assimp/code/AssetLib/IFC/IFCBoolean.cpp

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/// @file  IFCBoolean.cpp
/// @brief Implements a subset of Ifc boolean operations

#ifndef ASSIMP_BUILD_NO_IFC_IMPORTER

#include "AssetLib/IFC/IFCUtil.h"
#include "Common/PolyTools.h"
#include "PostProcessing/ProcessHelper.h"

#include <iterator>
#include <tuple>
#include <utility>

namespace Assimp {
namespace IFC {

// ------------------------------------------------------------------------------------------------
// Calculates intersection between line segment and plane. To catch corner cases, specify which side you prefer.
// The function then generates a hit only if the end is beyond a certain margin in that direction, filtering out
// "very close to plane" ghost hits as long as start and end stay directly on or within the given plane side.
bool IntersectSegmentPlane(const IfcVector3 &p, const IfcVector3 &n, const IfcVector3 &e0,
        const IfcVector3 &e1, bool assumeStartOnWhiteSide, IfcVector3 &out) {
    const IfcVector3 pdelta = e0 - p, seg = e1 - e0;
    const IfcFloat dotOne = n * seg, dotTwo = -(n * pdelta);

    // if segment ends on plane, do not report a hit. We stay on that side until a following segment starting at this
    // point leaves the plane through the other side
    if (std::abs(dotOne + dotTwo) < ai_epsilon) {
        return false;
    }

    // if segment starts on the plane, report a hit only if the end lies on the *other* side
    if (std::abs(dotTwo) < ai_epsilon) {
        if ((assumeStartOnWhiteSide && dotOne + dotTwo < ai_epsilon) || (!assumeStartOnWhiteSide && dotOne + dotTwo > -ai_epsilon)) {
            out = e0;
            return true;
        } else {
            return false;
        }
    }

    // ignore if segment is parallel to plane and far away from it on either side
    // Warning: if there's a few thousand of such segments which slowly accumulate beyond the epsilon, no hit would be registered
    if (std::abs(dotOne) < ai_epsilon) {
        return false;
    }

    // t must be in [0..1] if the intersection point is within the given segment
    const IfcFloat t = dotTwo / dotOne;
    if (t > 1.0 || t < 0.0) {
        return false;
    }

    out = e0 + t * seg;
    return true;
}

// ------------------------------------------------------------------------------------------------
void FilterPolygon(std::vector<IfcVector3> &resultpoly) {
    if (resultpoly.size() < 3) {
        resultpoly.clear();
        return;
    }

    IfcVector3 vmin, vmax;
    ArrayBounds(resultpoly.data(), static_cast<unsigned int>(resultpoly.size()), vmin, vmax);

    // filter our IfcFloat points - those may happen if a point lies
    // directly on the intersection line or directly on the clipping plane
    const IfcFloat epsilon = (vmax - vmin).SquareLength() / 1e6f;
    FuzzyVectorCompare fz(epsilon);
    std::vector<IfcVector3>::iterator e = std::unique(resultpoly.begin(), resultpoly.end(), fz);

    if (e != resultpoly.end()) {
        resultpoly.erase(e, resultpoly.end());
    }

    if (!resultpoly.empty() && fz(resultpoly.front(), resultpoly.back())) {
        resultpoly.pop_back();
    }
}

// ------------------------------------------------------------------------------------------------
void WritePolygon(std::vector<IfcVector3> &resultpoly, TempMesh &result) {
    FilterPolygon(resultpoly);

    if (resultpoly.size() > 2) {
        result.mVerts.insert(result.mVerts.end(), resultpoly.begin(), resultpoly.end());
        result.mVertcnt.push_back(static_cast<unsigned int>(resultpoly.size()));
    }
}

// ------------------------------------------------------------------------------------------------
void ProcessBooleanHalfSpaceDifference(const Schema_2x3::IfcHalfSpaceSolid *hs, TempMesh &result,
        const TempMesh &first_operand,
        ConversionData & /*conv*/) {
    ai_assert(hs != nullptr);

    const Schema_2x3::IfcPlane *const plane = hs->BaseSurface->ToPtr<Schema_2x3::IfcPlane>();
    if (!plane) {
        IFCImporter::LogError("expected IfcPlane as base surface for the IfcHalfSpaceSolid");
        return;
    }

    // extract plane base position vector and normal vector
    IfcVector3 p, n(0.f, 0.f, 1.f);
    if (plane->Position->Axis) {
        ConvertDirection(n, plane->Position->Axis.Get());
    }
    ConvertCartesianPoint(p, plane->Position->Location);

    if (!IsTrue(hs->AgreementFlag)) {
        n *= -1.f;
    }

    // clip the current contents of `meshout` against the plane we obtained from the second operand
    const std::vector<IfcVector3> &in = first_operand.mVerts;
    std::vector<IfcVector3> &outvert = result.mVerts;

    std::vector<unsigned int>::const_iterator begin = first_operand.mVertcnt.begin(),
                                              end = first_operand.mVertcnt.end(), iit;

    outvert.reserve(in.size());
    result.mVertcnt.reserve(first_operand.mVertcnt.size());

    unsigned int vidx = 0;
    for (iit = begin; iit != end; vidx += *iit++) {

        unsigned int newcount = 0;
        bool isAtWhiteSide = (in[vidx] - p) * n > -ai_epsilon;
        for (unsigned int i = 0; i < *iit; ++i) {
            const IfcVector3 &e0 = in[vidx + i], e1 = in[vidx + (i + 1) % *iit];

            // does the next segment intersect the plane?
            IfcVector3 isectpos;
            if (IntersectSegmentPlane(p, n, e0, e1, isAtWhiteSide, isectpos)) {
                if (isAtWhiteSide) {
                    // e0 is on the right side, so keep it
                    outvert.push_back(e0);
                    outvert.push_back(isectpos);
                    newcount += 2;
                } else {
                    // e0 is on the wrong side, so drop it and keep e1 instead
                    outvert.push_back(isectpos);
                    ++newcount;
                }
                isAtWhiteSide = !isAtWhiteSide;
            } else {
                if (isAtWhiteSide) {
                    outvert.push_back(e0);
                    ++newcount;
                }
            }
        }

        if (!newcount) {
            continue;
        }

        IfcVector3 vmin, vmax;
        ArrayBounds(&*(outvert.end() - newcount), newcount, vmin, vmax);

        // filter our IfcFloat points - those may happen if a point lies
        // directly on the intersection line. However, due to IfcFloat
        // precision a bitwise comparison is not feasible to detect
        // this case.
        const IfcFloat epsilon = (vmax - vmin).SquareLength() / 1e6f;
        FuzzyVectorCompare fz(epsilon);

        std::vector<IfcVector3>::iterator e = std::unique(outvert.end() - newcount, outvert.end(), fz);

        if (e != outvert.end()) {
            newcount -= static_cast<unsigned int>(std::distance(e, outvert.end()));
            outvert.erase(e, outvert.end());
        }
        if (fz(*(outvert.end() - newcount), outvert.back())) {
            outvert.pop_back();
            --newcount;
        }
        if (newcount > 2) {
            result.mVertcnt.push_back(newcount);
        } else
            while (newcount-- > 0) {
                result.mVerts.pop_back();
            }
    }
    IFCImporter::LogVerboseDebug("generating CSG geometry by plane clipping (IfcBooleanClippingResult)");
}

// ------------------------------------------------------------------------------------------------
// Check if e0-e1 intersects a sub-segment of the given boundary line.
// note: this functions works on 3D vectors, but performs its intersection checks solely in xy.
// New version takes the supposed inside/outside state as a parameter and treats corner cases as if
// the line stays on that side. This should make corner cases more stable.
// Two million assumptions! Boundary should have all z at 0.0, will be treated as closed, should not have
// segments with length <1e-6, self-intersecting might break the corner case handling... just don't go there, ok?
bool IntersectsBoundaryProfile(const IfcVector3 &e0, const IfcVector3 &e1, const std::vector<IfcVector3> &boundary,
        const bool isStartAssumedInside, std::vector<std::pair<size_t, IfcVector3>> &intersect_results,
        const bool halfOpen = false) {
    ai_assert(intersect_results.empty());

    // determine winding order - necessary to detect segments going "inwards" or "outwards" from a point directly on the border
    // positive sum of angles means clockwise order when looking down the -Z axis
    IfcFloat windingOrder = 0.0;
    for (size_t i = 0, bcount = boundary.size(); i < bcount; ++i) {
        IfcVector3 b01 = boundary[(i + 1) % bcount] - boundary[i];
        IfcVector3 b12 = boundary[(i + 2) % bcount] - boundary[(i + 1) % bcount];
        IfcVector3 b1_side = IfcVector3(b01.y, -b01.x, 0.0); // rotated 90° clockwise in Z plane
        // Warning: rough estimate only. A concave poly with lots of small segments each featuring a small counter rotation
        // could fool the accumulation. Correct implementation would be sum( acos( b01 * b2) * sign( b12 * b1_side))
        windingOrder += (b1_side.x * b12.x + b1_side.y * b12.y);
    }
    windingOrder = windingOrder > 0.0 ? 1.0 : -1.0;

    const IfcVector3 e = e1 - e0;

    for (size_t i = 0, bcount = boundary.size(); i < bcount; ++i) {
        // boundary segment i: b0-b1
        const IfcVector3 &b0 = boundary[i];
        const IfcVector3 &b1 = boundary[(i + 1) % bcount];
        IfcVector3 b = b1 - b0;

        // segment-segment intersection
        // solve b0 + b*s = e0 + e*t for (s,t)
        const IfcFloat det = (-b.x * e.y + e.x * b.y);
        if (std::abs(det) < ai_epsilon) {
            // no solutions (parallel lines)
            continue;
        }
        IfcFloat b_sqlen_inv = 1.0 / b.SquareLength();

        const IfcFloat x = b0.x - e0.x;
        const IfcFloat y = b0.y - e0.y;
        const IfcFloat s = (x * e.y - e.x * y) / det; // scale along boundary edge
        const IfcFloat t = (x * b.y - b.x * y) / det; // scale along given segment
        const IfcVector3 p = e0 + e * t;
#ifdef ASSIMP_BUILD_DEBUG
        const IfcVector3 check = b0 + b * s - p;
        ai_assert((IfcVector2(check.x, check.y)).SquareLength() < 1e-5);
#endif

        // also calculate the distance of e0 and e1 to the segment. We need to detect the "starts directly on segment"
        // and "ends directly at segment" cases
        bool startsAtSegment, endsAtSegment;
        {
            // calculate closest point to each end on the segment, clamp that point to the segment's length, then check
            // distance to that point. This approach is like testing if e0 is inside a capped cylinder.
            IfcFloat et0 = (b.x * (e0.x - b0.x) + b.y * (e0.y - b0.y)) * b_sqlen_inv;
            IfcVector3 closestPosToE0OnBoundary = b0 + std::max(IfcFloat(0.0), std::min(IfcFloat(1.0), et0)) * b;
            startsAtSegment = (closestPosToE0OnBoundary - IfcVector3(e0.x, e0.y, 0.0)).SquareLength() < 1e-12;
            IfcFloat et1 = (b.x * (e1.x - b0.x) + b.y * (e1.y - b0.y)) * b_sqlen_inv;
            IfcVector3 closestPosToE1OnBoundary = b0 + std::max(IfcFloat(0.0), std::min(IfcFloat(1.0), et1)) * b;
            endsAtSegment = (closestPosToE1OnBoundary - IfcVector3(e1.x, e1.y, 0.0)).SquareLength() < 1e-12;
        }

        // Line segment ends at boundary -> ignore any hit, it will be handled by possibly following segments
        if (endsAtSegment && !halfOpen) {
            continue;
        }

        // Line segment starts at boundary -> generate a hit only if following that line would change the INSIDE/OUTSIDE
        // state. This should catch the case where a connected set of segments has a point directly on the boundary,
        // one segment not hitting it because it ends there and the next segment not hitting it because it starts there
        // Should NOT generate a hit if the segment only touches the boundary but turns around and stays inside.
        if (startsAtSegment) {
            IfcVector3 inside_dir = IfcVector3(b.y, -b.x, 0.0) * windingOrder;
            bool isGoingInside = (inside_dir * e) > 0.0;
            if (isGoingInside == isStartAssumedInside) {
                continue;
            }

            // only insert the point into the list if it is sufficiently far away from the previous intersection point.
            // This way, we avoid duplicate detection if the intersection is directly on the vertex between two segments.
            if (!intersect_results.empty() && intersect_results.back().first == i - 1) {
                const IfcVector3 diff = intersect_results.back().second - e0;
                if (IfcVector2(diff.x, diff.y).SquareLength() < 1e-10) {
                    continue;
                }
            }
            intersect_results.emplace_back(i, e0);
            continue;
        }

        // for a valid intersection, s and t should be in range [0,1]. Including a bit of epsilon on s, potential double
        // hits on two consecutive boundary segments are filtered
        if (s >= -ai_epsilon * b_sqlen_inv && s <= 1.0 + ai_epsilon * b_sqlen_inv && t >= 0.0 && (t <= 1.0 || halfOpen)) {
            // only insert the point into the list if it is sufficiently far away from the previous intersection point.
            // This way, we avoid duplicate detection if the intersection is directly on the vertex between two segments.
            if (!intersect_results.empty() && intersect_results.back().first == i - 1) {
                const IfcVector3 diff = intersect_results.back().second - p;
                if (IfcVector2(diff.x, diff.y).SquareLength() < 1e-10) {
                    continue;
                }
            }
            intersect_results.emplace_back(i, p);
        }
    }

    return !intersect_results.empty();
}

// ------------------------------------------------------------------------------------------------
// note: this functions works on 3D vectors, but performs its intersection checks solely in xy.
bool PointInPoly(const IfcVector3 &p, const std::vector<IfcVector3> &boundary) {
    // even-odd algorithm: take a random vector that extends from p to infinite
    // and counts how many times it intersects edges of the boundary.
    // because checking for segment intersections is prone to numeric inaccuracies
    // or double detections (i.e. when hitting multiple adjacent segments at their
    // shared vertices) we do it thrice with different rays and vote on it.

    // the even-odd algorithm doesn't work for points which lie directly on
    // the border of the polygon. If any of our attempts produces this result,
    // we return false immediately.

    std::vector<std::pair<size_t, IfcVector3>> intersected_boundary;
    size_t votes = 0;

    IntersectsBoundaryProfile(p, p + IfcVector3(1.0, 0, 0), boundary, true, intersected_boundary, true);
    votes += intersected_boundary.size() % 2;

    intersected_boundary.clear();
    IntersectsBoundaryProfile(p, p + IfcVector3(0, 1.0, 0), boundary, true, intersected_boundary, true);
    votes += intersected_boundary.size() % 2;

    intersected_boundary.clear();
    IntersectsBoundaryProfile(p, p + IfcVector3(0.6, -0.6, 0.0), boundary, true, intersected_boundary, true);
    votes += intersected_boundary.size() % 2;

    return votes > 1;
}

// ------------------------------------------------------------------------------------------------
void ProcessPolygonalBoundedBooleanHalfSpaceDifference(const Schema_2x3::IfcPolygonalBoundedHalfSpace *hs, TempMesh &result,
        const TempMesh &first_operand,
        ConversionData &conv) {
    ai_assert(hs != nullptr);

    const Schema_2x3::IfcPlane *const plane = hs->BaseSurface->ToPtr<Schema_2x3::IfcPlane>();
    if (!plane) {
        IFCImporter::LogError("expected IfcPlane as base surface for the IfcHalfSpaceSolid");
        return;
    }

    // extract plane base position vector and normal vector
    IfcVector3 p, n(0.f, 0.f, 1.f);
    if (plane->Position->Axis) {
        ConvertDirection(n, plane->Position->Axis.Get());
    }
    ConvertCartesianPoint(p, plane->Position->Location);

    if (!IsTrue(hs->AgreementFlag)) {
        n *= -1.f;
    }

    n.Normalize();

    // obtain the polygonal bounding volume
    std::shared_ptr<TempMesh> profile = std::make_shared<TempMesh>();
    if (!ProcessCurve(hs->PolygonalBoundary, *profile, conv)) {
        IFCImporter::LogError("expected valid polyline for boundary of boolean halfspace");
        return;
    }

    // determine winding order by calculating the normal.
    IfcVector3 profileNormal = TempMesh::ComputePolygonNormal(profile->mVerts.data(), profile->mVerts.size());

    IfcMatrix4 proj_inv;
    ConvertAxisPlacement(proj_inv, hs->Position);

    // and map everything into a plane coordinate space so all intersection
    // tests can be done in 2D space.
    IfcMatrix4 proj = proj_inv;
    proj.Inverse();

    // clip the current contents of `meshout` against the plane we obtained from the second operand
    const std::vector<IfcVector3> &in = first_operand.mVerts;
    std::vector<IfcVector3> &outvert = result.mVerts;
    std::vector<unsigned int> &outvertcnt = result.mVertcnt;

    outvert.reserve(in.size());
    outvertcnt.reserve(first_operand.mVertcnt.size());

    unsigned int vidx = 0;
    std::vector<unsigned int>::const_iterator begin = first_operand.mVertcnt.begin();
    std::vector<unsigned int>::const_iterator end = first_operand.mVertcnt.end();
    std::vector<unsigned int>::const_iterator iit;
    for (iit = begin; iit != end; vidx += *iit++) {
        // Our new approach: we cut the poly along the plane, then we intersect the part on the black side of the plane
        // against the bounding polygon. All the white parts, and the black part outside the boundary polygon, are kept.
        std::vector<IfcVector3> whiteside, blackside;

        {
            const IfcVector3 *srcVertices = &in[vidx];
            const size_t srcVtxCount = *iit;
            if (srcVtxCount == 0)
                continue;

            IfcVector3 polyNormal = TempMesh::ComputePolygonNormal(srcVertices, srcVtxCount, true);

            // if the poly is parallel to the plane, put it completely on the black or white side
            if (std::abs(polyNormal * n) > 0.9999) {
                bool isOnWhiteSide = (srcVertices[0] - p) * n > -ai_epsilon;
                std::vector<IfcVector3> &targetSide = isOnWhiteSide ? whiteside : blackside;
                targetSide.insert(targetSide.end(), srcVertices, srcVertices + srcVtxCount);
            } else {
                // otherwise start building one polygon for each side. Whenever the current line segment intersects the plane
                // we put a point there as an end of the current segment. Then we switch to the other side, put a point there, too,
                // as a beginning of the current segment, and simply continue accumulating vertices.
                bool isCurrentlyOnWhiteSide = ((srcVertices[0]) - p) * n > -ai_epsilon;
                for (size_t a = 0; a < srcVtxCount; ++a) {
                    IfcVector3 e0 = srcVertices[a];
                    IfcVector3 e1 = srcVertices[(a + 1) % srcVtxCount];
                    IfcVector3 ei;

                    // put starting point to the current mesh
                    std::vector<IfcVector3> &trgt = isCurrentlyOnWhiteSide ? whiteside : blackside;
                    trgt.push_back(srcVertices[a]);

                    // if there's an intersection, put an end vertex there, switch to the other side's mesh,
                    // and add a starting vertex there, too
                    bool isPlaneHit = IntersectSegmentPlane(p, n, e0, e1, isCurrentlyOnWhiteSide, ei);
                    if (isPlaneHit) {
                        if (trgt.empty() || (trgt.back() - ei).SquareLength() > 1e-12)
                            trgt.push_back(ei);
                        isCurrentlyOnWhiteSide = !isCurrentlyOnWhiteSide;
                        std::vector<IfcVector3> &newtrgt = isCurrentlyOnWhiteSide ? whiteside : blackside;
                        newtrgt.push_back(ei);
                    }
                }
            }
        }

        // the part on the white side can be written into the target mesh right away
        WritePolygon(whiteside, result);

        // The black part is the piece we need to get rid of, but only the part of it within the boundary polygon.
        // So we now need to construct all the polygons that result from BlackSidePoly minus BoundaryPoly.
        FilterPolygon(blackside);

        // Complicated, II. We run along the polygon. a) When we're inside the boundary, we run on until we hit an
        // intersection, which means we're leaving it. We then start a new out poly there. b) When we're outside the
        // boundary, we start collecting vertices until we hit an intersection, then we run along the boundary until we hit
        // an intersection, then we switch back to the poly and run on on this one again, and so on until we got a closed
        // loop. Then we continue with the path we left to catch potential additional polys on the other side of the
        // boundary as described in a)
        if (!blackside.empty()) {
            // poly edge index, intersection point, edge index in boundary poly
            std::vector<std::tuple<size_t, IfcVector3, size_t>> intersections;
            bool startedInside = PointInPoly(proj * blackside.front(), profile->mVerts);
            bool isCurrentlyInside = startedInside;

            std::vector<std::pair<size_t, IfcVector3>> intersected_boundary;

            for (size_t a = 0; a < blackside.size(); ++a) {
                const IfcVector3 e0 = proj * blackside[a];
                const IfcVector3 e1 = proj * blackside[(a + 1) % blackside.size()];

                intersected_boundary.clear();
                IntersectsBoundaryProfile(e0, e1, profile->mVerts, isCurrentlyInside, intersected_boundary);
                // sort the hits by distance from e0 to get the correct in/out/in sequence. Manually :-( I miss you, C++11.
                if (intersected_boundary.size() > 1) {
                    bool keepSorting = true;
                    while (keepSorting) {
                        keepSorting = false;
                        for (size_t b = 0; b < intersected_boundary.size() - 1; ++b) {
                            if ((intersected_boundary[b + 1].second - e0).SquareLength() < (intersected_boundary[b].second - e0).SquareLength()) {
                                keepSorting = true;
                                std::swap(intersected_boundary[b + 1], intersected_boundary[b]);
                            }
                        }
                    }
                }
                // now add them to the list of intersections
                for (size_t b = 0; b < intersected_boundary.size(); ++b)
                    intersections.emplace_back(a, proj_inv * intersected_boundary[b].second, intersected_boundary[b].first);

                // and calculate our new inside/outside state
                if (intersected_boundary.size() & 1)
                    isCurrentlyInside = !isCurrentlyInside;
            }

            // we got a list of in-out-combinations of intersections. That should be an even number of intersections, or
            // we are facing a non-recoverable error.
            if ((intersections.size() & 1) != 0) {
                IFCImporter::LogWarn("Odd number of intersections, can't work with that. Omitting half space boundary check.");
                continue;
            }

            if (intersections.size() > 1) {
                // If we started outside, the first intersection is a out->in intersection. Cycle them so that it
                // starts with an intersection leaving the boundary
                if (!startedInside)
                    for (size_t b = 0; b < intersections.size() - 1; ++b)
                        std::swap(intersections[b], intersections[(b + intersections.size() - 1) % intersections.size()]);

                // Filter pairs of out->in->out that lie too close to each other.
                for (size_t a = 0; intersections.size() > 0 && a < intersections.size() - 1; /**/) {
                    if ((std::get<1>(intersections[a]) - std::get<1>(intersections[(a + 1) % intersections.size()])).SquareLength() < 1e-10)
                        intersections.erase(intersections.begin() + a, intersections.begin() + a + 2);
                    else
                        a++;
                }
                if (intersections.size() > 1 && (std::get<1>(intersections.back()) - std::get<1>(intersections.front())).SquareLength() < 1e-10) {
                    intersections.pop_back();
                    intersections.erase(intersections.begin());
                }
            }

            // no intersections at all: either completely inside the boundary, so everything gets discarded, or completely outside.
            // in the latter case we're implementional lost. I'm simply going to ignore this, so a large poly will not get any
            // holes if the boundary is smaller and does not touch it anywhere.
            if (intersections.empty()) {
                // starting point was outside -> everything is outside the boundary -> nothing is clipped -> add black side
                // to result mesh unchanged
                if (!startedInside) {
                    outvertcnt.push_back(static_cast<unsigned int>(blackside.size()));
                    outvert.insert(outvert.end(), blackside.begin(), blackside.end());
                    continue;
                } else {
                    // starting point was inside the boundary -> everything is inside the boundary -> nothing is spared from the
                    // clipping -> nothing left to add to the result mesh
                    continue;
                }
            }

            // determine the direction in which we're marching along the boundary polygon. If the src poly is faced upwards
            // and the boundary is also winded this way, we need to march *backwards* on the boundary.
            const IfcVector3 polyNormal = IfcMatrix3(proj) * TempMesh::ComputePolygonNormal(blackside.data(), blackside.size());
            bool marchBackwardsOnBoundary = (profileNormal * polyNormal) >= 0.0;

            // Build closed loops from these intersections. Starting from an intersection leaving the boundary we
            // walk along the polygon to the next intersection (which should be an IS entering the boundary poly).
            // From there we walk along the boundary until we hit another intersection leaving the boundary,
            // walk along the poly to the next IS and so on until we're back at the starting point.
            // We remove every intersection we "used up", so any remaining intersection is the start of a new loop.
            while (!intersections.empty()) {
                std::vector<IfcVector3> resultpoly;
                size_t currentIntersecIdx = 0;

                while (true) {
                    ai_assert(intersections.size() > currentIntersecIdx + 1);
                    std::tuple<size_t, IfcVector3, size_t> currintsec = intersections[currentIntersecIdx + 0];
                    std::tuple<size_t, IfcVector3, size_t> nextintsec = intersections[currentIntersecIdx + 1];
                    intersections.erase(intersections.begin() + currentIntersecIdx, intersections.begin() + currentIntersecIdx + 2);

                    // we start with an in->out intersection
                    resultpoly.push_back(std::get<1>(currintsec));
                    // climb along the polygon to the next intersection, which should be an out->in
                    size_t numPolyPoints = (std::get<0>(currintsec) > std::get<0>(nextintsec) ? blackside.size() : 0) + std::get<0>(nextintsec) - std::get<0>(currintsec);
                    for (size_t a = 1; a <= numPolyPoints; ++a)
                        resultpoly.push_back(blackside[(std::get<0>(currintsec) + a) % blackside.size()]);
                    // put the out->in intersection
                    resultpoly.push_back(std::get<1>(nextintsec));

                    // generate segments along the boundary polygon that lie in the poly's plane until we hit another intersection
                    IfcVector3 startingPoint = proj * std::get<1>(nextintsec);
                    size_t currentBoundaryEdgeIdx = (std::get<2>(nextintsec) + (marchBackwardsOnBoundary ? 1 : 0)) % profile->mVerts.size();
                    size_t nextIntsecIdx = SIZE_MAX;
                    while (nextIntsecIdx == SIZE_MAX) {
                        IfcFloat t = 1e10;

                        size_t nextBoundaryEdgeIdx = marchBackwardsOnBoundary ? (currentBoundaryEdgeIdx + profile->mVerts.size() - 1) : currentBoundaryEdgeIdx + 1;
                        nextBoundaryEdgeIdx %= profile->mVerts.size();
                        // vertices of the current boundary segments
                        IfcVector3 currBoundaryPoint = profile->mVerts[currentBoundaryEdgeIdx];
                        IfcVector3 nextBoundaryPoint = profile->mVerts[nextBoundaryEdgeIdx];
                        // project the two onto the polygon
                        if (std::abs(polyNormal.z) > 1e-5) {
                            currBoundaryPoint.z = startingPoint.z + (currBoundaryPoint.x - startingPoint.x) * polyNormal.x / polyNormal.z + (currBoundaryPoint.y - startingPoint.y) * polyNormal.y / polyNormal.z;
                            nextBoundaryPoint.z = startingPoint.z + (nextBoundaryPoint.x - startingPoint.x) * polyNormal.x / polyNormal.z + (nextBoundaryPoint.y - startingPoint.y) * polyNormal.y / polyNormal.z;
                        }

                        // build a direction that goes along the boundary border but lies in the poly plane
                        IfcVector3 boundaryPlaneNormal = ((nextBoundaryPoint - currBoundaryPoint) ^ profileNormal).Normalize();
                        IfcVector3 dirAtPolyPlane = (boundaryPlaneNormal ^ polyNormal).Normalize() * (marchBackwardsOnBoundary ? -1.0 : 1.0);
                        // if we can project the direction to the plane, we can calculate a maximum marching distance along that dir
                        // until we finish that boundary segment and continue on the next
                        if (std::abs(polyNormal.z) > 1e-5) {
                            t = std::min(t, (nextBoundaryPoint - startingPoint).Length());
                        }

                        // check if the direction hits the loop start - if yes, we got a poly to output
                        IfcVector3 dirToThatPoint = proj * resultpoly.front() - startingPoint;
                        IfcFloat tpt = dirToThatPoint * dirAtPolyPlane;
                        if (tpt > -1e-6 && tpt <= t && (dirToThatPoint - tpt * dirAtPolyPlane).SquareLength() < 1e-10) {
                            nextIntsecIdx = intersections.size(); // dirty hack to end marching along the boundary and signal the end of the loop
                            t = tpt;
                        }

                        // also check if the direction hits any in->out intersections earlier. If we hit one, we can switch back
                        // to marching along the poly border from that intersection point
                        for (size_t a = 0; a < intersections.size(); a += 2) {
                            dirToThatPoint = proj * std::get<1>(intersections[a]) - startingPoint;
                            tpt = dirToThatPoint * dirAtPolyPlane;
                            if (tpt > -1e-6 && tpt <= t && (dirToThatPoint - tpt * dirAtPolyPlane).SquareLength() < 1e-10) {
                                nextIntsecIdx = a; // switch back to poly and march on from this in->out intersection
                                t = tpt;
                            }
                        }

                        // if we keep marching on the boundary, put the segment end point to the result poly and well... keep marching
                        if (nextIntsecIdx == SIZE_MAX) {
                            resultpoly.push_back(proj_inv * nextBoundaryPoint);
                            currentBoundaryEdgeIdx = nextBoundaryEdgeIdx;
                            startingPoint = nextBoundaryPoint;
                        }

                        // quick endless loop check
                        if (resultpoly.size() > blackside.size() + profile->mVerts.size()) {
                            IFCImporter::LogError("Encountered endless loop while clipping polygon against poly-bounded half space.");
                            break;
                        }
                    }

                    // we're back on the poly - if this is the intersection we started from, we got a closed loop.
                    if (nextIntsecIdx >= intersections.size()) {
                        break;
                    }

                    // otherwise it's another intersection. Continue marching from there.
                    currentIntersecIdx = nextIntsecIdx;
                }

                WritePolygon(resultpoly, result);
            }
        }
    }
    IFCImporter::LogVerboseDebug("generating CSG geometry by plane clipping with polygonal bounding (IfcBooleanClippingResult)");
}

// ------------------------------------------------------------------------------------------------
void ProcessBooleanExtrudedAreaSolidDifference(const Schema_2x3::IfcExtrudedAreaSolid *as, 
        TempMesh &result,
        const TempMesh &first_operand,
        ConversionData &conv) {
    ai_assert(as != nullptr);

    // This case is handled by reduction to an instance of the quadrify() algorithm.
    // Obviously, this won't work for arbitrarily complex cases. In fact, the first
    // operand should be near-planar. Luckily, this is usually the case in Ifc
    // buildings.

    std::shared_ptr<TempMesh> meshtmp = std::make_shared<TempMesh>();
    ProcessExtrudedAreaSolid(*as, *meshtmp, conv, false);

    std::vector<TempOpening> openings(1, TempOpening(as, IfcVector3(0, 0, 0), std::move(meshtmp), std::shared_ptr<TempMesh>()));

    result = first_operand;

    TempMesh temp;

    std::vector<IfcVector3>::const_iterator vit = first_operand.mVerts.begin();
    for (unsigned int pcount : first_operand.mVertcnt) {
        temp.Clear();

        temp.mVerts.insert(temp.mVerts.end(), vit, vit + pcount);
        temp.mVertcnt.push_back(pcount);

        // The algorithms used to generate mesh geometry sometimes
        // spit out lines or other degenerates which must be
        // filtered to avoid running into assertions later on.

        // ComputePolygonNormal returns the Newell normal, so the
        // length of the normal is the area of the polygon.
        const IfcVector3 &normal = temp.ComputeLastPolygonNormal(false);
        if (normal.SquareLength() < static_cast<IfcFloat>(1e-5)) {
            IFCImporter::LogWarn("skipping degenerate polygon (ProcessBooleanExtrudedAreaSolidDifference)");
            continue;
        }

        GenerateOpenings(openings, temp, false, true);
        result.Append(temp);

        vit += pcount;
    }

    IFCImporter::LogVerboseDebug("generating CSG geometry by geometric difference to a solid (IfcExtrudedAreaSolid)");
}

// ------------------------------------------------------------------------------------------------
void ProcessBoolean(const Schema_2x3::IfcBooleanResult &boolean, TempMesh &result, ConversionData &conv) {
    // supported CSG operations:
    //   DIFFERENCE
    if (const Schema_2x3::IfcBooleanResult *const clip = boolean.ToPtr<Schema_2x3::IfcBooleanResult>()) {
        if (clip->Operator != "DIFFERENCE") {
            IFCImporter::LogWarn("encountered unsupported boolean operator: ", (std::string)clip->Operator);
            return;
        }

        // supported cases (1st operand):
        //  IfcBooleanResult -- call ProcessBoolean recursively
        //  IfcSweptAreaSolid -- obtain polygonal geometry first

        // supported cases (2nd operand):
        //  IfcHalfSpaceSolid -- easy, clip against plane
        //  IfcExtrudedAreaSolid -- reduce to an instance of the quadrify() algorithm

        const Schema_2x3::IfcHalfSpaceSolid *const hs = clip->SecondOperand->ResolveSelectPtr<Schema_2x3::IfcHalfSpaceSolid>(conv.db);
        const Schema_2x3::IfcExtrudedAreaSolid *const as = clip->SecondOperand->ResolveSelectPtr<Schema_2x3::IfcExtrudedAreaSolid>(conv.db);
        if (!hs && !as) {
            IFCImporter::LogError("expected IfcHalfSpaceSolid or IfcExtrudedAreaSolid as second clipping operand");
            return;
        }

        TempMesh first_operand;
        if (const Schema_2x3::IfcBooleanResult *const op0 = clip->FirstOperand->ResolveSelectPtr<Schema_2x3::IfcBooleanResult>(conv.db)) {
            ProcessBoolean(*op0, first_operand, conv);
        } else if (const Schema_2x3::IfcSweptAreaSolid *const swept = clip->FirstOperand->ResolveSelectPtr<Schema_2x3::IfcSweptAreaSolid>(conv.db)) {
            ProcessSweptAreaSolid(*swept, first_operand, conv);
        } else {
            IFCImporter::LogError("expected IfcSweptAreaSolid or IfcBooleanResult as first clipping operand");
            return;
        }

        if (hs) {

            const Schema_2x3::IfcPolygonalBoundedHalfSpace *const hs_bounded = clip->SecondOperand->ResolveSelectPtr<Schema_2x3::IfcPolygonalBoundedHalfSpace>(conv.db);
            if (hs_bounded) {
                ProcessPolygonalBoundedBooleanHalfSpaceDifference(hs_bounded, result, first_operand, conv);
            } else {
                ProcessBooleanHalfSpaceDifference(hs, result, first_operand, conv);
            }
        } else {
            ProcessBooleanExtrudedAreaSolidDifference(as, result, first_operand, conv);
        }
    } else {
        IFCImporter::LogWarn("skipping unknown IfcBooleanResult entity, type is ", boolean.GetClassName());
    }
}

} // namespace IFC
} // namespace Assimp

#endif // ASSIMP_BUILD_NO_IFC_IMPORTER