Go back to the "simplified" determinant formula in an attempt to avoid overflows.

[spline3.git] / src / Tetrahedron.hs

diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index e84b09103d7ad1bb850bed4b9380aeb47d6bb3b3..a7b4047398d5a12d5102618c03aad60bddbcd0d6 100644 (file)
--- a/src/Tetrahedron.hs
+++ b/src/Tetrahedron.hs
@@ -281,21 +281,35 @@ c _ _ _ _ _ = error "coefficient index out of bounds"
 
 
 
+-- | Compute the determinant of the 4x4 matrix,
+--
+--   [1]
+--   [x]
+--   [y]
+--   [z]
+--
+--   where [1] = [1, 1, 1, 1],
+--         [x] = [x1,x2,x3,x4],
+--
+--   et cetera.
+--
+--   The termX nonsense is an attempt to prevent Double overflow.
+--   which has been observed to happen with large coordinates.
+--
 det :: Point -> Point -> Point -> Point -> Double
 det p0 p1 p2 p3 =
---  Both of these results are just copy/pasted from Sage. One of them
---  might be more numerically stable, faster, or both.
---
---  x1*y2*z4 - x1*y2*z3 + x1*y3*z2 - x1*y3*z4 - x1*y4*z2 + x1*y4*z3 +
---  x2*y1*z3 - x2*y1*z4 - x2*y3*z1 + x2*y3*z4 +
---  x2*y4*z1 - x2*y4*z3 - x3*y1*z2 + x3*y1*z4 + x3*y2*z1 - x3*y2*z4 - x3*y4*z1 +
---  x3*y4*z2 + x4*y1*z2 - x4*y1*z3 - x4*y2*z1 + x4*y2*z3 + x4*y3*z1 - x4*y3*z2
-  -((x2 - x3)*y1 - (x1 - x3)*y2 + (x1 - x2)*y3)*z4 + ((x2 - x4)*y1 - (x1 - x4)*y2 + (x1 - x2)*y4)*z3 + ((x3 - x4)*y2 - (x2 - x4)*y3 + (x2 - x3)*y4)*z1 - ((x3 - x4)*y1 - (x1 - x4)*y3 + (x1 - x3)*y4)*z2
+  term5 + term6
   where
     (x1, y1, z1) = p0
     (x2, y2, z2) = p1
     (x3, y3, z3) = p2
     (x4, y4, z4) = p3
+    term1 = ((x2 - x4)*y1 - (x1 - x4)*y2 + (x1 - x2)*y4)*z3
+    term2 = ((x2 - x3)*y1 - (x1 - x3)*y2 + (x1 - x2)*y3)*z4
+    term3 = ((x3 - x4)*y2 - (x2 - x4)*y3 + (x2 - x3)*y4)*z1
+    term4 = ((x3 - x4)*y1 - (x1 - x4)*y3 + (x1 - x3)*y4)*z2
+    term5 = term1 - term2
+    term6 = term3 - term4
 
 
 -- | Computed using the formula from Lai & Schumaker, Definition 15.4,