From e6cf08a9b3535bbb2c2b364f669e76534a123dce Mon Sep 17 00:00:00 2001
From: Aaron Fenyes <aaron.fenyes@fareycircles.ooo>
Date: Mon, 15 Jul 2024 23:54:59 -0700
Subject: [PATCH] Make tetrahedron faces planar

---
 .../gram-test/sphere-in-tetrahedron.jl        | 46 +++++++++++++------
 1 file changed, 33 insertions(+), 13 deletions(-)

diff --git a/engine-proto/gram-test/sphere-in-tetrahedron.jl b/engine-proto/gram-test/sphere-in-tetrahedron.jl
index 273d3ad..1d02d45 100644
--- a/engine-proto/gram-test/sphere-in-tetrahedron.jl
+++ b/engine-proto/gram-test/sphere-in-tetrahedron.jl
@@ -8,16 +8,32 @@ using Random
 J = Int64[]
 K = Int64[]
 values = BigFloat[]
-for j in 1:5
-  for k in 1:5
-    push!(J, j)
-    push!(K, k)
-    if j == k
+for j in 1:6
+  for k in 1:6
+    filled = false
+    if j == 6
+      if k <= 4
+        push!(values, 0)
+        filled = true
+      end
+    elseif k == 6
+      if j <= 4
+        push!(values, 0)
+        filled = true
+      end
+    elseif j == k
       push!(values, 1)
+      filled = true
     elseif (j <= 4 && k <= 4)
       push!(values, -1/BigFloat(3))
+      filled = true
     else
       push!(values, -1)
+      filled = true
+    end
+    if filled
+      push!(J, j)
+      push!(K, k)
     end
   end
 end
@@ -25,19 +41,23 @@ gram = sparse(J, K, values)
 
 # set initial guess
 Random.seed!(99230)
-guess = sqrt(1/BigFloat(3)) * BigFloat[
-  1  1 -1 -1  0
-  1 -1  1 -1  0
-  1 -1 -1  1  0
-  1  1  1  1 -2
-  1  1  1  1  1
-] + 0.2*Engine.rand_on_shell(fill(BigFloat(-1), 5))
+guess = hcat(
+  sqrt(1/BigFloat(3)) * BigFloat[
+    1  1 -1 -1  0
+    1 -1  1 -1  0
+    1 -1 -1  1  0
+    1  1  1  1 -2
+    1  1  1  1  1
+  ] + 0.2*Engine.rand_on_shell(fill(BigFloat(-1), 5)),
+  BigFloat[0, 0, 0, 1, 1]
+)
+frozen = [CartesianIndex(j, 6) for j in 1:5]
 
 # complete the gram matrix
 #=
 L, history = Engine.realize_gram_newton(gram, guess)
 =#
-L, success, history = Engine.realize_gram(gram, guess)
+L, success, history = Engine.realize_gram(gram, guess, frozen)
 completed_gram = L'*Engine.Q*L
 println("Completed Gram matrix:\n")
 display(completed_gram)