Clifford torus embedding (needs to be configured manually and on a straight square for now)

geometry.cpp

@@ -1080,7 +1080,7 @@ EX namespace geom3 {
     seProduct,
     seNil,
     seSol, seNIH, seSolN,
-    seNIH_inv
+    seCliffordTorus
     };
   #endif
 
@@ -1094,6 +1094,7 @@ EX namespace geom3 {
     {"Sol",              "Embed into Sol. Works only with Euclidean. You need to set the variation to Pure."},
     {"stretched hyperbolic",              "Embed into stretched hyperbolic geometry. Works only with Euclidean. You need to set the variation to Pure."},
     {"stretched Sol",              "Embed into stretched Sol geometry. Works only with Euclidean. You need to set the variation to Pure."},
+    {"Clifford Torus",              "Embed Euclidean torus into S3. You need to set the variation to Pure."},
     };
 
   EX eSpatialEmbedding spatial_embedding = seDefault;
@@ -1132,13 +1133,17 @@ EX namespace geom3 {
     }
 
   EX bool euc_in_noniso() {
-    return among(ggclass(), gcNil, gcSol, gcNIH, gcSolN) && mgclass() == gcEuclid;
+    return among(ggclass(), gcNil, gcSol, gcNIH, gcSolN, gcSphere) && mgclass() == gcEuclid;
     }
 
   EX bool sph_in_euc() {
     return ggclass() == gcEuclid && mgclass() == gcSphere;
     }
 
+  EX bool euc_in_sph() {
+    return ggclass() == gcSphere && mgclass() == gcEuclid;
+    }
+
   EX bool sph_in_hyp() {
     return ggclass() == gcHyperbolic && mgclass() == gcSphere;
     }
@@ -1220,6 +1225,11 @@ EX namespace geom3 {
             g.gameplay_dimension = 2;
             }
 
+          if(spatial_embedding == seCliffordTorus && ieuclid) {
+            g = ginf[gCell120].g;
+            g.gameplay_dimension = 2;
+            }
+
           bool ieuc_or_binary = ieuclid || (gi.flags & qBINARY);
 
           if(spatial_embedding == seSol && ieuc_or_binary) {

geometry2.cpp

@@ -442,7 +442,7 @@ EX bool no_easy_spin() {
   return NONSTDVAR || arcm::in() || WDIM == 3 || bt::in() || kite::in();
   }
 
-EX bool dont_inverse() { return geometry == 1 && PURE && geom3::euc_in_noniso(); }
+EX bool dont_inverse() { return meuclid && PURE && geom3::euc_in_noniso(); }
 
 ld hrmap_standard::spin_angle(cell *c, int d) {
   if(WDIM == 3) return SPIN_NOT_AVAILABLE;

hyperpoint.cpp

@@ -572,6 +572,15 @@ EX hyperpoint normalize_flat(hyperpoint h) {
   if(geom3::euc_in_nil()) h[1] = 0;
   if(geom3::euc_in_solnih()) h[2] = 0;
   if(geom3::hyp_in_solnih()) h[0] = 0;
+  if(geom3::euc_in_sph()) {
+    ld tx = hypot(h[0], h[2]);
+    ld ty = hypot(h[1], h[3]);
+    h[0] = h[0] / tx * sin(1);
+    h[1] = h[1] / ty * cos(1);
+    h[2] = h[2] / tx * sin(1);
+    h[3] = h[3] / ty * cos(1);
+    return h;
+    }
   if(geom3::euc_in_hyp()) {
     h = normalize(h);
     auto h1 = deparabolic13(h);
@@ -837,6 +846,19 @@ EX hyperpoint orthogonal_move(const hyperpoint& h, ld z) {
     hf[3] = cosh(z0 + z);
     return hf;
     }
+  if(geom3::euc_in_sph()) {
+    // cspin(0,2,x) * cspin(1,3,y) * cspin0(2, 3, z)
+    ld tx = hypot(h[0], h[2]);
+    ld ty = hypot(h[1], h[3]);
+    ld z0 = atan2(ty, tx);
+    z0 -= z;
+    hyperpoint hf;
+    hf[0] = h[0] / tx * cos(z0);
+    hf[1] = h[1] / ty * sin(z0);
+    hf[2] = h[2] / tx * cos(z0);
+    hf[3] = h[3] / ty * sin(z0);
+    return hf;
+    }
   if(GDIM == 2) return scale_point(h, geom3::scale_at_lev(z));
   if(gproduct) return scale_point(h, exp(z));
   if(sl2) return slr::translate(h) * cpush0(2, z);
@@ -874,6 +896,11 @@ EX transmatrix matrix4(ld a, ld b, ld c, ld d, ld e, ld f, ld g, ld h, ld i, ld
   #endif
   }
 
+EX void euc_in_sph_rescale(hyperpoint& h) {
+  h[0] *= TAU * geom3::euclid_embed_scale;
+  h[1] *= TAU * geom3::euclid_embed_scale;
+  }
+
 #if MAXMDIM >= 4
 /** Transform a matrix between the 'embedded_plane' and underlying representation. Switches to the current variant. */
 EX void swapmatrix(transmatrix& T) {
@@ -916,6 +943,11 @@ EX void swapmatrix(transmatrix& T) {
   else if(geom3::in_product()) {
     /* just do nothing */
     }
+  else if(geom3::euc_in_sph()) {
+    hyperpoint h1 = get_column(T, 2);
+    euc_in_sph_rescale(h1);
+    T = cspin(0, 2, h1[0]) * cspin(1, 3, h1[1]);
+    }
   else {
     for(int i=0; i<4; i++) swap(T[i][2], T[i][3]);
     for(int i=0; i<4; i++) swap(T[2][i], T[3][i]);
@@ -934,6 +966,10 @@ EX void swapmatrix(hyperpoint& h) {
   if(geom3::sph_in_euc()) { h[3] = 1; return; }
   if(geom3::sph_in_hyp()) { h[0] *= sinh(1); h[1] *= sinh(1); h[2] *= sinh(1); h[3] = cosh(1); return; }
   if(geom3::euc_in_nil()) { h[3] = 1; h[2] = h[1] * geom3::euclid_embed_scale; h[1] = 0; h[0] *= geom3::euclid_embed_scale; return; }
+  if(geom3::euc_in_sph()) {
+    euc_in_sph_rescale(h); h = cspin(0, 2, h[0]) * cspin(1, 3, h[1]) * lzpush(1) * C0;
+    return;
+    }
   if(geom3::euc_in_solnih()) { h[3] = 1; h[1] = h[1] * geom3::euclid_embed_scale; h[2] = 0; h[0] *= geom3::euclid_embed_scale; return; }
   if(geom3::hyp_in_solnih()) {
     // copied from deparabolic13
@@ -1524,12 +1560,14 @@ EX hyperpoint scale_point(const hyperpoint& h, ld scale_factor) {
 EX bool moved_center() {
   if(geom3::sph_in_euc()) return true;
   if(geom3::sph_in_hyp()) return true;
+  if(geom3::euc_in_sph()) return true;
   return false;
   }
 
 /** Returns the intended center of the tile, relative to its local matrix. Usually C0 but may be different, e.g. when embedding a sphere in E3 or H3. */
 EX hyperpoint tile_center() {
   if(geom3::sph_in_euc()) return C02 + C03;
+  if(geom3::euc_in_sph()) return zpush0(1);
   if(geom3::sph_in_hyp()) return zpush0(1);
   return C0;
   }

hypgraph.cpp

@@ -2028,7 +2028,7 @@ EX void adjust_eye(transmatrix& T, cell *c, ld sign) {
   geom3::do_auto_eye();
   int sl = snakelevel(c);
   if(isWorm(c->monst) && sl < 3) sl++;
-  int i = geom3::sph_in_low() ? 1 : 0;
+  int i = moved_center() ? 1 : 0;
   if(sl || vid.eye || i)
     T = T * lzpush(sign * (cgi.SLEV[sl] - cgi.FLOOR - vid.eye + i));
   }
@@ -2917,7 +2917,7 @@ EX namespace dq {
   EX set<unsigned> visited_by_matrix;
   EX void enqueue_by_matrix(heptagon *h, const shiftmatrix& T) {
     if(!h) return;
-    unsigned b = bucketer(tC0(T));
+    unsigned b = bucketer(T * tile_center());
     if(visited_by_matrix.count(b)) { return; }
     visited_by_matrix.insert(b);
     drawqueue.emplace(h, T);
@@ -2934,7 +2934,7 @@ EX namespace dq {
 
   EX void enqueue_by_matrix_c(cell *c, const shiftmatrix& T) {
     if(!c) return;
-    unsigned b = bucketer(tC0(T));
+    unsigned b = bucketer(T * tile_center());
     if(visited_by_matrix.count(b)) { return; }
     visited_by_matrix.insert(b);
     drawqueue_c.emplace(c, T);
@@ -3368,6 +3368,11 @@ EX transmatrix map_relative_push(hyperpoint h) {
     geom3::light_flip(false);
     return T * zpush(z);
     }
+  if(geom3::euc_in_sph()) {
+    ld tx = hypot(h[0], h[2]);
+    ld ty = hypot(h[1], h[3]);
+    return cspin(0, 2, atan2(h[0], h[2])) * cspin(1, 3, atan2(h[1], h[3])) * cspin(2, 3, atan2(tx, ty));
+    }
   return rgpushxto0(h);
   }