p);
      transmatrix V = get<1>(p);
      dynamicval<ld> b(band_shift, get<2>(p));
      bandfixer bf(V);
      dq::drawqueue.pop();
      
      
      cell *c = h->c7;
      if(!do_draw(c, V)) continue;
      drawcell(c, V, 0, false);

      if(DIM == 2) {
        dq::enqueue(h->move(bd_up), V * xpush(-log(2)));
        dq::enqueue(h->move(bd_right), V * parabolic(1));
        dq::enqueue(h->move(bd_left), V * parabolic(-1));
        if(c->type == 6)
          dq::enqueue(h->move(bd_down), V * xpush(log(2)));
        if(c->type == 7) {
          dq::enqueue(h->move(bd_down_left), V * parabolic(-1) * xpush(log(2)));
          dq::enqueue(h->move(bd_down_right), V * parabolic(1) * xpush(log(2)));
          }
        }
      else {
        for(int i=0; i<9; i++)
          dq::enqueue(h->move(i), V * tmatrix(h, i));
        }
      }
    }
  
  transmatrix relative_matrix(heptagon *h2, heptagon *h1) {
    if(gmatrix0.count(h2->c7) && gmatrix0.count(h1->c7))
      return inverse(gmatrix0[h1->c7]) * gmatrix0[h2->c7];
    transmatrix gm = Id, where = Id;
    while(h1 != h2) {
      if(h1->distance <= h2->distance) {
        if(DIM == 3)
          where = itmatrix(h2, 8) * where, h2 = hr::createStep(h2, 8);
        else {
          if(type_of(h2) == 6)
            h2 = hr::createStep(h2, bd_down), where = xpush(-log(2)) * where;
          else if(mapside(h2) == 1)
            h2 = hr::createStep(h2, bd_left), where = parabolic(+1) * where;
          else if(mapside(h2) == -1)
            h2 = hr::createStep(h2, bd_right), where = parabolic(-1) * where;
          }
        }
      else {
        if(DIM == 3)
          gm = gm * tmatrix(h1, 8), h1 = hr::createStep(h1, 8);
        else {
          if(type_of(h1) == 6)
            h1 = hr::createStep(h1, bd_down), gm = gm * xpush(log(2));
          else if(mapside(h1) == 1)
            h1 = hr::createStep(h1, bd_left), gm = gm * parabolic(-1);
          else if(mapside(h1) == -1)
            h1 = hr::createStep(h1, bd_right), gm = gm * parabolic(+1);
          }
        }
      }
    return gm * where;
    }

#if CAP_COMMANDLINE
auto bt_config = addHook(hooks_args, 0, [] () {
  using namespace arg;
  if(argis("-btwidth")) {
    shift_arg_formula(vid.binary_width, delayed_geo_reset);
    return 0;
    }
  return 1;
  });
#endif

bool pseudohept(cell *c) {
  if(DIM == 2)
    return c->type & c->master->distance & 1;
  else
    return (c->master->zebraval == 1) && (c->master->distance & 1);
  }

int celldistance3(heptagon *c1, heptagon *c2) {
  int steps = 0;
  int d1 = c1->distance;
  int d2 = c2->distance;
  while(d1 > d2) c1 = c1->cmove(8), steps++, d1--;
  while(d2 > d1) c2 = c2->cmove(8), steps++, d2--;
  vector<int> dx, dy;
  while(c1 != c2) {
    dx.push_back((c1->c.spin(8) & 1) - (c2->c.spin(8) & 1));
    dy.push_back((c1->c.spin(8) >> 1) - (c2->c.spin(8) >> 1));
    c1 = c1->cmove(8);
    c2 = c2->cmove(8);
    steps += 2;
    }
  int xsteps = steps, sx = 0, sy = 0;
  while(isize(dx)) {
    xsteps -= 2;
    sx *= 2;
    sy *= 2;
    sx += dx.back(); sy += dy.back();
    dx.pop_back(); dy.pop_back();
    int ysteps = xsteps + abs(sx) + abs(sy);
    if(ysteps < steps) steps = ysteps;
    if(sx >= 8 || sx <= -8 || sy >= 8 || sy <= -8) break;
    }
  return steps;
  }

int celldistance3(cell *c1, cell *c2) { return celldistance3(c1->master, c2->master); }
#endif

void virtualRebaseSimple(heptagon*& base, transmatrix& at) {

  while(true) {
  
    double currz = at[DIM][DIM];
    
    heptagon *h = base;
    
    heptagon *newbase = NULL;
    
    transmatrix bestV;
    
    for(int d=0; d<S7; d++) {
      transmatrix V2 = itmatrix(h, d) * at;
      double newz = V2[DIM][DIM];
      if(newz < currz) {
        currz = newz;
        bestV = V2;
        newbase = h->cmove(d);
        }
      }

    if(newbase) {
      base = newbase;
      at = bestV;
      continue;
      }

    return;
    }
  }


  }
}