diff --git a/celldrawer.cpp b/celldrawer.cpp
index 562457d1..f61e71fc 100644
--- a/celldrawer.cpp
+++ b/celldrawer.cpp
@@ -1861,7 +1861,7 @@ void celldrawer::draw_features_and_walls_3d() {
             case 6: case 7: if (pmodel == mdPerspective && V[2][LDIM] <= -l) continue; break;
             }
           }
-        else if(mproduct) {
+        else if(mproduct && !models::conformal_product_model()) {
           if(a < c->type-2 && !in_s2xe()) {
             ld d = in_e2xe() ? sqhypot_d(2, unshift(tC0(V))) : V[2][2];
             hyperpoint h = (unshift(V) * cgi.walltester[ofs + a]);
diff --git a/classes.cpp b/classes.cpp
index c6b1bf53..ba87f453 100644
--- a/classes.cpp
+++ b/classes.cpp
@@ -1045,8 +1045,8 @@ enum eModel : int {
 
 /** list of available models (i.e., projections) */
 EX vector<modelinfo> mdinf = {
-  {"disk/Gans", "general perspective", "general perspective", mf::azimuthal | mf::conformal},
-  {"half-plane", "inversion", "stereographic projection [VR]", mf::conformal | mf::orientation | mf::horocyclic},
+  {"disk/Gans", "general perspective", "general perspective", mf::azimuthal | mf::conformal | mf::product_special},
+  {"half-plane", "inversion", "stereographic projection [VR]", mf::conformal | mf::orientation | mf::horocyclic | mf::product_special},
   {"band", "band", "Mercator", mf::band | mf::conformal | mf::transition},
   {X3("polygonal"), mf::conformal | mf::orientation},
   {X3("formula"), 0},
diff --git a/hypgraph.cpp b/hypgraph.cpp
index 2cb8b34e..2e4b9f7e 100644
--- a/hypgraph.cpp
+++ b/hypgraph.cpp
@@ -609,6 +609,31 @@ EX hyperpoint hyperboloid_form(hyperpoint ret) {
   return ret;
   }
 
+EX void product_projection(hyperpoint H, hyperpoint& ret, eModel proj) {
+  ld zlev = zlevel(H);
+  H /= exp(zlev);
+  H = space_to_perspective(H);
+  H[1] += 1;
+  double rad = sqhypot_d(2, H);
+  H /= rad;
+  H[1] -= 0.5;
+  H[1] = -H[1];
+  H[2] = 0; H[3] = 1; ret = H;
+  tie(H[1], H[2]) = make_pair( H[1] * cos(zlev), H[1] * sin(zlev) );
+
+  if(proj == mdDisk) {
+    H[1] = -H[1];
+    H[1] += 0.5;
+    rad = sqhypot_d(3, H);
+    H[0] /= rad; H[1] /= rad; H[2] /= rad;
+    H[1] -= 1;
+    }
+
+  H[3] = 1;
+
+  ret = NLP * H;
+  }
+
 EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
 
   hyperpoint H = H_orig.h;
@@ -687,6 +712,10 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       }
     
     case mdDisk: {
+      if(mproduct && pconf.alpha == 1) {
+        product_projection(H, ret, mdDisk);
+        break;
+        }
       if(nonisotropic) {
         ret = lp_apply(inverse_exp(H_orig, pNORMAL | pfNO_DISTANCE));
         ld w;
@@ -740,6 +769,10 @@ EX void apply_other_model(shiftpoint H_orig, hyperpoint& ret, eModel md) {
       }
     
     case mdHalfplane: {
+      if(mproduct) {
+        product_projection(H, ret, mdHalfplane);
+        break;
+        }
       if(sphere && vrhr::rendering()) {
         vr_sphere(ret, H, md);
         return;
@@ -3280,6 +3313,12 @@ EX bool do_draw(cell *c, const shiftmatrix& T) {
   if(h) return h > 0;
 
   if(WDIM == 3) {
+
+    if(models::conformal_product_model()) {
+      ld z = zlevel(T.T * C0);
+      if(z > M_PI + 0.01 || z <= 0.01 - M_PI) return false;
+      }
+
     // do not care about cells outside of the track
     if(GDIM == 3 && racing::on && c->land == laMemory && cells_drawn >= S7+1) return false;
 
diff --git a/models.cpp b/models.cpp
index 29dd0352..9d4c4716 100644
--- a/models.cpp
+++ b/models.cpp
@@ -267,10 +267,16 @@ EX namespace models {
   
   EX bool product_model(eModel m) {
     if(!gproduct) return false;
-    if(mdinf[m].flags & mf::product_special) return false;
+    if(mdinf[m].flags & mf::product_special && !(pmodel == mdDisk && pconf.alpha != 1)) return false;
     return true;
     }
   
+  EX bool conformal_product_model() {
+    if(!in_h2xe()) return false;
+    if(pmodel == mdDisk && pconf.alpha == 1) return true;
+    return pmodel == mdHalfplane;
+    }
+
   int editpos = 0;
   
   EX string get_model_name(eModel m) {