diff --git a/commandline.cpp b/commandline.cpp
index cc664a61..600970ae 100644
--- a/commandline.cpp
+++ b/commandline.cpp
@@ -119,6 +119,10 @@ EX namespace arg {
     #endif
     if(old != x && r) r();
     }
+
+  EX void shift_arg_formula_matrix(struct hr::trans23& x) {
+    shift(); x = parsematrix23(args()); // TODO animate
+    }
   
   #if HDR
 
diff --git a/drawing.cpp b/drawing.cpp
index 53d9acfd..063882d4 100644
--- a/drawing.cpp
+++ b/drawing.cpp
@@ -925,13 +925,29 @@ ld period_at(ld y) {
     }     
   }
 
+void apply_ori_gl(glvertex& g) {
+  auto Ori = pconf.mori().v2;
+  tie(g[0], g[1]) = make_pair(
+    Ori[0][0] * g[0] + Ori[0][1] * g[1],
+    Ori[1][0] * g[0] + Ori[1][1] * g[1]
+    );
+  }
+
+void apply_iori_gl(glvertex& g) {
+  auto Ori = pconf.mori().v2;
+  tie(g[0], g[1]) = make_pair(
+    Ori[0][0] * g[0] + Ori[1][0] * g[1],
+    Ori[0][1] * g[0] + Ori[1][1] * g[1]
+    );
+  }
+
 void adjust(bool tinf) {
 
   periods.resize(isize(glcoords));
   
   if(!models::model_straight)
     for(auto& g: glcoords)
-      models::apply_orientation(g[0], g[1]);
+      apply_ori_gl(g);
 
   for(int i = 0; i<isize(glcoords); i++) periods[i] = period_at(glcoords[i][1]);  
     
@@ -989,7 +1005,7 @@ void adjust(bool tinf) {
   if(abs(first - last) < 1e-6) {
     if(!models::model_straight)
       for(auto& g: glcoords)
-        models::apply_orientation(g[1], g[0]);
+        apply_iori_gl(g);
     }
   else {
     if(tinf) { 
@@ -1020,7 +1036,7 @@ void adjust(bool tinf) {
       }
     if(!models::model_straight)
       for(auto& g: glcoords)
-        models::apply_orientation(g[1], g[0]);
+        apply_iori_gl(g);
     // we have already looped
     loop_min = loop_max = 0;  
     }
@@ -1667,7 +1683,7 @@ bool broken_projection(dqi_poly& p0) {
     int fail = 0;
     int last_fail;
 
-    for(auto& h: all) models::apply_orientation(h[0], h[1]);
+    for(auto& h: all) models::apply_ori(h);
 
     auto break_in_xz = [&] (hyperpoint a, hyperpoint b, int xcoord, int zcoord) {
       return a[xcoord] * b[xcoord] <= 0 && (a[xcoord] * (b[zcoord]+zlow) - b[xcoord] * (a[zcoord]+zlow)) * (a[xcoord] - b[xcoord]) < 0;
@@ -1692,7 +1708,7 @@ bool broken_projection(dqi_poly& p0) {
 
     /* we don't rotate h's back, just change p.V */
     for(int i=0; i<3; i++)
-      models::apply_orientation(p.V.T[i][0], p.V.T[i][1]);
+      models::apply_ori(p.V.T[i]);
 
     if(fail) {
       if(p0.tinf) return true;
@@ -1875,8 +1891,8 @@ void dqi_poly::draw() {
           shiftpoint h2 = V * glhr::gltopoint((*tab)[offset+(i+1)%cnt]);
           
           hyperpoint ah1 = h1.h, ah2 = h2.h;
-          models::apply_orientation(ah1[0], ah1[1]);
-          models::apply_orientation(ah2[0], ah2[1]);
+          models::apply_ori(ah1);
+          models::apply_ori(ah2);
           if(ah1[1] * ah2[1] > 0) continue;
           ld c1 = ah1[1], c2 = -ah2[1];
           if(c1 < 0) c1 = -c1, c2 = -c2;
@@ -2030,8 +2046,8 @@ void dqi_poly::draw() {
   
     if(l || lastl) { 
       for(int i=0; i<isize(glcoords); i++) {
-        glcoords[i][0] += models::ocos * cyl::periods[i] * (l - lastl);
-        glcoords[i][1] += models::osin * cyl::periods[i] * (l - lastl);
+        glcoords[i][0] += pconf.mori().get()[0][0] * cyl::periods[i] * (l - lastl);
+        glcoords[i][1] += pconf.mori().get()[1][0] * cyl::periods[i] * (l - lastl);
         }
       lastl = l;
       }
diff --git a/graph.cpp b/graph.cpp
index 65226bb2..3bf7bcfd 100644
--- a/graph.cpp
+++ b/graph.cpp
@@ -3400,11 +3400,12 @@ EX void drawaura() {
     ld s = sin(rr);
 
     if(joukowsky) {
-      ld c1 = c, s1 = s;
+      hyperpoint v(c, s, 0, 1);
       if(inversion)
-        models::apply_orientation(s1, c1);
+        models::apply_iori(v);
       else        
-        models::apply_orientation(c1, s1);
+        models::apply_ori(v);
+      ld c1 = v[0], s1 = v[1];
 
       ld& mt = pconf.model_transition;
       ld mt2 = 1 - mt;
diff --git a/hyperpoint.cpp b/hyperpoint.cpp
index d3b7c513..74cdab33 100644
--- a/hyperpoint.cpp
+++ b/hyperpoint.cpp
@@ -203,6 +203,25 @@ constexpr transmatrix Id = diag(1,1,1,1);
 /** zero matrix */
 constexpr transmatrix Zero = diag(0,0,0,0);
 
+/** a transmatrix with 2D and 3D version, useful for configuration */
+struct trans23 {
+  transmatrix v2, v3;
+  transmatrix& get() { return MDIM == 3 ? v2 : v3; }
+  trans23() { v2 = Id; v3 = Id; }
+  trans23(const transmatrix& T) { v2 = T; v3 = T; }
+  trans23(const transmatrix& T2, const transmatrix& T3) { v2 = T2; v3 = T3; }
+  trans23 operator * (trans23 T) {
+    trans23 t;
+    auto& dim = cginf.g.homogeneous_dimension;
+    dynamicval<int> d1(dim, dim);
+    dim = 3; t.v2 = v2 * T.v2;
+    dim = 4; t.v3 = v3 * T.v3;
+    return t;
+    }
+  };
+
+inline trans23 *gen_trans23() { return new trans23; }
+
 /** mirror image */
 constexpr transmatrix Mirror = diag(1,-1,1,1);
 
@@ -1167,6 +1186,16 @@ EX transmatrix iso_inverse(const transmatrix& T) {
   return inverse(T);
   }
 
+/** inverse a guaranteed rotation */
+EX transmatrix rot_inverse(const transmatrix& T) {
+  return transpose(T);
+  }
+
+/** inverse a guaranteed rotation */
+EX trans23 rot_inverse(const trans23& T) {
+  return trans23(rot_inverse(T.v2), rot_inverse(T.v3));
+  }
+
 /** \brief T inverse a matrix T = O*S, where O is isometry and S is a scaling matrix (todo optimize) */
 EX transmatrix z_inverse(const transmatrix& T) {
   return inverse(T);
diff --git a/hypgraph.cpp b/hypgraph.cpp
index f12934db..7db31524 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -253,8 +253,7 @@ void move_y_to_z(hyperpoint& H, pair<ld, ld> coef) {
 
 template<class T> void makeband(shiftpoint H, hyperpoint& ret, const T& f) {
   ld zlev = find_zlev(H.h);
-  models::apply_orientation_yz(H[1], H[2]);
-  models::apply_orientation(H[0], H[1]);
+  models::apply_ori(H.h);
   auto r = move_z_to_y(H.h);
   
   ld x, y, yf, zf=0;
@@ -272,8 +271,7 @@ template<class T> void makeband(shiftpoint H, hyperpoint& ret, const T& f) {
   ld yzf = y * zf; y *= yf;
   ret = hpxyz(x / M_PI, y / M_PI, 0);
   move_y_to_z(ret, r);
-  models::apply_orientation(ret[1], ret[0]);
-  models::apply_orientation_yz(ret[2], ret[1]);
+  models::apply_iori(ret);
   if(zlev != 1 && use_z_coordinate()) 
     apply_depth(ret, yzf / M_PI);
   return;
@@ -397,9 +395,9 @@ EX void apply_perspective(const hyperpoint& H, hyperpoint& ret) {
 EX void apply_nil_rotation(hyperpoint& H) {
   if(nil) {
     nilv::convert_ref(H, nilv::model_used, nilv::nmSym);
-    models::apply_orientation(H[0], H[1]);
+    models::apply_ori(H);
     nilv::convert_ref(H, nilv::nmSym, pconf.rotational_nil);
-    models::apply_orientation(H[1], H[0]);        
+    models::apply_iori(H);  
     }
   }
 
@@ -454,8 +452,7 @@ EX void threepoint_projection(const hyperpoint& H, hyperpoint& ret) {
   hyperpoint H1 = H;
   find_zlev(H1);
   if(true) {
-    models::apply_orientation_yz(H1[1], H1[2]);
-    models::apply_orientation(H1[0], H1[1]);
+    models::apply_ori(H1);
     }
 
   auto p = pconf.twopoint_param;
@@ -501,16 +498,14 @@ EX void threepoint_projection(const hyperpoint& H, hyperpoint& ret) {
   geometry = gCubeTiling;
   
   ret = sxy;
-  models::apply_orientation(ret[1], ret[0]);
-  models::apply_orientation_yz(ret[2], ret[1]);
+  models::apply_iori(ret);
   }
 #endif
 
 EX vector<hr::function<void(shiftpoint& H_orig, hyperpoint& H, hyperpoint& ret)>> extra_projections;
 
 EX void make_axial(hyperpoint H, hyperpoint& ret, const hr::function<ld(hyperpoint)>& f) {
-  models::apply_orientation_yz(H[1], H[2]);
-  models::apply_orientation(H[0], H[1]);
+  models::apply_ori(H);
 
   ret[0] = f(H);
   ld axi = pconf.axial_angle;
@@ -531,8 +526,7 @@ EX void make_axial(hyperpoint H, hyperpoint& ret, const hr::function<ld(hyperpoi
 
   ret[3] = 1;
 
-  models::apply_orientation(ret[1], ret[0]);
-  models::apply_orientation_yz(ret[2], ret[1]);
+  models::apply_iori(ret);
   }
 
 // according to https://github.com/cspersonal/peirce-quincuncial-projection/blob/master/peirceQuincuncialProjection.R
@@ -655,8 +649,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       #endif
       if(!computing_semidirect) S = lp_apply(S);
       if(hyperbolic) {
-        models::apply_orientation(ret[1], ret[0]);
-        models::apply_orientation_yz(ret[2], ret[1]);
+        models::apply_iori(ret);
         }
       apply_perspective(S, ret);
       return;
@@ -751,8 +744,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       ld zlev = find_zlev(H);
       H = space_to_perspective(H);
       
-      models::apply_orientation_yz(H[1], H[2]);
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
   
       H[1] += 1;
       double rad = sqhypot_d(GDIM, H);
@@ -766,26 +758,27 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         ret[1] = 1 + H[1];
         ret[2] = H[2];
         ret[3] = 1;
-        models::apply_orientation(ret[1], ret[0]);
-        models::apply_orientation_yz(ret[2], ret[1]);
+        models::apply_iori(ret);
         break;
         }
       
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
       
       H *= pconf.halfplane_scale;
-      
-      ret[0] = -models::osin - H[0];
+      auto ocos = pconf.mori().get()[0][0];
+      auto osin = pconf.mori().get()[1][0];
+
+      ret[0] = -osin - H[0];
       ld height = 0;
       if(zlev != 1) {
-        if(abs(models::ocos) > 1e-9)
-          height += H[1] * (pow(zlev, models::ocos) - 1);
-        if(abs(models::ocos) > 1e-9 && models::osin)
-          height += H[0] * models::osin * (pow(zlev, models::ocos) - 1) / models::ocos;
-        else if(models::osin)
-          height += H[0] * models::osin * log(zlev);
+        if(abs(ocos) > 1e-9)
+          height += H[1] * (pow(zlev, ocos) - 1);
+        if(abs(ocos) > 1e-9 && osin)
+          height += H[0] * osin * (pow(zlev, ocos) - 1) / ocos;
+        else if(osin)
+          height += H[0] * osin * log(zlev);
         }
-      ret[1] = models::ocos + H[1];
+      ret[1] = ocos + H[1];
       ret[2] = GDIM == 3 ? H[2] : 0;
       if(MAXMDIM == 4) ret[3] = 1;
        if(zlev != 1 && use_z_coordinate())
@@ -824,8 +817,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
     
     case mdQuadrant: {
       H = space_to_perspective(H);
-      models::apply_orientation_yz(H[1], H[2]);
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
       
       tie(H[0], H[1]) = make_pair((H[0] + H[1]) / sqrt(2), (H[1] - H[0]) / sqrt(2));
 
@@ -840,8 +832,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       ret[0] = -H[1] * x - 1;
       ret[1] = H[1] / x + 1;
 
-      models::apply_orientation(ret[1], ret[0]);
-      models::apply_orientation_yz(ret[2], ret[1]);
+      models::apply_iori(ret);
       break;
       }
     
@@ -858,19 +849,13 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
 
       apply_nil_rotation(H);
       
-      if(hyperbolic) {
-        models::apply_orientation_yz(H[1], H[2]);
-        models::apply_orientation(H[0], H[1]);
-        }
+      if(hyperbolic) models::apply_ori(H);
       
       ret = hyperbolic ? deparabolic13(H) : H;
       ret *= .5;
       ret[LDIM] = 1;
       
-      if(hyperbolic) {  
-        models::apply_orientation(ret[1], ret[0]);
-        models::apply_orientation_yz(ret[2], ret[1]);
-        }
+      if(hyperbolic) models::apply_iori(ret);
       
       if(!vrhr::rendering()) ret = lp_apply(ret);
 
@@ -879,32 +864,24 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
 
     case mdHorocyclicEqa: {
 
-      if(hyperbolic) {
-        models::apply_orientation_yz(H[1], H[2]);
-        models::apply_orientation(H[0], H[1]);
-        }
+      if(hyperbolic) models::apply_ori(H);
 
       ret = hyperbolic ? deparabolic13(H) : H;
       ret[0] = exp(-ret[0]) - 1;
       ret *= .5;
       ret[LDIM] = 1;
 
-      if(hyperbolic) {
-        models::apply_orientation(ret[1], ret[0]);
-        models::apply_orientation_yz(ret[2], ret[1]);
-        }
+      if(hyperbolic) models::apply_iori(ret);
 
       break;
       }
 
     case mdConformalSquare: {
       find_zlev(H);
-      models::apply_orientation_yz(H[1], H[2]);
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
       if(euclid) H[0] /= pconf.fisheye_param, H[1] /= pconf.fisheye_param;
       ret = to_square(H);
-      models::apply_orientation(ret[1], ret[0]);
-      models::apply_orientation_yz(ret[2], ret[1]);
+      models::apply_iori(ret);
       break;
       }
 
@@ -914,10 +891,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       ret *= .5;
       ret[LDIM] = 1;
 
-      if(hyperbolic) {
-        models::apply_orientation(ret[1], ret[0]);
-        models::apply_orientation_yz(ret[2], ret[1]);
-        }
+      if(hyperbolic) models::apply_iori(ret);
 
       if(!vrhr::rendering()) ret = lp_apply(ret);
 
@@ -1080,8 +1054,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       }
     
     case mdSimulatedPerspective: {
-      models::apply_orientation_yz(H[1], H[2]);
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
       auto yz = move_z_to_y(H);
       hyperpoint Hl = xpush(-pconf.twopoint_param) * H;
       hyperpoint Hr = xpush(+pconf.twopoint_param) * H;
@@ -1100,28 +1073,24 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       ret[0] = -ret[0]; ret[1] = -ret[1];
 
       move_y_to_z(ret, yz);      
-      models::apply_orientation(ret[1], ret[0]);
-      models::apply_orientation_yz(ret[2], ret[1]);
+      models::apply_iori(ret);
       break;
       }
     
     case mdTwoHybrid: {
-      models::apply_orientation_yz(H[1], H[2]);
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
       auto yz = move_z_to_y(H);
       
       ret = compute_hybrid(H, whateveri[0]); 
       
       move_y_to_z(ret, yz);      
-      models::apply_orientation(ret[1], ret[0]);
-      models::apply_orientation_yz(ret[2], ret[1]);
+      models::apply_iori(ret);
       break;
       }
     
     case mdJoukowsky: 
     case mdJoukowskyInverted: {
-      models::apply_orientation_yz(H[1], H[2]);
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
       // with equal speed skiprope: models::apply_orientation(H[1], H[0]);
   
       if(pconf.skiprope) {
@@ -1168,7 +1137,6 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         ret[0] = ret[0] / r2;
         ret[1] = -ret[1] / r2;
         move_y_to_z(ret, yz);      
-        models::apply_orientation(ret[1], ret[0]);
         
         /*
   
@@ -1181,10 +1149,9 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         ret[1] = log(mod); */
         }
       else {
-        move_y_to_z(ret, yz);      
-        models::apply_orientation(ret[0], ret[1]);
+        move_y_to_z(ret, yz);
         }
-      models::apply_orientation_yz(ret[2], ret[1]);
+      models::apply_iori(ret);
   
       break;
       }
@@ -1193,14 +1160,14 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
     
       H = space_to_perspective(H);
 
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
   
       pair<long double, long double> p = polygonal::compute(H[0], H[1]);
   
-      models::apply_orientation(p.second, p.first);
       ret[0] = p.first;
       ret[1] = p.second;
       ret[2] = 0;
+      models::apply_iori(ret);
       break;
       }  
       
@@ -1211,7 +1178,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         
         H = space_to_perspective(H);
         
-        models::apply_orientation(H[0], H[1]);
+        models::apply_ori(H);
     
         H[0] += 1;
         double rad = H[0]*H[0] + H[1]*H[1];
@@ -1232,7 +1199,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
         ret[0] /= -(1-mt) * 90._deg;
         ret[1] /= (1-mt) * 90._deg;
         
-        models::apply_orientation(ret[1], ret[0]);
+        models::apply_iori(ret);
         }
       else 
         makeband(H_orig, ret, band_conformal);
@@ -1329,8 +1296,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
     
     case mdWerner: {
 
-      models::apply_orientation_yz(H[1], H[2]);
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
 
       find_zlev(H); // ignored for now
       
@@ -1344,8 +1310,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       ret[2] = 0;
       ret[3] = 1;
 
-      models::apply_orientation(ret[1], ret[0]);
-      models::apply_orientation_yz(ret[2], ret[1]);
+      models::apply_iori(ret);
       break;
       }
 
@@ -1417,7 +1382,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
     case mdRotatedHyperboles: {
       // ld zlev =  <- not implemented
       find_zlev(H); // + vid.depth;
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
       
       ld y = asin_auto(H[1]);
       ld x = asin_auto_clamp(H[0] / cos_auto(y));
@@ -1532,8 +1497,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
     
     case mdPanini: {
       find_zlev(H);
-      models::apply_orientation_yz(H[1], H[2]);
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
 
       ld proh = sqrt(H[2]*H[2] + curvature() * H[0] * H[0]);
       H /= proh;
@@ -1541,8 +1505,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       ret = H;
       ret[2] = 0; ret[3] = 1;
 
-      models::apply_orientation(ret[1], ret[0]);
-      models::apply_orientation_yz(ret[2], ret[1]);
+      models::apply_iori(ret);
       break;
       }
     
@@ -1550,8 +1513,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       find_zlev(H);
       H = space_to_perspective(H);
       
-      models::apply_orientation_yz(H[1], H[2]);
-      models::apply_orientation(H[0], H[1]);
+      models::apply_ori(H);
       
       ld u = H[0], v = H[1];
       if(abs(u) > 1e-3 && abs(v) > 1e-3) {
@@ -1564,8 +1526,7 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       ret[2] = 0;
       ret[3] = 1;
   
-      models::apply_orientation(ret[1], ret[0]);
-      models::apply_orientation_yz(ret[2], ret[1]);
+      models::apply_iori(ret);
       break;
       }
     
@@ -2264,11 +2225,11 @@ EX void centerpc(ld aspd) {
     }
 
   if(set_multi && multi::two_focus) {
-    pconf.model_orientation = atan2(multi_point) / degree;
+    pconf.mori() = spin( atan2(multi_point) );
     auto& d = pconf.twopoint_param;
     d = hdist0(multi_point);
     if(among(pmodel, mdJoukowsky, mdJoukowskyInverted)) {
-      pconf.model_orientation += 90;
+      pconf.mori() = pconf.mori() * spin90();
       pconf.model_transition = sinh(d) / (1 + cosh(d));
       pconf.dualfocus_autoscale = true;
       }
@@ -2603,8 +2564,7 @@ EX void draw_model_elements() {
           hyperpoint H = xpush(p * pconf.twopoint_param) * ypush0(h);
           
           hyperpoint res = compute_hybrid(H, 2 | mode);
-          models::apply_orientation(res[0], res[1]);
-          models::apply_orientation_yz(res[2], res[1]);
+          models::apply_iori(res);
           curvepoint(res * current_display->radius);
           }
         queuecurve(shiftless(Id), ringcolor, 0, PPR::CIRCLE);
@@ -2616,9 +2576,9 @@ EX void draw_model_elements() {
 
     case mdTwoPoint: case mdSimulatedPerspective: fallthrough: {
       if(set_multi) return; /* no need */
-      ld a = -pconf.model_orientation * degree;
-      put_x(shiftless(xspinpush(a, +pconf.twopoint_param)), ringcolor >> 8);
-      put_x(shiftless(xspinpush(a, -pconf.twopoint_param)), ringcolor >> 8);
+      auto T = rot_inverse(pconf.mori().get());
+      put_x(shiftless(T * xpush(+pconf.twopoint_param)), ringcolor >> 8);
+      put_x(shiftless(T * xpush(-pconf.twopoint_param)), ringcolor >> 8);
       return;
       }
     
@@ -2626,8 +2586,7 @@ EX void draw_model_elements() {
       vid.linewidth *= 5;
       for(int i=0; i<=3; i++) {
         hyperpoint h = xspinpush0(120._deg*i, pconf.twopoint_param);
-        models::apply_orientation(h[1], h[0]);
-        models::apply_orientation_yz(h[2], h[1]);
+        models::apply_iori(h);
         curvepoint(h);
         }
       
@@ -2773,7 +2732,7 @@ EX void draw_boundary(int w) {
         h[broken_coord] = -sin_auto(a*degree) * rem;
         h[0] = sin_auto(a*degree) * eps * s;
         h[unbroken_coord] = cos_auto(a*degree);
-        models::apply_orientation(h[1], h[0]);
+        models::apply_iori(h);
         curvepoint(h);
         }
       queuecurve(shiftless(Id), periodcolor, 0, PPR::CIRCLE).flags |= POLY_FORCEWIDE;
@@ -2793,13 +2752,14 @@ EX void draw_boundary(int w) {
         ld x = sin(a * pconf.twopoint_param * b / 90);
         ld y = 0;
         ld z = -sqrt(1 - x*x);
-        models::apply_orientation(y, x);
+        hyperpoint h0 = hpxyz(x, y, z);
+        models::apply_iori(h0);
         hyperpoint h1;
-        applymodel(shiftless(hpxyz(x,y,z)), h1);
+        applymodel(shiftless(h0), h1);
         
-        models::apply_orientation(h1[0], h1[1]);      
+        models::apply_ori(h1);
         h1[1] = abs(h1[1]) * b;
-        models::apply_orientation(h1[1], h1[0]);
+        models::apply_iori(h1);
         curvepoint(h1);
         }
   
@@ -2814,7 +2774,7 @@ EX void draw_boundary(int w) {
       if(GDIM == 3) return;
       if(pmodel == mdBand && pconf.model_transition != 1) return;
       bool bndband = (among(pmodel, mdBand, mdMiller, mdGallStereographic, mdCentralCyl) ? hyperbolic : sphere);
-      transmatrix T = spin(-pconf.model_orientation * degree);
+      transmatrix T = rot_inverse(pconf.mori().get());
       ld right = 90._deg - 1e-5;
       if(bndband) 
         queuestraight(T * ypush0(hyperbolic ? 10 : right), 2, lc, fc, p);
@@ -2840,7 +2800,8 @@ EX void draw_boundary(int w) {
     
     case mdHalfplane: 
       if(hyperbolic && GDIM == 2) {
-        queuestraight(xspinpush0(-pconf.model_orientation * degree - 90._deg, fakeinf), 1, lc, fc, p);
+        transmatrix Ori = rot_inverse(pconf.mori().get());
+        queuestraight(Ori * spin270() * xpush0(fakeinf), 1, lc, fc, p);
         return;
         }
       break;
@@ -2982,9 +2943,9 @@ EX void change_shift(shiftpoint& h, ld by) {
     tie(h[0], h[1]) = make_pair(h[0] * ca - h[1] * sa, h[1] * ca + h[0] * sa);
     }
   else if((mdinf[pmodel].flags & mf::uses_bandshift) || (sphere && pmodel == mdSpiral)) {
-    h.h = spin(pconf.model_orientation * degree) * h.h;
+    h.h = pconf.mori().get() * h.h;
     h.h = xpush(-by) * h.h;
-    h.h = spin(-pconf.model_orientation * degree) * h.h;
+    h.h = rot_inverse(pconf.mori().get()) * h.h;
     }
   }
 
@@ -2999,10 +2960,10 @@ EX void change_shift(shiftmatrix& T, ld by) {
       }
     }
   else if((mdinf[pmodel].flags & mf::uses_bandshift) || (sphere && pmodel == mdSpiral)) {
-    T.T = spin(pconf.model_orientation * degree) * T.T;
+    T.T = pconf.mori().get() * T.T;
     T.T = xpush(-by) * T.T;
     fixmatrix(T.T);
-    T.T = spin(-pconf.model_orientation * degree) * T.T;
+    T.T = rot_inverse(pconf.mori().get()) * T.T;
     }
   }
 
@@ -3045,7 +3006,7 @@ EX void optimize_shift(shiftmatrix& T) {
     }
 
   else if(((mdinf[pmodel].flags & mf::uses_bandshift) && T[LDIM][LDIM] > 30) || (sphere && pmodel == mdSpiral)) {
-    T.T = spin(pconf.model_orientation * degree) * T.T;
+    T.T = pconf.mori().get() * T.T;
     hyperpoint H = tC0(T.T);
     find_zlev(H);
     
@@ -3058,7 +3019,7 @@ EX void optimize_shift(shiftmatrix& T) {
     T.shift += x;
     T.T = xpush(-x) * T.T;
     fixmatrix(T.T);
-    T.T = spin(-pconf.model_orientation * degree) * T.T;
+    T.T = rot_inverse(pconf.mori().get()) * T.T;
     }
   }
 
@@ -3436,8 +3397,7 @@ EX hyperpoint lie_log(const shiftpoint h1) {
 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]);
+    models::apply_ori(H);
     return lie_log(shiftless(H));
     }
   return lie_log(H_orig);
diff --git a/menus.cpp b/menus.cpp
index 77da41f2..0832b9f8 100644
--- a/menus.cpp
+++ b/menus.cpp
@@ -953,7 +953,7 @@ EX void showStartMenu() {
       specialland = racing::race_lands[rand() % isize(racing::race_lands)];
       start_game();
       pmodel = mdBand;
-      pconf.model_orientation = racing::race_angle;
+      pconf.mori() = racing::race_angle;
       racing::race_advance = 1;
       vid.yshift = 0;
       pconf.camera_angle = 0;
diff --git a/models.cpp b/models.cpp
index e3068ae7..c44815c8 100644
--- a/models.cpp
+++ b/models.cpp
@@ -119,18 +119,15 @@ EX namespace models {
   EX ld rotation_xz = 90;
   EX ld rotation_xy2 = 90;
   EX int do_rotate = 1;
-  EX ld ocos, osin, ocos_yz, osin_yz;
   EX ld cos_ball, sin_ball;
   EX bool model_straight, model_straight_yz;
 
+  EX void apply_ori(hyperpoint& h) { if(!model_straight) h = pconf.mori().get() * h; }
+  EX void apply_iori(hyperpoint& h) { if(!model_straight) h = iso_inverse(pconf.mori().get()) * h; }
   #if HDR
-    // screen coordinates to logical coordinates: apply_orientation(x,y)
+  // screen coordinates to logical coordinates: apply_orientation(x,y)
   // logical coordinates back to screen coordinates: apply_orientation(y,x)
   template<class A>
-  void apply_orientation(A& x, A& y) { if(!model_straight) tie(x,y) = make_pair(x*ocos + y*osin, y*ocos - x*osin); }
-  template<class A>
-  void apply_orientation_yz(A& x, A& y) { if(!model_straight_yz) tie(x,y) = make_pair(x*ocos_yz + y*osin_yz, y*ocos_yz - x*osin_yz); }
-  template<class A>
   void apply_ball(A& x, A& y) { tie(x,y) = make_pair(x*cos_ball + y*sin_ball, y*cos_ball - x*sin_ball); }
   #endif
 
@@ -151,12 +148,8 @@ EX namespace models {
   EX void configure() {
     ld ball = -pconf.ballangle * degree;
     cos_ball = cos(ball), sin_ball = sin(ball);
-    ocos = cos(pconf.model_orientation * degree);
-    osin = sin(pconf.model_orientation * degree);
-    ocos_yz = cos(pconf.model_orientation_yz * degree);
-    osin_yz = sin(pconf.model_orientation_yz * degree);
-    model_straight = (ocos > 1 - 1e-9);
-    model_straight_yz = GDIM == 2 || (ocos_yz > 1-1e-9);
+    model_straight = (pconf.mori().get()[0][0] > 1 - 1e-9);
+    model_straight_yz = GDIM == 2 || (pconf.mori().get()[2][2] > 1-1e-9);
     if(history::on) history::apply();
     
     if(!euclid) {
@@ -474,7 +467,7 @@ EX namespace models {
       add_edit(vpconf.alpha);
       }
                                   
-    if(has_orientation(vpmodel)) {
+    /* TODO if(has_orientation(vpmodel)) {
       dialog::addSelItem(XLAT("model orientation"), fts(vpconf.model_orientation) + "°", 'l');
       dialog::add_action([] () {
         dialog::editNumber(vpconf.model_orientation, 0, 360, 90, 0, XLAT("model orientation"), "");
@@ -485,13 +478,13 @@ EX namespace models {
           dialog::editNumber(vpconf.model_orientation_yz, 0, 360, 90, 0, XLAT("model orientation (y/z plane)"), "");
           });
         }
-      }
+      } */
      
     if(among(vpmodel, mdPerspective, mdHorocyclic) && nil) {
-      dialog::addSelItem(XLAT("model orientation"), fts(vpconf.model_orientation) + "°", 'l');
+      /* TODO dialog::addSelItem(XLAT("model orientation"), fts(vpconf.model_orientation) + "°", 'l');
       dialog::add_action([] () {
         dialog::editNumber(vpconf.model_orientation, 0, 360, 90, 0, XLAT("model orientation"), "");
-        });
+        }); */
       dialog::addSelItem(XLAT("rotational or Heisenberg"), fts(vpconf.rotational_nil), 'L');
       dialog::add_action([] () {
         dialog::editNumber(vpconf.rotational_nil, 0, 1, 1, 1, XLAT("1 = Heisenberg, 0 = rotational"), "");
@@ -850,7 +843,7 @@ EX namespace models {
       }
     else if(argis("-mori")) { 
       PHASEFROM(2); 
-      shift_arg_formula(vpconf.model_orientation);
+      shift_arg_formula_matrix(vpconf.mori());
       }
     else if(argis("-mets")) { 
       PHASEFROM(2); 
@@ -868,11 +861,6 @@ EX namespace models {
       PHASEFROM(2); 
       shift_arg_formula(vpconf.rotational_nil);
       }
-    else if(argis("-mori2")) { 
-      PHASEFROM(2); 
-      shift_arg_formula(vpconf.model_orientation);
-      shift_arg_formula(vpconf.model_orientation_yz);
-      }
     else if(argis("-crot")) { 
       PHASEFROM(2); 
       shift_arg_formula(models::rotation);
@@ -987,8 +975,8 @@ EX namespace models {
       addsaverenum(p.model, pp+"used model", mdDisk);
       if(&p.model == &pmodel) param_custom(pmodel, "projection|Poincare|Klein|half-plane|perspective", menuitem_projection, '1');
 
-      param_f(p.model_orientation, pp+"mori", sp+"model orientation", 0);
-      param_f(p.model_orientation_yz, pp+"mori_yz", sp+"model orientation-yz", 0);
+      // TODO param_f(p.model_orientation, pp+"mori", sp+"model orientation", 0);
+      // TODO param_f(p.model_orientation_yz, pp+"mori_yz", sp+"model orientation-yz", 0);
 
       param_f(p.top_z, sp+"topz", 5)
       -> editable(1, 20, .25, "maximum z coordinate to show", "maximum z coordinate to show", 'l');       
diff --git a/racing.cpp b/racing.cpp
index 90ed0524..996703be 100644
--- a/racing.cpp
+++ b/racing.cpp
@@ -698,7 +698,7 @@ EX void reset_race() {
 
 bool inrec = false;
 
-EX ld race_angle = 90;
+EX trans23 race_angle = cspin90(0, 1);
 
 EX bool force_standard_centering() {
   return nonisotropic || mhybrid || quotient || closed_or_bounded;
@@ -793,7 +793,7 @@ EX bool set_view() {
     }
   if(GDIM == 3 && WDIM == 2)
     View = spin180() * cspin(2, 1, 90._deg + shmup::playerturny[multi::cpid]) * spin270() * View;
-  else if(GDIM == 2) View = spin(race_angle * degree) * View;
+  else if(GDIM == 2) View = race_angle.v2 * View;
   return true;
   }
 
@@ -846,7 +846,7 @@ auto hook =
     })
 + addHook(hooks_configfile, 100, [] {
     param_f(racing::race_advance, "race_advance");
-    param_f(racing::race_angle, "race_angle");
+    // TODO param_f(racing::race_angle, "race_angle");
     param_i(racing::ghosts_to_show, "race_ghosts_to_show");
     param_i(racing::ghosts_to_save, "race_ghosts_to_save");
     param_b(racing::guiding, "race_guiding");
@@ -982,7 +982,7 @@ void race_projection() {
   dialog::addBoolItem(XLAT("band"), pmodel == mdBand, '2');
   dialog::add_action([] () {
     pmodel = mdBand;
-    pconf.model_orientation = race_angle;
+    pconf.mori() = race_angle;
     race_advance = 1;
     vid.yshift = 0;
     pconf.camera_angle = 0;
@@ -996,7 +996,7 @@ void race_projection() {
   dialog::addBoolItem(XLAT("half-plane"), pmodel == mdHalfplane, '3');
   dialog::add_action([] () {
     pmodel = mdHalfplane;
-    pconf.model_orientation = race_angle + 90;
+    pconf.mori() = race_angle * spin90();
     race_advance = 0.5;
     vid.yshift = 0;
     pconf.camera_angle = 0;
@@ -1035,11 +1035,11 @@ void race_projection() {
   else dialog::addBreak(100);
         
   if(GDIM == 2) {
-    dialog::addSelItem(XLAT("race angle"), fts(race_angle), 'a');
+    // TODO dialog::addSelItem(XLAT("race angle"), fts(race_angle), 'a');
     dialog::add_action([] () { 
-      dialog::editNumber(race_angle, 0, 360, 15, 90, XLAT("race angle"), "");
-      int q = pconf.model_orientation - race_angle;
-      dialog::reaction = [q] () { pconf.model_orientation = race_angle + q; };
+      // TODO dialog::editNumber(race_angle, 0, 360, 15, 90, XLAT("race angle"), "");
+      auto q = rot_inverse(race_angle) * pconf.mori();
+      dialog::reaction = [q] () { pconf.mori() = race_angle * q; };
       });
     }
 
diff --git a/screenshot.cpp b/screenshot.cpp
index 64c85a33..e4aad960 100644
--- a/screenshot.cpp
+++ b/screenshot.cpp
@@ -1365,7 +1365,7 @@ EX void apply() {
 
   if(ballangle_rotation) {
     if(models::has_orientation(vpconf.model))
-      vpconf.model_orientation += ballangle_rotation * 360 * t / period;
+      vpconf.mori() = trans23(spin(ballangle_rotation * 360 * t / period)) * vpconf.mori();
     else
       vpconf.ballangle += ballangle_rotation * 360 * t / period;
     }
@@ -1925,7 +1925,7 @@ startanim null_animation { "", no_init, [] { gamescreen(); }};
 #if CAP_STARTANIM
 startanim joukowsky { "Joukowsky transform", no_init, [] {
   dynamicval<eModel> dm(pmodel, mdJoukowskyInverted);
-  dynamicval<ld> dt(pconf.model_orientation, ticks / 25.);
+  dynamicval<trans23> dt(pconf.mori(), spin( ticks / 25. ));
   dynamicval<int> dv(vid.use_smart_range, 2);
   dynamicval<ld> ds(pconf.scale, 1/4.);
   models::configure();
@@ -1936,7 +1936,7 @@ startanim joukowsky { "Joukowsky transform", no_init, [] {
 
 startanim bandspin { "spinning in the band model", no_init, [] {
   dynamicval<eModel> dm(pmodel, mdBand);
-  dynamicval<ld> dt(pconf.model_orientation, ticks / 25.);
+  dynamicval<trans23> dt(pconf.mori(), spin( ticks / 25. ));
   dynamicval<int> dv(vid.use_smart_range, 2);
   models::configure();
   gamescreen();
diff --git a/shaders.cpp b/shaders.cpp
index ab705ff0..19697cc1 100644
--- a/shaders.cpp
+++ b/shaders.cpp
@@ -56,10 +56,12 @@ EX map<unsigned, shared_ptr<glhr::GLprogram>> matched_programs;
 
 glhr::glmatrix model_orientation_gl() {
   glhr::glmatrix s = glhr::id;
-  for(int a=0; a<GDIM; a++)
-    models::apply_orientation(s[a][1], s[a][0]);
-  if(GDIM == 3) for(int a=0; a<GDIM; a++)
-    models::apply_orientation_yz(s[a][2], s[a][1]);
+  for(int a=0; a<GDIM; a++) {
+    hyperpoint row;
+    for(int b=0; b<4; b++) row[b] = s[a][b];
+    models::apply_iori(row);
+    for(int b=0; b<4; b++) s[a][b] = row[b];
+    }
   return s;
   }
 
@@ -769,8 +771,8 @@ void display_data::set_projection(int ed, ld shift) {
     }
 
   if(selected->uRotNil != -1) {
-    glUniform1f(selected->uRotCos, models::ocos);
-    glUniform1f(selected->uRotSin, models::osin);
+    glUniform1f(selected->uRotCos, pconf.mori().get()[0][0]);
+    glUniform1f(selected->uRotSin, pconf.mori().get()[1][0]);
     glUniform1f(selected->uRotNil, pconf.rotational_nil);
     }
 
@@ -786,10 +788,12 @@ void display_data::set_projection(int ed, ld shift) {
       pp = glhr::tmtogl_transpose(NLP) * pp;
 
     if(get_shader_flags() & SF_ORIENT) {
-      if(GDIM == 3) for(int a=0; a<4; a++) 
-        models::apply_orientation_yz(pp[a][1], pp[a][2]);
-      for(int a=0; a<4; a++) 
-        models::apply_orientation(pp[a][0], pp[a][1]);
+      for(int a=0; a<4; a++)  {
+        hyperpoint row;
+        for(int b=0; b<4; b++) row[b] = pp[a][b];
+        models::apply_ori(row);
+        for(int b=0; b<4; b++) pp[a][b] = row[b];
+        }
       }
     
     glUniformMatrix4fv(selected->uPP, 1, 0, pp.as_array());
diff --git a/util.cpp b/util.cpp
index f9ec73fa..22ad46be 100644
--- a/util.cpp
+++ b/util.cpp
@@ -129,6 +129,8 @@ struct exp_parser {
 
   cld parse(int prio = 0);
 
+  transmatrix parsematrix(int prio = 0);
+
   ld rparse(int prio = 0) { return validate_real(parse(prio)); }
   int iparse(int prio = 0) { return int(floor(rparse(prio) + .5)); }
 
@@ -470,12 +472,80 @@ cld exp_parser::parse(int prio) {
   return res;
   }
 
+int coord_id(char ch) {
+  if(ch == 'x') return 0;
+  if(ch == 'y') return 1;
+  if(ch == 'z') return 2;
+  if(ch == 'w') return 3;
+  if(ch == 't') return MDIM-1;
+  return -1;
+  }
+
+ld angle_unit(char ch) {
+  if(ch == 'r') return 1;
+  if(ch == 'd') return degree;
+  if(ch == 't') return TAU;
+  if(ch == 'l') return -1;
+  return 0;
+  }
+
+transmatrix exp_parser::parsematrix(int prio) {
+  skip_white();
+  if(s[at] && s[at+1] && s[at+2] && s[at+3] == '(') {
+    ld unit = angle_unit(s[at]);
+    int c0 = coord_id(s[at+1]);
+    int c1 = coord_id(s[at+2]);
+    if(c0 >= 0 && c1 >= 0 && c0 != c1 && unit) {
+      at += 4;
+      ld angle = validate_real(parsepar());
+      if(unit == -1) return lorentz(c0, c1, angle);
+      else return cspin(c0, c1, angle);
+      }
+    }
+  transmatrix res;
+  if(next() == '(') {
+    at++;
+    res = parsematrix(); 
+    force_eat(")");
+    }
+  else {
+    string token = next_token();
+    if(token == "id") res = Id;
+    else if(token == "view") res = View;
+    else throw hr_parse_exception("unknown matrix: " + token);
+    }
+  while(true) {
+    skip_white();
+    if(next() == '*' && prio <= 20) at++, res = res * parsematrix(30);
+    }
+  return res;
+  }
+
 EX ld parseld(const string& s) {
   exp_parser ep;
   ep.s = s;
   return ep.rparse();
   }
 
+EX transmatrix parsematrix(const string& s) {
+  exp_parser ep;
+  ep.s = s;
+  return ep.parsematrix();
+  }
+
+EX trans23 parsematrix23(const string& s) {
+  trans23 t;
+  #if MAXMDIM == 3
+  t.v2 = t.v3 = parsematrix(s);
+  #else
+  auto& dim = cginf.g.homogeneous_dimension;
+  dynamicval<int> d1(dim, dim);
+  dim = 3; t.v2 = parsematrix(s);
+  dim = 4; t.v3 = parsematrix(s);
+  #endif
+  return t;
+  }
+
 EX int parseint(const string& s) {
   exp_parser ep;
   ep.s = s;