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 // This file is part of the ACTS project.
 //
 // Copyright (C) 2016 CERN for the benefit of the ACTS project
 //
 // This Source Code Form is subject to the terms of the Mozilla Public
 // License, v. 2.0. If a copy of the MPL was not distributed with this
 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 #include "Acts/Surfaces/LineSurface.hpp"
 
 #include "Acts/Definitions/Algebra.hpp"
 #include "Acts/Geometry/GeometryObject.hpp"
 #include "Acts/Surfaces/InfiniteBounds.hpp"
 #include "Acts/Surfaces/LineBounds.hpp"
 #include "Acts/Surfaces/SurfaceBounds.hpp"
 #include "Acts/Surfaces/SurfaceError.hpp"
 #include "Acts/Surfaces/detail/AlignmentHelper.hpp"
 #include "Acts/Utilities/AlgebraHelpers.hpp"
 #include "Acts/Utilities/Intersection.hpp"
 #include "Acts/Utilities/ThrowAssert.hpp"
 
 #include <cmath>
 #include <limits>
 #include <utility>
 
 namespace Acts {
 
 LineSurface::LineSurface(const Transform3& transform, double radius,
                          double halez)
     : Surface(transform),
       m_bounds(std::make_shared<const LineBounds>(radius, halez)) {}
 
 LineSurface::LineSurface(const Transform3& transform,
                          std::shared_ptr<const LineBounds> lbounds)
     : Surface(transform), m_bounds(std::move(lbounds)) {}
 
 LineSurface::LineSurface(std::shared_ptr<const LineBounds> lbounds,
                          const SurfacePlacementBase& placement)
     : Surface{placement}, m_bounds(std::move(lbounds)) {
   throw_assert(m_bounds, "LineBounds must not be nullptr");
 }
 
 LineSurface::LineSurface(const LineSurface& other)
     : GeometryObject{}, Surface(other), m_bounds(other.m_bounds) {}
 
 LineSurface::LineSurface(const GeometryContext& gctx, const LineSurface& other,
                          const Transform3& shift)
     : Surface(gctx, other, shift), m_bounds(other.m_bounds) {}
 
 LineSurface& LineSurface::operator=(const LineSurface& other) {
   if (this != &other) {
     Surface::operator=(other);
     m_bounds = other.m_bounds;
   }
   return *this;
 }
 
 Vector3 LineSurface::localToGlobal(const GeometryContext& gctx,
                                    const Vector2& lposition,
                                    const Vector3& direction) const {
   Vector3 unitZ0 = lineDirection(gctx);
 
   // get the vector perpendicular to the momentum direction and the straw axis
   Vector3 radiusAxisGlobal = unitZ0.cross(direction);
   Vector3 locZinGlobal =
       localToGlobalTransform(gctx) * Vector3(0., 0., lposition[1]);
   // add loc0 * radiusAxis
   return Vector3(locZinGlobal + lposition[0] * radiusAxisGlobal.normalized());
 }
 
 Result<Vector2> LineSurface::globalToLocal(const GeometryContext& gctx,
                                            const Vector3& position,
                                            const Vector3& direction,
                                            double tolerance) const {
   using VectorHelpers::perp;
 
   // Bring the global position into the local frame. First remove the
   // translation then the rotation.
   Vector3 localPosition =
       referenceFrame(gctx, position, direction).inverse() *
       (position - localToGlobalTransform(gctx).translation());
 
   // `localPosition.z()` is not the distance to the PCA but the smallest
   // distance between `position` and the imaginary plane surface defined by the
   // local x,y axes in the global frame and the position of the line surface.
   //
   // This check is also done for the `PlaneSurface` so I aligned the
   // `LineSurface` to do the same thing.
   if (std::abs(localPosition.z()) > std::abs(tolerance)) {
     return Result<Vector2>::failure(SurfaceError::GlobalPositionNotOnSurface);
   }
 
   // Construct result from local x,y
   Vector2 localXY = localPosition.head<2>();
 
   return Result<Vector2>::success(localXY);
 }
 
 std::string LineSurface::name() const {
   return "Acts::LineSurface";
 }
 
 RotationMatrix3 LineSurface::referenceFrame(const GeometryContext& gctx,
                                             const Vector3& /*position*/,
                                             const Vector3& direction) const {
   Vector3 unitZ0 = lineDirection(gctx);
   Vector3 unitD0 = unitZ0.cross(direction).normalized();
   Vector3 unitDistance = unitD0.cross(unitZ0);
 
   RotationMatrix3 mFrame;
   mFrame.col(0) = unitD0;
   mFrame.col(1) = unitZ0;
   mFrame.col(2) = unitDistance;
 
   return mFrame;
 }
 
 double LineSurface::pathCorrection(const GeometryContext& /*gctx*/,
                                    const Vector3& /*pos*/,
                                    const Vector3& /*mom*/) const {
   return 1.;
 }
 
 Vector3 LineSurface::referencePosition(const GeometryContext& gctx,
                                        AxisDirection /*aDir*/) const {
   return center(gctx);
 }
 
 Vector3 LineSurface::normal(const GeometryContext& gctx, const Vector3& pos,
                             const Vector3& direction) const {
   auto ref = referenceFrame(gctx, pos, direction);
   return ref.col(2);
 }
 
 const SurfaceBounds& LineSurface::bounds() const {
   if (m_bounds) {
     return *m_bounds;
   }
   return s_noBounds;
 }
 
 MultiIntersection3D LineSurface::intersect(
     const GeometryContext& gctx, const Vector3& position,
     const Vector3& direction, const BoundaryTolerance& boundaryTolerance,
     double tolerance) const {
   // The nomenclature is following the header file and doxygen documentation
 
   const Vector3& ma = position;
   const Vector3& ea = direction;
 
   // Origin of the line surface
   Vector3 mb = localToGlobalTransform(gctx).translation();
   // Line surface axis
   Vector3 eb = lineDirection(gctx);
 
   // Now go ahead and solve for the closest approach
   Vector3 mab = mb - ma;
   double eaTeb = ea.dot(eb);
   double denom = 1 - eaTeb * eaTeb;
 
   // `tolerance` does not really have a meaning here it is just a sufficiently
   // small number so `u` does not explode
   if (std::abs(denom) < std::abs(tolerance)) {
     // return a false intersection
     return MultiIntersection3D(Intersection3D::Invalid());
   }
 
   double u = (mab.dot(ea) - mab.dot(eb) * eaTeb) / denom;
   // Check if we are on the surface already
   IntersectionStatus status = std::abs(u) > std::abs(tolerance)
                                   ? IntersectionStatus::reachable
                                   : IntersectionStatus::onSurface;
   Vector3 result = ma + u * ea;
   // Evaluate the boundary check if requested
   // m_bounds == nullptr prevents unnecessary calculations for PerigeeSurface
   if (m_bounds && !boundaryTolerance.isInfinite()) {
     Vector3 vecLocal = result - mb;
     double cZ = vecLocal.dot(eb);
     double cR = (vecLocal - cZ * eb).norm();
     if (!m_bounds->inside({cR, cZ}, boundaryTolerance)) {
       status = IntersectionStatus::unreachable;
     }
   }
 
   return MultiIntersection3D(Intersection3D(result, u, status));
 }
 
 BoundToFreeMatrix LineSurface::boundToFreeJacobian(
     const GeometryContext& gctx, const Vector3& position,
     const Vector3& direction) const {
   assert(isOnSurface(gctx, position, direction, BoundaryTolerance::Infinite()));
 
   // retrieve the reference frame
   auto rframe = referenceFrame(gctx, position, direction);
 
   Vector2 local = *globalToLocal(gctx, position, direction,
                                  std::numeric_limits<double>::max());
 
   // For the derivative of global position with bound angles, refer the
   // following white paper:
   // https://acts.readthedocs.io/en/latest/white_papers/line-surface-jacobian.html
 
   BoundToFreeMatrix jacToGlobal =
       Surface::boundToFreeJacobian(gctx, position, direction);
 
   // 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 * local.x() * ipdn;
   jacToGlobal.block<3, 1>(eFreePos0, eBoundTheta) = dDThetaY * local.x() * ipdn;
 
   return jacToGlobal;
 }
 
 FreeToPathMatrix LineSurface::freeToPathDerivative(
     const GeometryContext& gctx, const Vector3& position,
     const Vector3& direction) const {
   assert(isOnSurface(gctx, position, direction, BoundaryTolerance::Infinite()));
 
   // The vector between position and center
   Vector3 pcRowVec = position - center(gctx);
   // The local frame z axis
   Vector3 localZAxis = lineDirection(gctx);
   // The local z coordinate
   double pz = pcRowVec.dot(localZAxis);
   // Cosine of angle between momentum direction and local frame z axis
   double dz = localZAxis.dot(direction);
   double norm = 1 / (1 - dz * dz);
 
   // Initialize the derivative of propagation path w.r.t. free parameter
   FreeToPathMatrix freeToPath = FreeToPathMatrix::Zero();
 
   // The derivative of path w.r.t. position
   freeToPath.segment<3>(eFreePos0) =
       norm * (dz * localZAxis.transpose() - direction.transpose());
 
   // The derivative of path w.r.t. direction
   freeToPath.segment<3>(eFreeDir0) =
       norm * (pz * localZAxis.transpose() - pcRowVec.transpose());
 
   return freeToPath;
 }
 
 AlignmentToPathMatrix LineSurface::alignmentToPathDerivative(
     const GeometryContext& gctx, const Vector3& position,
     const Vector3& direction) const {
   assert(isOnSurface(gctx, position, direction, BoundaryTolerance::Infinite()));
 
   // The vector between position and center
   Vector3 pcRowVec = position - center(gctx);
   // The local frame z axis
   Vector3 localZAxis = lineDirection(gctx);
   // The local z coordinate
   double pz = pcRowVec.dot(localZAxis);
   // Cosine of angle between momentum direction and local frame z axis
   double dz = localZAxis.dot(direction);
   double norm = 1 / (1 - dz * dz);
   // Calculate the derivative of local frame axes w.r.t its rotation
   auto [rotToLocalXAxis, rotToLocalYAxis, rotToLocalZAxis] =
       detail::rotationToLocalAxesDerivative(
           localToGlobalTransform(gctx).rotation());
 
   // Initialize the derivative of propagation path w.r.t. local frame
   // translation (origin) and rotation
   AlignmentToPathMatrix alignToPath = AlignmentToPathMatrix::Zero();
   alignToPath.segment<3>(eAlignmentCenter0) =
       norm * (direction.transpose() - dz * localZAxis.transpose());
   alignToPath.segment<3>(eAlignmentRotation0) =
       norm * (dz * pcRowVec.transpose() + pz * direction.transpose()) *
       rotToLocalZAxis;
 
   return alignToPath;
 }
 
 Matrix<2, 3> LineSurface::localCartesianToBoundLocalDerivative(
     const GeometryContext& gctx, const Vector3& position) const {
   // calculate the transformation to local coordinates
   Vector3 localPosition = localToGlobalTransform(gctx).inverse() * position;
   double localPhi = VectorHelpers::phi(localPosition);
 
   Matrix<2, 3> loc3DToLocBound = Matrix<2, 3>::Zero();
   loc3DToLocBound << std::cos(localPhi), std::sin(localPhi), 0, 0, 0, 1;
 
   return loc3DToLocBound;
 }
 
 Vector3 LineSurface::lineDirection(const GeometryContext& gctx) const {
   return localToGlobalTransform(gctx).linear().col(2);
 }
 
 const std::shared_ptr<const LineBounds>& LineSurface::boundsPtr() const {
   return m_bounds;
 }
 
 void LineSurface::assignSurfaceBounds(
     std::shared_ptr<const LineBounds> newBounds) {
   m_bounds = std::move(newBounds);
 }
 
 }  // namespace Acts

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