From badccdd0eda969dc1489e34d778b36880a573a79 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Thu, 12 Jan 2012 11:05:22 +0000
Subject: [PATCH] Reimplement mixed third derivative method
New implementation properly handles the two sheets.
Now the TargetSpace test passes again. Yay!
[[Imported from SVN: r8375]]
---
dune/gfe/rotation.hh | 40 ++++++++++++++++++++++++++++++++++------
1 file changed, 34 insertions(+), 6 deletions(-)
diff --git a/dune/gfe/rotation.hh b/dune/gfe/rotation.hh
index d4fbfc6b..394ee544 100644
--- a/dune/gfe/rotation.hh
+++ b/dune/gfe/rotation.hh
@@ -737,14 +737,42 @@ public:
Unlike the distance itself the squared distance is differentiable at zero
*/
static Tensor3<T,4,4,4> thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(const Rotation<T,3>& p, const Rotation<T,3>& q) {
- // use the functionality from the unitvector class
- Tensor3<T,4,4,4> result = UnitVector<T,4>::thirdDerivativeOfDistanceSquaredWRTFirst1AndSecond2Argument(p.globalCoordinates(),
- q.globalCoordinates());
- // 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.
+
+ Tensor3<T,4,4,4> result;
+
+ T sp = p.globalCoordinates() * q.globalCoordinates();
+
+ // The projection matrix onto the tangent space at p and q
+ Dune::FieldMatrix<T,4,4> Pp, Pq;
+ for (int i=0; i<4; i++)
+ for (int j=0; j<4; j++) {
+ Pp[i][j] = (i==j) - p.globalCoordinates()[i]*p.globalCoordinates()[j];
+ Pq[i][j] = (i==j) - q.globalCoordinates()[i]*q.globalCoordinates()[j];
+ }
+
+ EmbeddedTangentVector pProjected = q.projectOntoTangentSpace(p.globalCoordinates());
+ EmbeddedTangentVector qProjected = p.projectOntoTangentSpace(q.globalCoordinates());
+
+ Tensor3<T,4,4,4> derivativeOfPqOTimesPq;
+ for (int i=0; i<4; i++)
+ for (int j=0; j<4; j++)
+ for (int k=0; k<4; k++) {
+ derivativeOfPqOTimesPq[i][j][k] = 0;
+ for (int l=0; l<4; l++)
+ derivativeOfPqOTimesPq[i][j][k] += Pp[i][l] * (Pq[j][l]*pProjected[k] + pProjected[j]*Pq[k][l]);
+ }
+
+ double plusMinus = (sp < 0) ? -1 : 1;
+
+ result = plusMinus * UnitVector<T,4>::thirdDerivativeOfArcCosSquared(std::fabs(sp)) * Tensor3<T,4,4,4>::product(qProjected,pProjected,pProjected)
+ + UnitVector<T,4>::secondDerivativeOfArcCosSquared(std::fabs(sp)) * derivativeOfPqOTimesPq
+ - UnitVector<T,4>::secondDerivativeOfArcCosSquared(std::fabs(sp)) * sp * Tensor3<T,4,4,4>::product(qProjected,Pq)
+ - plusMinus * UnitVector<T,4>::derivativeOfArcCosSquared(std::fabs(sp)) * Tensor3<T,4,4,4>::product(qProjected,Pq);
+
result *= 4;
+
return result;
+
}
--
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