From 963d338922e9ef1addcd29c1b43e9b66243207c0 Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Fri, 20 Jun 2014 15:09:42 +0200
Subject: [PATCH] Fix bug #827: improve accuracy of quaternion to angle-axis
 conversion

---
 Eigen/src/Geometry/AngleAxis.h | 28 ++++++++++++++--------------
 1 file changed, 14 insertions(+), 14 deletions(-)

diff --git a/Eigen/src/Geometry/AngleAxis.h b/Eigen/src/Geometry/AngleAxis.h
index b42048c55..636712c2b 100644
--- a/Eigen/src/Geometry/AngleAxis.h
+++ b/Eigen/src/Geometry/AngleAxis.h
@@ -77,7 +77,9 @@ public:
     *          represents an invalid rotation. */
   template<typename Derived>
   inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
-  /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */
+  /** Constructs and initialize the angle-axis rotation from a quaternion \a q.
+    * This function implicitly normalizes the quaternion \a q.
+    */
   template<typename QuatDerived> inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }
   /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
   template<typename Derived>
@@ -149,29 +151,27 @@ typedef AngleAxis<float> AngleAxisf;
 typedef AngleAxis<double> AngleAxisd;
 
 /** Set \c *this from a \b unit quaternion.
-  * The axis is normalized.
+  * The resulting axis is normalized.
   * 
-  * \warning As any other method dealing with quaternion, if the input quaternion
-  *          is not normalized then the result is undefined.
+  * This function implicitly normalizes the quaternion \a q.
   */
 template<typename Scalar>
 template<typename QuatDerived>
 AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)
 {
-  using std::acos;
-  EIGEN_USING_STD_MATH(min);
-  EIGEN_USING_STD_MATH(max);
-  using std::sqrt;
-  Scalar n2 = q.vec().squaredNorm();
-  if (n2 < NumTraits<Scalar>::dummy_precision()*NumTraits<Scalar>::dummy_precision())
+  using std::atan2;
+  Scalar n = q.vec().norm();
+  if(n<NumTraits<Scalar>::epsilon())
+    n = q.vec().stableNorm();
+  if (n > Scalar(0))
   {
-    m_angle = Scalar(0);
-    m_axis << Scalar(1), Scalar(0), Scalar(0);
+    m_angle = Scalar(2)*atan2(n, q.w());
+    m_axis  = q.vec() / n;
   }
   else
   {
-    m_angle = Scalar(2)*acos((min)((max)(Scalar(-1),q.w()),Scalar(1)));
-    m_axis = q.vec() / sqrt(n2);
+    m_angle = 0;
+    m_axis << 1, 0, 0;
   }
   return *this;
 }