diff --git a/geom-exp.cpp b/geom-exp.cpp
index 2767e939..783068c9 100644
--- a/geom-exp.cpp
+++ b/geom-exp.cpp
@@ -279,8 +279,12 @@ void set_or_configure_geometry(eGeometry g) {
   #endif
   else {
     if(among(g, gProduct, gRotSpace)) {
-      if(WDIM == 3 || euclid) {
-        addMessage(XLAT("Only works with 2D non-Euclidean geometries"));
+      if(WDIM == 3 || (g == gRotSpace && euclid)) {
+        addMessage(XLAT(          
+          g == gRotSpace ?
+            "Only works with 2D non-Euclidean geometries"
+          : "Only works with 2D geometries"
+            ));
         return;
         }
       if(g == gRotSpace) {
diff --git a/hyperpoint.cpp b/hyperpoint.cpp
index 780afb84..384253fe 100644
--- a/hyperpoint.cpp
+++ b/hyperpoint.cpp
@@ -373,6 +373,7 @@ EX ld zlevel(const hyperpoint &h) {
   if(sl2) return sqrt(-intval(h, Hypc));
   else if(translatable) return h[LDIM];
   else if(sphere) return sqrt(intval(h, Hypc));
+  else if(in_e2xe()) return log(h[2]);
   else if(prod) return log(sqrt(abs(intval(h, Hypc)))); /* abs works with both underlying spherical and hyperbolic */
   else return (h[LDIM] < 0 ? -1 : 1) * sqrt(-intval(h, Hypc));
   }
diff --git a/nonisotropic.cpp b/nonisotropic.cpp
index 65e52bb9..a8531aea 100644
--- a/nonisotropic.cpp
+++ b/nonisotropic.cpp
@@ -1226,15 +1226,17 @@ EX namespace product {
     cell *c = cw.at;
     if(sphere) gmatrix[c] = V; /* some computations need gmatrix0 for underlying geometry */
     bool s = sphere || pmodel != mdPerspective;
+    bool euc = euclid;
     hybrid::in_actual([&] { 
       cell *c0 = hybrid::get_at(c, z0);
       cwall_offset = hybrid::wall_offset(c0);
       if(s) cwall_mask = (1<<c->type) - 1;
       else {
         cwall_mask = 0;
-        ld d = V[2][2];
+        ld d = euc ? sqhypot_d(2, tC0(V)) : V[2][2];
         for(int i=0; i<c->type; i++) {
-          ld d1 = (V * cgi.walltester[cwall_offset + i])[2];
+          hyperpoint h = (V * cgi.walltester[cwall_offset + i]);
+          ld d1 = euc ? sqhypot_d(2, h) : h[2];
           if(d1 < d - 1e-6) cwall_mask |= (1<<i);
           }
         }
@@ -1256,7 +1258,11 @@ EX namespace product {
     res[2] = zlevel(h);
     h = zshift(h, -res[2]);
     ld r = hypot_d(2, h);
-    if(r < 1e-6) {
+    if(hybrid::under_class() == gcEuclid) {
+      res[0] = h[0];
+      res[1] = h[1];
+      }
+    else if(r < 1e-6) {
       res[0] = h[0];
       res[1] = h[1];
       }
diff --git a/shaders.cpp b/shaders.cpp
index d641c868..5db62b30 100644
--- a/shaders.cpp
+++ b/shaders.cpp
@@ -209,6 +209,14 @@ shared_ptr<glhr::GLprogram> write_shader(flagtype shader_flags) {
     distfun = "sqrt(z*z+d*d)";
     treset = true;
     }
+  else if(in_e2xe() && pmodel == mdPerspective) {
+    shader_flags |= SF_PERS3 | SF_DIRECT;
+    coordinator +=      
+      "t.xy /= t.z;\n"
+      "t.z = log(t.z);\n";
+    distfun = "length(t.xyz)";
+    treset = true;
+    }
   else if(in_s2xe() && pmodel == mdPerspective) {
     shader_flags |= SF_PERS3 | SF_DIRECT;
     distfun = "length(t.xyz)", treset = true;