VolumeConverter.cxx

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/*
  Copyright (C) 2002-2024 CERN for the benefit of the ATLAS collaboration
*/
 
#include "TrkDetDescrGeoModelCnv/VolumeConverter.h"
 
#include "GeoPrimitives/GeoPrimitivesHelpers.h"
// Trk
#include "TrkGeometry/TrackingVolume.h"
#include "TrkVolumes/BevelledCylinderVolumeBounds.h"
#include "TrkVolumes/BoundarySurface.h"
#include "TrkVolumes/CombinedVolumeBounds.h"
#include "TrkVolumes/CuboidVolumeBounds.h"
#include "TrkVolumes/CylinderVolumeBounds.h"
#include "TrkVolumes/DoubleTrapezoidVolumeBounds.h"
#include "TrkVolumes/PrismVolumeBounds.h"
#include "TrkVolumes/SimplePolygonBrepVolumeBounds.h"
#include "TrkVolumes/SubtractedVolumeBounds.h"
#include "TrkVolumes/TrapezoidVolumeBounds.h"
// GeoModel
#include "GeoModelKernel/GeoShapeIntersection.h"
#include "GeoModelKernel/GeoShapeShift.h"
#include "GeoModelKernel/GeoShapeSubtraction.h"
#include "GeoModelKernel/GeoShapeUnion.h"
#include "GeoModelKernel/GeoTrd.h"
#include "GeoModelUtilities/GeoVisitVolumes.h"
 
// STL
#include <algorithm>
#include <iostream>
namespace {
    const Trk::Material dummyMaterial{1.e10, 1.e10, 0., 0., 0.};
 
    Amg::Transform3D* makeTransform(const Amg::Transform3D& trf) {
        return std::make_unique<Amg::Transform3D>(trf).release();
    }
}
 
namespace Trk {
VolumeConverter::VolumeConverter() : AthMessaging("VolumeConverter") {}
 
std::unique_ptr<TrackingVolume> VolumeConverter::translate(const GeoVPhysVol* gv, 
                                                           bool simplify, bool blend,
                                                           double blendMassLimit) const {
 
    const std::string name = gv->getLogVol()->getName();
 
    Amg::Transform3D ident{Amg::Transform3D::Identity()};
    std::unique_ptr<Volume> volGeo{m_geoShapeConverter.translateGeoShape(
        gv->getLogVol()->getShape(), ident)};
 
    // resolve volume structure into a set of non-overlapping subtractions from
    // analytically calculable shapes
    VolumePairVec constituents = splitComposedVolume(*volGeo);
 
    // material properties
    Material mat = Trk::GeoMaterialConverter::convert(gv->getLogVol()->getMaterial());
 
    // calculate precision of volume estimate  taking into account material
    // properties
    double precision = s_precisionInX0 * mat.X0;  // required precision in mm
 
    // volume estimate from GeoShape
    double volumeFromGeoShape =
        -1;  // replace with database info when available
 
    // volume estimate from resolveBoolean
    // double volumeBoolean = calculateVolume(volGeo,false,pow(precision,3)); //
    // TODO : test on inert material
 
    // volume estimate from Volume
    double volume = volumeFromGeoShape >= 0 ? volumeFromGeoShape : -1.;
    if ((simplify || blend) && volumeFromGeoShape < 0) {
        double fraction = 0.;
        volume = 0.;
        for (const VolumePair& cs : constituents) {
            fraction = estimateFraction(cs, precision);
            if (fraction < 0) {
                volume = -1;
                break;
            } else
                volume += fraction * calculateVolume(*cs.first);
        }
    }
 
    // evaluate complexity of shape
    // simple case
    if (constituents.size() == 1 && !constituents[0].second) {
        return std::make_unique<TrackingVolume>(*volGeo, mat, nullptr, nullptr,
                                                name);
    }
    // build envelope
    std::unique_ptr<Volume> envelope{};
    std::string envName = name;
 
    std::unique_ptr<TrackingVolume> trEnv{};
 
    bool blended = false;
 
    if (constituents.size() == 1) {
 
        envelope = std::make_unique<Volume>(*(constituents.front().first),
                                            volGeo->transform());
        double volEnv = calculateVolume(*constituents.front().first);
 
        if (blend && volume > 0 && volEnv > 0 &&
            volume * mat.rho < blendMassLimit)
            blended = true;
 
        if ((simplify || blended) && volume > 0 && volEnv > 0) {
            // simplified material rescales X0, l0 and density
            double fraction = volume / volEnv;
            Material matScaled(mat.X0 / fraction, mat.L0 / fraction, mat.A,
                               mat.Z, fraction * mat.rho);
            if (blend && !blended)
                envName = envName + "_PERM";
            trEnv = std::make_unique<TrackingVolume>(*envelope, matScaled,
                                                     nullptr, nullptr, envName);
        } else {
            auto confinedVols =std::make_unique<std::vector<TrackingVolume*>>();
            confinedVols->push_back(std::make_unique<TrackingVolume>(*volGeo, mat, nullptr, nullptr, name).release());
            envName = name + "_envelope";
            trEnv = std::make_unique<TrackingVolume>(*envelope, dummyMaterial, confinedVols.release(), envName);
        }
 
        return trEnv;
    }
 
    // composed shapes : derive envelope from span
    Amg::Transform3D transf = volGeo->transform();
    std::unique_ptr<VolumeSpan> span =
        findVolumeSpan(volGeo->volumeBounds(), transf, 0., 0.);
 
    bool isCyl = false;
    for (const auto& fv : constituents) {
        const CylinderVolumeBounds* cyl =
            dynamic_cast<const CylinderVolumeBounds*>(
                &(fv.first->volumeBounds()));
        if (cyl) {
            isCyl = true;
            break;
        }
    }
 
    ATH_MSG_DEBUG(__FILE__ << ":" << __LINE__
                           << "envelope estimate: object contains cylinder:"
                           << name << ":" << isCyl);
    ATH_MSG_DEBUG(__FILE__ << ":" << __LINE__
                           << "complex volume span for envelope:" << name
                           << ":x range:" << (*span).xMin << ","
                           << (*span).xMax);
    ATH_MSG_DEBUG(__FILE__ << ":" << __LINE__
                           << "complex volume span for envelope:" << name
                           << ":y range:" << (*span).yMin << ","
                           << (*span).yMax);
    ATH_MSG_DEBUG(__FILE__ << ":" << __LINE__
                           << "complex volume span for envelope:" << name
                           << ":z range:" << (*span).zMin << ","
                           << (*span).zMax);
    ATH_MSG_DEBUG(__FILE__ << ":" << __LINE__
                           << "complex volume span for envelope:" << name
                           << ":R range:" << (*span).rMin << ","
                           << (*span).rMax);
    ATH_MSG_DEBUG(__FILE__ << ":" << __LINE__
                           << "complex volume span for envelope:" << name
                           << ":phi range:" << (*span).phiMin << ","
                           << (*span).phiMax);
 
    if (!isCyl) {  // cuboid envelope
        Amg::Transform3D cylTrf{
            transf * Amg::Translation3D{0.5 * ((*span).xMin + (*span).xMax),
                                        0.5 * ((*span).yMin + (*span).yMax),
                                        0.5 * ((*span).zMin + (*span).zMax)}};
 
        std::unique_ptr<VolumeBounds> bounds =
            std::make_unique<CuboidVolumeBounds>(
                0.5 * ((*span).xMax - (*span).xMin),
                0.5 * ((*span).yMax - (*span).yMin),
                0.5 * ((*span).zMax - (*span).zMin));
        envelope = std::make_unique<Volume>(
            makeTransform(cylTrf), bounds.release());
    } else {
        double dPhi = (*span).phiMin > (*span).phiMax
                          ? (*span).phiMax - (*span).phiMin + 2 * M_PI
                          : (*span).phiMax - (*span).phiMin;
        std::unique_ptr<VolumeBounds> cylBounds{};
        Amg::Transform3D cylTrf{transf};
        if (dPhi < 2 * M_PI) {
            double aPhi = 0.5 * ((*span).phiMax + (*span).phiMin);
            cylBounds = std::make_unique<CylinderVolumeBounds>(
                (*span).rMin, (*span).rMax, 0.5 * dPhi,
                0.5 * ((*span).zMax - (*span).zMin));
            cylTrf = cylTrf * Amg::getRotateZ3D(aPhi);
        } else {
            cylBounds = std::make_unique<CylinderVolumeBounds>(
                (*span).rMin, (*span).rMax,
                0.5 * ((*span).zMax - (*span).zMin));
        }
        envelope = std::make_unique<Volume>(
            makeTransform(cylTrf), cylBounds.release());
    }
 
    double volEnv = calculateVolume(*envelope);
 
    if (blend && volume > 0 && volEnv > 0 && volume * mat.rho < blendMassLimit)
        blended = true;
 
    if ((simplify || blended) && volume > 0 && volEnv > 0) {
        double fraction = volume / volEnv;
        Material matScaled(mat.X0 / fraction, mat.L0 / fraction, mat.A, mat.Z,
                           fraction * mat.rho);
        if (blend && !blended)
            envName = envName + "_PERM";
        trEnv = std::make_unique<TrackingVolume>(*envelope, mat, nullptr,
                                                 nullptr, envName);
    } else {
        auto confinedVols = std::make_unique<std::vector<TrackingVolume*>>();
        confinedVols->push_back( std::make_unique<TrackingVolume>(*volGeo, mat, nullptr, nullptr, name).release());
        envName = envName + "_envelope";
        trEnv = std::make_unique<TrackingVolume>(*envelope, dummyMaterial, confinedVols.release(), envName);
    }
 
    return trEnv;
}
 
double VolumeConverter::resolveBooleanVolume(const Volume& trVol,
                                             double tolerance) const {
 
    VolumePartVec constituents{};
    VolumePart inputVol{};
    inputVol.parts.push_back(std::make_unique<Volume>(trVol));
    constituents.push_back(std::move(inputVol));
    VolumePartVec::iterator sIter = constituents.begin();
 
    double volume = 0;
    while (sIter != constituents.end()) {
        bool update = false;
        for (unsigned int ii = 0; ii < (*sIter).parts.size(); ++ii) {
            const VolumeBounds& bounds{((*sIter).parts[ii]->volumeBounds())};
            const CombinedVolumeBounds* comb =
                dynamic_cast<const CombinedVolumeBounds*>(&bounds);
            const SubtractedVolumeBounds* sub =
                dynamic_cast<const SubtractedVolumeBounds*>(&bounds);
            if (comb) {
                (*sIter).parts[ii].reset(comb->first()->clone());
                VolumePart vp = (*sIter);
                constituents.push_back(vp);
                constituents.back().parts[ii].reset(comb->second()->clone());
                constituents.push_back(vp);
                constituents.back().parts.emplace_back(comb->second()->clone());
                constituents.back().sign = -1. * constituents.back().sign;
                update = true;
                break;
            } else if (sub) {
                (*sIter).parts[ii].reset(sub->outer()->clone());
                double volSub = calculateVolume(*sub->inner(), true, tolerance);
                if (volSub < tolerance) {
                    volume += -1. * (*sIter).sign * volSub;
                } else {
                    constituents.emplace_back(*sIter);
                    constituents.back().parts.emplace_back(
                        sub->inner()->clone());
                    constituents.back().sign = -1. * constituents.back().sign;
                }
                update = true;
                break;
            } else {
                // component small, below tolerance
                double volSmall = calculateVolume(*(*sIter).parts[ii]);
                if (volSmall < tolerance) {
                    sIter=constituents.erase(sIter);
                    update = true;
                    break;
                }
            }
        }  //
        if (update)
            sIter = constituents.begin();
        else if ((*sIter).parts.size() == 1) {
            double volSingle = calculateVolume(*(*sIter).parts[0]);
            volume += (*sIter).sign * volSingle;
            sIter=constituents.erase(sIter);
        } else {
            std::vector<std::shared_ptr<Volume>>::iterator tit =
                (*sIter).parts.begin();
            bool noovrlp = false;
            while (tit + 1 != (*sIter).parts.end()) {
                std::pair<bool, std::unique_ptr<Volume>> overlap =
                    Trk::VolumeIntersection::intersect(**tit, **(tit + 1));
                if (overlap.first && !overlap.second) {
                    sIter=constituents.erase(sIter);
                    noovrlp = true;
                    break;
                }  // no intersection
                else if (overlap.first && overlap.second) {
                    (*sIter).parts.erase(tit, tit + 2);
                    (*sIter).parts.push_back(std::move(overlap.second));
                    tit = (*sIter).parts.begin();
                } else {
                    if (calculateVolume(**tit) < tolerance) {
                        sIter=constituents.erase(sIter);
                        noovrlp = true;
                        break;
                    }
                    if (calculateVolume(**(tit + 1)) < tolerance) {
                        sIter=constituents.erase(sIter);
                        noovrlp = true;
                        break;
                    }
                    std::pair<bool, std::unique_ptr<Volume>> overlap =
                        Trk::VolumeIntersection::intersectApproximative(
                            **tit, **(tit + 1));
                    if (overlap.first) {
                        if (overlap.second) {
                            (*sIter).parts.erase(tit, tit + 2);
                            (*sIter).parts.push_back(std::move(overlap.second));
                            tit = (*sIter).parts.begin();
                        } else {
                            sIter=constituents.erase(sIter);
                            noovrlp = true;
                            break;  // no intersection
                        }
                    } else
                        ++tit;
                }
            }
            if (noovrlp) {
            } else if ((*sIter).parts.size() == 1) {
                double volSingle = calculateVolume(*(*sIter).parts[0]);
                volume += (*sIter).sign * volSingle;
                sIter=constituents.erase(sIter);
            } else {
                ++sIter;
            }
        }
    }
 
    if (!constituents.empty()) {
        ATH_MSG_VERBOSE("boolean volume resolved to "
                        << constituents.size() << " items "
                        << ":volume estimate:" << volume);
    }
    return volume;
}
 
VolumeConverter::VolumePairVec VolumeConverter::splitComposedVolume(
    const Trk::Volume& trVol) {
 
    VolumePairVec constituents;
    constituents.emplace_back(std::make_unique<Volume>(trVol), nullptr);
    VolumePairVec::iterator sIter = constituents.begin();
    std::unique_ptr<VolumeBounds> newBounds{};
    while (sIter != constituents.end()) {
        const CombinedVolumeBounds* comb =
            dynamic_cast<const Trk::CombinedVolumeBounds*>(
                &((*sIter).first->volumeBounds()));
        const Trk::SubtractedVolumeBounds* sub =
            dynamic_cast<const Trk::SubtractedVolumeBounds*>(
                &((*sIter).first->volumeBounds()));
        if (comb) {
            std::shared_ptr<Volume> subVol = (*sIter).second;
            sIter = constituents.erase(sIter);
            std::shared_ptr<Volume> combFirst{comb->first()->clone()};
            std::shared_ptr<Volume> combSecond{comb->second()->clone()};
            if (comb->intersection()) {
                newBounds = std::make_unique<Trk::SubtractedVolumeBounds>(
                    combFirst->clone(), combSecond->clone());
                std::unique_ptr<Trk::Volume> newSubVol =
                    std::make_unique<Volume>(nullptr, newBounds.release());
                if (subVol) {
                    newBounds = std::make_unique<CombinedVolumeBounds>(
                        subVol->clone(), newSubVol.release(), false);
                    std::shared_ptr<Volume> newCSubVol =
                        std::make_unique<Volume>(nullptr, newBounds.release());
                    constituents.insert(sIter,
                                        std::make_pair(combFirst, newCSubVol));
                } else {
                    constituents.insert(
                        sIter, std::make_pair(combFirst, std::move(newSubVol)));
                }
            } else {
                constituents.insert(sIter, std::make_pair(combFirst, subVol));
                if (subVol) {
                    newBounds = std::make_unique<CombinedVolumeBounds>(
                        subVol->clone(), combFirst->clone(), false);
                    std::unique_ptr<Trk::Volume> newSubVol =
                        std::make_unique<Volume>(nullptr, newBounds.release());
                    constituents.insert(
                        sIter,
                        std::make_pair(combSecond, std::move(newSubVol)));
                } else {
                    constituents.insert(sIter,
                                        std::make_pair(combSecond, combFirst));
                }
            }
            sIter = constituents.begin();
        } else if (sub) {
            std::shared_ptr<Volume> subVol = (*sIter).second;
            sIter = constituents.erase(sIter);
            std::shared_ptr<Volume> innerVol{sub->inner()->clone()};
            std::shared_ptr<Volume> outerVol{sub->outer()->clone()};
            if (subVol) {
                newBounds = std::make_unique<CombinedVolumeBounds>(
                    subVol->clone(), innerVol->clone(), false);
                std::unique_ptr<Volume> newSubVol =
                    std::make_unique<Trk::Volume>(nullptr, newBounds.release());
                constituents.insert(
                    sIter, std::make_pair(outerVol, std::move(newSubVol)));
            } else {
                constituents.insert(sIter, std::make_pair(outerVol, innerVol));
            }
            sIter = constituents.begin();
        } else {
            ++sIter;
        }
    }
    return constituents;
}
 
std::unique_ptr<VolumeSpan> VolumeConverter::findVolumeSpan(
    const VolumeBounds& volBounds, const Amg::Transform3D& transform,
    double zTol, double phiTol) const {
    // volume shape
    const CuboidVolumeBounds* box =
        dynamic_cast<const CuboidVolumeBounds*>(&volBounds);
    const TrapezoidVolumeBounds* trd =
        dynamic_cast<const TrapezoidVolumeBounds*>(&volBounds);
    const DoubleTrapezoidVolumeBounds* dtrd =
        dynamic_cast<const DoubleTrapezoidVolumeBounds*>(&volBounds);
    const BevelledCylinderVolumeBounds* bcyl =
        dynamic_cast<const BevelledCylinderVolumeBounds*>(&volBounds);
    const CylinderVolumeBounds* cyl =
        dynamic_cast<const CylinderVolumeBounds*>(&volBounds);
    const SubtractedVolumeBounds* sub =
        dynamic_cast<const SubtractedVolumeBounds*>(&volBounds);
    const CombinedVolumeBounds* comb =
        dynamic_cast<const CombinedVolumeBounds*>(&volBounds);
    const SimplePolygonBrepVolumeBounds* spb =
        dynamic_cast<const SimplePolygonBrepVolumeBounds*>(&volBounds);
    const PrismVolumeBounds* prism =
        dynamic_cast<const PrismVolumeBounds*>(&volBounds);
 
    double dPhi = 0.;
 
    if (sub) {
        return findVolumeSpan(sub->outer()->volumeBounds(),
                              transform * sub->outer()->transform(), zTol,
                              phiTol);
    }
 
    if (comb) {
        std::unique_ptr<VolumeSpan> s1 = findVolumeSpan(
            comb->first()->volumeBounds(),
            transform * comb->first()->transform(), zTol, phiTol);
        std::unique_ptr<VolumeSpan> s2 = findVolumeSpan(
            comb->second()->volumeBounds(),
            transform * comb->second()->transform(), zTol, phiTol);
 
        VolumeSpan scomb;
        scomb.rMin = std::min((*s1).rMin, (*s2).rMin);
        scomb.rMax = std::max((*s1).rMax, (*s2).rMax);
        scomb.xMin = std::min((*s1).xMin, (*s2).xMin);
        scomb.xMax = std::max((*s1).xMax, (*s2).xMax);
        scomb.yMin = std::min((*s1).yMin, (*s2).yMin);
        scomb.yMax = std::max((*s1).yMax, (*s2).yMax);
        scomb.zMin = std::min((*s1).zMin, (*s2).zMin);
        scomb.zMax = std::max((*s1).zMax, (*s2).zMax);
        if ((*s1).phiMin < (*s1).phiMax && (*s2).phiMin < (*s2).phiMax) {
            scomb.phiMin = std::min((*s1).phiMin, (*s2).phiMin);
            scomb.phiMax = std::max((*s1).phiMax, (*s2).phiMax);
        } else if ((*s1).phiMin < (*s1).phiMax && (*s2).phiMin > (*s2).phiMax) {
            if ((*s1).phiMin > (*s2).phiMax) {
                scomb.phiMin = std::min((*s1).phiMin, (*s2).phiMin);
                scomb.phiMax = (*s2).phiMax;
            } else if ((*s1).phiMax < (*s2).phiMin) {
                scomb.phiMin = (*s2).phiMin;
                scomb.phiMax = std::max((*s1).phiMax, (*s2).phiMax);
            } else {
                scomb.phiMin = 0.;
                scomb.phiMax = 2 * M_PI;
            }
        } else if ((*s1).phiMin > (*s1).phiMax && (*s2).phiMin < (*s2).phiMax) {
            if ((*s2).phiMin > (*s1).phiMax) {
                scomb.phiMin = std::min((*s1).phiMin, (*s2).phiMin);
                scomb.phiMax = (*s1).phiMax;
            } else if ((*s2).phiMax < (*s1).phiMin) {
                scomb.phiMin = (*s1).phiMin;
                scomb.phiMax = std::max((*s1).phiMax, (*s2).phiMax);
            } else {
                scomb.phiMin = 0.;
                scomb.phiMax = 2 * M_PI;
            }
        } else {
            scomb.phiMin = std::min((*s1).phiMin, (*s2).phiMin);
            scomb.phiMax = std::max((*s1).phiMax, (*s2).phiMax);
        }
        return std::make_unique<VolumeSpan>(scomb);
    }
 
    //
    double minZ{1.e6}, maxZ{-1.e6}, minPhi{2 * M_PI}, maxPhi{0.}, minR{1.e6},
        maxR{0.}, minX{1.e6}, maxX{-1.e6}, minY{1.e6}, maxY{-1.e6};
 
    // defined vertices and edges
    std::vector<Amg::Vector3D> vtx;
    std::vector<std::pair<int, int>> edges;
    VolumeSpan span;
 
    if (box) {
        vtx.emplace_back(box->halflengthX(), box->halflengthY(),
                         box->halflengthZ());
        vtx.emplace_back(-box->halflengthX(), box->halflengthY(),
                         box->halflengthZ());
        vtx.emplace_back(box->halflengthX(), -box->halflengthY(),
                         box->halflengthZ());
        vtx.emplace_back(-box->halflengthX(), -box->halflengthY(),
                         box->halflengthZ());
        vtx.emplace_back(box->halflengthX(), box->halflengthY(),
                         -box->halflengthZ());
        vtx.emplace_back(-box->halflengthX(), box->halflengthY(),
                         -box->halflengthZ());
        vtx.emplace_back(box->halflengthX(), -box->halflengthY(),
                         -box->halflengthZ());
        vtx.emplace_back(-box->halflengthX(), -box->halflengthY(),
                         -box->halflengthZ());
        edges.emplace_back(0, 1);
        edges.emplace_back(0, 2);
        edges.emplace_back(1, 3);
        edges.emplace_back(2, 3);
        edges.emplace_back(4, 5);
        edges.emplace_back(4, 6);
        edges.emplace_back(5, 7);
        edges.emplace_back(6, 7);
        edges.emplace_back(0, 4);
        edges.emplace_back(1, 5);
        edges.emplace_back(2, 6);
        edges.emplace_back(3, 7);
    }
    if (trd) {
        vtx.emplace_back(trd->maxHalflengthX(), trd->halflengthY(),
                         trd->halflengthZ());
        vtx.emplace_back(-trd->maxHalflengthX(), trd->halflengthY(),
                         trd->halflengthZ());
        vtx.emplace_back(trd->minHalflengthX(), -trd->halflengthY(),
                         trd->halflengthZ());
        vtx.emplace_back(-trd->minHalflengthX(), -trd->halflengthY(),
                         trd->halflengthZ());
        vtx.emplace_back(trd->maxHalflengthX(), trd->halflengthY(),
                         -trd->halflengthZ());
        vtx.emplace_back(-trd->maxHalflengthX(), trd->halflengthY(),
                         -trd->halflengthZ());
        vtx.emplace_back(trd->minHalflengthX(), -trd->halflengthY(),
                         -trd->halflengthZ());
        vtx.emplace_back(-trd->minHalflengthX(), -trd->halflengthY(),
                         -trd->halflengthZ());
        edges.emplace_back(0, 1);
        edges.emplace_back(0, 2);
        edges.emplace_back(1, 3);
        edges.emplace_back(2, 3);
        edges.emplace_back(4, 5);
        edges.emplace_back(4, 6);
        edges.emplace_back(5, 7);
        edges.emplace_back(6, 7);
        edges.emplace_back(0, 4);
        edges.emplace_back(1, 5);
        edges.emplace_back(2, 6);
        edges.emplace_back(3, 7);
    }
    if (dtrd) {
        vtx.emplace_back(dtrd->maxHalflengthX(), 2 * dtrd->halflengthY2(),
                         dtrd->halflengthZ());
        vtx.emplace_back(-dtrd->maxHalflengthX(), 2 * dtrd->halflengthY2(),
                         dtrd->halflengthZ());
        vtx.emplace_back(dtrd->medHalflengthX(), 0., dtrd->halflengthZ());
        vtx.emplace_back(-dtrd->medHalflengthX(), 0., dtrd->halflengthZ());
        vtx.emplace_back(dtrd->minHalflengthX(), -2 * dtrd->halflengthY1(),
                         dtrd->halflengthZ());
        vtx.emplace_back(-dtrd->minHalflengthX(), -2 * dtrd->halflengthY1(),
                         dtrd->halflengthZ());
        vtx.emplace_back(dtrd->maxHalflengthX(), 2 * dtrd->halflengthY2(),
                         -dtrd->halflengthZ());
        vtx.emplace_back(-dtrd->maxHalflengthX(), 2 * dtrd->halflengthY2(),
                         -dtrd->halflengthZ());
        vtx.emplace_back(dtrd->medHalflengthX(), 0., -dtrd->halflengthZ());
        vtx.emplace_back(-dtrd->medHalflengthX(), 0., -dtrd->halflengthZ());
        vtx.emplace_back(dtrd->minHalflengthX(), -2 * dtrd->halflengthY1(),
                         -dtrd->halflengthZ());
        vtx.emplace_back(-dtrd->minHalflengthX(), -2 * dtrd->halflengthY1(),
                         -dtrd->halflengthZ());
        edges.emplace_back(0, 1);
        edges.emplace_back(0, 2);
        edges.emplace_back(1, 3);
        edges.emplace_back(2, 4);
        edges.emplace_back(3, 5);
        edges.emplace_back(4, 5);
        edges.emplace_back(6, 7);
        edges.emplace_back(6, 8);
        edges.emplace_back(7, 9);
        edges.emplace_back(8, 10);
        edges.emplace_back(9, 11);
        edges.emplace_back(10, 11);
        edges.emplace_back(0, 6);
        edges.emplace_back(1, 7);
        edges.emplace_back(2, 8);
        edges.emplace_back(3, 9);
        edges.emplace_back(4, 10);
        edges.emplace_back(5, 11);
    }
    if (bcyl) {
        dPhi = bcyl->halfPhiSector();
        vtx.emplace_back(0., 0., bcyl->halflengthZ());
        vtx.emplace_back(0., 0., -bcyl->halflengthZ());
        edges.emplace_back(0, 1);
        if (dPhi < M_PI) {
            const double cosDphi = std::cos(dPhi);
            const double sinDphi = std::sin(dPhi);
            vtx.emplace_back(bcyl->outerRadius() * cosDphi,
                             bcyl->outerRadius() * sinDphi,
                             bcyl->halflengthZ());
            vtx.emplace_back(bcyl->innerRadius() * cosDphi,
                             bcyl->innerRadius() * sinDphi,
                             bcyl->halflengthZ());
            vtx.emplace_back(bcyl->outerRadius() * cosDphi,
                             -bcyl->outerRadius() * sinDphi,
                             bcyl->halflengthZ());
            vtx.emplace_back(bcyl->innerRadius() * cosDphi,
                             -bcyl->innerRadius() * sinDphi,
                             bcyl->halflengthZ());
            vtx.emplace_back(bcyl->outerRadius() * cosDphi,
                             bcyl->outerRadius() * sinDphi,
                             -bcyl->halflengthZ());
            vtx.emplace_back(bcyl->innerRadius() * cosDphi,
                             bcyl->innerRadius() * sinDphi,
                             -bcyl->halflengthZ());
            vtx.emplace_back(bcyl->outerRadius() * cosDphi,
                             -bcyl->outerRadius() * sinDphi,
                             -bcyl->halflengthZ());
            vtx.emplace_back(bcyl->innerRadius() * cosDphi,
                             -bcyl->innerRadius() * sinDphi,
                             -bcyl->halflengthZ());
            vtx.emplace_back(bcyl->outerRadius(), 0.,
                             0.);  // to distinguish phi intervals for cylinders
                                   // aligned with z axis
            edges.emplace_back(2, 3);
            edges.emplace_back(4, 5);
            edges.emplace_back(6, 7);
            edges.emplace_back(8, 9);
            if (bcyl->type() == 1 || bcyl->type() == 3) {
                edges.emplace_back(3, 5);
                edges.emplace_back(7, 9);
            }
            if (bcyl->type() == 2 || bcyl->type() == 3) {
                edges.emplace_back(2, 4);
                edges.emplace_back(6, 8);
            }
        }
    }
    if (cyl) {
        dPhi = cyl->halfPhiSector();
        vtx.emplace_back(0., 0., cyl->halflengthZ());
        vtx.emplace_back(0., 0., -cyl->halflengthZ());
        edges.emplace_back(0, 1);
        if (dPhi < M_PI) {
            const double cosDphi = std::cos(dPhi);
            const double sinDphi = std::sin(dPhi);
            vtx.emplace_back(cyl->outerRadius() * cosDphi,
                             cyl->outerRadius() * sinDphi, cyl->halflengthZ());
            vtx.emplace_back(cyl->innerRadius() * cosDphi,
                             cyl->innerRadius() * sinDphi, cyl->halflengthZ());
            vtx.emplace_back(cyl->outerRadius() * cosDphi,
                             -cyl->outerRadius() * sinDphi, cyl->halflengthZ());
            vtx.emplace_back(cyl->outerRadius() * cosDphi,
                             -cyl->outerRadius() * sinDphi, cyl->halflengthZ());
            vtx.emplace_back(cyl->outerRadius() * cosDphi,
                             cyl->outerRadius() * sinDphi, -cyl->halflengthZ());
            vtx.emplace_back(cyl->innerRadius() * cosDphi,
                             cyl->innerRadius() * sinDphi, -cyl->halflengthZ());
            vtx.emplace_back(cyl->outerRadius() * cosDphi,
                             -cyl->outerRadius() * sinDphi,
                             -cyl->halflengthZ());
            vtx.emplace_back(cyl->outerRadius() * cosDphi,
                             -cyl->outerRadius() * sinDphi,
                             -cyl->halflengthZ());
            vtx.emplace_back(cyl->outerRadius(), 0.,
                             0.);  // to distinguish phi intervals for cylinders
                                   // aligned with z axis
            edges.emplace_back(2, 3);
            edges.emplace_back(4, 5);
            edges.emplace_back(6, 7);
            edges.emplace_back(8, 9);
        }
    }
 
    if (spb) {
        const std::vector<std::pair<double, double>> vtcs = spb->xyVertices();
        for (const auto& vtc : vtcs) {
            vtx.emplace_back(vtc.first, vtc.second, spb->halflengthZ());
            vtx.emplace_back(vtc.first, vtc.second, -spb->halflengthZ());
            edges.emplace_back(vtx.size() - 2, vtx.size() - 1);
            if (vtx.size() > 2) {
                edges.emplace_back(
                    vtx.size() - 4, vtx.size() - 2);
                edges.emplace_back(
                    vtx.size() - 3, vtx.size() - 1);
            }
            if (vtx.size() > 4) {  // some diagonals
                edges.emplace_back(vtx.size() - 2, 1);
                edges.emplace_back(vtx.size() - 1, 0);
            }
        }
        edges.emplace_back(0, vtx.size() - 2);
        edges.emplace_back(1, vtx.size() - 1);
    }
 
    if (prism) {
        const std::vector<std::pair<double, double>> vtcs = prism->xyVertices();
        for (const auto& vtc : vtcs) {
            vtx.emplace_back(vtc.first, vtc.second, prism->halflengthZ());
            vtx.emplace_back(vtc.first, vtc.second, -prism->halflengthZ());
            edges.emplace_back(vtx.size() - 2, vtx.size() - 1);
            if (vtx.size() > 2) {
                edges.emplace_back(
                    vtx.size() - 4, vtx.size() - 2);
                edges.emplace_back(
                    vtx.size() - 3, vtx.size() - 1);
            }
        }
        edges.emplace_back(0, vtx.size() - 2);
        edges.emplace_back(1, vtx.size() - 1);
    }
 
    std::vector<Amg::Vector3D> vtxt;
 
    for (unsigned int ie = 0; ie < vtx.size(); ie++) {
        Amg::Vector3D gp = transform * vtx[ie];
        vtxt.push_back(gp);
 
        double phi = gp.phi() + M_PI;
        double rad = gp.perp();
 
        // collect limits from vertices
        minX = std::min(minX, gp[0]);
        maxX = std::max(maxX, gp[0]);
        minY = std::min(minY, gp[1]);
        maxY = std::max(maxY, gp[1]);
        minZ = std::min(minZ, gp[2]);
        maxZ = std::max(maxZ, gp[2]);
        minR = std::min(minR, rad);
        maxR = std::max(maxR, rad);
        maxPhi = std::max(maxPhi, phi);
        minPhi = std::min(minPhi, phi);
    }
 
    if (cyl || bcyl) {
 
        double ro = cyl ? cyl->outerRadius() : bcyl->outerRadius();
        double ri = cyl ? cyl->innerRadius() : bcyl->innerRadius();
        // z span corrected for theta inclination
        Amg::Vector3D dir =
            (vtxt[edges[0].first] - vtxt[edges[0].second]).unit();
        maxZ += ro * sin(dir.theta());
        minZ += -ro * sin(dir.theta());
        // azimuthal & radial extent
        if (ro < minR) {  // excentric object, phi span driven by z-R extent
            // calculate point of closest approach
            PerigeeSurface peri;
            Intersection closest = peri.straightLineIntersection(vtxt[1], dir);
            double le = (vtxt[0] - vtxt[1]).norm();
            if ((closest.position - vtxt[0]).norm() < le &&
                (closest.position - vtxt[1]).norm() < le) {
                if (minR > closest.position.perp() - ro)
                    minR = std::max(0., closest.position.perp() - ro);
                // use for phi check
                double phiClosest = closest.position.phi() + M_PI;
                if (phiClosest < minPhi || phiClosest > maxPhi) {
                    double phiTmp = minPhi;
                    minPhi = maxPhi;
                    maxPhi = phiTmp;
                }
            } else
                minR = std::max(0., minR - ro * std::abs(dir.z()));
 
            const double aTan = std::atan2(ro, minR);
            minPhi += -aTan;
            maxPhi += aTan;
            if (minPhi < 0)
                minPhi += 2 * M_PI;
            if (maxPhi > 2 * M_PI)
                maxPhi += -2 * M_PI;
 
            maxR += ro * std::abs(cos(dir.theta()));
        } else {
 
            double rAx = std::max(vtxt[0].perp(), vtxt[1].perp());
            if (rAx < ri)
                minR = ri - rAx;
            else
                minR = std::max(0., minR - ro * std::abs(cos(dir.theta())));
 
            // loop over edges to check inner radial extent
            PerigeeSurface peri;
            for (unsigned int ie = 0; ie < edges.size(); ie++) {
                Amg::Vector3D dir =
                    (vtxt[edges[ie].first] - vtxt[edges[ie].second]).unit();
                Intersection closest =
                    peri.straightLineIntersection(vtxt[edges[ie].second], dir);
                double le =
                    (vtxt[edges[ie].first] - vtxt[edges[ie].second]).norm();
                if ((closest.position - vtxt[edges[ie].first]).norm() < le &&
                    (closest.position - vtxt[edges[ie].second]).norm() < le)
                    if (minR > closest.position.perp())
                        minR = closest.position.perp();
            }
 
            if (vtxt.size() > 10) {  // cylindrical section
                // find spread of phi extent at section (-) boundary : vertices
                // 4,5,8,9
                double phiSecLmin = std::min(
                    std::min(vtxt[4].phi() + M_PI, vtxt[5].phi() + M_PI),
                    std::min(vtxt[8].phi() + M_PI, vtxt[9].phi() + M_PI));
                double phiSecLmax = std::max(
                    std::max(vtxt[4].phi() + M_PI, vtxt[5].phi() + M_PI),
                    std::max(vtxt[8].phi() + M_PI, vtxt[9].phi() + M_PI));
                // find spread of phi extent at section (+) boundary : vertices
                // 2,3,6,7
                double phiSecUmin = std::min(
                    std::min(vtxt[2].phi() + M_PI, vtxt[3].phi() + M_PI),
                    std::min(vtxt[6].phi() + M_PI, vtxt[7].phi() + M_PI));
                double phiSecUmax = std::max(
                    std::max(vtxt[2].phi() + M_PI, vtxt[3].phi() + M_PI),
                    std::max(vtxt[6].phi() + M_PI, vtxt[7].phi() + M_PI));
                minPhi = std::min(std::min(phiSecLmin, phiSecLmax),
                                  std::min(phiSecUmin, phiSecUmax));
                maxPhi = std::max(std::max(phiSecLmin, phiSecLmax),
                                  std::max(phiSecUmin, phiSecUmax));
                if (vtxt[10].phi() + M_PI < minPhi ||
                    vtxt[10].phi() + M_PI > maxPhi) {
                    minPhi = 3 * M_PI;
                    maxPhi = 0.;
                    double phiTmp;
                    for (unsigned int iv = 2; iv < vtxt.size(); iv++) {
                        phiTmp = vtxt[iv].phi() + M_PI;
                        if (phiTmp < M_PI)
                            phiTmp += 2 * M_PI;
                        minPhi = phiTmp < minPhi ? phiTmp : minPhi;
                        maxPhi = phiTmp > maxPhi ? phiTmp : maxPhi;
                    }
                    if (minPhi > 2 * M_PI)
                        minPhi += -2 * M_PI;
                    if (maxPhi > 2 * M_PI)
                        maxPhi += -2 * M_PI;
                }
            } else {
                minPhi = 0.;
                maxPhi = 2 * M_PI;
                maxR += ro * std::abs(std::cos(dir.theta()));
            }
            if (minPhi >= maxPhi && (minPhi - maxPhi) < M_PI) {
                minPhi = 0.;
                maxPhi = 2 * M_PI;
            }
        }
    }  // end cyl & bcyl
 
    if (!cyl && !bcyl) {
        // loop over edges to check inner radial extent
        PerigeeSurface peri;
        for (unsigned int ie = 0; ie < edges.size(); ie++) {
            Amg::Vector3D dir =
                (vtxt[edges[ie].first] - vtxt[edges[ie].second]).unit();
            Intersection closest =
                peri.straightLineIntersection(vtxt[edges[ie].second], dir);
            double le = (vtxt[edges[ie].first] - vtxt[edges[ie].second]).norm();
            if ((closest.position - vtxt[edges[ie].first]).norm() < le &&
                (closest.position - vtxt[edges[ie].second]).norm() < le)
                if (minR > closest.position.perp())
                    minR = closest.position.perp();
        }  // end loop over edges
        // verify phi span - may run across step
        if (std::abs(maxPhi - minPhi) > M_PI) {
            double phiTmp = minPhi;
            minPhi = 3 * M_PI;
            maxPhi = 0.;  // redo the search
            for (unsigned int iv = 0; iv < vtxt.size(); iv++) {
                phiTmp = vtxt[iv].phi() + M_PI;
                if (phiTmp < M_PI)
                    phiTmp += 2 * M_PI;
                minPhi = phiTmp < minPhi ? phiTmp : minPhi;
                maxPhi = phiTmp > maxPhi ? phiTmp : maxPhi;
            }
            if (minPhi > 2 * M_PI)
                minPhi += -2 * M_PI;
            if (maxPhi > 2 * M_PI)
                maxPhi += -2 * M_PI;
            if (minPhi >= maxPhi && (minPhi - maxPhi) < M_PI) {
                minPhi = 0.;
                maxPhi = 2 * M_PI;
            }
        }
    }
 
    if (cyl || bcyl || box || trd || dtrd || spb || prism) {
        span.zMin = minZ - zTol;
        span.zMax = maxZ - +zTol;
        minPhi = (minPhi - phiTol) < 0 ? minPhi - phiTol + 2 * M_PI
                                       : minPhi - phiTol;
        span.phiMin = minPhi;
        maxPhi = (maxPhi + phiTol) > 2 * M_PI ? maxPhi + phiTol - 2 * M_PI
                                              : maxPhi + phiTol;
        span.phiMax = maxPhi;
        span.rMin = std::max(70.001, minR - zTol);
        span.rMax = maxR + zTol;
        span.xMin = minX - zTol;
        span.xMax = maxX - +zTol;
        span.yMin = minY - zTol;
        span.yMax = maxY - +zTol;
    } else {
        ATH_MSG_WARNING("VolumeConverter::volume shape not recognized ");
    }
    return std::make_unique<VolumeSpan>(span);
}
 
double VolumeConverter::calculateVolume(const Volume& vol, bool nonBooleanOnly,
                                        double precision) const {
 
    double volume = -1.;
 
    const CylinderVolumeBounds* cyl = dynamic_cast<const CylinderVolumeBounds*>(&(vol.volumeBounds()));
    const CuboidVolumeBounds* box = dynamic_cast<const CuboidVolumeBounds*>(&(vol.volumeBounds()));
    const TrapezoidVolumeBounds* trd = dynamic_cast<const TrapezoidVolumeBounds*>(&(vol.volumeBounds()));
    const BevelledCylinderVolumeBounds* bcyl =dynamic_cast<const BevelledCylinderVolumeBounds*>(&(vol.volumeBounds()));
    const PrismVolumeBounds* prism =dynamic_cast<const PrismVolumeBounds*>(&(vol.volumeBounds()));
    const SimplePolygonBrepVolumeBounds* spb = dynamic_cast<const SimplePolygonBrepVolumeBounds*>(&(vol.volumeBounds()));
    const CombinedVolumeBounds* comb =dynamic_cast<const CombinedVolumeBounds*>(&(vol.volumeBounds()));
    const SubtractedVolumeBounds* sub = dynamic_cast<const SubtractedVolumeBounds*>(&(vol.volumeBounds()));
 
    if (cyl) {
        return 2 * cyl->halfPhiSector() * cyl->halflengthZ() *
               (std::pow(cyl->outerRadius(), 2) -
                std::pow(cyl->innerRadius(), 2));
    }
    if (box) {
        return 8 * box->halflengthX() * box->halflengthY() * box->halflengthZ();
    }
    if (trd) {
        return 4 * (trd->minHalflengthX() + trd->maxHalflengthX()) *
               trd->halflengthY() * trd->halflengthZ();
    }
    if (bcyl) {
        int type = bcyl->type();
        if (type < 1)
            return 2 * bcyl->halfPhiSector() *
                   (std::pow(bcyl->outerRadius(), 2) -
                    std::pow(bcyl->innerRadius(), 2)) *
                   bcyl->halflengthZ();
        if (type == 1)
            return 2 * bcyl->halflengthZ() *
                   (bcyl->halfPhiSector() * std::pow(bcyl->outerRadius(), 2) -
                    std::pow(bcyl->innerRadius(), 2) *
                        std::tan(bcyl->halfPhiSector()));
        if (type == 2)
            return 2 * bcyl->halflengthZ() *
                   (-bcyl->halfPhiSector() * std::pow(bcyl->innerRadius(), 2) +
                    std::pow(bcyl->outerRadius(), 2) *
                        std::tan(bcyl->halfPhiSector()));
        if (type == 3)
            return 2 * bcyl->halflengthZ() * std::tan(bcyl->halfPhiSector()) *
                   (std::pow(bcyl->outerRadius(), 2) -
                    std::pow(bcyl->innerRadius(), 2));
    }
    if (prism) {
 
        std::vector<std::pair<double, double>> v = prism->xyVertices();
        double vv = v[0].first * (v[1].second - v.back().second);
        for (unsigned int i = 1; i < v.size() - 1; i++) {
            vv += v[i].first * (v[i + 1].second - v[i - 1].second);
        }
        vv += v.back().first * (v[0].second - v[v.size() - 2].second);
        return vv * prism->halflengthZ();
    }
    if (spb) {
        std::vector<std::pair<double, double>> v = spb->xyVertices();
        double vv = v[0].first * (v[1].second - v.back().second);
        for (unsigned int i = 1; i < v.size() - 1; i++) {
            vv += v[i].first * (v[i + 1].second - v[i - 1].second);
        }
        vv += v.back().first * (v[0].second - v[v.size() - 2].second);
        return vv * spb->halflengthZ();
    }
 
    if (nonBooleanOnly)
        return volume;
 
    if (comb || sub) {
        return resolveBooleanVolume(vol, precision);
    }
    return volume;
}
 
double VolumeConverter::estimateFraction(const VolumePair& sub,
                                         double precision) const {
 
    if (!sub.first)
        return 0.;
 
    if (sub.first && !sub.second)
        return 1.;
    double fraction = -1.;
 
    std::pair<bool, std::unique_ptr<Volume>> overlap =
        Trk::VolumeIntersection::intersect(*sub.first, *sub.second);
 
    if (overlap.first && !overlap.second)
        return fraction = 1.;
    else if (overlap.first && overlap.second) {
        fraction = 1. - calculateVolume(*overlap.second, true, precision) /
                            calculateVolume(*sub.first, true, precision);
        return fraction;
    }
    //  resolve embedded volumes
 
    // trivial within required precision
    double volA = calculateVolume(*sub.first, true, precision);
    double volB = calculateVolume(*sub.second, true, precision);
    if ((volA > 0 && volA < precision) || (volB > 0 && volB < precision))
        return 1.;
 
    return fraction;
}
 
void VolumeConverter::collectMaterial(const GeoVPhysVol* pv,
                                      MaterialProperties& layMat,
                                      double sf) const {
    // sf is the area of the layer collecting the material
 
    // solution relying on GeoModel
    // currently involves hit&miss on-fly calculation of boolean volumes
    // GeoModelTools::MaterialComponent  mat =
    // gm_materialHelper.collectMaterial(pv); Material newMP =
    // convert(mat.first); double d = mat.second / sf; layMat.addMaterial(newMP,
    // d / newMP.x0()); return;
 
    std::vector<MaterialComponent> materialContent;
    collectMaterialContent(pv, materialContent);
 
    for (const auto& mat : materialContent) {
        if (mat.second < 0)
            continue;  // protection unsolved booleans
        double d = sf > 0 ? mat.second / sf : 0.;
        if (d > 0)
            layMat.addMaterial(mat.first,
                               (mat.first.X0 > 0 ? d / mat.first.X0 : 0.));
    }
}
 
void VolumeConverter::collectMaterialContent(
    const GeoVPhysVol* gv,
    std::vector<MaterialComponent>& materialContent) const {
 
    // solution relying on GeoModel
    // currently involves hit&miss on-fly calculation of boolean volumes
    // GeoModelTools::MaterialComponent  mat =
    // gm_materialHelper.collectMaterial(pv); Material newMP =
    // convert(mat.first); materialContent.push_back( MaterialComponent( newMP,
    // mat.second) ); return;
 
    const GeoLogVol* lv = gv->getLogVol();
    Material mat = Trk::GeoMaterialConverter::convert(lv->getMaterial());
 
    double motherVolume = 0.;
 
    // skip volume calculation for dummy material configuration
    if (!Trk::GeoMaterialConverter::dummy_material(lv->getMaterial())) {
        const GeoShape* sh = lv->getShape();
        while (sh && sh->type() == "Shift") {
            const GeoShapeShift* shift = dynamic_cast<const GeoShapeShift*>(sh);
            sh = shift ? shift->getOp() : nullptr;
        }
 
        bool isBoolean =
            sh && (sh->type() == "Subtraction" || sh->type() == "Union" ||
                   sh->type() == "Intersection");
 
        if (isBoolean) {
            Amg::Transform3D transf{Amg::Transform3D::Identity()};
            std::unique_ptr<Volume> vol{
                m_geoShapeConverter.translateGeoShape(sh, transf)};
            motherVolume =
                calculateVolume(*vol, false, std::pow(1.e-3 * mat.X0, 3));
            if (motherVolume < 0) {
                //  m_geoShapeConverter.decodeShape(sh);
            }
        } else
            motherVolume = lv->getShape()->volume();
    }
 
    double childVol = 0;
    std::string cPrevious = " ";
    size_t nIdentical = 0;
    std::vector<Trk::MaterialComponent> childMat;
    std::vector<const GeoVPhysVol*> children = geoGetVolumesNoXform (gv);
    for (const GeoVPhysVol* cv : children) {
        std::string cname = cv->getLogVol()->getName();
        if (cname == cPrevious)
            nIdentical++;  // assuming identity for identical name and branching
                           // history
        else {             // scale and collect material from previous item
            for (const auto& cmat : childMat) {
                materialContent.emplace_back(cmat.first, nIdentical * cmat.second);
                childVol += materialContent.back().second;
            }
            childMat.clear();  // reset
            nIdentical = 1;    // current
            collectMaterialContent(cv, childMat);
        }
    }
    for (const auto& cmat : childMat) {
        materialContent.emplace_back(cmat.first, nIdentical * cmat.second);
        childVol += materialContent.back().second;
    }
    if (motherVolume > 0 && childVol > 0)
        motherVolume += -1. * childVol;
 
    ATH_MSG_DEBUG("collected material:" << lv->getName() << ":made of:"
                                        << lv->getMaterial()->getName()
                                        << ":density(g/mm3)" << mat.rho
                                        << ":mass:" << mat.rho * motherVolume);
    materialContent.emplace_back(mat, motherVolume);
}
 
double VolumeConverter::leadingVolume(const GeoShape* sh) const {
 
    if (sh->type() == "Subtraction") {
        const GeoShapeSubtraction* sub =
            dynamic_cast<const GeoShapeSubtraction*>(sh);
        if (sub)
            return leadingVolume(sub->getOpA());
    }
    if (sh->type() == "Union") {
        const GeoShapeUnion* uni = dynamic_cast<const GeoShapeUnion*>(sh);
        if (uni)
            return leadingVolume(uni->getOpA()) + leadingVolume(uni->getOpB());
    }
    if (sh->type() == "Intersection") {
        const GeoShapeIntersection* intr =
            dynamic_cast<const GeoShapeIntersection*>(sh);
        if (intr)
            return std::min(leadingVolume(intr->getOpA()),
                            leadingVolume(intr->getOpB()));
    }
    if (sh->type() == "Shift") {
        const GeoShapeShift* shift = dynamic_cast<const GeoShapeShift*>(sh);
        if (shift)
            return leadingVolume(shift->getOp());
    }
 
    return sh->volume();
}
}  // namespace Trk