Excellent!  Something to bite into, rather than vague generalities...  Examples are
good.

I generated mutually exclusive regions with cgi.

========================================================
global_settings {max_trace_level 255}

camera {
   perspective
   location  <-6, 2, -10> // change x to 0 or +6
   look_at   <0, 1.3,  0>
   right     x*image_width/image_height
   angle 18
}

light_source {
   <0, 0, 0>
   color rgb <1, 1, 1>
   translate <-30, 30, -30>
              }


sky_sphere {
    pigment {
       radial
       frequency 100
       color_map{
        [0.0 rgb 0]
        [0.5 rgb 0]
        [0.5 rgb 1]
        [1.0 rgb 1]
       }
     }
   }

plane {
   y, 0
   pigment { checker
        rgb 1
        rgb 1.5
      }
    }

#declare pigment_1 =
     pigment{ color rgbf <.5,.5,1,1> }

#declare pigment_2 =
     pigment{ color rgbf <1,.5,.5,1> }

#declare ior_1 = 1.3;
#declare ior_2 = 1.0;

#declare r1 = <-.4,1.3,0>;
#declare r2 = <.4,1.3,0>;

#declare sphere_1 =
sphere{
   0,1
   translate r1
}

#declare sphere_2 =
sphere{
   0,1
   translate r2
}

#declare region_1 =
   difference {
     object { sphere_1 }
     object { sphere_2 }
     texture { pigment { pigment_1 } }
     interior { ior ior_1 }
   }

#declare region_2 =
   difference {
     object { sphere_2 }
     object { sphere_1 }
     texture { pigment { pigment_2 } }
     interior { ior ior_2 }
   }

#declare region_12 =
   intersection {
     object { sphere_1 }
     object { sphere_2 }
     texture {
       pigment {
	average
	pigment_map {
	  [0.5 pigment_1]
	  [0.5 pigment_2]
	}
       }
     }
     interior {
       ior ior_1 + ior_2
     }
   }

// consider two options: 1 and 2
#declare option = 1;
#if (option = 1)
   union {
     object { region_1 }
     object { region_2 }
     object { region_12 }
   }
#end
#if (option = 2)
   merge {
     object { region_1 translate -r1 scale 1.0001 translate r1}
     object { region_2 translate -r2 scale 1.0001 translate r2}
     object { region_12 scale 1.0001 }
   }
#end

============================================================

These two cases give much different results.

Dan

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