hyperrogue/sol.cpp

// implementation of the Solv space

// Copyright (C) 2011-2019 Zeno Rogue, see 'hyper.cpp' for details

namespace hr {

namespace solv {
  
  int PRECX, PRECY, PRECZ;
  
  typedef hyperpoint pt;
  typedef array<float, 3> ptlow;

  vector<ptlow> inverse_exp_table;
  
  bool table_loaded;
  
  string solfname = "solv-geodesics.dat";
  
  pt inverse_exp(pt h);

  void load_table() {
    if(table_loaded) return;
    FILE *f = fopen(solfname.c_str(), "rb");
    // if(!f) f = fopen("/usr/lib/soltable.dat", "rb");
    if(!f) { addMessage(XLAT("geodesic table missing")); pmodel = mdPerspective; return; }
    fread(&PRECX, 4, 1, f);
    fread(&PRECY, 4, 1, f);
    fread(&PRECZ, 4, 1, f);
    inverse_exp_table.resize(PRECX * PRECY * PRECZ);
    fread(&inverse_exp_table[0], sizeof(ptlow) * PRECX * PRECY * PRECZ, 1, f);
    fclose(f);
    table_loaded = true;    
    }
  
  void step2(ld& x, ld &y, ld &z, ld &vx, ld &vy, ld &vz) {
  
    ld ax = -2 * vx * vz;
    ld ay = 2 * vy * vz;
    ld az = exp(2*z) * vx * vx - exp(-2*z) * vy * vy;
  
    // ld x2 = x + vx/2;
    // ld y2 = y + vy/2;
    ld z2 = z + vz/2;
    
    ld vx2 = vx + ax/2;
    ld vy2 = vy + ay/2;
    ld vz2 = vz + az/2;
    
    ld ax2 = -2 * vx2 * vz2;
    ld ay2 = 2 * vy2 * vz2;
    ld az2 = exp(2*z2) * vx2 * vx2 - exp(-2*z2) * vy2 * vy2;
    
    x += vx + ax/2;
    y += vy + ay/2;
    z += vz + az/2;
    
    vx += ax2;
    vy += ay2;
    vz += az2;
    }
  
  pt direct_exp(pt v, int steps) {
    pt at;
    at[0] = 0;
    at[1] = 0;
    at[2] = 0;
    at[3] = 1;
    v[0] /= steps;
    v[1] /= steps;
    v[2] /= steps;
    for(int i=0; i<steps; i++) step2(at[0], at[1], at[2], v[0],v[1],v[2]);
    return at;
    }

  void parallel(ld x, ld y, ld z, ld vx, ld vy, ld vz, ld& wx, ld& wy, ld& wz, ld t) {
    // ld dax = -dz * gxyz * ay;
    
    ld dwx = -vz * wx - vx * wz;
    ld dwy =  vz * wy + vy * wz;
    ld dwz = vx * wx * exp(2*z) - vy * wy * exp(-2*z);
      
    wx += dwx * t;
    wy += dwy * t;
    wz += dwz * t;
    }

  pt direct_exp(pt v, int steps, vector<pt> transported) {
    ld x = 0, y = 0, z = 0;
    v[0] /= steps;
    v[1] /= steps;
    v[2] /= steps;
    for(int i=0; i<steps; i++) {
      for(auto t: transported) parallel(x,y,z, v[0],v[1],v[2], t[0], t[1], t[2], 1);
      step2(x,y,z, v[0],v[1],v[2]);
      }
    return hpxy3(x, y, z);
    }

  ld x_to_ix(ld u) {
    if(u == 0.) return 0.;
    ld diag = u*u/2.;
 
    ld x = diag;
    ld y = u;
    ld z = diag+1.;
  
    x /= (1.+z);
    y /= (1.+z);
  
    return 0.5 - atan((0.5-x) / y) / M_PI;
    }

  pt inverse_exp(pt h, bool lazy) {
    load_table();
    
    ld ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);
    ld iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);
    ld iz = tanh(h[2]);
    
    if(h[2] < 0.) { iz = -iz; swap(ix, iy); }
    
    ix *= PRECX-1;
    iy *= PRECY-1;
    iz *= PRECZ-1;
    
    hyperpoint res = C0;

    if(lazy) {
      auto r = inverse_exp_table[(int(iz)*PRECY+int(iy))*PRECX+int(ix)];
      for(int i=0; i<3; i++) res[i] = r[i];
      }
    
    else {

      if(ix >= PRECX-1) ix = PRECX-2;
      if(iy >= PRECX-1) iy = PRECX-2;
      if(iz >= PRECZ-1) iz = PRECZ-2;
      
      int ax = ix, bx = ax+1;
      int ay = iy, by = ay+1;
      int az = iz, bz = az+1;
      
      #define S0(x,y,z) inverse_exp_table[(z*PRECY+y)*PRECX+x][t]
      #define S1(x,y) (S0(x,y,az) * (bz-iz) + S0(x,y,bz) * (iz-az))
      #define S2(x) (S1(x,ay) * (by-iy) + S1(x,by) * (iy-ay))
  
      for(int t=0; t<3; t++)
        res[t] = S2(ax) * (bx-ix) + S2(bx) * (ix-ax);
      }
  
    if(h[2] < 0.) { swap(res[0], res[1]); res[2] = -res[2]; }
    if(h[0] < 0.) res[0] = -res[0];
    if(h[1] < 0.) res[1] = -res[1];
    
    return res;

    /* ld r = sqrt(res[0] * res[0] + res[1] * res[1] + res[2] * res[2]);
    if(r == 0.) return res;
    return res * atanh(r) / r; */
    }

  transmatrix local_perspective;
  
  bool geodesic_movement = true;

  struct hrmap_sol : hrmap {
    hrmap *binary_map;
    unordered_map<pair<heptagon*, heptagon*>, heptagon*> at;
    unordered_map<heptagon*, pair<heptagon*, heptagon*>> coords;
    
    heptagon *origin;
    
    heptagon *getOrigin() override { return origin; }
    
    heptagon *get_at(heptagon *x, heptagon *y) {
      auto& h = at[make_pair(x, y)];
      if(h) return h;
      h = tailored_alloc<heptagon> (S7);
      h->c7 = newCell(S7, h);
      coords[h] = make_pair(x, y);
      h->distance = x->distance;
      h->dm4 = 0;
      h->zebraval = x->emeraldval;
      h->emeraldval = y->emeraldval;
      h->fieldval = 0;
      h->cdata = NULL;
      h->alt = NULL;
      return h;      
      }

    hrmap_sol() {
    
      heptagon *alt;
    
      if(true) {
        dynamicval<eGeometry> g(geometry, gBinary4); 
        alt = tailored_alloc<heptagon> (S7);
        alt->s = hsOrigin;
        alt->alt = alt;
        alt->cdata = NULL;
        alt->c7 = NULL;
        alt->zebraval = 0;
        alt->distance = 0;
        alt->emeraldval = 0;
        binary_map = binary::new_alt_map(alt);
        }
      
      origin = get_at(alt, alt);
      }
    
    heptagon *altstep(heptagon *h, int d) {
      dynamicval<eGeometry> g(geometry, gBinary4); 
      dynamicval<hrmap*> cm(currentmap, binary_map);
      return h->cmove(d);
      }
    
    heptagon *create_step(heptagon *parent, int d) override {
      auto p = coords[parent];
      auto pf = p.first, ps = p.second;
      auto rule = [&] (heptagon *c1, heptagon *c2, int d1) {
        auto g = get_at(c1, c2);
        parent->c.connect(d, g, d1, false);
        return g;
        };

      switch(d) {
        case 0: // right
          return rule(altstep(pf, 2), ps, 4);
        case 1: // up
          return rule(pf, altstep(ps, 2), 5);
        case 2: // front left
          return rule(altstep(pf, 0), altstep(ps, 3), ps->zebraval ? 7 : 6);
        case 3: // front right
          return rule(altstep(pf, 1), altstep(ps, 3), ps->zebraval ? 7 : 6);
        case 4: // left
          return rule(altstep(pf, 4), ps, 0);
        case 5: // down
          return rule(pf, altstep(ps, 4), 1);
        case 6: // back down
          return rule(altstep(pf, 3), altstep(ps, 0), pf->zebraval ? 3 : 2);
        case 7: // back up
          return rule(altstep(pf, 3), altstep(ps, 1), pf->zebraval ? 3 : 2);
        default:
          return NULL;
        }
      }

    ~hrmap_sol() {
      delete binary_map;
      }
    
    transmatrix adjmatrix(int i, int j) {
      ld z = log(2);
      ld bw = vid.binary_width * z;
      ld bwh = bw / 4;
      switch(i) {
        case 0: return xpush(+bw);
        case 1: return ypush(+bw);
        case 2: return xpush(-bwh) * zpush(+z) * ypush(j == 6 ? +bwh : -bwh);
        case 3: return xpush(+bwh) * zpush(+z) * ypush(j == 6 ? +bwh : -bwh);
        case 4: return xpush(-bw);
        case 5: return ypush(-bw);
        case 6: return ypush(-bwh) * zpush(-z) * xpush(j == 2 ? +bwh : -bwh);
        case 7: return ypush(+bwh) * zpush(-z) * xpush(j == 2 ? +bwh : -bwh);
        default:return Id;
        }
      }
    
    virtual transmatrix relative_matrix(heptagon *h2, heptagon *h1) override { 
      for(int i=0; i<h1->type; i++) if(h1->move(i) == h2) return adjmatrix(i, h1->c.spin(i));
      if(gmatrix0.count(h2->c7) && gmatrix0.count(h1->c7))
        return inverse(gmatrix0[h1->c7]) * gmatrix0[h2->c7];
      return Id; // not implemented yet
      }

    void draw() override {
      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);
        dq::drawqueue.pop();
        
        cell *c = h->c7;
        if(!do_draw(c, V)) continue;
        drawcell(c, V, 0, false);
  
        for(int i=0; i<S7; i++) {
          // note: need do cmove before c.spin
          heptagon *h1 = h->cmove(i);
          dq::enqueue(h1, V * adjmatrix(i, h->c.spin(i)));
          }
        }
      }

    };

  hrmap *new_map() { return new hrmap_sol; }
  
  ld solrange_xy = 15;
  ld solrange_z = 4;
  
  ld glitch_xy = 2, glitch_z = 0.6;

  bool in_table_range(hyperpoint h) {
    if(abs(h[0]) > glitch_xy && abs(h[1]) > glitch_xy && abs(h[2]) < glitch_z) return false;
    return abs(h[0]) < solrange_xy && abs(h[1]) < solrange_xy && abs(h[2]) < solrange_z;
    }

  transmatrix get_solmul(const transmatrix T, const transmatrix V) {
    if(!geodesic_movement) return V * eupush(inverse(V) * T * V * C0);

    transmatrix push_back = eupush( tC0(inverse(V)) );
    transmatrix space_to_view = V * push_back;
    
    for(int x=0; x<3; x++) for(int y=0; y<=x; y++) {
      auto& T = space_to_view;
      ld dp = 0;
      for(int z=0; z<3; z++) dp += T[z][x] * T[z][y];
      
      if(y == x) dp = 1 - sqrt(1/dp);
      
      for(int z=0; z<3; z++) T[z][x] -= dp * T[z][y];
      }
    
    transmatrix view_to_space = inverse(space_to_view);
    using namespace hyperpoint_vec;
    hyperpoint shift = /* inverse(V) * T * V * C0; */ view_to_space * T * C0;
    
    transmatrix push_to = inverse(push_back);

    int steps = 100;
    
    // hyperpoint units[3] = { point3(1,0,0), point3(0,1,0), point3(0,0,1) };
    
    /*
    println(hlog, "shift = ", kz(shift));
    println(hlog, "space_to_view = ", kz(space_to_view));

    for(int i=0; i<3; i++)
      println(hlog, "view_to_space[", i, "] = ", kz(view_to_space * units[i]));
    */

    for(int s=0; s<3; s++) shift[s] /= steps;
    ld x = 0, y = 0, z = 0;
    

    for(int i=0; i<steps; i++) {
      for(int j=0; j<3; j++) 
        parallel(x, y, z, shift[0], shift[1], shift[2], view_to_space[0][j], view_to_space[1][j], view_to_space[2][j], -1);
      step2(x, y, z, shift[0], shift[1], shift[2]);
      }
    
    space_to_view = inverse(view_to_space);
    
    /*
    println(hlog, "arrive at = ", kz(pt({x, y, z})), " with vel = ", (shift * steps));

    for(int i=0; i<3; i++)
      println(hlog, "view_to_space[", i, "] = ", kz(view_to_space * units[i]));
    println(hlog, "space_to_view = ", kz(space_to_view));
    */

    // println(hlog, "view_to_space = ", view_to_space);
    
    transmatrix npush = Id;
    npush[0][GDIM] = x;
    npush[1][GDIM] = y;
    npush[2][GDIM] = z;

    // println(hlog, "result = ", space_to_view * npush * push_to);
    // println(hlog, "naive = ", V * eupush(inverse(V) * T * V * C0));
    return space_to_view * npush * push_to;
    }

  transmatrix get_solmul_pt(const transmatrix Position, const transmatrix T) {
    return inverse(get_solmul(inverse(T), inverse(Position)));
    }
  
  transmatrix spin_towards(const transmatrix Position, const hyperpoint goal) {

    hyperpoint at = tC0(Position);
    transmatrix push_back = inverse(eupush(at));
    hyperpoint back_goal = push_back * goal;
    back_goal = inverse_exp(back_goal, false);
    
    transmatrix back_Position = push_back * Position;

    return rspintox(inverse(back_Position) * back_goal);
    }

  string solshader = 
    "uniform mediump sampler3D tInvExpTable;"    
    "uniform mediump float PRECX, PRECY, PRECZ;"

    "float x_to_ix(float u) {"
    "  if(u < 1e-6) return 0.;"
    "  float diag = u*u/2.;"
   
    "  float x = diag;"
    "  float y = u;"
    "  float z = diag+1.;"
    
    "  x /= (1.+z);"
    "  y /= (1.+z);"
    
    "  return 0.5 - atan((0.5-x) / y) / 3.1415926535897932384626433832795;"
    "  }"


    "vec4 inverse_exp(vec4 h) {"
    
    "float ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);"
    "float iy = h[1] >= 0. ? x_to_ix(h[1]) : x_to_ix(-h[1]);"
    "float iz = tanh(h[2]);"
    
    "if(h[2] < 1e-6) { iz = -iz; float s = ix; ix = iy; iy = s; }"
    "if(iz < 0.) iz = 0.;"
  
    "vec4 res = texture3D(tInvExpTable, vec3(ix*(1.-1./PRECX) + 0.5/PRECX, iy*(1.-1./PRECY) + .5/PRECY, iz*(1.-1./PRECZ) + .5/PRECZ));"
  
    "if(h[2] < 1e-6) { res.xy = res.yx; res[2] = -res[2]; }"
    "if(h[0] < 0.) res[0] = -res[0];"
    "if(h[1] < 0.) res[1] = -res[1];"
    
    "return res;"
    "}";

auto sol_config = addHook(hooks_args, 0, [] () {
  using namespace arg;
  if(argis("-solrange")) {
    shift_arg_formula(solrange_xy);
    shift_arg_formula(solrange_z);
    return 0;
    }
  else if(argis("-fsol")) {
    shift(); solfname = args();
    return 0;
    }
  else if(argis("-solglitch")) {
    shift_arg_formula(glitch_xy);
    shift_arg_formula(glitch_z);
    return 0;
    }
  else if(argis("-solgeo")) {
    geodesic_movement = true;
    pmodel = mdSolPerspective;
    return 0;
    }
  else if(argis("-solnogeo")) {
    geodesic_movement = false;
    pmodel = mdPerspective;
    return 0;
    }
  return 1;
  });
  
  }

}