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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/TrackParametrization.hpp"
 #include "Acts/Utilities/MathHelpers.hpp"
 
 Acts::FreeVector Acts::estimateTrackParamsFromSeed(const Vector3& sp0,
                                                    const Vector3& sp1,
                                                    const Vector3& sp2,
                                                    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 trans(sp0);
   // The transform which constructs the new frame
   const Transform3 transform(trans * rotation);
 
   // The coordinate of the middle and top space point in the new frame
   const Vector3 local1 = transform.inverse() * sp1;
   const Vector3 local2 = transform.inverse() * sp2;
 
   // We determine the center of the circle directly given the 3 points and using
   // Cramer's rule.
   Vector2 circleCenter = Vector2::Zero();
   {
     const double det = 2 * (local1.x() * local2.y() - local2.x() * local1.y());
 
     // Check if points are aligned and return straight line estimate if so
     if (std::abs(det) < 1e-12) {
       FreeVector params = FreeVector::Zero();
       params.segment<3>(eFreePos0) = sp0;
       params.segment<3>(eFreeDir0) = (sp2 - sp0).normalized();
       params[eFreeQOverP] = 0;
       return params;
     }
 
     const double z1 = local1.head<2>().squaredNorm();
     const double z2 = local2.head<2>().squaredNorm();
 
     const double nom1 = local1.y() * z2 - local2.y() * z1;
     const double nom2 = local2.x() * z1 - local1.x() * z2;
 
     circleCenter.x() = nom1 / det;
     circleCenter.y() = nom2 / det;
   }
   const int sign = circleCenter.y() >= 0 ? 1 : -1;
   const double R = circleCenter.norm();
 
   const double invTanTheta =
       local2.z() / (2 * R * std::asin(local2.head<2>().norm() / (2 * R)));
   // The momentum direction in the new frame (the center of the circle has the
   // coordinate (-1.*A/(2*B), 1./(2*B)))
   const double A = -circleCenter.x() / circleCenter.y();
   const Vector3 transDirection(1., A, fastHypot(1, A) * invTanTheta);
   // Transform it back to the original frame
   const Vector3 direction = rotation * transDirection.normalized();
 
   // 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 = sign / (bField.norm() * R);
   // The estimated q/p in [GeV/c]^-1
   params[eFreeQOverP] = qOverPt / fastHypot(1., invTanTheta);
 
   return params;
 }
 
 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)");
 
   BoundSquareMatrix result = BoundSquareMatrix::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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