ConeSurface.cpp

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// This file is part of the Acts project.
//
// Copyright (C) 2016-2020 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 http://mozilla.org/MPL/2.0/.

#include "Acts/Surfaces/ConeSurface.hpp"

#include "Acts/Surfaces/SurfaceError.hpp"
#include "Acts/Surfaces/detail/FacesHelper.hpp"
#include "Acts/Surfaces/detail/VerticesHelper.hpp"
#include "Acts/Utilities/ThrowAssert.hpp"
#include "Acts/Utilities/detail/RealQuadraticEquation.hpp"

#include <cassert>
#include <cmath>

using Acts::VectorHelpers::perp;
using Acts::VectorHelpers::phi;

Acts::ConeSurface::ConeSurface(const ConeSurface& other)
    : GeometryObject(), Surface(other), m_bounds(other.m_bounds) {}

Acts::ConeSurface::ConeSurface(const GeometryContext& gctx,
                               const ConeSurface& other,
                               const Transform3D& shift)
    : GeometryObject(), Surface(gctx, other, shift), m_bounds(other.m_bounds) {}

Acts::ConeSurface::ConeSurface(const Transform3D& transform, double alpha,
                               bool symmetric)
    : GeometryObject(),
      Surface(transform),
      m_bounds(std::make_shared<const ConeBounds>(alpha, symmetric)) {}

Acts::ConeSurface::ConeSurface(const Transform3D& transform, double alpha,
                               double zmin, double zmax, double halfPhi)
    : GeometryObject(),
      Surface(transform),
      m_bounds(std::make_shared<const ConeBounds>(alpha, zmin, zmax, halfPhi)) {
}

Acts::ConeSurface::ConeSurface(const Transform3D& transform,
                               const std::shared_ptr<const ConeBounds>& cbounds)
    : GeometryObject(), Surface(transform), m_bounds(cbounds) {
  throw_assert(cbounds, "ConeBounds must not be nullptr");
}

Acts::Vector3D Acts::ConeSurface::binningPosition(
    const GeometryContext& gctx, Acts::BinningValue bValue) const {
  const Vector3D& sfCenter = center(gctx);

  // special binning type for R-type methods
  if (bValue == Acts::binR || bValue == Acts::binRPhi) {
    return Vector3D(sfCenter.x() + bounds().r(sfCenter.z()), sfCenter.y(),
                    sfCenter.z());
  }
  // give the center as default for all of these binning types
  // binX, binY, binZ, binR, binPhi, binRPhi, binH, binEta
  return sfCenter;
}

Acts::Surface::SurfaceType Acts::ConeSurface::type() const {
  return Surface::Cone;
}

Acts::ConeSurface& Acts::ConeSurface::operator=(const ConeSurface& other) {
  if (this != &other) {
    Surface::operator=(other);
    m_bounds = other.m_bounds;
  }
  return *this;
}

Acts::Vector3D Acts::ConeSurface::rotSymmetryAxis(
    const GeometryContext& gctx) const {
  return std::move(transform(gctx).matrix().block<3, 1>(0, 2));
}

Acts::RotationMatrix3D Acts::ConeSurface::referenceFrame(
    const GeometryContext& gctx, const Vector3D& position,
    const Vector3D& /*unused*/) const {
  RotationMatrix3D mFrame;
  // construct the measurement frame
  // measured Y is the local z axis
  Vector3D measY = rotSymmetryAxis(gctx);
  // measured z is the position transverse normalized
  Vector3D measDepth = Vector3D(position.x(), position.y(), 0.).normalized();
  // measured X is what comoes out of it
  Acts::Vector3D measX(measY.cross(measDepth).normalized());
  // the columnes
  mFrame.col(0) = measX;
  mFrame.col(1) = measY;
  mFrame.col(2) = measDepth;
  // return the rotation matrix
  // return it
  return mFrame;
}

Acts::Vector3D Acts::ConeSurface::localToGlobal(
    const GeometryContext& gctx, const Vector2D& lposition,
    const Vector3D& /*unused*/) const {
  // create the position in the local 3d frame
  double r = lposition[Acts::eBoundLoc1] * bounds().tanAlpha();
  double phi = lposition[Acts::eBoundLoc0] / r;
  Vector3D loc3Dframe(r * cos(phi), r * sin(phi), lposition[Acts::eBoundLoc1]);
  return transform(gctx) * loc3Dframe;
}

Acts::Result<Acts::Vector2D> Acts::ConeSurface::globalToLocal(
    const GeometryContext& gctx, const Vector3D& position,
    const Vector3D& /*unused*/) const {
  Vector3D loc3Dframe = transform(gctx).inverse() * position;
  double r = loc3Dframe.z() * bounds().tanAlpha();
  if (std::abs(perp(loc3Dframe) - r) > s_onSurfaceTolerance) {
    return Result<Vector2D>::failure(SurfaceError::GlobalPositionNotOnSurface);
  }
  return Result<Vector2D>::success(
      {r * atan2(loc3Dframe.y(), loc3Dframe.x()), loc3Dframe.z()});
}

double Acts::ConeSurface::pathCorrection(const GeometryContext& gctx,
                                         const Vector3D& position,
                                         const Vector3D& direction) const {
  // (cos phi cos alpha, sin phi cos alpha, sgn z sin alpha)
  Vector3D posLocal = transform(gctx).inverse() * position;
  double phi = VectorHelpers::phi(posLocal);
  double sgn = posLocal.z() > 0. ? -1. : +1.;
  double cosAlpha = std::cos(bounds().get(ConeBounds::eAlpha));
  double sinAlpha = std::sin(bounds().get(ConeBounds::eAlpha));
  Vector3D normalC(cos(phi) * cosAlpha, sin(phi) * cosAlpha, sgn * sinAlpha);
  normalC = transform(gctx) * normalC;
  // Back to the global frame
  double cAlpha = normalC.dot(direction);
  return std::abs(1. / cAlpha);
}

std::string Acts::ConeSurface::name() const {
  return "Acts::ConeSurface";
}

Acts::Vector3D Acts::ConeSurface::normal(
    const GeometryContext& gctx, const Acts::Vector2D& lposition) const {
  // (cos phi cos alpha, sin phi cos alpha, sgn z sin alpha)
  double phi = lposition[Acts::eBoundLoc0] /
               (bounds().r(lposition[Acts::eBoundLoc1])),
         sgn = lposition[Acts::eBoundLoc1] > 0 ? -1. : +1.;
  double cosAlpha = std::cos(bounds().get(ConeBounds::eAlpha));
  double sinAlpha = std::sin(bounds().get(ConeBounds::eAlpha));
  Vector3D localNormal(cos(phi) * cosAlpha, sin(phi) * cosAlpha,
                       sgn * sinAlpha);
  return Vector3D(transform(gctx).linear() * localNormal);
}

Acts::Vector3D Acts::ConeSurface::normal(const GeometryContext& gctx,
                                         const Acts::Vector3D& position) const {
  // get it into the cylinder frame if needed
  // @todo respect opening angle
  Vector3D pos3D = transform(gctx).inverse() * position;
  pos3D.z() = 0;
  return pos3D.normalized();
}

const Acts::ConeBounds& Acts::ConeSurface::bounds() const {
  // is safe because no constructor w/o bounds exists
  return (*m_bounds.get());
}

Acts::Polyhedron Acts::ConeSurface::polyhedronRepresentation(
    const GeometryContext& gctx, size_t lseg) const {
  // Prepare vertices and faces
  std::vector<Vector3D> vertices;
  std::vector<Polyhedron::FaceType> faces;
  std::vector<Polyhedron::FaceType> triangularMesh;

  double minZ = bounds().get(ConeBounds::eMinZ);
  double maxZ = bounds().get(ConeBounds::eMaxZ);

  if (minZ == -std::numeric_limits<double>::infinity() or
      maxZ == std::numeric_limits<double>::infinity()) {
    throw std::domain_error(
        "Polyhedron repr of boundless surface not possible");
  }

  auto ctransform = transform(gctx);

  // The tip - created only once and only, if the it's not a cut-off cone
  bool tipExists = false;
  if (minZ * maxZ <= s_onSurfaceTolerance) {
    vertices.push_back(ctransform * Vector3D(0., 0., 0.));
    tipExists = true;
  }

  // Cone parameters
  double hPhiSec = bounds().get(ConeBounds::eHalfPhiSector);
  double avgPhi = bounds().get(ConeBounds::eAveragePhi);
  bool fullCone = (hPhiSec == M_PI);

  // Get the phi segments from the helper
  auto phiSegs = fullCone ? detail::VerticesHelper::phiSegments()
                          : detail::VerticesHelper::phiSegments(
                                avgPhi - hPhiSec, avgPhi + hPhiSec, {avgPhi});

  // Negative cone if exists
  std::vector<double> coneSides;
  if (std::abs(minZ) > s_onSurfaceTolerance) {
    coneSides.push_back(minZ);
  }
  if (std::abs(maxZ) > s_onSurfaceTolerance) {
    coneSides.push_back(maxZ);
  }
  for (auto& z : coneSides) {
    // Remember the first vertex
    size_t firstIv = vertices.size();
    // Radius and z offset
    double r = std::abs(z) * bounds().tanAlpha();
    Vector3D zoffset(0., 0., z);
    for (unsigned int iseg = 0; iseg < phiSegs.size() - 1; ++iseg) {
      int addon = (iseg == phiSegs.size() - 2 and not fullCone) ? 1 : 0;
      detail::VerticesHelper::createSegment(vertices, {r, r}, phiSegs[iseg],
                                            phiSegs[iseg + 1], lseg, addon,
                                            zoffset, ctransform);
    }
    // Create the faces
    if (tipExists) {
      for (size_t iv = firstIv + 2; iv < vertices.size() + 1; ++iv) {
        size_t one = 0, two = iv - 1, three = iv - 2;
        if (z < 0.) {
          std::swap(two, three);
        }
        faces.push_back({one, two, three});
      }
      // Complete cone if necessary
      if (fullCone) {
        if (z > 0.) {
          faces.push_back({0, firstIv, vertices.size() - 1});
        } else {
          faces.push_back({0, vertices.size() - 1, firstIv});
        }
      }
    }
  }
  // if no tip exists, connect the two bows
  if (tipExists) {
    triangularMesh = faces;
  } else {
    auto facesMesh =
        detail::FacesHelper::cylindricalFaceMesh(vertices, fullCone);
    faces = facesMesh.first;
    triangularMesh = facesMesh.second;
  }
  return Polyhedron(vertices, faces, triangularMesh, false);
}