From 82593c052d8a0d927bbde40bf317118343c5aace Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Fri, 14 Jan 2011 10:14:55 +0000
Subject: [PATCH] implement exp for a quaternion tangent vector
[[Imported from SVN: r6741]]
---
dune/gfe/rotation.hh | 24 ++++++++++++++++++++++--
1 file changed, 22 insertions(+), 2 deletions(-)
diff --git a/dune/gfe/rotation.hh b/dune/gfe/rotation.hh
index d30bd9e2..1e03ce2e 100644
--- a/dune/gfe/rotation.hh
+++ b/dune/gfe/rotation.hh
@@ -230,9 +230,29 @@ public:
return p.mult(corr);
}
- /** \brief The exponential map from a given point $p \in SO(3)$. */
+ /** \brief The exponential map from a given point $p \in SO(3)$.
+
+ There may be a more direct way to implement this
+
+ \param v A tangent vector in quaternion coordinates
+ */
static Rotation<3,T> exp(const Rotation<3,T>& p, const EmbeddedTangentVector& v) {
- DUNE_THROW(Dune::NotImplemented, "exp... EmbeddedTangentVector");
+
+ // The vector v as a quaternion
+ Quaternion<T> vQuat(v);
+
+ // left multiplication by the inverse base point yields a tangent vector at the identity
+ Quaternion<T> vAtIdentity = p.inverse().mult(vQuat);
+ assert( std::fabs(vAtIdentity[3] < 1e-8) );
+
+ // vAtIdentity as a skew matrix
+ TangentVector vMatrix;
+ vMatrix[0] = 2*vAtIdentity[0];
+ vMatrix[1] = 2*vAtIdentity[1];
+ vMatrix[2] = 2*vAtIdentity[2];
+
+ // The actual exponential map
+ return exp(p, vMatrix);
}
static Dune::FieldMatrix<T,4,3> Dexp(const Dune::FieldVector<T,3>& v) {
--
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