From: Wolfgang Bangerth <bangerth@math.tamu.edu>
Date: Tue, 19 Aug 2014 16:00:58 +0000 (-0500)
Subject: Further improve test to avoid square roots.
X-Git-Tag: v8.2.0-rc1~197^2
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=1488b1fa19eefa88c001e2edcf71f0cfaff1dcde;p=dealii.git

Further improve test to avoid square roots.
---

diff --git a/source/grid/tria_accessor.cc b/source/grid/tria_accessor.cc
index 09008f51f8..8eb5fbae4c 100644
--- a/source/grid/tria_accessor.cc
+++ b/source/grid/tria_accessor.cc
@@ -983,9 +983,17 @@ namespace
     Point<3> normal;
     cross_product(normal, v01, v02);
 
-    const Point<3> v03 = accessor.vertex(3) - accessor.vertex(0); //1st diagonal
-
-    if (std::abs((v03 * normal) / (v03.norm() * v01.norm() * v02.norm())) >= 1e-12)
+    const Point<3> v03 = accessor.vertex(3) - accessor.vertex(0);
+
+    // check whether v03 does not lie in the plane of v01 and v02
+    // (i.e., whether the face is not planar). we do so by checking
+    // whether the triple product (v01 x v02) * v03 forms a positive
+    // volume relative to |v01|*|v02|*|v03|. the test checks the
+    // squares of these to avoid taking norms/square roots:
+    if (std::abs((v03 * normal) * (v03 * normal) /
+		 (v03.square() * v01.square() * v02.square()))
+	>=
+	1e-24)
       {
 	Assert (false,
 		ExcMessage("Computing the measure of a nonplanar face is not implemented!"));