Revert "Give spheres positive radii in examples"

This reverts commit 4728959ae0, which
actually gave the spheres negative radii! I got confused by the sign
convention differences between the notes and the engine.

engine-proto/ConstructionViewer.jl

@@ -213,8 +213,8 @@ elements = begin
     1    1   -1   -1    0
     1   -1    1   -1    0
     1   -1   -1    1    0
-    0.5  0.5  0.5  0.5  a+1
-   -0.5 -0.5 -0.5 -0.5  a-1
+   -0.5 -0.5 -0.5 -0.5 -a-1
+    0.5  0.5  0.5  0.5 -a+1
   ]
 end
 

engine-proto/gram-test/overlapping-pyramids.jl

@@ -23,7 +23,13 @@ end
 gram = sparse(J, K, values)
 
 # set the independent variable
-indep_val = 2//5
+#
+# using gram[6, 2] or gram[7, 1] as the independent variable seems to stall
+# convergence, even if its value comes from a known solution, like
+#
+#   gram[6, 2] = 0.9936131705272925
+#
+indep_val = -9//5
 gram[6, 1] = BigFloat(indep_val)
 gram[1, 6] = gram[6, 1]
 
@@ -37,8 +43,8 @@ guess = begin
       1    1   -1   -1    0
       1   -1    1   -1    0
       1   -1   -1    1    0
-      0.5  0.5  0.5  0.5  a+1
-     -0.5 -0.5 -0.5 -0.5  a-1
+     -0.5 -0.5 -0.5 -0.5 -a-1
+      0.5  0.5  0.5  0.5 -a+1
     ] + 0.2*Engine.rand_on_shell(fill(BigFloat(-1), 5)),
     Engine.rand_on_shell(fill(BigFloat(-1), 2))
   )

engine-proto/gram-test/sphere-in-tetrahedron.jl

@@ -28,7 +28,7 @@ for j in 1:6
       push!(values, -1/BigFloat(3))
       filled = true
     else
-      push!(values, 1)
+      push!(values, -1)
       filled = true
     end
     if filled
@@ -46,8 +46,8 @@ guess = hcat(
     1  1 -1 -1  0
     1 -1  1 -1  0
     1 -1 -1  1  0
-    0  0  0  0  1.5
-    1  1  1  1  0.5
+    0  0  0  0 -1.5
+    1  1  1  1 -0.5
   ] + 0.2*Engine.rand_on_shell(fill(BigFloat(-1), 5)),
   BigFloat[0, 0, 0, 0, 1]
 )