From 48f2efb23ca81c038dfaf1ceef15975fb912b135 Mon Sep 17 00:00:00 2001
From: Oliver Sander <oliver.sander@tu-dresden.de>
Date: Thu, 3 Jan 2019 14:18:50 +0100
Subject: [PATCH] Implement projectOnto and derivativeOfProjection
WARNING: These methods implement the projection in quaternion
space. This is NOT the canonical projection in matrix space.
---
dune/gfe/rotation.hh | 24 ++++++++++++++++++++++++
1 file changed, 24 insertions(+)
diff --git a/dune/gfe/rotation.hh b/dune/gfe/rotation.hh
index c9f11e4b..aa023750 100644
--- a/dune/gfe/rotation.hh
+++ b/dune/gfe/rotation.hh
@@ -1148,6 +1148,30 @@ public:
return result;
}
+ /** \brief Project a vector in R^4 onto the unit quaternions
+ *
+ * \warning This is NOT the standard projection from R^{3 \times 3} onto SO(3)!
+ */
+ static Rotation<T,3> projectOnto(const CoordinateType& p)
+ {
+ Rotation<T,3> result(p);
+ result /= result.two_norm();
+ return result;
+ }
+
+ /** \brief Derivative of the projection of a vector in R^4 onto the unit quaternions
+ *
+ * \warning This is NOT the standard projection from R^{3 \times 3} onto SO(3)!
+ */
+ static auto derivativeOfProjection(const Dune::FieldVector<T,4>& p)
+ {
+ Dune::FieldMatrix<T,4,4> result;
+ for (int i=0; i<4; i++)
+ for (int j=0; j<4; j++)
+ result[i][j] = ( (i==j) - p[i]*p[j] / p.two_norm2() ) / p.two_norm();
+ return result;
+ }
+
/** \brief The global coordinates, if you really want them */
const CoordinateType& globalCoordinates() const {
return *this;
--
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