From eadf8986f6dd7498b9f32078dbb71a26355b528e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Vladim=C3=ADr=20Vondru=C5=A1?= <mosra@centrum.cz>
Date: Mon, 3 Sep 2018 22:18:12 +0200
Subject: [PATCH] Math: fuzzy compare for division-by-zero in quaternion
 s(c)lerp.

Also remove a totally unneeded conversion.
---
 src/Magnum/Math/DualQuaternion.h | 4 ++--
 src/Magnum/Math/Quaternion.h     | 6 ++++--
 2 files changed, 6 insertions(+), 4 deletions(-)

diff --git a/src/Magnum/Math/DualQuaternion.h b/src/Magnum/Math/DualQuaternion.h
index ab806d3a6a..b268c9a267 100644
--- a/src/Magnum/Math/DualQuaternion.h
+++ b/src/Magnum/Math/DualQuaternion.h
@@ -84,7 +84,7 @@ template<class T> inline DualQuaternion<T> sclerp(const DualQuaternion<T>& norma
 
     /* Avoid division by zero: interpolate just the translation part */
     /** @todo could this be optimized somehow? */
-    if(std::abs(cosHalfAngle) >= T(1))
+    if(std::abs(cosHalfAngle) >= T(1) - TypeTraits<T>::epsilon())
         return DualQuaternion<T>::translation(Implementation::lerp(normalizedA.translation(), normalizedB.translation(), t))*DualQuaternion<T>{normalizedA.real()};
 
     /* l + εm = q_A^**q_B */
@@ -151,7 +151,7 @@ template<class T> inline DualQuaternion<T> sclerpShortestPath(const DualQuaterni
 
     /* Avoid division by zero: interpolate just the translation part */
     /** @todo could this be optimized somehow? */
-    if(std::abs(cosHalfAngle) >= T(1))
+    if(std::abs(cosHalfAngle) >= T(1) - TypeTraits<T>::epsilon())
         return DualQuaternion<T>::translation(Implementation::lerp(normalizedA.translation(), normalizedB.translation(), t))*DualQuaternion<T>{normalizedA.real()};
 
     /* l + εm = q_A^**q_B, multiplying with -1 ensures shortest path when dot < 0 */
diff --git a/src/Magnum/Math/Quaternion.h b/src/Magnum/Math/Quaternion.h
index 4f1b600a10..325b68ce78 100644
--- a/src/Magnum/Math/Quaternion.h
+++ b/src/Magnum/Math/Quaternion.h
@@ -163,7 +163,8 @@ template<class T> inline Quaternion<T> slerp(const Quaternion<T>& normalizedA, c
     const T cosHalfAngle = dot(normalizedA, normalizedB);
 
     /* Avoid division by zero */
-    if(std::abs(cosHalfAngle) >= T(1)) return Quaternion<T>{normalizedA};
+    if(std::abs(cosHalfAngle) >= T(1) - TypeTraits<T>::epsilon())
+        return normalizedA;
 
     const T a = std::acos(cosHalfAngle);
     return (std::sin((T(1) - t)*a)*normalizedA + std::sin(t*a)*normalizedB)/std::sin(a);
@@ -206,7 +207,8 @@ template<class T> inline Quaternion<T> slerpShortestPath(const Quaternion<T>& no
     const T cosHalfAngle = dot(normalizedA, normalizedB);
 
     /* Avoid division by zero */
-    if(std::abs(cosHalfAngle) >= T(1)) return Quaternion<T>{normalizedA};
+    if(std::abs(cosHalfAngle) >= T(1) - TypeTraits<T>::epsilon())
+        return normalizedA;
 
     const Quaternion<T> shortestNormalizedA = cosHalfAngle < 0 ? -normalizedA : normalizedA;