Class Acts::LineSurface¶
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class Acts::LineSurface : public Acts::Surface¶
Base class for a linear surfaces in the TrackingGeometry to describe dirft tube, straw like detectors or the Perigee It inherits from Surface.
Note
It leaves the type() method virtual, so it can not be instantiated
Subclassed by Acts::PerigeeSurface, Acts::StrawSurface
Public Functions
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LineSurface() = delete¶
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~LineSurface() override = default¶
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virtual AlignmentToPathMatrix alignmentToPathDerivative(const GeometryContext &gctx, const FreeVector ¶meters) const final¶
Calculate the derivative of path length at the geometry constraint or point-of-closest-approach w.r.t.
alignment parameters of the surface (i.e. local frame origin in global 3D Cartesian coordinates and its rotation represented with extrinsic Euler angles)
- Parameters
gctx – The current geometry context object, e.g. alignment
parameters – is the free parameters
- Returns
Derivative of path length w.r.t. the alignment parameters
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virtual Vector3 binningPosition(const GeometryContext &gctx, BinningValue bValue) const final¶
The binning position is the position calcualted for a certain binning type.
- Parameters
gctx – The current geometry context object, e.g. alignment
bValue – is the binning type to be used
- Returns
position that can beused for this binning
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virtual const SurfaceBounds &bounds() const final¶
This method returns the bounds of the Surface by reference */.
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virtual BoundToFreeMatrix boundToFreeJacobian(const GeometryContext &gctx, const BoundVector &boundParams) const final¶
Calculate the jacobian from local to global which the surface knows best, hence the calculation is done here.
- Parameters
gctx – The current geometry context object, e.g. alignment
boundParams – is the bound parameters vector
- Returns
Jacobian from local to global
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virtual FreeToPathMatrix freeToPathDerivative(const GeometryContext &gctx, const FreeVector ¶meters) const final¶
Calculate the derivative of path length at the geometry constraint or point-of-closest-approach w.r.t.
free parameters
- Parameters
gctx – The current geometry context object, e.g. alignment
parameters – is the free parameters
- Returns
Derivative of path length w.r.t. free parameters
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virtual Result<Vector2> globalToLocal(const GeometryContext &gctx, const Vector3 &position, const Vector3 &momentum, double tolerance = s_onSurfaceTolerance) const final¶
Specified for LineSurface: global to local method without dynamic memory allocation.
This method is the true global->local transformation.
makes use of globalToLocal and indicates the sign of the Acts::eBoundLoc0 by the given momentum
The calculation of the sign of the radius (or \( d_0 \)
) can be done as follows:
May
\( \vec d = \vec m - \vec c \) denote the difference between the center of the line and the global position of the measurement/predicted state, then \( \vec d \) lies within the so called measurement plane. The measurement plane is determined by the two orthogonal vectors \( \vec{measY}= \vec{Acts::eBoundLoc1} \) and \( \vec{measX} = \vec{measY} \times \frac{\vec{p}}{|\vec{p}|} \).The sign of the radius ( \( d_{0} \) ) is then defined by the projection of \( \vec{d} \) onto \( \vec{measX} \):\( sign = -sign(\vec{d} \cdot \vec{measX}) \)
- Parameters
gctx – The current geometry context object, e.g. alignment
position – global 3D position - considered to be on surface but not inside bounds (check is done)
momentum – global 3D momentum representation (optionally ignored)
tolerance – (unused)
- Returns
a Result<Vector2> which can be !ok() if the operation fails
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virtual SurfaceIntersection intersect(const GeometryContext &gctx, const Vector3 &position, const Vector3 &direction, const BoundaryCheck &bcheck = false) const final¶
Straight line intersection schema.
mathematical motivation: Given two lines in parameteric form:
\( \vec l_{a}(\lambda) = \vec m_a + \lambda \cdot \vec e_{a} \)
\( \vec l_{b}(\mu) = \vec m_b + \mu \cdot \vec e_{b} \) the vector between any two points on the two lines is given by:
\( \vec s(\lambda, \mu) = \vec l_{b} - l_{a} = \vec m_{ab} + \mu \cdot \vec e_{b} - \lambda \cdot \vec e_{a} \)
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when
\( \vec m_{ab} = \vec m_{b} - \vec m_{a} \).\( \vec s(u, \mu_0) \) denotes the vector between the two closest points \( \vec l_{a,0} = l_{a}(u) \) and \( \vec l_{b,0} = l_{b}(\mu_0) \) and is perpendicular to both, \( \vec e_{a} \) and \( \vec e_{b} \).
This results in a system of two linear equations:
(i) \( 0 = \vec s(u, \mu_0) \cdot \vec e_a = \vec m_ab \cdot \vec e_a + \mu_0 \vec e_a \cdot \vec e_b - u \)
(ii) \( 0 = \vec s(u, \mu_0) \cdot \vec e_b = \vec m_ab \cdot \vec e_b + \mu_0 - u \vec e_b \cdot \vec e_a \)
Solving (i), (ii) for \( u \) and \( \mu_0 \) yields:
\( u = \frac{(\vec m_ab \cdot \vec e_a)-(\vec m_ab \cdot \vec e_b)(\vec e_a \cdot \vec e_b)}{1-(\vec e_a \cdot \vec e_b)^2} \)
\( \mu_0 = - \frac{(\vec m_ab \cdot \vec e_b)-(\vec m_ab \cdot \vec e_a)(\vec e_a \cdot \vec e_b)}{1-(\vec e_a \cdot \vec e_b)^2} \)
Note
exptected to be normalized
- Parameters
gctx – The current geometry context object, e.g. alignment
position – The global position as a starting point
direction – The global direction at the starting point
bcheck – The boundary check directive for the estimate
- Returns
is the intersection object
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virtual ActsMatrix<2, 3> localCartesianToBoundLocalDerivative(const GeometryContext &gctx, const Vector3 &position) const final¶
Calculate the derivative of bound track parameters local position w.r.t.
position in local 3D Cartesian coordinates
- Parameters
gctx – The current geometry context object, e.g. alignment
position – The position of the paramters in global
- Returns
Derivative of bound local position w.r.t. position in local 3D cartesian coordinates
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virtual Vector3 localToGlobal(const GeometryContext &gctx, const Vector2 &lposition, const Vector3 &momentum) const final¶
Local to global transformation for line surfaces the momentum is used in order to interpret the drift radius.
- Parameters
gctx – The current geometry context object, e.g. alignment
lposition – is the local position to be transformed
momentum – is the global momentum (used to sign the closest approach)
- Returns
global position by value
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virtual std::string name() const override¶
Return properly formatted class name for screen output */.
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virtual Vector3 normal(const GeometryContext &gctx, const Vector2 &lposition) const final¶
Normal vector return.
- Parameters
gctx – The current geometry context object, e.g. alignment
lposition – is the local position is ignored
- Returns
a Vector3 by value
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LineSurface &operator=(const LineSurface &other)¶
Assignment operator.
- Parameters
other – is the source surface dor copying
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virtual double pathCorrection(const GeometryContext &gctx, const Vector3 &position, const Vector3 &momentum) const override¶
the pathCorrection for derived classes with thickness is by definition 1 for LineSurfaces
Note
input parameters are ignored
Note
there’s no material associated to the line surface
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virtual RotationMatrix3 referenceFrame(const GeometryContext &gctx, const Vector3 &position, const Vector3 &momentum) const final¶
Return the measurement frame - this is needed for alignment, in particular.
for StraightLine and Perigee Surface
the default implementation is the the RotationMatrix3 of the transform
- Parameters
gctx – The current geometry context object, e.g. alignment
position – is the global position where the measurement frame is constructed
momentum – is the momentum used for the measurement frame construction
- Returns
is a rotation matrix that indicates the measurement frame
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LineSurface() = delete¶