--- | The matrix used in the tetrahedron volume calculation as given in
--- Lai & Schumaker, Definition 15.4, page 436.
-vol_matrix :: Tetrahedron -> Matrix Double
-vol_matrix t = (4><4)
- [1, 1, 1, 1,
- x1, x2, x3, x4,
- y1, y2, y3, y4,
- z1, z2, z3, z4 ]
- where
- (x1, y1, z1) = v0 t
- (x2, y2, z2) = v1 t
- (x3, y3, z3) = v2 t
- (x4, y4, z4) = v3 t
+-- | Compute the determinant of the 4x4 matrix,
+--
+-- [1]
+-- [x]
+-- [y]
+-- [z]
+--
+-- where [1] = [1, 1, 1, 1],
+-- [x] = [x1,x2,x3,x4],
+--
+-- et cetera.
+--
+det :: Point -> Point -> Point -> Point -> Double
+det p0 p1 p2 p3 =
+ 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 + x3*y1*z4 +
+ x3*y2*z1 - x3*y2*z4 - x3*y4*z1 - x2*y4*z3 - x3*y1*z2 + x3*y4*z2 +
+ x4*y1*z2 - x4*y1*z3 - x4*y2*z1 + x4*y2*z3 + x4*y3*z1 - x4*y3*z2
+ where
+ (x1, y1, z1) = p0
+ (x2, y2, z2) = p1
+ (x3, y3, z3) = p2
+ (x4, y4, z4) = p3
+