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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/Seeding/EstimateTrackParamsFromSeed.hpp"
 
 #include "Acts/Definitions/Algebra.hpp"
 #include "Acts/Definitions/TrackParametrization.hpp"
 #include "Acts/Utilities/MathHelpers.hpp"
 
 #include <cmath>
 
 namespace Acts {
 
 namespace {
 
 Transform3 estimationFrameLocalToGlobal(const Vector3& sp0, const Vector3& sp1,
                                         const Vector3& bField) {
   // Define a new coordinate frame with its origin at the bottom space point, z
   // axis long the magnetic field direction and y axis perpendicular to vector
   // from the bottom to middle space point. Hence, the projection of the middle
   // space point on the transverse plane will be located at the x axis of the
   // new frame.
   const Vector3 relVec = sp1 - sp0;
   const Vector3 newZAxis = bField.normalized();
   const Vector3 newYAxis = newZAxis.cross(relVec).normalized();
   const Vector3 newXAxis = newYAxis.cross(newZAxis);
   RotationMatrix3 rotation;
   rotation.col(0) = newXAxis;
   rotation.col(1) = newYAxis;
   rotation.col(2) = newZAxis;
   // The center of the new frame is at the bottom space point
   const Translation3 translation(sp0);
   // The transform which constructs the new frame
   return translation * rotation;
 }
 
 double computeDzDs(double A, double B, const Vector3& local0,
                    const Vector3& local2) {
   const auto computeLocalPhi = [&](const Vector2& local) -> double {
     // Scaled radius vector from circle center
     const Vector2 r = 2 * B * local - Vector2(-A, 1);
 
     return std::atan2(r.y(), r.x());
   };
 
   const double localPhi0 = computeLocalPhi(local0.head<2>());
   const double localPhi2 = computeLocalPhi(local2.head<2>());
 
   const double dZ = local2.z() - local0.z();
   const double dPhi = localPhi2 - localPhi0;
 
   // Apply the sinc correction to account for the fact that the particle do not
   // follow a straight line in the R-Z plane. This is especially important for
   // high delta phi and/or strongly bent tracks.
   const double sincCorrection = sinc(dPhi / 2);
 
   const double dzds =
       sincCorrection * dZ / (local2.head<2>() - local0.head<2>()).norm();
 
   return dzds;
 }
 
 struct ConformalMappingResult {
   Vector2 uv1;
   Vector2 uv2;
   Vector2 duv;
   double A;
   double B;
   double bOverS;
   double dzds;
 };
 
 ConformalMappingResult performConformalMapping(const Vector3& local1,
                                                const Vector3& local2) {
   ConformalMappingResult r{};
   r.uv1 = local1.head<2>() / local1.head<2>().squaredNorm();
   r.uv2 = local2.head<2>() / local2.head<2>().squaredNorm();
   r.duv = r.uv2 - r.uv1;
   r.A = r.duv.y() / r.duv.x();
   r.B = r.uv1.y() - r.A * r.uv1.x();
   r.bOverS = (r.uv1.y() * r.uv2.x() - r.uv2.y() * r.uv1.x()) / r.duv.norm();
   r.dzds = computeDzDs(r.A, r.B, local1, local2);
   return r;
 }
 
 Vector3 computeLocalTangent(const ConformalMappingResult& cm,
                             const Vector2& local) {
   // Scaled radius vector from circle center
   const Vector2 r = 2 * cm.B * local - Vector2(-cm.A, 1);
 
   // Tangent perpendicular to radius
   const Vector3 t(-r.y(), r.x(), r.norm() * cm.dzds);
 
   return t.normalized();
 }
 
 }  // namespace
 
 }  // namespace Acts
 
 Acts::FreeVector Acts::estimateTrackParamsFromSeed(const Vector3& sp0,
                                                    const Vector3& sp1,
                                                    const Vector3& sp2,
                                                    const Vector3& bField) {
   return estimateTrackParamsFromSeed(sp0, 0, sp1, sp2, bField);
 }
 
 Acts::FreeVector Acts::estimateTrackParamsFromSeed(
     const Vector3& sp0, const double t0, const Vector3& sp1, const Vector3& sp2,
     const Vector3& bField, Vector3* tangent0, Vector3* tangent1,
     Vector3* tangent2) {
   const Transform3 transform = estimationFrameLocalToGlobal(sp0, sp1, bField);
 
   // Local coordinates
   const Vector3 local0 = Vector3::Zero();
   const Vector3 local1 = transform.inverse() * sp1;
   const Vector3 local2 = transform.inverse() * sp2;
 
   // Conformal mapping
   const ConformalMappingResult cm = performConformalMapping(local1, local2);
 
   // The tangent vector at the bottom space point
   const Vector3 direction =
       transform.linear() * computeLocalTangent(cm, local0.head<2>());
 
   // Initialize the free parameters vector
   FreeVector params = FreeVector::Zero();
 
   // The bottom space point position
   params.segment<3>(eFreePos0) = sp0;
 
   // The estimated direction
   params.segment<3>(eFreeDir0) = direction;
 
   // The estimated q/pt in [GeV/c]^-1 (note that the pt is the projection of
   // momentum on the transverse plane of the new frame)
   const double qOverPt = 2 * cm.bOverS / bField.norm();
   // The estimated q/p in [GeV/c]^-1
   params[eFreeQOverP] = qOverPt / fastHypot(1, cm.dzds);
 
   // The time parameter is set to the time of the bottom space point
   params[eFreeTime] = t0;
 
   if (tangent0 != nullptr) {
     *tangent0 = direction;
   }
   if (tangent1 != nullptr) {
     *tangent1 = transform.linear() * computeLocalTangent(cm, local1.head<2>());
   }
   if (tangent2 != nullptr) {
     *tangent2 = transform.linear() * computeLocalTangent(cm, local2.head<2>());
   }
 
   return params;
 }
 
 Acts::Result<Acts::BoundVector> Acts::estimateTrackParamsFromSeed(
     const GeometryContext& gctx, const Surface& surface, const Vector3& sp0,
     const double t0, const Vector3& sp1, const Vector3& sp2,
     const Vector3& bField) {
   const FreeVector freeParams =
       estimateTrackParamsFromSeed(sp0, t0, sp1, sp2, bField);
   return transformFreeToBoundParameters(freeParams, surface, gctx);
 }
 
 Acts::BoundMatrix Acts::estimateTrackParamCovariance(
     const EstimateTrackParamCovarianceConfig& config, const BoundVector& params,
     bool hasTime) {
   assert((params[eBoundTheta] > 0 && params[eBoundTheta] < std::numbers::pi) &&
          "Theta must be in the range (0, pi)");
 
   BoundMatrix result = BoundMatrix::Zero();
 
   for (std::size_t i = eBoundLoc0; i < eBoundSize; ++i) {
     double sigma = config.initialSigmas[i];
     double variance = sigma * sigma;
 
     if (i == eBoundQOverP) {
       // note that we rely on the fact that sigma theta is already computed
       double varianceTheta = result(eBoundTheta, eBoundTheta);
 
       // contribution from sigma(q/pt)
       variance += std::pow(
           config.initialSigmaQoverPt * std::sin(params[eBoundTheta]), 2);
 
       // contribution from sigma(pt)/pt
       variance += std::pow(config.initialSigmaPtRel * params[eBoundQOverP], 2);
 
       // contribution from sigma(theta)
       variance +=
           varianceTheta *
           std::pow(params[eBoundQOverP] / std::tan(params[eBoundTheta]), 2);
     }
 
     if (i == eBoundTime && !hasTime) {
       // Inflate the time uncertainty if no time measurement is available
       variance *= config.noTimeVarInflation;
     }
 
     // Inflate the initial covariance
     variance *= config.initialVarInflation[i];
 
     result(i, i) = variance;
   }
 
   return result;
 }

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