From f80b7798fb386e6a11218bf074eeadc1104824a8 Mon Sep 17 00:00:00 2001
From: Jonathan Youett <youett@mi.fu-berlin.de>
Date: Mon, 17 Oct 2011 09:46:06 +0000
Subject: [PATCH] add methods to transform axial vectors to tangent vectors and
back
[[Imported from SVN: r7931]]
---
dune/gfe/rotation.hh | 42 ++++++++++++++++++++++++++++++++++++++++++
1 file changed, 42 insertions(+)
diff --git a/dune/gfe/rotation.hh b/dune/gfe/rotation.hh
index f7212a62..668675cb 100644
--- a/dune/gfe/rotation.hh
+++ b/dune/gfe/rotation.hh
@@ -270,6 +270,48 @@ public:
// The actual exponential map
return exp(p, vMatrix);
}
+
+ /** \brief Compute tangent vector from given basepoint and axial vector. */
+ static TangentVector axialToTangentVector(const Rotation<3,T>& p, const Dune::FieldVector<T,3> axialVector) {
+
+ // embedded tangent vector at identity
+ Quaternion<T> vAtIdentity(0);
+ vAtIdentity[0] = 0.5*axialVector[0];
+ vAtIdentity[1] = 0.5*axialVector[1];
+ vAtIdentity[2] = 0.5*axialVector[2];
+
+ // multiply with base point to get real embedded tangent vector
+ Quaternion<T> vQuat = p.mult(vAtIdentity);
+
+ //get basis of the tangent space
+ Dune::FieldMatrix<T,3,4> basis = p.orthonormalFrame();
+
+ // transform coordinates
+ TangentVector tang;
+ basis.mv(vQuat,tang);
+
+ return tang;
+ }
+
+ /** \brief Compute axial vector from given basepoint and tangent vector. */
+ static Dune::FieldVector<T,3> tangentToAxialVector(const Rotation<3,T>& p, const TangentVector& tangent) {
+
+ // embedded tangent vector
+ Dune::FieldMatrix<T,3,4> basis = p.orthonormalFrame();
+ Quaternion<T> embeddedTangent;
+ basis.mtv(tangent, embeddedTangent);
+
+ // left multiplication by the inverse base point yields a tangent vector at the identity
+ Quaternion<T> vAtIdentity = p.inverse().mult(embeddedTangent);
+ assert( std::fabs(vAtIdentity[3]) < 1e-8 );
+
+ Dune::FieldVector<T,3> axial;
+ axial[0] = 2*vAtIdentity[0];
+ axial[1] = 2*vAtIdentity[1];
+ axial[2] = 2*vAtIdentity[2];
+
+ return axial;
+ }
static Rotation<3,T> exp(const Rotation<3,T>& p, const Dune::FieldVector<T,4>& v) {
--
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