From a981a02c5ae9262bc91dd283195fe36a214ccec9 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Thu, 12 Jan 2012 09:25:43 +0000
Subject: [PATCH] replace an 'I'm not really sure'-style comment by a proper
explanation
[[Imported from SVN: r8368]]
---
dune/gfe/rotation.hh | 24 ++++++++++++------------
1 file changed, 12 insertions(+), 12 deletions(-)
diff --git a/dune/gfe/rotation.hh b/dune/gfe/rotation.hh
index e4f030a9..9d2196f7 100644
--- a/dune/gfe/rotation.hh
+++ b/dune/gfe/rotation.hh
@@ -651,9 +651,9 @@ public:
// use the functionality from the unitvector class
Dune::FieldMatrix<T,4,4> result = UnitVector<T,4>::secondDerivativeOfDistanceSquaredWRTSecondArgument(p.globalCoordinates(),
q.globalCoordinates());
- // for some reason that I don't really understand, the distance we have defined for the rotations (== Unit quaternions)
- // is twice the corresponding distance on the unit quaternions seen as a sphere. Hence the derivative of the
- // squared distance needs to be multiplied by 4.
+ // The unit quaternions form a double cover of SO(3). That means going once around the unit sphere (2\pi)
+ // means going twice around SO(3) (4\pi). Hence there is a factor 2, which in addition we need to square,
+ // because we are considering the squared distance.
result *= 4;
return result;
}
@@ -666,9 +666,9 @@ public:
// use the functionality from the unitvector class
Dune::FieldMatrix<T,4,4> result = UnitVector<T,4>::secondDerivativeOfDistanceSquaredWRTFirstAndSecondArgument(p.globalCoordinates(),
q.globalCoordinates());
- // for some reason that I don't really understand, the distance we have defined for the rotations (== Unit quaternions)
- // is twice the corresponding distance on the unit quaternions seen as a sphere. Hence the derivative of the
- // squared distance needs to be multiplied by 4.
+ // The unit quaternions form a double cover of SO(3). That means going once around the unit sphere (2\pi)
+ // means going twice around SO(3) (4\pi). Hence there is a factor 2, which in addition we need to square,
+ // because we are considering the squared distance.
result *= 4;
return result;
}
@@ -681,9 +681,9 @@ public:
// use the functionality from the unitvector class
Tensor3<T,4,4,4> result = UnitVector<T,4>::thirdDerivativeOfDistanceSquaredWRTSecondArgument(p.globalCoordinates(),
q.globalCoordinates());
- // for some reason that I don't really understand, the distance we have defined for the rotations (== Unit quaternions)
- // is twice the corresponding distance on the unit quaternions seen as a sphere. Hence the derivative of the
- // squared distance needs to be multiplied by 4.
+ // The unit quaternions form a double cover of SO(3). That means going once around the unit sphere (2\pi)
+ // means going twice around SO(3) (4\pi). Hence there is a factor 2, which in addition we need to square,
+ // because we are considering the squared distance.
result *= 4;
return result;
}
@@ -696,9 +696,9 @@ public:
// use the functionality from the unitvector class
Tensor3<T,4,4,4> result = UnitVector<T,4>::thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(p.globalCoordinates(),
q.globalCoordinates());
- // for some reason that I don't really understand, the distance we have defined for the rotations (== Unit quaternions)
- // is twice the corresponding distance on the unit quaternions seen as a sphere. Hence the derivative of the
- // squared distance needs to be multiplied by 4.
+ // The unit quaternions form a double cover of SO(3). That means going once around the unit sphere (2\pi)
+ // means going twice around SO(3) (4\pi). Hence there is a factor 2, which in addition we need to square,
+ // because we are considering the squared distance.
result *= 4;
return result;
}
--
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