refactored all the operations on View

3d-models.cpp

@@ -622,37 +622,25 @@ void geometry_information::animate_bird(hpcshape& orig, hpcshape_animated& anima
   // shift_shape(orig, BIRD);
   }
 
-EX hyperpoint forward_dir(ld x) { return hybri ? point3(x, 0, 0) : xpush0(x); }
-EX hyperpoint zforward_dir(ld z) { return hybri ? point3(0, 0, z) : zpush0(z); }
-
-EX hyperpoint dir_to_point(hyperpoint h) { return hybri ? nisot::direct_exp(h, 100) : h; }
-
-EX hyperpoint dir_setlength(hyperpoint dir, ld length) {
-  if(dir[0] == 0 && dir[1] == 0 && dir[2] == 0) return dir;
-  if(prod) return dir * (length / hypot_d(3, dir));
-  return rspintox(dir) * xpush0(length);
-  }
-
 void geometry_information::slimetriangle(hyperpoint a, hyperpoint b, hyperpoint c, ld rad, int lev) {
   dynamicval<int> d(vid.texture_step, 8);
   texture_order([&] (ld x, ld y) {
     ld z = 1-x-y;
     ld r = scalefactor * hcrossf7 * (0 + pow(max(x,max(y,z)), .3) * 0.8) * (hybri ? .5 : 1);
-    hyperpoint h = dir_to_point(dir_setlength(a*x+b*y+c*z, r));
+    hyperpoint h = direct_exp(tangent_length(a*x+b*y+c*z, r), 10);
     hpcpush(h);
     });  
   }
 
 void geometry_information::balltriangle(hyperpoint a, hyperpoint b, hyperpoint c, ld rad, int lev) {
   if(lev == 0) {
-    hpcpush(dir_to_point(a));
+    hpcpush(direct_exp(a, 10));
-    hpcpush(dir_to_point(b));
+    hpcpush(direct_exp(b, 10));
-    hpcpush(dir_to_point(c));
+    hpcpush(direct_exp(c, 10));
     }
   else {
     auto midpoint = [&] (hyperpoint h1, hyperpoint h2) {
-      if(prod) return dir_setlength(h1+h2, rad);
+      return tangent_length(h1+h2, rad);
-      else return rspintox(mid(h1,h2)) * xpush0(rad);
       };
     hyperpoint cx = midpoint(a, b);
     hyperpoint ax = midpoint(b, c);
@@ -667,8 +655,8 @@ void geometry_information::balltriangle(hyperpoint a, hyperpoint b, hyperpoint c
 void geometry_information::make_ball(hpcshape& sh, ld rad, int lev) {
   bshape(sh, sh.prio);
   sh.flags |= POLY_TRIANGLES;
-  hyperpoint tip = forward_dir(rad);
+  hyperpoint tip = xtangent(rad);
-  hyperpoint atip = forward_dir(-rad);
+  hyperpoint atip = xtangent(-rad);
   ld z = 63.43 * degree;
   for(int i=0; i<5; i++) {
     hyperpoint a = cspin(1, 2, (72 * i   ) * degree) * spin(z) * tip;
@@ -1125,14 +1113,14 @@ void geometry_information::make_3d_models() {
 
   DEBB(DF_POLY, ("slime"));
   bshape(shSlime, PPR::MONSTER_BODY);
-  hyperpoint tip = xpush0(1);
+  hyperpoint tip = xtangent(1);
-  hyperpoint atip = xpush0(-1);
+  hyperpoint atip = xtangent(-1);
   ld z = 63.43 * degree;
   for(int i=0; i<5; i++) {
-    auto a = cspin(1, 2, (72 * i   ) * degree) * spin(z) * forward_dir(1);
+    auto a = cspin(1, 2, (72 * i   ) * degree) * spin(z) * xtangent(1);
-    auto b = cspin(1, 2, (72 * i-72) * degree) * spin(z) * forward_dir(1);
+    auto b = cspin(1, 2, (72 * i-72) * degree) * spin(z) * xtangent(1);
-    auto c = cspin(1, 2, (72 * i+36) * degree) * spin(M_PI-z) * forward_dir(1);
+    auto c = cspin(1, 2, (72 * i+36) * degree) * spin(M_PI-z) * xtangent(1);
-    auto d = cspin(1, 2, (72 * i-36) * degree) * spin(M_PI-z) * forward_dir(1);
+    auto d = cspin(1, 2, (72 * i-36) * degree) * spin(M_PI-z) * xtangent(1);
     slimetriangle(tip, a, b, 1, 0);
     slimetriangle(a, b, c, 1, 0);
     slimetriangle(b, c, d, 1, 0);

control.cpp

@@ -75,8 +75,7 @@ EX movedir vectodir(hyperpoint P) {
   transmatrix U = ggmatrix(cwt.at);
   if(GDIM == 3 && WDIM == 2)  U = radar_transform * U;
 
-  if(nisot::local_perspective_used()) P = inverse(nisot::local_perspective) * P;
+  P = direct_exp(lp_iapply(P), 100);
-  if(prod) P = product::direct_exp(P);
 
   hyperpoint H = sphereflip * tC0(U);
   transmatrix Centered = sphereflip * rgpushxto0(H);
@@ -113,12 +112,11 @@ EX void remission() {
  }
 
 EX hyperpoint move_destination_vec(int d) {
-  hyperpoint Forward = prod ? forward_dir(.5) : tC0(pushone());
+  if(WDIM == 2) return spin(-d * M_PI/4) * smalltangent();
-  if(WDIM == 2) return spin(-d * M_PI/4) * tC0(pushone());
   // else if(WDIM == 2 && pmodel == mdPerspective) return cspin(0, 2, d * M_PI/4) * tC0(pushone());
   // else if(WDIM == 2) return spin(-d * M_PI/4) * tC0(pushone());
-  else if(d&1) return cspin(0, 1, d > 4 ? M_PI/2 : -M_PI/2) * Forward;
+  else if(d&1) return cspin(0, 1, d > 4 ? M_PI/2 : -M_PI/2) * smalltangent();
-  else return cspin(0, 2, d * M_PI/4) * Forward;
+  else return cspin(0, 2, d * M_PI/4) * smalltangent();
   }
 
 EX void movepckeydir(int d) {
@@ -292,31 +290,28 @@ transmatrix zforward_push(ld z) {
   }
 
 EX void handlePanning(int sym, int uni) {
-  auto& LPe = nisot::local_perspective;
   if(mousepan && dual::split([=] { handlePanning(sym, uni); })) return;
   if(GDIM == 3) {
-    if(sym == PSEUDOKEY_WHEELUP) View = solmul(cpush(2, -0.05*shiftmul), LPe, View), didsomething = true, playermoved = false;
+    if(sym == PSEUDOKEY_WHEELUP) shift_view(ztangent(-0.05*shiftmul)), didsomething = true, playermoved = false;
-    if(sym == PSEUDOKEY_WHEELDOWN) View = solmul(cpush(2, 0.05*shiftmul), LPe, View), didsomething = true, playermoved = false;
+    if(sym == PSEUDOKEY_WHEELDOWN) shift_view(ztangent(0.05*shiftmul)), didsomething = true, playermoved = false;
     }
 
   if(rug::rugged || smooth_scrolling) {
     return;
     }
     
-  auto& LPV = prod ? nisot::local_perspective : View;
-  
 #if !ISPANDORA
   if(sym == SDLK_END && GDIM == 3) { 
-    View = solmul(zforward_push(-0.2*shiftmul), LPe, View), didsomething = true, playermoved = false;
+    shift_view(ztangent(-0.2*shiftmul)), didsomething = true, playermoved = false;
     }
   if(sym == SDLK_HOME && GDIM == 3) { 
-    View = solmul(zforward_push(+0.2*shiftmul), LPe, View), didsomething = true, playermoved = false;
+    shift_view(ztangent(+0.2*shiftmul)), didsomething = true, playermoved = false;
     }
   if(sym == SDLK_RIGHT) { 
     if(history::on)
       history::lvspeed += 0.1 * shiftmul;
     else if(GDIM == 3)
-      LPV = cspin(0, 2, -0.2*shiftmul) * LPV, didsomething = true;
+      rotate_view(cspin(0, 2, -0.2*shiftmul)), didsomething = true;
     else
       View = xpush(-0.2*shiftmul) * View, playermoved = false, didsomething = true;
     }
@@ -324,7 +319,7 @@ EX void handlePanning(int sym, int uni) {
     if(history::on)
       history::lvspeed -= 0.1 * shiftmul;
     else if(GDIM == 3)
-      LPV = cspin(0, 2, 0.2*shiftmul) * LPV, didsomething = true;
+      rotate_view(cspin(0, 2, 0.2*shiftmul)), didsomething = true;
     else
       View = xpush(+0.2*shiftmul) * View, playermoved = false, didsomething = true;
     }
@@ -332,7 +327,7 @@ EX void handlePanning(int sym, int uni) {
     if(history::on)
       history::lvspeed += 0.1 * shiftmul;
     else if(GDIM == 3)
-      LPV = cspin(1, 2, 0.2*shiftmul) * LPV, didsomething = true;
+      rotate_view(cspin(1, 2, 0.2*shiftmul)), didsomething = true;
     else
       View = ypush(+0.2*shiftmul) * View, playermoved = false, didsomething = true;
     }
@@ -340,7 +335,7 @@ EX void handlePanning(int sym, int uni) {
     if(history::on)
       history::lvspeed -= 0.1 * shiftmul;
     else if(GDIM == 3)
-      LPV = cspin(1, 2, -0.2*shiftmul) * LPV, didsomething = true;
+      rotate_view(cspin(1, 2, -0.2*shiftmul)), didsomething = true;
     else
       View = ypush(-0.2*shiftmul) * View, playermoved = false, didsomething = true;
     }
@@ -349,13 +344,13 @@ EX void handlePanning(int sym, int uni) {
     if(history::on)
       models::rotation++;
     else
-      LPV = spin(M_PI/cgi.S21/2*shiftmul) * LPV, didsomething = true;
+      rotate_view(spin(M_PI/cgi.S21/2*shiftmul)), didsomething = true;
     }
   if(sym == SDLK_PAGEDOWN) {
     if(history::on)
       models::rotation++;
     else
-      LPV = spin(-M_PI/cgi.S21/2*shiftmul) * LPV, didsomething = true;
+      rotate_view(spin(-M_PI/cgi.S21/2*shiftmul)), didsomething = true;
     }
   
   if(sym == SDLK_PAGEUP || sym == SDLK_PAGEDOWN) 
@@ -683,8 +678,7 @@ EX void mainloopiter() {
   
   if(GDIM == 3 && !shmup::on && !rug::rugged) {
     #if CAP_MOUSEGRAB
-    auto &LPV = prod ? nisot::local_perspective : View;
+    rotate_view(cspin(0, 2, -mouseaim_x) * cspin(1, 2, -mouseaim_y));
-    LPV = cspin(0, 2, -mouseaim_x) * cspin(1, 2, -mouseaim_y) * LPV;
     mouseaim_x = mouseaim_y = 0;
     #endif
     }

graph.cpp

@@ -756,7 +756,7 @@ pair<bool, hyperpoint> makeradar(hyperpoint h) {
   ld d = hdist0(h);
 
   if(sol && nisot::geodesic_movement) {
-    h = nisot::inverse_exp(h, nisot::iLazy);
+    h = inverse_exp(h, iLazy);
     ld r = hypot_d(3, h);
     if(r < 1) h = h * (atanh(r) / r);
     else return {false, h};
@@ -3270,7 +3270,7 @@ void drawMovementArrows(cell *c, transmatrix V) {
 
   for(int d=0; d<8; d++) {
   
-    movedir md = vectodir(spin(-d * M_PI/4) * tC0(pushone()));
+    movedir md = vectodir(spin(-d * M_PI/4) * smalltangent());
     int u = md.d;
     cellwalker xc = cwt + u + wstep;
     if(xc.at == c) {
@@ -5100,7 +5100,7 @@ EX void drawcell(cell *c, transmatrix V, int spinv, bool mirrored) {
     hyperpoint H = tC0(V);
     if(abs(H[0]) <= 3 && abs(H[1]) <= 3 && abs(H[2]) <= 3 ) ;
     else {
-      hyperpoint H2 = nisot::inverse_exp(H, nisot::iLazy);
+      hyperpoint H2 = inverse_exp(H, iLazy);
       for(hyperpoint& cpoint: clipping_planes) if((H2|cpoint) < -.2) return;
       }
     noclipped++;
@@ -5109,7 +5109,7 @@ EX void drawcell(cell *c, transmatrix V, int spinv, bool mirrored) {
     hyperpoint H = tC0(V);
     if(abs(H[0]) <= 3 && abs(H[1]) <= 3 && abs(H[2]) <= 3 ) ;
     else {
-      hyperpoint H2 = nisot::inverse_exp(H, nisot::iLazy);
+      hyperpoint H2 = inverse_exp(H, iLazy);
       for(hyperpoint& cpoint: clipping_planes) if((H2|cpoint) < -2) return;
       }
     noclipped++;
@@ -7209,7 +7209,7 @@ EX void make_actual_view() {
     if(max) {
       transmatrix Start = inverse(actualV(viewctr, actual_view_transform * View));
       ld d = wall_radar(viewcenter(), Start, nisot::local_perspective, max);
-      actual_view_transform = solmul(zpush(d), nisot::local_perspective, actual_view_transform * View) * inverse(View); 
+      actual_view_transform = get_shift_view_of(ztangent(d), actual_view_transform * View) * inverse(View); 
       }
     camera_level = asin_auto(tC0(inverse(actual_view_transform * View))[2]);
     }
@@ -7246,10 +7246,7 @@ EX void precise_mouseover() {
   if(WDIM == 3) { 
     mouseover2 = mouseover = viewcenter();
     ld best = HUGE_VAL;
-    hyperpoint h = 
+    hyperpoint h = direct_exp(lp_iapply(ztangent(1)), 100);
-      prod ? product::direct_exp( inverse(nisot::local_perspective) * zforward_dir(1) ) :
-      
-      nisot::local_perspective_used() ? inverse(nisot::local_perspective) * zpush0(1) : zpush0(1);
     forCellEx(c1, mouseover2) {
       ld dist = hdist(tC0(ggmatrix(c1)), h);
       if(dist < best) mouseover = c1, best = dist;

hyperpoint.cpp

@@ -81,6 +81,8 @@ struct hyperpoint : array<ld, MAXMDIM> {
   inline friend hyperpoint operator + (hyperpoint h, hyperpoint h2) { return h += h2; }
   inline friend hyperpoint operator - (hyperpoint h, hyperpoint h2) { return h -= h2; }
 
+  inline friend hyperpoint operator - (hyperpoint h) { return h * -1; }
+
   // cross product  
   inline friend hyperpoint operator ^ (hyperpoint h1, hyperpoint h2) {
     return hyperpoint(
@@ -929,8 +931,6 @@ EX transmatrix mzscale(const transmatrix& t, double fac) {
   return res;
   }
 
-EX transmatrix pushone() { return xpush(sphere?.5 : 1); }
-
 EX hyperpoint mid3(hyperpoint h1, hyperpoint h2, hyperpoint h3) {
   return mid(h1+h2+h3, h1+h2+h3);
   }
@@ -978,18 +978,13 @@ bool asign(ld y1, ld y2) { return signum(y1) != signum(y2); }
 
 ld xcross(ld x1, ld y1, ld x2, ld y2) { return x1 + (x2 - x1) * y1 / (y1 - y2); }
 
-EX transmatrix solmul(const transmatrix T, const transmatrix LPe, const transmatrix V) {
-  if(nonisotropic || prod) return nisot::transport_view(T, LPe, V);
-  else return T * V;
-  }
-
 EX transmatrix solmul_pt(const transmatrix Position, const transmatrix T) {
-  if(nonisotropic) return nisot::parallel_transport(Position, Id, T);
+  if(nonisotropic) return nisot::parallel_transport(Position, Id, tC0(T));
   else return Position * T;
   }
 
 EX transmatrix solmul_pt(const transmatrix Position, const transmatrix LPe, const transmatrix T) {
-  if(nonisotropic || prod) return nisot::parallel_transport(Position, LPe, T);
+  if(nonisotropic || prod) return nisot::parallel_transport(Position, LPe, tC0(T));
   else return Position * T;
   }
 
@@ -1065,4 +1060,64 @@ inline hyperpoint tC0(const transmatrix &T) {
   }
 #endif
 
+/** tangent vector in the given direction */
+EX hyperpoint ctangent(int c, ld x) { return point3(c==0?x:0, c==1?x:0, c==2?x:0); }
+
+/** tangent vector in direction X */
+EX hyperpoint xtangent(ld x) { return ctangent(0, x); }
+
+/** tangent vector in direction Y */
+EX hyperpoint ztangent(ld z) { return ctangent(2, z); }
+
+/** change the length of the targent vector */
+EX hyperpoint tangent_length(hyperpoint dir, ld length) {
+  ld r = hypot_d(GDIM, dir);
+  if(!r) return dir;
+  return dir * (length / r);
+  }
+
+/** exponential function: follow the geodesic given by v */
+EX hyperpoint direct_exp(hyperpoint v, int steps) {
+  if(sol) return nisot::numerical_exp(v, steps);
+  if(nil) return nilv::formula_exp(v);
+  if(sl2) return slr::formula_exp(v);
+  if(prod) return product::direct_exp(v);
+  ld d = hypot_d(GDIM, v);
+  if(d > 0) for(int i=0; i<GDIM; i++) v[i] = v[i] * sin_auto(d) / d;
+  v[3] = cos_auto(d);
+  return v;
+  }
+
+#if HDR
+enum iePrecision { iLazy, iTable };
+#endif
+  
+/** inverse exponential function \see hr::direct_exp */
+EX hyperpoint inverse_exp(const hyperpoint h, iePrecision p, bool just_direction IS(true)) {
+  if(sol) return solv::get_inverse_exp(h, p == iLazy, just_direction);
+  if(nil) return nilv::get_inverse_exp(h, p == iLazy ? 5 : 20);
+  if(sl2) return slr::get_inverse_exp(h);
+  if(prod) return product::inverse_exp(h);
+  ld d = acos_auto_clamp(h[GDIM]);
+  hyperpoint v;
+  if(d && sin_auto(d)) for(int i=0; i<GDIM; i++) v[i] = h[i] * d / sin_auto(d);
+  v[3] = 0;
+  return v;
+  }
+
+EX ld geo_dist(const hyperpoint h1, const hyperpoint h2, iePrecision p) {
+  if(!nonisotropic) return hdist(h1, h2);
+  return hypot_d(3, inverse_exp(inverse(nisot::translate(h1)) * h2, p, false));
+  }
+
+hyperpoint lp_iapply(const hyperpoint h) {
+  return nisot::local_perspective_used() ? inverse(nisot::local_perspective) * h : h;
+  }
+
+hyperpoint lp_apply(const hyperpoint h) {
+  return nisot::local_perspective_used() ? nisot::local_perspective * h : h;
+  }
+
+EX hyperpoint smalltangent() { return xtangent((sphere || hybri) ?.5 : 1); }
+
 }

hypgraph.cpp

@@ -320,7 +320,7 @@ EX void applymodel(hyperpoint H, hyperpoint& ret) {
     case mdPerspective: {
       ld ratio = vid.xres / current_display->tanfov / current_display->radius / 2;
       if(prod) H = product::inverse_exp(H);
-      if(nisot::local_perspective_used()) H = nisot::local_perspective * H;
+      H = lp_apply(H);
       if(H[2] == 0) { ret[0] = 1e6; ret[1] = 1e6; ret[2] = 1; return; }
       ret[0] = H[0]/H[2] * ratio;
       ret[1] = H[1]/H[2] * ratio;
@@ -329,8 +329,7 @@ EX void applymodel(hyperpoint H, hyperpoint& ret) {
       }
 
     case mdGeodesic: {
-      auto S = nisot::inverse_exp(H, nisot::iTable);
+      auto S = lp_apply(inverse_exp(H, iTable));
-      if(nisot::local_perspective_used()) S = nisot::local_perspective * S;
       ld ratio = vid.xres / current_display->tanfov / current_display->radius / 2;
       ret[0] = S[0]/S[2] * ratio;
       ret[1] = S[1]/S[2] * ratio;
@@ -711,9 +710,8 @@ EX void applymodel(hyperpoint H, hyperpoint& ret) {
     
     case mdEquidistant: case mdEquiarea: case mdEquivolume: {
       if(nonisotropic) {
-        H = nisot::inverse_exp(H, nisot::iTable, false);
+        ret = lp_apply(inverse_exp(H, iTable, false));
-        if(nisot::local_perspective_used()) H = nisot::local_perspective * H;
+        ret[3] = 1;
-        ret = H; ret[3] = 1;
         break;
         }
       ld zlev = find_zlev(H);
@@ -939,9 +937,9 @@ EX transmatrix actualV(const heptspin& hs, const transmatrix& V) {
 EX bool point_behind(hyperpoint h) {
   if(sphere) return false;
   if(!in_perspective()) return false;
-  if(pmodel == mdGeodesic) h = nisot::inverse_exp(h, nisot::iLazy);
+  if(pmodel == mdGeodesic) h = inverse_exp(h, iLazy);
   if(pmodel == mdPerspective && prod) h = product::inverse_exp(h);
-  if(nisot::local_perspective_used()) h = nisot::local_perspective * h;
+  h = lp_apply(h);
   return h[2] < 1e-8;
   }
 
@@ -1238,7 +1236,6 @@ EX transmatrix eumovedir(int d) {
 
 EX void spinEdge(ld aspd) { 
   ld downspin = 0;
-  auto& LPV = prod ? nisot::local_perspective : View;
   if(dual::state == 2 && dual::currently_loaded != dual::main_side) {
     transmatrix our   = dual::get_orientation();
     transmatrix their = dual::player_orientation[dual::main_side];
@@ -1249,7 +1246,7 @@ EX void spinEdge(ld aspd) {
       hyperpoint H = T * xpush0(1);
       downspin = -atan2(H[1], H[0]);
       }
-    else LPV = their * inverse(our) * LPV;
+    else rotate_view(their * inverse(our));
     }
   else if(playerfound && vid.fixed_facing) {
     hyperpoint H = gpushxto0(playerV * C0) * playerV * xpush0(5);
@@ -1262,15 +1259,16 @@ EX void spinEdge(ld aspd) {
     }
   else if((WDIM == 2 || prod) && GDIM == 3 && vid.fixed_yz && !CAP_ORIENTATION) {
     aspd = 999999;
+    auto& vo = get_view_orientation();
     if(straightDownSeek) {
       auto sdp = straightDownPoint;
-      if(prod) sdp = LPV * product::inverse_exp(sdp);
+      if(prod) sdp = vo * product::inverse_exp(sdp);
       if(sdp[0])
         downspin = models::rotation * degree - atan2(sdp[0], sdp[1]);
       }
     else {
-      if(LPV[0][2]) 
+      if(vo[0][2]) 
-        downspin = -atan2(LPV[0][2], LPV[1][2]);
+        downspin = -atan2(vo[0][2], vo[1][2]);
       }
     }
   else if(straightDownSeek) {
@@ -1283,7 +1281,7 @@ EX void spinEdge(ld aspd) {
     }
   if(downspin >  aspd) downspin =  aspd;
   if(downspin < -aspd) downspin = -aspd;
-  LPV = spin(downspin) * LPV;
+  rotate_view(spin(downspin));
   }
 
 EX void centerpc(ld aspd) { 
@@ -1365,11 +1363,10 @@ EX void centerpc(ld aspd) {
       aspd *= sqrt(R*R - d.first * d.first) / R;
       }
 
-    if(R < aspd) {
+    if(R < aspd) 
-      View = solmul(gpushxto0(H), Id, View);
+      shift_view_to(H);
-      }
     else 
-      View = solmul(rspintox(H) * xpush(-aspd) * spintox(H), Id, View);
+      shift_view_towards(H, aspd);
       
     fixmatrix(View);
     spinEdge(aspd);
@@ -1991,7 +1988,7 @@ EX bool do_draw(cell *c, const transmatrix& T) {
   if(WDIM == 3) {
     if(cells_drawn > vid.cells_drawn_limit) return false;
     if(nil && pmodel == mdGeodesic) {
-      ld dist = hdist0(nisot::inverse_exp(tC0(T), nisot::iLazy));
+      ld dist = hypot_d(3, inverse_exp(tC0(T), iLazy));
       if(dist > sightranges[geometry] + (vid.sloppy_3d ? 0 : 0.9)) return false;
       if(dist <= extra_generation_distance && !limited_generation(c)) return false;
       }
@@ -2063,4 +2060,54 @@ EX int cone_side(const hyperpoint H) {
   return (ret1[1] - ret0[1]) * (ret2[0] - ret0[0]) < (ret2[1] - ret0[1]) * (ret1[0] - ret0[0]) ? 1 : -1;
   }
 
+/** get the current orientation of the view */
+EX transmatrix& get_view_orientation() {
+  return prod ? nisot::local_perspective : View;
+  }
+
+/** rotate the view using the given rotation matrix */
+EX void rotate_view(transmatrix T) {
+  transmatrix& which = get_view_orientation();
+  which = T * which;
+  }
+
+/** shift the view according to the given tangent vector */
+EX transmatrix get_shift_view_of(const hyperpoint H, const transmatrix V) {
+  if(prod) {
+    hyperpoint h = product::direct_exp(inverse(nisot::local_perspective) * H);
+    return rgpushxto0(h) * V;
+    }
+  else if(!nonisotropic) {
+    return gpushxto0(direct_exp(H, 100)) * V;
+    }
+  else if(!nisot::geodesic_movement) {
+    transmatrix IV = inverse(V);
+    nisot::fixmatrix(IV);
+    const transmatrix V1 = inverse(IV);
+    return V1 * eupush(IV * eupush(H) * V1 * C0);
+    }
+  else {
+    return inverse(nisot::parallel_transport(inverse(V), Id, -H));
+    }
+  }
+
+/** shift the view according to the given tangent vector */
+EX void shift_view(hyperpoint H) {
+  View = get_shift_view_of(H, View);
+  }
+
+EX void shift_view_to(hyperpoint H) {
+  if(!nonisotropic) View = gpushxto0(H) * View;
+  else shift_view(-inverse_exp(H, iTable, false));
+  }
+
+EX void shift_view_towards(hyperpoint H, ld l) {
+  if(!nonisotropic && !prod) 
+    View = rspintox(H) * xpush(-l) * spintox(H) * View;
+  else {
+    hyperpoint ie = nisot::geodesic_movement ? inverse_exp(H, iTable, false) : H-C0;
+    shift_view(tangent_length(ie, -l));
+    }
+  }
+
 }

mapeditor.cpp

@@ -1114,9 +1114,7 @@ namespace mapeditor {
   unsigned gridcolor = 0xC0C0C040;
   
   hyperpoint in_front_dist(ld d) {
-    hyperpoint h = prod ? product::direct_exp( inverse(nisot::local_perspective) * zforward_dir(d) ) : zpush0(d);
+    return direct_exp(lp_iapply(ztangent(d)), 100);
-    if(nonisotropic && nisot::geodesic_movement) h = nisot::get_exp(inverse(nisot::local_perspective) * h, 100);
-    return h;
     }
   
   hyperpoint find_mouseh3() {
@@ -1131,7 +1129,7 @@ namespace mapeditor {
       ld d1 = front_edit;
       hyperpoint h1 = in_front_dist(d);
       if(front_config == eFront::sphere_center) 
-        d1 = nisot::geo_dist(drawtrans * C0, h1, nisot::iTable);
+        d1 = geo_dist(drawtrans * C0, h1, iTable);
       if(front_config == eFront::equidistants) {
         hyperpoint h = idt * in_front_dist(d);
         d1 = asin_auto(h[2]);
@@ -1174,9 +1172,7 @@ namespace mapeditor {
         }
       if(front_config == eFront::sphere_center) for(int i=0; i<4; i+=2) {
         auto pt = [&] (ld a, ld b) {
-          hyperpoint h = dir_to_point(spin(a*degree) * cspin(0, 2, b*degree) * forward_dir(front_edit));
+          return d2 * direct_exp(spin(a*degree) * cspin(0, 2, b*degree) * xtangent(front_edit), 100);
-          if(nonisotropic && nisot::geodesic_movement) return d2 * nisot::get_exp(h, 100);
-          return d2 * h;
           };
         for(int ai=0; ai<parallels; ai++) {
           ld a = ai * 360 / parallels;
@@ -1197,7 +1193,7 @@ namespace mapeditor {
       for(int i=0; i<4; i+=2) {
         for(int u=2; u<=20; u++) {
           PRING(d) {
-            curvepoint(d2 * T * xspinpush(M_PI*d/cgi.S42, u/20.) * zpush(front_edit) * C0);
+            curvepoint(d2 * T * xspinpush(M_PI*d/cgi.S42, u/20.) * zpush0(front_edit));
             }
           queuecurve(cols[i + (u%5 != 0)], 0, i < 2 ? PPR::LINE : PPR::SUPERLINE);
           }
@@ -1454,9 +1450,8 @@ namespace mapeditor {
       displayfr(vid.xres-8, vid.yres-8-fs*5, 2, vid.fsize, XLAT("z: %1", fts(mh[2],4)), 0xC0C0C0, 16);
       if(MDIM == 4)
         displayfr(vid.xres-8, vid.yres-8-fs*4, 2, vid.fsize, XLAT("w: %1", fts(mh[3],4)), 0xC0C0C0, 16);
-      if(prod) mh = product::inverse_exp(mh);
+      mh = inverse_exp(mh, iTable, false);
-      else if(nonisotropic) mh = nisot::inverse_exp(mh, nisot::iTable, false);
+      displayfr(vid.xres-8, vid.yres-8-fs*3, 2, vid.fsize, XLAT("r: %1", fts(hypot_d(3, mh),4)), 0xC0C0C0, 16);
-      displayfr(vid.xres-8, vid.yres-8-fs*3, 2, vid.fsize, XLAT("r: %1", fts(prod ? hypot_d(3, mh) : hdist0(mh),4)), 0xC0C0C0, 16);
       if(GDIM == 3) {
         displayfr(vid.xres-8, vid.yres-8-fs, 2, vid.fsize, XLAT("ϕ: %1°", fts(-atan2(mh[2], hypot_d(2, mh)) / degree,4)), 0xC0C0C0, 16);
         displayfr(vid.xres-8, vid.yres-8-fs*2, 2, vid.fsize, XLAT("λ: %1°", fts(-atan2(mh[1], mh[0]) / degree,4)), 0xC0C0C0, 16);

nonisotropic.cpp

@@ -80,7 +80,7 @@ EX namespace solv {
     return 0.5 - atan((0.5-x) / y) / M_PI;
     }
 
-  hyperpoint get_inverse_exp(hyperpoint h, bool lazy, bool just_direction) {
+  EX hyperpoint get_inverse_exp(hyperpoint h, bool lazy, bool just_direction) {
     load_table();
     
     ld ix = h[0] >= 0. ? x_to_ix(h[0]) : x_to_ix(-h[0]);
@@ -1089,23 +1089,6 @@ EX namespace nisot {
     return true;
     }
   
-  #if HDR
-  enum iePrecision { iLazy, iTable };
-  #endif
-  
-  EX hyperpoint inverse_exp(const hyperpoint h, iePrecision p, bool just_direction IS(true)) {
-    if(sol) return solv::get_inverse_exp(h, p == iLazy, just_direction);
-    if(nil) return nilv::get_inverse_exp(h, p == iLazy ? 5 : 20);
-    if(sl2) return slr::get_inverse_exp(h);
-    if(prod) return product::inverse_exp(h);
-    return point3(h[0], h[1], h[2]);
-    }
-  
-  EX ld geo_dist(const hyperpoint h1, const hyperpoint h2, iePrecision p) {
-    if(!nonisotropic) return hdist(h1, h2);
-    return hypot_d(3, inverse_exp(inverse(translate(h1)) * h2, p, false));
-    }
-
   EX void geodesic_step(hyperpoint& at, hyperpoint& velocity) {
     auto acc = christoffel(at, velocity, velocity);
     
@@ -1119,7 +1102,7 @@ EX namespace nisot {
     velocity = velocity + acc;
     }
   
-  EX hyperpoint direct_exp(hyperpoint v, int steps) {
+  EX hyperpoint numerical_exp(hyperpoint v, int steps) {
     hyperpoint at = point31(0, 0, 0);
     v /= steps;
     v[3] = 0;
@@ -1127,17 +1110,8 @@ EX namespace nisot {
     return at;
     }
 
-  EX hyperpoint get_exp(hyperpoint v, int steps) {
+  EX transmatrix parallel_transport_bare(transmatrix Pos, hyperpoint h) {
-    if(sol) return direct_exp(v, steps);
-    if(nil) return nilv::formula_exp(v);
-    if(sl2) return slr::formula_exp(v);
-    if(prod) return product::direct_exp(v);
-    return v;
-    }
   
-  EX transmatrix parallel_transport_bare(transmatrix Pos, transmatrix T) {
-  
-    hyperpoint h = tC0(T);
     h[3] = 0;
   
     auto tPos = transpose(Pos);
@@ -1180,29 +1154,15 @@ EX namespace nisot {
     T = push * gtl;
     }
 
-  EX transmatrix parallel_transport(const transmatrix Position, const transmatrix LPe, const transmatrix T) {
+  EX transmatrix parallel_transport(const transmatrix Position, const transmatrix LPe, hyperpoint h) {
     if(prod) {
-      hyperpoint h = product::direct_exp(inverse(LPe) * product::inverse_exp(tC0(T)));
+      hyperpoint h = product::direct_exp(inverse(LPe) * product::inverse_exp(h));
       return Position * rgpushxto0(h);
       }
     auto P = Position;
     nisot::fixmatrix(P);  
-    if(!geodesic_movement) return inverse(eupush(Position * inverse(T) * inverse(Position) * C0)) * Position;
+    if(!geodesic_movement) return inverse(eupush(Position * translate(-h) * inverse(Position) * C0)) * Position;
-    return parallel_transport_bare(P, T);
+    return parallel_transport_bare(P, h);
-    }
-  
-  EX transmatrix transport_view(const transmatrix T, const transmatrix LPe, const transmatrix V) {
-    if(prod) {
-      hyperpoint h = product::direct_exp(inverse(LPe) * product::inverse_exp(tC0(T)));
-      return rgpushxto0(h) * V;
-      }
-    if(!geodesic_movement) {
-      transmatrix IV = inverse(V);
-      nisot::fixmatrix(IV);
-      const transmatrix V1 = inverse(IV);
-      return V1 * eupush(IV * T * V1 * C0);
-      }
-    return inverse(parallel_transport(inverse(V), Id, inverse(T)));
     }
   
   EX transmatrix spin_towards(const transmatrix Position, const hyperpoint goal) {

screenshot.cpp

@@ -590,8 +590,6 @@ EX void apply() {
   int t = ticks - lastticks;
   lastticks = ticks;
 
-  auto& LPV = prod ? nisot::local_perspective : View;
-
   switch(ma) {
     case maTranslation:
       if(history::on) {
@@ -611,8 +609,9 @@ EX void apply() {
             fullcenter(); View = spin(rand() % 1000) * View;
             }
           }
-        View = solmul(cspin(0, GDIM-1, movement_angle * degree) * ypush(shift_angle * degree) * xpush(cycle_length * t / period) * ypush(-shift_angle * degree) * 
+        shift_view(
-          cspin(0, GDIM-1, -movement_angle * degree), nisot::local_perspective, View);
+          cspin(0, GDIM-1, movement_angle * degree) * spin(shift_angle * degree) * xtangent(cycle_length * t / period)
+          );
         moved();
         if(clearup) {
           viewcenter()->wall = waNone;
@@ -623,21 +622,22 @@ EX void apply() {
 
     case maRotation:
       if(GDIM == 3) {
-        LPV = spin(-movement_angle * degree) * LPV;
+        rotate_view(spin(-movement_angle * degree));
-        LPV = cspin(1, 2, normal_angle * degree) * LPV;
+        rotate_view(cspin(1, 2, normal_angle * degree));
         }
-      LPV = spin(2 * M_PI * t / period) * LPV;
+      rotate_view(spin(2 * M_PI * t / period));
       if(GDIM == 3) {
-        LPV = cspin(2, 1, normal_angle * degree) * LPV;
+        rotate_view(cspin(2, 1, normal_angle * degree));
-        LPV = spin(movement_angle * degree) * LPV;
+        rotate_view(spin(movement_angle * degree));
         }
       break;
     
     case maTranslationRotation:
-      View = solmul(cspin(0, GDIM-1, movement_angle * degree) * ypush(shift_angle * degree) * xpush(cycle_length * t / period) * ypush(-shift_angle * degree) * 
+      shift_view(
-        cspin(0, GDIM-1, -movement_angle * degree), nisot::local_perspective, View);
+        cspin(0, GDIM-1, movement_angle * degree) * spin(shift_angle * degree) * xtangent(cycle_length * t / period)
+        );
       moved();
-      LPV = cspin(0, GDIM-1, 2 * M_PI * t / period) * LPV;
+      rotate_view(cspin(0, GDIM-1, 2 * M_PI * t / period));
       if(clearup) {
         viewcenter()->wall = waNone;
         }