LineSurface jacobians seem incomplete

[andiwand]

In the LineSurface we define a boundToFreeJacobian but not a freeToBoundJacobian which seems incorrect to me. If the jacobian is different compared to the one from a plane surface in one direction it should also be the case in the other direction

acts/Core/include/Acts/Surfaces/LineSurface.hpp

Lines 120 to 128 in f7106bc

	/// Calculate the jacobian from local to global which the surface knows best,
	/// hence the calculation is done here.
	///
	/// @param gctx The current geometry context object, e.g. alignment
	/// @param boundParams is the bound parameters vector
	///
	/// @return Jacobian from local to global
	BoundToFreeMatrix boundToFreeJacobian(
	const GeometryContext& gctx, const BoundVector& boundParams) const final;

acts/Core/src/Surfaces/LineSurface.cpp

Lines 198 to 249 in f7106bc

	Acts::BoundToFreeMatrix Acts::LineSurface::boundToFreeJacobian(
	const GeometryContext& gctx, const BoundVector& boundParams) const {
	// Transform from bound to free parameters
	FreeVector freeParams =
	detail::transformBoundToFreeParameters(*this, gctx, boundParams);
	// The global position
	Vector3 position = freeParams.segment<3>(eFreePos0);
	// The direction
	Vector3 direction = freeParams.segment<3>(eFreeDir0);
	// Get the sines and cosines directly
	double cosTheta = std::cos(boundParams[eBoundTheta]);
	double sinTheta = std::sin(boundParams[eBoundTheta]);
	double cosPhi = std::cos(boundParams[eBoundPhi]);
	double sinPhi = std::sin(boundParams[eBoundPhi]);
	// retrieve the reference frame
	auto rframe = referenceFrame(gctx, position, direction);
	// Initialize the jacobian from local to global
	BoundToFreeMatrix jacToGlobal = BoundToFreeMatrix::Zero();
	// the local error components - given by the reference frame
	jacToGlobal.topLeftCorner<3, 2>() = rframe.topLeftCorner<3, 2>();
	// the time component
	jacToGlobal(eFreeTime, eBoundTime) = 1;
	// the momentum components
	jacToGlobal(eFreeDir0, eBoundPhi) = -sinTheta * sinPhi;
	jacToGlobal(eFreeDir0, eBoundTheta) = cosTheta * cosPhi;
	jacToGlobal(eFreeDir1, eBoundPhi) = sinTheta * cosPhi;
	jacToGlobal(eFreeDir1, eBoundTheta) = cosTheta * sinPhi;
	jacToGlobal(eFreeDir2, eBoundTheta) = -sinTheta;
	jacToGlobal(eFreeQOverP, eBoundQOverP) = 1;
	// the projection of direction onto ref frame normal
	double ipdn = 1. / direction.dot(rframe.col(2));
	// build the cross product of d(D)/d(eBoundPhi) components with y axis
	Vector3 dDPhiY = rframe.block<3, 1>(0, 1).cross(
	jacToGlobal.block<3, 1>(eFreeDir0, eBoundPhi));
	// and the same for the d(D)/d(eTheta) components
	Vector3 dDThetaY = rframe.block<3, 1>(0, 1).cross(
	jacToGlobal.block<3, 1>(eFreeDir0, eBoundTheta));
	// and correct for the x axis components
	dDPhiY -= rframe.block<3, 1>(0, 0) * (rframe.block<3, 1>(0, 0).dot(dDPhiY));
	dDThetaY -=
	rframe.block<3, 1>(0, 0) * (rframe.block<3, 1>(0, 0).dot(dDThetaY));
	// set the jacobian components for global d/ phi/Theta
	jacToGlobal.block<3, 1>(eFreePos0, eBoundPhi) =
	dDPhiY * boundParams[eBoundLoc0] * ipdn;
	jacToGlobal.block<3, 1>(eFreePos0, eBoundTheta) =
	dDThetaY * boundParams[eBoundLoc0] * ipdn;
	return jacToGlobal;
	}

[paulgessinger]

Maybe @beomki-yeo has thoughts on this.

[beomki-yeo]

Indeed. I will update my PR on line surface jacobian soon so you can check the details there (#2657)

Summary:
It should not be defined and it's OK not to be defined. J_{G->L} X J_{L->G} is always identical matrix in the current implementation

[andiwand]

thanks I will check. still seems odd to me as there should be a correlation between direction error and position error for both transformations

[beomki-yeo]

That's a funny behavior of two different transforms - it will be described in the Discussion section. 😉

[andiwand]

thanks for your derivation @beomki-yeo ! I think it makes some sense now to me. I might still need to check this manually to be 100% convinced but it is enough to close this ticket 😄