From 86492d1181a2ae68510eac006ad942c373c765d3 Mon Sep 17 00:00:00 2001
From: Zeno Rogue <zeno@attnam.com>
Date: Sun, 25 Dec 2022 12:14:36 +0100
Subject: [PATCH] Improved the UI for 'geodesic movement' setting, and also
 make it work correctly in SL2 and hyperbolic geometries

---
 config.cpp       |  7 ++++-
 drawing.cpp      |  4 +--
 geom-exp.cpp     |  9 ++----
 graph.cpp        |  7 +++--
 hyperpoint.cpp   |  7 +++--
 hypgraph.cpp     | 79 ++++++++++++++++++++++++++++++++++++------------
 nonisotropic.cpp |  4 +--
 radar.cpp        |  2 +-
 shaders.cpp      |  6 ++--
 vr.cpp           |  3 +-
 10 files changed, 84 insertions(+), 44 deletions(-)

diff --git a/config.cpp b/config.cpp
index 28083612..738486bf 100644
--- a/config.cpp
+++ b/config.cpp
@@ -1111,7 +1111,12 @@ EX void initConfig() {
 
   addsaver(bounded_mine_percentage, "bounded_mine_percentage");
 
-  param_b(nisot::geodesic_movement, "solv_geodesic_movement", true);
+  param_enum(nisot::geodesic_movement, "solv_geodesic_movement", "solv_geodesic_movement", true)
+  -> editable({{"Lie group", "light, camera, and objects move in lines of constant direction, in the Lie group sense"}, {"geodesics", "light, camera, and objects always take the shortest path"}}, "straight lines", 'G')
+  -> set_reaction([] {
+    if(pmodel == mdLiePerspective && nisot::geodesic_movement) pmodel = hyperbolic ? mdPerspective : mdGeodesic;
+    if(among(pmodel, mdGeodesic, mdPerspective) && !nisot::geodesic_movement) pmodel = mdLiePerspective;
+    });
 
   addsaver(s2xe::qrings, "s2xe-rings");
   addsaver(rots::underlying_scale, "rots-underlying-scale");
diff --git a/drawing.cpp b/drawing.cpp
index 48c7a7d7..dc20ee6e 100644
--- a/drawing.cpp
+++ b/drawing.cpp
@@ -482,9 +482,9 @@ bool behind3(shiftpoint h) {
   if(pmodel == mdGeodesic) 
     return lp_apply(inverse_exp(h))[2] < 0;
   if(pmodel == mdLiePerspective)
-    return lp_apply(lie_log(unshift(h)))[2] < 0;
+    return lp_apply(lie_log(h))[2] < 0;
   if(pmodel == mdRelPerspective)
-    return lp_apply(rel_log(h))[2] < 0;
+    return lp_apply(rel_log(h, false))[2] < 0;
   return h[2] < 0;
   }
 
diff --git a/geom-exp.cpp b/geom-exp.cpp
index 904a0c99..8f0afb4b 100644
--- a/geom-exp.cpp
+++ b/geom-exp.cpp
@@ -1108,13 +1108,8 @@ EX void showEuclideanMenu() {
     dialog::add_action_push(show3D);
     }
   menuitem_projection('1');
-  if(nonisotropic && !sl2 && !embedded_plane) {
-    dialog::addBoolItem(XLAT("geodesic movement in Sol/Nil"), nisot::geodesic_movement, 'G');
-    dialog::add_action([] {
-      nisot::geodesic_movement = !nisot::geodesic_movement;
-      if(pmodel == mdLiePerspective && nisot::geodesic_movement) pmodel = mdGeodesic;
-      if(pmodel == mdGeodesic && !nisot::geodesic_movement) pmodel = mdLiePerspective;
-      });
+  if(lie_movement_available()) {
+    add_edit(nisot::geodesic_movement);
     }
   #if CAP_CRYSTAL && MAXMDIM >= 4
   crystal::add_crystal_transform('x');  
diff --git a/graph.cpp b/graph.cpp
index 3cce1ab0..04f39cc6 100644
--- a/graph.cpp
+++ b/graph.cpp
@@ -4093,7 +4093,7 @@ void make_clipping_planes() {
     sx /= hypot_d(3, sx);
     sx[3] = 0;
     sx = T * sx;
-    if(nisot::local_perspective_used()) sx = ortho_inverse(nlp) * sx;
+    if(nisot::local_perspective_used) sx = ortho_inverse(nlp) * sx;
     clipping_plane_sets.back().push_back(sx);
     };
 
@@ -5059,6 +5059,8 @@ EX ld wall_radar(cell *c, transmatrix T, transmatrix LPe, ld max) {
 EX bool nonisotropic_weird_transforms;
 
 EX void make_actual_view() {
+  nisot::local_perspective_used = gproduct;
+  if(!nisot::local_perspective_used) NLP = Id;
   sphereflip = Id;
   sphere_flipped = flip_sphere();
   if(sphere_flipped) sphereflip[LDIM][LDIM] = -1;
@@ -5083,11 +5085,12 @@ EX void make_actual_view() {
 
     camera_sign = cgi.FLOOR > cgi.WALL;
     }
-  if(nonisotropic && !nonisotropic_weird_transforms) {
+  if((nonisotropic || (hyperbolic && bt::in() && !nisot::geodesic_movement)) && !nonisotropic_weird_transforms) {
     transmatrix T = actual_view_transform * View;
     transmatrix T2 = eupush( tC0(view_inverse(T)) );
     NLP = T * T2;
     actual_view_transform = ortho_inverse(NLP) * actual_view_transform;
+    nisot::local_perspective_used = true;
     }
   #endif
   #if MAXMDIM >= 4
diff --git a/hyperpoint.cpp b/hyperpoint.cpp
index 65ecc2db..ed61ba0a 100644
--- a/hyperpoint.cpp
+++ b/hyperpoint.cpp
@@ -731,6 +731,7 @@ EX transmatrix euscale3(ld x, ld y, ld z) {
 
 EX transmatrix eupush(hyperpoint h, ld co IS(1)) {
   if(nonisotropic) return nisot::translate(h, co);
+  if(hyperbolic) { return co ? parabolic13_at(deparabolic13(h)) : inverse(parabolic13_at(deparabolic13(h))); }
   transmatrix T = Id;
   for(int i=0; i<GDIM; i++) T[i][LDIM] = h[i] * co;
   return T;
@@ -1651,7 +1652,7 @@ EX eShiftMethod shift_method(eShiftMethodApplication sma) {
   if(gproduct) return smProduct;
   if(embedded_plane && sma == smaObject) return geom3::same_in_same() ? smIsotropic : smEmbedded;
   if(embedded_plane && use_embedded_shift(sma)) return nonisotropic ? smLie : smEmbedded;
-  if(!nonisotropic && !stretch::in()) return smIsotropic;
+  if(!nonisotropic && !stretch::in() && !(!nisot::geodesic_movement && hyperbolic && bt::in())) return smIsotropic;
   if(!nisot::geodesic_movement && !embedded_plane) return smLie;
   return smGeodesic;
   }
@@ -1897,11 +1898,11 @@ EX ld geo_dist_q(const hyperpoint h1, const hyperpoint h2, flagtype prec IS(pNOR
   }
 
 EX hyperpoint lp_iapply(const hyperpoint h) {
-  return nisot::local_perspective_used() ? inverse(NLP) * h : h;
+  return nisot::local_perspective_used ? inverse(NLP) * h : h;
   }
 
 EX hyperpoint lp_apply(const hyperpoint h) {
-  return nisot::local_perspective_used() ? NLP * h : h;
+  return nisot::local_perspective_used ? NLP * h : h;
   }
 
 EX hyperpoint smalltangent() { return xtangent(.1); }
diff --git a/hypgraph.cpp b/hypgraph.cpp
index 03d81f2e..d6f7b086 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -539,11 +539,8 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         exit(1);
         /* x wanes as z grows! */
         }
-      if(hyperbolic) {
-        models::apply_orientation_yz(H[1], H[2]);
-        models::apply_orientation(H[0], H[1]);
-        }
-      auto S = lie_log(H); S[3] = 1;
+      hyperpoint S = lie_log_correct(H_orig, H);
+      S[3] = 1;
       S = lp_apply(S);
       if(hyperbolic) {
         models::apply_orientation(ret[1], ret[0]);
@@ -554,7 +551,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       }
 
     case mdRelPerspective: {
-      auto S = rel_log(H_orig); S[3] = 1;
+      auto S = rel_log(H_orig, true); S[3] = 1;
       S = lp_apply(S);
       apply_perspective(S, ret);
       return;
@@ -778,20 +775,14 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         models::apply_orientation_yz(ret[2], ret[1]);
         }
       
-      if(nonisotropic && !vrhr::rendering()) ret = lp_apply(ret);
+      if(!vrhr::rendering()) ret = lp_apply(ret);
 
       break;
       }
 
     case mdLieOrthogonal: {
-      find_zlev(H);
+      ret = lie_log_correct(H_orig, H);
 
-      if(hyperbolic) {
-        models::apply_orientation_yz(H[1], H[2]);
-        models::apply_orientation(H[0], H[1]);
-        }
-
-      ret = lie_log(H);
       ret *= .5;
       ret[LDIM] = 1;
 
@@ -800,18 +791,18 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         models::apply_orientation_yz(ret[2], ret[1]);
         }
 
-      if(nonisotropic && !vrhr::rendering()) ret = lp_apply(ret);
+      if(!vrhr::rendering()) ret = lp_apply(ret);
 
       break;
       }
 
     case mdRelOrthogonal: {
 
-      ret = rel_log(H_orig);
+      ret = rel_log(H_orig, true);
       ret *= .5;
       ret[LDIM] = 1;
 
-      if(nonisotropic && !vrhr::rendering()) ret = lp_apply(ret);
+      if(!vrhr::rendering()) ret = lp_apply(ret);
       break;
       }
 
@@ -2299,6 +2290,7 @@ EX int flat_on;
 eGeometry backup_geometry;
 eVariation backup_variation;
 videopar backup_vid;
+bool backup_lpu;
 
 /** \brief enable the 'flat' model for drawing HUD. See hr::flat_model_enabler */
 EX void enable_flat_model(int val) {
@@ -2308,9 +2300,12 @@ EX void enable_flat_model(int val) {
     #endif
     backup_geometry = geometry;
     backup_variation = variation;
+    backup_lpu = nisot::local_perspective_used;
     backup_vid = vid;
     geometry = gNormal;
     variation = eVariation::bitruncated;
+    nisot::local_perspective_used = false;
+
     pmodel = mdDisk;
     pconf.alpha = 1;
     pconf.scale = 1;
@@ -2330,6 +2325,7 @@ EX void enable_flat_model(int val) {
   if(flat_on >= 1 && flat_on + val < 1) {
     geometry = backup_geometry;
     variation = backup_variation;
+    nisot::local_perspective_used = backup_lpu;
     vid = backup_vid;
     geom3::apply_always3();
     calcparam();
@@ -3121,6 +3117,20 @@ EX hyperpoint lie_exp(hyperpoint h) {
       h[1] *= (exp(+z) - 1) / z;
       }
     }
+  else if(sl2) {
+    h[3] = 0;
+    ld v = h[0] * h[0] + h[1] * h[1] - h[2] * h[2];
+    if(v > 0) {
+      h *= sin(v) / sqrt(v);
+      h[3] += cos(v);
+      }
+    else if(v < 0) {
+      h *= sinh(v) / sqrt(-v);
+      h[3] += cosh(v);
+      }
+    else h[3]++;
+    return h;
+    }
   else {
     /* not implemented -- approximate for now */
     const int steps = 16;
@@ -3134,7 +3144,11 @@ EX hyperpoint lie_exp(hyperpoint h) {
   return h;
   }
 
-EX hyperpoint rel_log(shiftpoint h) {
+/** With relativistic_length off, compute the Lie logarithm in SL(2,R) or de Sitter space.
+ *  With relativistic_length on, this corresponds to a geodesic in AdS/dS, so make it as long as the length of the geodesic in AdS/dS space.
+ **/
+
+EX hyperpoint rel_log(shiftpoint h, bool relativistic_length) {
   if(sl2) {
     optimize_shift(h);
     ld cycles = floor(h.shift / TAU + .5);
@@ -3148,6 +3162,7 @@ EX hyperpoint rel_log(shiftpoint h) {
       z += cycles * TAU;
       }
     else if(cycles || h1[3] < -1 || choice == 0) {
+      if(!relativistic_length) return h1 - C0;
       /* impossible, or light-like */
       r = 1; z = 0;
       }
@@ -3155,6 +3170,7 @@ EX hyperpoint rel_log(shiftpoint h) {
       r = sqrt(-choice);
       z = asinh(r);
       }
+    if(!relativistic_length) r = sqhypot_d(3, h1);
     h1 = h1 * z / r;
     h1[3] = 0;
     return h1;
@@ -3165,13 +3181,22 @@ EX hyperpoint rel_log(shiftpoint h) {
     ld r, z;
     if(choice > 0) { r = sqrt(choice); z = asinh(r); }
     else { r = sqrt(-choice); z = asin_clamp(r); if(h1[2] < 0) z = M_PI - z; }
+    if(!relativistic_length) r = sqrt(h1[3] * h1[3] + h1[0] * h1[0] + h1[1] * h1[1]);
     h1 = h1 * z / r; h1[2] = h1[3]; h1[3] = 0;
     return h1;
     }
   throw hr_exception("rel_log in wrong geometry");
   }
 
-EX hyperpoint lie_log(hyperpoint h) {
+/** Is Lie movement available? Depends on map geometry, not ambient geometry. */
+EX bool lie_movement_available() {
+  if(nonisotropic && !embedded_plane) return true;
+  if(mhyperbolic && bt::in()) return true;
+  return false;
+  };
+
+EX hyperpoint lie_log(const shiftpoint h1) {
+  hyperpoint h = unshift(h1);
   if(nil) {
     h[3] = 0;
     h[2] -= h[0] * h[1] / 2;
@@ -3210,12 +3235,26 @@ EX hyperpoint lie_log(hyperpoint h) {
       for(int i=1; i<LDIM; i++)
         h[i] *= h[0] / (exp(h[0])-1);
     }
+  else if(sl2) {
+    return rel_log(h1, false);
+    }
   else {
     /* not implemented */
     }
   return h;
   }
 
+/** Like lie_log but includes orientation and level in hyperbolic space. May modify H */
+EX hyperpoint lie_log_correct(const shiftpoint H_orig, hyperpoint& H) {
+  find_zlev(H);
+  if(hyperbolic) {
+    models::apply_orientation_yz(H[1], H[2]);
+    models::apply_orientation(H[0], H[1]);
+    return lie_log(shiftless(H));
+    }
+  return lie_log(H_orig);
+  }
+
 /** shift the view according to the given tangent vector */
 EX transmatrix get_shift_view_of(const hyperpoint H, const transmatrix V, eShiftMethod sm IS(shift_method(smaManualCamera))) {
   switch(sm) {
@@ -3328,7 +3367,7 @@ EX void shift_view_to(shiftpoint H, eShiftMethod sm IS(shift_method(smaManualCam
       shift_view_by_matrix(gpushxto0(unshift(H)), sm);
       return;
     case smLie:
-      shift_view(-lie_log(unshift(H)), sm);
+      shift_view(-lie_log(H), sm);
       return;
     case smGeodesic:
       shift_view(-inverse_exp(H), sm);
diff --git a/nonisotropic.cpp b/nonisotropic.cpp
index d7334ddd..d2b3e571 100644
--- a/nonisotropic.cpp
+++ b/nonisotropic.cpp
@@ -10,9 +10,7 @@ namespace hr {
 
 EX namespace nisot {
 
-  #if HDR
-  inline bool local_perspective_used() { return nonisotropic || gproduct; }
-  #endif
+  EX bool local_perspective_used;
   
   EX bool geodesic_movement = true;
 
diff --git a/radar.cpp b/radar.cpp
index f996e780..1ea586b3 100644
--- a/radar.cpp
+++ b/radar.cpp
@@ -19,7 +19,7 @@ pair<bool, hyperpoint> makeradar(shiftpoint h) {
   else if(sl2) h1 = slr::get_inverse_exp(h);
   else h1 = unshift(h);
   
-  if(nisot::local_perspective_used() && !embedded_plane) {
+  if(nisot::local_perspective_used && !embedded_plane) {
     h1 = NLP * h1;
     }
   
diff --git a/shaders.cpp b/shaders.cpp
index d3b02f3a..848694bb 100644
--- a/shaders.cpp
+++ b/shaders.cpp
@@ -660,7 +660,7 @@ void display_data::set_projection(int ed, ld shift) {
       }
     else M[2][2] /= 10000;
     glhr::projection_multiply(M);
-    if(nisot::local_perspective_used() && (shader_flags & SF_BOX))
+    if(nisot::local_perspective_used && (shader_flags & SF_BOX))
       glhr::projection_multiply(glhr::tmtogl_transpose(NLP));
     if(ed && vid.stereo_mode != sODS) {
       glhr::glmatrix m = glhr::id;
@@ -712,7 +712,7 @@ void display_data::set_projection(int ed, ld shift) {
     else {
       glhr::projection_multiply(glhr::frustum(cd->tanfov, cd->tanfov * cd->ysize / cd->xsize));
       glhr::projection_multiply(glhr::scale(1, -1, -1));
-      if(nisot::local_perspective_used()) {
+      if(nisot::local_perspective_used) {
         if(gproduct) {
           for(int i=0; i<3; i++) NLP[3][i] = NLP[i][3] = 0;
           NLP[3][3] = 1;
@@ -758,7 +758,7 @@ void display_data::set_projection(int ed, ld shift) {
 
     pp = pp * pp0;    
 
-    if(nisot::local_perspective_used()) 
+    if(nisot::local_perspective_used)
       pp = glhr::tmtogl_transpose(NLP) * pp;
 
     if(get_shader_flags() & SF_ORIENT) {
diff --git a/vr.cpp b/vr.cpp
index 455003e7..3fc7374d 100644
--- a/vr.cpp
+++ b/vr.cpp
@@ -1007,10 +1007,9 @@ EX void gen_mv() {
   if(!pers) mu[1][1] *= pconf.stretch;
 
   hmd_mv = Id;
-  bool nlpu = nisot::local_perspective_used();
   if(1) {
     E4;
-    if(nlpu) {
+    if(nisot::local_perspective_used) {
       be_33(NLP);
       hmd_mv = NLP * hmd_mv;          
       }