Get Ganja.js to display planes

engine-proto/ConstructionViewer.jl

@@ -123,12 +123,24 @@ mutable struct ConstructionViewer
   end
 end
 
+mprod(v, w) =
+  v[1]*w[1] + v[2]*w[2] + v[3]*w[3] + v[4]*w[4] - v[5]*w[5]
+
 function display!(viewer::ConstructionViewer, elements::Matrix)
   # load elements
-  elements_full = [
-    [0; elt; fill(0, 26)]
-    for elt in eachcol(elements)
-  ]
+  elements_full = []
+  for elt in eachcol(elements)
+    if mprod(elt, elt) < 0.5
+      elt_full = [0; elt; fill(0, 26)]
+    else
+      # `elt` is a spacelike vector, representing a generalized sphere, so we
+      # take its Hodge dual before passing it to Ganja.js. the dual represents
+      # the same generalized sphere, but Ganja.js only displays planes when
+      # they're represented by vectors in grade 4 rather than grade 1
+      elt_full = [fill(0, 26); -elt[5]; -elt[4]; elt[3]; -elt[2]; elt[1]; 0]
+    end
+    push!(elements_full, elt_full)
+  end
   @js viewer.win elements = $elements_full.map((elt) -> @new CGA3(elt))
   
   # generate palette. this is Gadfly's `default_discrete_colors` palette,