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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/.
 
 namespace Acts {
 template <typename external_spacepoint_t, typename callable_t>
 inline LinCircle transformCoordinates(Acts::SpacePointMutableData& mutableData,
                                       const external_spacepoint_t& sp,
                                       const external_spacepoint_t& spM,
                                       bool bottom,
                                       callable_t&& extractFunction) {
   // The computation inside this function is exactly identical to that in the
   // vectorized version of this function, except that it operates on a single
   // spacepoint. Please see the other version of this function for more
   // detailed comments.
 
   auto [xM, yM, zM, rM, varianceRM, varianceZM] = extractFunction(spM);
   auto [xSP, ySP, zSP, rSP, varianceRSP, varianceZSP] = extractFunction(sp);
 
   float cosPhiM = xM / rM;
   float sinPhiM = yM / rM;
   float deltaX = xSP - xM;
   float deltaY = ySP - yM;
   float deltaZ = zSP - zM;
   float xNewFrame = deltaX * cosPhiM + deltaY * sinPhiM;
   float yNewFrame = deltaY * cosPhiM - deltaX * sinPhiM;
   float deltaR2 = (xNewFrame * xNewFrame + yNewFrame * yNewFrame);
   float iDeltaR2 = 1. / (deltaX * deltaX + deltaY * deltaY);
   float iDeltaR = std::sqrt(iDeltaR2);
   int bottomFactor = bottom ? -1 : 1;
   float cotTheta = deltaZ * iDeltaR * bottomFactor;
 
   // conformal transformation u=x/(x²+y²) v=y/(x²+y²) transform the
   // circle into straight lines in the u/v plane the line equation can
   // be described in terms of aCoef and bCoef, where v = aCoef * u +
   // bCoef
   const float U = xNewFrame * iDeltaR2;
   const float V = yNewFrame * iDeltaR2;
 
   // error term for sp-pair without correlation of middle space point
   const float Er = ((varianceZM + varianceZSP) +
                     (cotTheta * cotTheta) * (varianceRM + varianceRSP)) *
                    iDeltaR2;
 
   mutableData.setDeltaR(sp.index(), std::sqrt(deltaR2 + (deltaZ * deltaZ)));
   return LinCircle(cotTheta, iDeltaR, Er, U, V, xNewFrame, yNewFrame);
 }
 
 template <typename external_spacepoint_t>
 inline void transformCoordinates(
     Acts::SpacePointMutableData& mutableData,
     const std::vector<const external_spacepoint_t*>& vec,
     const external_spacepoint_t& spM, bool bottom,
     std::vector<LinCircle>& linCircleVec) {
   const float xM = spM.x();
   const float yM = spM.y();
   const float zM = spM.z();
   const float rM = spM.radius();
   const float varianceRM = spM.varianceR();
   const float varianceZM = spM.varianceZ();
 
   // resize + operator[] is faster than reserve and push_back
   linCircleVec.resize(vec.size());
 
   float cosPhiM = xM / rM;
   float sinPhiM = yM / rM;
 
   int bottomFactor = bottom ? -1 : 1;
 
   for (std::size_t idx(0); idx < vec.size(); ++idx) {
     const external_spacepoint_t* sp = vec[idx];
 
     const float xSP = sp->x();
     const float ySP = sp->y();
     const float zSP = sp->z();
     const float varianceRSP = sp->varianceR();
     const float varianceZSP = sp->varianceZ();
 
     const float deltaX = xSP - xM;
     const float deltaY = ySP - yM;
     const float deltaZ = zSP - zM;
     // calculate projection fraction of spM->sp vector pointing in same
     // direction as
     // vector origin->spM (x) and projection fraction of spM->sp vector pointing
     // orthogonal to origin->spM (y)
     const float xNewFrame = deltaX * cosPhiM + deltaY * sinPhiM;
     const float yNewFrame = deltaY * cosPhiM - deltaX * sinPhiM;
     // 1/(length of M -> SP)
     const float deltaR2 = (xNewFrame * xNewFrame + yNewFrame * yNewFrame);
     const float iDeltaR2 = 1. / deltaR2;
     const float iDeltaR = std::sqrt(iDeltaR2);
     //
     // cot_theta = (deltaZ/deltaR)
     const float cotTheta = deltaZ * iDeltaR * bottomFactor;
     // transformation of circle equation (x,y) into linear equation (u,v)
     // x^2 + y^2 - 2x_0*x - 2y_0*y = 0
     // is transformed into
     // 1 - 2x_0*u - 2y_0*v = 0
     // using the following m_U and m_V
     // (u = A + B*v); A and B are created later on
     const float U = xNewFrame * iDeltaR2;
     const float V = yNewFrame * iDeltaR2;
     // error term for sp-pair without correlation of middle space point
     const float Er = ((varianceZM + varianceZSP) +
                       (cotTheta * cotTheta) * (varianceRM + varianceRSP)) *
                      iDeltaR2;
 
     // Fill Line Circle
     linCircleVec[idx].cotTheta = cotTheta;
     linCircleVec[idx].iDeltaR = iDeltaR;
     linCircleVec[idx].Er = Er;
     linCircleVec[idx].U = U;
     linCircleVec[idx].V = V;
     linCircleVec[idx].x = xNewFrame;
     linCircleVec[idx].y = yNewFrame;
     mutableData.setDeltaR(sp->index(), std::sqrt(deltaR2 + (deltaZ * deltaZ)));
   }
 }
 
 template <typename external_spacepoint_t>
 inline bool xyzCoordinateCheck(
     const Acts::SeedFinderConfig<external_spacepoint_t>& m_config,
     const external_spacepoint_t& sp, const double* spacepointPosition,
     double* outputCoordinates) {
   // check the compatibility of SPs coordinates in xyz assuming the
   // Bottom-Middle direction with the strip measurement details
 
   using namespace Acts::HashedStringLiteral;
   const Acts::Vector3& topStripVector = sp.topStripVector();
   const Acts::Vector3& bottomStripVector = sp.bottomStripVector();
   const Acts::Vector3& stripCenterDistance = sp.stripCenterDistance();
 
   const double xTopStripVector = topStripVector[0];
   const double yTopStripVector = topStripVector[1];
   const double zTopStripVector = topStripVector[2];
   const double xBottomStripVector = bottomStripVector[0];
   const double yBottomStripVector = bottomStripVector[1];
   const double zBottomStripVector = bottomStripVector[2];
 
   // cross product between top strip vector and spacepointPosition
   double d1[3] = {yTopStripVector * spacepointPosition[2] -
                       zTopStripVector * spacepointPosition[1],
                   zTopStripVector * spacepointPosition[0] -
                       xTopStripVector * spacepointPosition[2],
                   xTopStripVector * spacepointPosition[1] -
                       yTopStripVector * spacepointPosition[0]};
 
   // scalar product between bottom strip vector and d1
   double bd1 = xBottomStripVector * d1[0] + yBottomStripVector * d1[1] +
                zBottomStripVector * d1[2];
 
   // compatibility check using distance between strips to evaluate if
   // spacepointPosition is inside the bottom detector element
   double s1 = (stripCenterDistance[0] * d1[0] + stripCenterDistance[1] * d1[1] +
                stripCenterDistance[2] * d1[2]);
   if (std::abs(s1) > std::abs(bd1) * m_config.toleranceParam) {
     return false;
   }
 
   // cross product between bottom strip vector and spacepointPosition
   double d0[3] = {yBottomStripVector * spacepointPosition[2] -
                       zBottomStripVector * spacepointPosition[1],
                   zBottomStripVector * spacepointPosition[0] -
                       xBottomStripVector * spacepointPosition[2],
                   xBottomStripVector * spacepointPosition[1] -
                       yBottomStripVector * spacepointPosition[0]};
 
   // compatibility check using distance between strips to evaluate if
   // spacepointPosition is inside the top detector element
   double s0 = (stripCenterDistance[0] * d0[0] + stripCenterDistance[1] * d0[1] +
                stripCenterDistance[2] * d0[2]);
   if (std::abs(s0) > std::abs(bd1) * m_config.toleranceParam) {
     return false;
   }
 
   // if arrive here spacepointPosition is compatible with strip directions and
   // detector elements
 
   const Acts::Vector3& topStripCenterPosition = sp.topStripCenterPosition();
 
   // spacepointPosition corrected with respect to the top strip position and
   // direction and the distance between the strips
   s0 = s0 / bd1;
   outputCoordinates[0] = topStripCenterPosition[0] + xTopStripVector * s0;
   outputCoordinates[1] = topStripCenterPosition[1] + yTopStripVector * s0;
   outputCoordinates[2] = topStripCenterPosition[2] + zTopStripVector * s0;
   return true;
 }
 }  // namespace Acts

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