From 74aefd9c23dadd12ee654c7d0206b0a96d22040c Mon Sep 17 00:00:00 2001
From: Simon Puchert <simonpuchert@alice.de>
Date: Sun, 31 Mar 2019 10:32:34 +0200
Subject: [PATCH] Improve precision of UnitQuaternion::angle (#569)

The previous implementation had stability problems for small angles due
to the behaviour of the arccosine it used. In particular, it needs a
hack to handle "cosines" greater than 1 and the smallest obtainable
nonzero angle for e.g. f32 is acos(1-2^-22) = 0.00069...
These problems can be fixed by using an arctangent-based formula.
---
 src/geometry/quaternion.rs | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/src/geometry/quaternion.rs b/src/geometry/quaternion.rs
index 6460a446..4a2007e0 100644
--- a/src/geometry/quaternion.rs
+++ b/src/geometry/quaternion.rs
@@ -602,13 +602,7 @@ impl<N: Real> UnitQuaternion<N> {
     #[inline]
     pub fn angle(&self) -> N {
         let w = self.quaternion().scalar().abs();
-
-        // Handle inaccuracies that make break `.acos`.
-        if w >= N::one() {
-            N::zero()
-        } else {
-            w.acos() * ::convert(2.0f64)
-        }
+	self.quaternion().imag().norm().atan2(w) * ::convert(2.0f64)
     }
 
     /// The underlying quaternion.