diff --git a/app-proto/inversive-display/src/inversive.frag b/app-proto/inversive-display/src/inversive.frag
index a4cbe8d..12b4129 100644
--- a/app-proto/inversive-display/src/inversive.frag
+++ b/app-proto/inversive-display/src/inversive.frag
@@ -121,29 +121,31 @@ vec2 sphere_cast(vecInv v, vec3 dir) {
 }
 
 void main() {
+    const int sphere_cnt = 2;
+    
     vec2 scr = (2.*gl_FragCoord.xy - resolution) / shortdim;
     vec3 dir = vec3(focal_slope * scr, -1.);
     
     // initialize two spheres
-    vecInv v [2];
-    v[0] = sphere(vec3(0.5, 0.5, -5. + ctrl.x), radius.x);
-    v[1] = sphere(vec3(-0.5, -0.5, -5. + ctrl.y), radius.y);
-    vec3 color0 = vec3(1., 0.214, 0.);
-    vec3 color1 = vec3(0., 0.214, 1.);
+    vecInv sphere_list [sphere_cnt];
+    sphere_list[0] = sphere(vec3(0.5, 0.5, -5. + ctrl.x), radius.x);
+    sphere_list[1] = sphere(vec3(-0.5, -0.5, -5. + ctrl.y), radius.y);
+    vec3 color_list [sphere_cnt];
+    color_list[0] = vec3(1., 0.214, 0.);
+    color_list[1] = vec3(0., 0.214, 1.);
     
     // cast rays through the spheres
-    vec2 u0 = sphere_cast(v[0], dir);
-    vec2 u1 = sphere_cast(v[1], dir);
+    vec2 depth_pairs [sphere_cnt];
+    taggedFrag frags [2*sphere_cnt];
+    for (int i = 0; i < sphere_cnt; i++) {
+        vec2 hit_depths = sphere_cast(sphere_list[i], dir);
+        frags[2*i] = sphere_shading(sphere_list[i], hit_depths[0] * dir, color_list[i], i);
+        frags[2*i+1] = sphere_shading(sphere_list[i], hit_depths[1] * dir, color_list[i], i);
+    }
     
     // shade and depth-sort the impact points
-    taggedFrag front_hits[2] = sort(
-        sphere_shading(v[0], u0[0] * dir, color0, 0),
-        sphere_shading(v[1], u1[0] * dir, color1, 1)
-    );
-    taggedFrag back_hits[2] = sort(
-        sphere_shading(v[0], u0[1] * dir, color0, 0),
-        sphere_shading(v[1], u1[1] * dir, color1, 1)
-    );
+    taggedFrag front_hits[2] = sort(frags[0], frags[2]);
+    taggedFrag back_hits[2] = sort(frags[1], frags[3]);
     taggedFrag middle_frags[2] = sort(front_hits[1], back_hits[0]);
     
     // finish depth sorting
@@ -170,7 +172,7 @@ void main() {
         
         // cusps
         float cusp_cos = abs(dot(dir, frag0.normal));
-        float cusp_threshold = 2.*sqrt(ixn_threshold * v[frag0.id].lt.s);
+        float cusp_threshold = 2.*sqrt(ixn_threshold * sphere_list[frag0.id].lt.s);
         float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
         frags_by_depth[i].color = mix(frags_by_depth[i].color, vec4(1.), cusp_highlight);
     }