From c98fd7a6cae853f1ca8570994ae9ba3c13e9c4bd Mon Sep 17 00:00:00 2001
From: Gael Guennebaud <g.gael@free.fr>
Date: Sun, 9 Jun 2013 23:14:45 +0200
Subject: Fix bug #609: avoid if statement and improve consistency of
 eulerAngles method

---
 Eigen/src/Geometry/EulerAngles.h | 58 +++++++++++++++++++++++++++-------------
 1 file changed, 39 insertions(+), 19 deletions(-)

(limited to 'Eigen/src/Geometry')

diff --git a/Eigen/src/Geometry/EulerAngles.h b/Eigen/src/Geometry/EulerAngles.h
index 216307706..3f6ecc6d9 100644
--- a/Eigen/src/Geometry/EulerAngles.h
+++ b/Eigen/src/Geometry/EulerAngles.h
@@ -27,12 +27,18 @@ namespace Eigen {
   *      * AngleAxisf(ea[1], Vector3f::UnitX())
   *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
   * This corresponds to the right-multiply conventions (with right hand side frames).
+  * 
+  * The returned angles are in the ranges [0:pi]x[0:pi]x[-pi:pi].
+  * 
+  * \sa class AngleAxis
   */
 template<typename Derived>
 inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
 MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
 {
   using std::atan2;
+  using std::sin;
+  using std::cos;
   /* Implemented from Graphics Gems IV */
   EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
 
@@ -44,39 +50,53 @@ MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
   const Index i = a0;
   const Index j = (a0 + 1 + odd)%3;
   const Index k = (a0 + 2 - odd)%3;
-
+  
   if (a0==a2)
   {
-    Scalar s = Vector2(coeff(j,i) , coeff(k,i)).norm();
-    res[1] = atan2(s, coeff(i,i));
-    if (s > epsilon)
+    res[0] = atan2(coeff(j,i), coeff(k,i));
+    if((odd && res[0]<0) || ((!odd) && res[0]>0))
     {
-      res[0] = atan2(coeff(j,i), coeff(k,i));
-      res[2] = atan2(coeff(i,j),-coeff(i,k));
+      res[0] = (res[0] > 0) ? res[0] - M_PI : res[0] +  M_PI;
+      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
+      res[1] = -atan2(s2, coeff(i,i));
     }
     else
     {
-      res[0] = Scalar(0);
-      res[2] = (coeff(i,i)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
+      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
+      res[1] = atan2(s2, coeff(i,i));
     }
-  }
+    
+    // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
+    // we can compute their respective rotation, and apply its inverse to M. Since the result must
+    // be a rotation around x, we have:
+    //
+    //  c2  s1.s2 c1.s2                   1  0   0 
+    //  0   c1    -s1       *    M    =   0  c3  s3
+    //  -s2 s1.c2 c1.c2                   0 -s3  c3
+    //
+    //  Thus:  m11.c1 - m21.s1 = c3  &   m12.c1 - m22.s1 = s3
+    
+    Scalar s1 = sin(res[0]);
+    Scalar c1 = cos(res[0]);
+    res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
+  } 
   else
   {
-    Scalar c = Vector2(coeff(i,i) , coeff(i,j)).norm();
-    res[1] = atan2(-coeff(i,k), c);
-    if (c > epsilon)
-    {
-      res[0] = atan2(coeff(j,k), coeff(k,k));
-      res[2] = atan2(coeff(i,j), coeff(i,i));
+    res[0] = atan2(coeff(j,k), coeff(k,k));
+    Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
+    if((odd && res[0]<0) || ((!odd) && res[0]>0)) {
+      res[0] = (res[0] > 0) ? res[0] - M_PI : res[0] +  M_PI;
+      res[1] = atan2(-coeff(i,k), -c2);
     }
     else
-    {
-      res[0] = Scalar(0);
-      res[2] = (coeff(i,k)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
-    }
+      res[1] = atan2(-coeff(i,k), c2);
+    Scalar s1 = sin(res[0]);
+    Scalar c1 = cos(res[0]);
+    res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
   }
   if (!odd)
     res = -res;
+  
   return res;
 }
 
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