diff --git a/embeddings.cpp b/embeddings.cpp
index 1290e363..7797bda9 100644
--- a/embeddings.cpp
+++ b/embeddings.cpp
@@ -500,21 +500,17 @@ struct emb_euc_in_product : emb_euclid_noniso {
 
 struct emb_euc_in_sl2 : emb_euclid_noniso {
 
-  /** used in esl2_ita */
-  EX transmatrix esl2_zpush(ld z) { return cspin(2, 3, z) * cspin(0, 1, z); }
+  transmatrix esl2_zpush(ld z) { return cspin(2, 3, z) * cspin(0, 1, z); }
 
-  /** see esl2_ita; equal to esl2_ita * C0 */
-  EX hyperpoint esl2_ita0(hyperpoint h1) {
-    return esl2_zpush(h1[2]) * xpush(h1[0]) * ypush0(h1[1]);
+  hyperpoint intermediate_to_actual(hyperpoint i) override {
+    return esl2_zpush(i[2]) * xpush(i[0]) * ypush0(i[1]);
     }
 
-  /** in embedded-in-sl2, convert from intermediate to actual coordinates */
-  EX transmatrix esl2_ita(hyperpoint h1) {
-    return esl2_zpush(h1[2]) * xpush(h1[0]) * ypush(h1[1]);
+  transmatrix intermediate_to_actual_translation(hyperpoint i) override {
+    return esl2_zpush(i[2]) * xpush(i[0]) * ypush(i[1]);
     }
 
-  /** in embedded-in-sl2, convert from actual to intermediate coordinates */
-  EX hyperpoint esl2_ati(hyperpoint h) {
+  hyperpoint actual_to_intermediate(hyperpoint h) override {
     ld a1 = (h[0] * h[3] - h[1] * h[2]) / (-h[2] * h[2] - h[1] * h[1] -h[0] * h[0] - h[3] * h[3]);
     // a1 is S*sqrt(1+S*S) / (1+2*S*S), where S = sinh(-x) and C = cosh(-x); U is S*S
     ld a = a1 * a1;
@@ -532,20 +528,6 @@ struct emb_euc_in_sl2 : emb_euclid_noniso {
   bool is_euc_in_sl2() override { return true; }
   bool no_spin() override { return true; }
   transmatrix get_lsti() override { return cspin90(2, 1); }
-  hyperpoint actual_to_intermediate(hyperpoint a) override { return esl2_ati(a); }
-  transmatrix intermediate_to_actual_translation(hyperpoint i) override { return esl2_zpush(i[2]) * xpush(i[0]) * ypush(i[1]); }
-
-  ld get_logical_z(hyperpoint a) override { return esl2_ati(a)[1]; }
-  hyperpoint orthogonal_move(const hyperpoint& a, ld z) override {
-    hyperpoint h1 = esl2_ati(a);
-    h1[1] += z;
-    return esl2_ita0(h1);
-    }
-  hyperpoint flatten(hyperpoint h) {
-    hyperpoint h1 = esl2_ati(h);
-    h1[1] = 0;
-    return esl2_ita0(h1);
-    }
   };
 
 /* for both seCylinderH and seCylinderE. Possibly actually works for CliffordTorus too */
diff --git a/hypgraph.cpp b/hypgraph.cpp
index 448ded00..3c72cf41 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -3306,7 +3306,7 @@ EX void shift_v_by_vector(transmatrix& V, const hyperpoint H, eShiftMethod sm IS
       V = iview_inverse(nisot::parallel_transport(view_inverse(V), -H));
       return;
     case smESL2: {
-      hyperpoint H1 = esl2_ita0(lp_iapply(-H));
+      hyperpoint H1 = cgi.emb->intermediate_to_actual(lp_iapply(-H));
       transmatrix IV = view_inverse(V);
       transmatrix rot = V * cgi.emb->map_relative_push(IV * C0);
       transmatrix V1 = gpushxto0(H1) * gpushxto0(IV*C0);
@@ -3376,7 +3376,7 @@ EX void shift_v_to(transmatrix& V, shiftpoint H, eShiftMethod sm IS(shift_method
     case smProduct:
       return shift_v_by_matrix(V, gpushxto0(unshift(H)), sm);
     case smESL2:
-      return shift_v_by_vector(V, -lp_apply(esl2_ati(lp_iapply(unshift(H)))), sm);
+      return shift_v_by_vector(V, -lp_apply(cgi.emb->actual_to_intermediate(lp_iapply(unshift(H)))), sm);
     case smLie:
       return shift_v_by_vector(V, -lie_log(H), sm);
       return;
@@ -3398,7 +3398,7 @@ EX void shift_v_towards(transmatrix& V, shiftpoint H, ld l, eShiftMethod sm IS(s
     case smEmbedded:
       return shift_v_by_matrix(V, rspintox(unshift(H)) * xpush(-l) * spintox(unshift(H)), sm);
     case smESL2:
-      return shift_v_by_vector(V, -lp_apply(tangent_length(esl2_ati(lp_iapply(unshift(H))), l)), sm);
+      return shift_v_by_vector(V, -lp_apply(tangent_length(cgi.emb->actual_to_intermediate(lp_iapply(unshift(H))), l)), sm);
     case smLie:
       return shift_v_by_vector(V, tangent_length(lie_log(H), -l), sm);
     case smGeodesic:
diff --git a/radar.cpp b/radar.cpp
index 5b5613a9..98599cf3 100644
--- a/radar.cpp
+++ b/radar.cpp
@@ -73,7 +73,7 @@ pair<bool, hyperpoint> makeradar(shiftpoint h) {
       if(d) h1 = h1 / (vid.radarrange + cgi.scalefactor/4);
       }
     else if(cgi.emb->is_euc_in_sl2()) {
-      h1 = cgi.emb->intermediate_to_logical * esl2_ati(unshift(h)); h1[1] = -h1[1];
+      h1 = cgi.emb->intermediate_to_logical * cgi.emb->actual_to_intermediate(unshift(h)); h1[1] = -h1[1];
       d = hypot_d(2, h1);
       if(d > vid.radarrange) return {false, h1};
       if(d) h1 = h1 / (vid.radarrange + cgi.scalefactor/4);