From afa57ab9ff086379a9570ddcb4bbb8caac42db71 Mon Sep 17 00:00:00 2001
From: Julius Nehring-Wirxel <julius.nehring-wirxel@rwth-aachen.de>
Date: Mon, 30 Mar 2020 19:52:05 +0200
Subject: [PATCH] Fixed are_orthogonal for real.

---
 src/typed-geometry/functions/tests/vec_tests.hh | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/typed-geometry/functions/tests/vec_tests.hh b/src/typed-geometry/functions/tests/vec_tests.hh
index 7b39982..bf6cacd 100644
--- a/src/typed-geometry/functions/tests/vec_tests.hh
+++ b/src/typed-geometry/functions/tests/vec_tests.hh
@@ -32,7 +32,9 @@ template <int D, class ScalarT, class = enable_if<is_floating_point<ScalarT>>>
 template <int D, class ScalarT>
 [[nodiscard]] constexpr bool are_orthogonal(vec<D, ScalarT> const& a, vec<D, ScalarT> const& b, ScalarT eps = 100 * D * tg::epsilon<ScalarT>)
 {
-    return abs(dot(a, b)) < max(max_element(abs(a)), max_element(abs(b))) * eps;
+    // the error scales with the square of the magnitude of the inputs
+    auto const scale = max(max_element(abs(a)), max_element(abs(b)));
+    return abs(dot(a, b)) < scale * scale * eps;
 }
 
 template <int D, class ScalarT>
-- 
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