From a06fe3af24267d872138065e440c6f1dcd4a2b9b Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Tue, 27 Apr 2010 15:11:37 +0000
Subject: [PATCH] add method to get an orthonormal frame at each point (for
dim==2 only)
[[Imported from SVN: r5964]]
---
dune/gfe/unitvector.hh | 32 ++++++++++++++++++++++++++++++++
1 file changed, 32 insertions(+)
diff --git a/dune/gfe/unitvector.hh b/dune/gfe/unitvector.hh
index 98d4553f..8491f688 100644
--- a/dune/gfe/unitvector.hh
+++ b/dune/gfe/unitvector.hh
@@ -39,7 +39,11 @@ public:
/** \brief The type used for coordinates */
typedef double ctype;
+ /** \brief Global coordinates wrt an isometric embedding function are available */
+ static const bool isometricallyEmbedded = true;
+
typedef Dune::FieldVector<double,dim-1> TangentVector;
+
typedef Dune::FieldVector<double,dim> EmbeddedTangentVector;
UnitVector<dim>& operator=(const Dune::FieldVector<double,dim>& vector)
@@ -49,6 +53,17 @@ public:
return *this;
}
+ /** \brief The exponential map */
+ static UnitVector exp(const UnitVector& p, const TangentVector& v) {
+
+ Dune::FieldMatrix<double,dim-1,dim> frame = p.orthonormalFrame();
+
+ EmbeddedTangentVector ev;
+ frame.mtv(v,ev);
+
+ return exp(p,ev);
+ }
+
/** \brief The exponential map */
static UnitVector exp(const UnitVector& p, const EmbeddedTangentVector& v) {
@@ -146,6 +161,23 @@ public:
return data_;
}
+ /** \brief Compute an orthonormal basis of the tangent space of S^n.
+
+ This basis is of course not globally continuous.
+ */
+ Dune::FieldMatrix<double,dim-1,dim> orthonormalFrame() const {
+
+ Dune::FieldMatrix<double,dim-1,dim> result;
+
+ if (dim==2) {
+ result[0][0] = -data_[1];
+ result[0][1] = data_[0];
+ } else
+ DUNE_THROW(Dune::NotImplemented, "orthonormalFrame for dim!=2!");
+
+ return result;
+ }
+
/** \brief Write LocalKey object to output stream */
friend std::ostream& operator<< (std::ostream& s, const UnitVector& unitVector)
{
--
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