TopologyKernel.cc 46.3 KB
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/*===========================================================================*\
 *                                                                           *
 *                            OpenVolumeMesh                                 *
 *        Copyright (C) 2011 by Computer Graphics Group, RWTH Aachen         *
 *                        www.openvolumemesh.org                             *
 *                                                                           *
 *---------------------------------------------------------------------------*
 *  This file is part of OpenVolumeMesh.                                     *
 *                                                                           *
 *  OpenVolumeMesh is free software: you can redistribute it and/or modify   *
 *  it under the terms of the GNU Lesser General Public License as           *
 *  published by the Free Software Foundation, either version 3 of           *
 *  the License, or (at your option) any later version with the              *
 *  following exceptions:                                                    *
 *                                                                           *
 *  If other files instantiate templates or use macros                       *
 *  or inline functions from this file, or you compile this file and         *
 *  link it with other files to produce an executable, this file does        *
 *  not by itself cause the resulting executable to be covered by the        *
 *  GNU Lesser General Public License. This exception does not however       *
 *  invalidate any other reasons why the executable file might be            *
 *  covered by the GNU Lesser General Public License.                        *
 *                                                                           *
 *  OpenVolumeMesh is distributed in the hope that it will be useful,        *
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of           *
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the            *
 *  GNU Lesser General Public License for more details.                      *
 *                                                                           *
 *  You should have received a copy of the GNU LesserGeneral Public          *
 *  License along with OpenVolumeMesh.  If not,                              *
 *  see <http://www.gnu.org/licenses/>.                                      *
 *                                                                           *
\*===========================================================================*/

/*===========================================================================*\
 *                                                                           *
 *   $Revision$                                                         *
 *   $Date$                    *
 *   $LastChangedBy$                                                *
 *                                                                           *
\*===========================================================================*/

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#include <OpenVolumeMesh/System/FunctionalInclude.hh>
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#include <queue>

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#include "TopologyKernel.hh"

namespace OpenVolumeMesh {

// Initialize constants
const VertexHandle      TopologyKernel::InvalidVertexHandle   = VertexHandle(-1);
const EdgeHandle        TopologyKernel::InvalidEdgeHandle     = EdgeHandle(-1);
const HalfEdgeHandle    TopologyKernel::InvalidHalfEdgeHandle = HalfEdgeHandle(-1);
const FaceHandle        TopologyKernel::InvalidFaceHandle     = FaceHandle(-1);
const HalfFaceHandle    TopologyKernel::InvalidHalfFaceHandle = HalfFaceHandle(-1);
const CellHandle        TopologyKernel::InvalidCellHandle     = CellHandle(-1);

TopologyKernel::TopologyKernel() :
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    n_vertices_(0u),
    n_edges_(0u),
    n_faces_(0u),
    n_cells_(0u),
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    v_bottom_up_(true),
    e_bottom_up_(true),
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    f_bottom_up_(true) {
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}

TopologyKernel::~TopologyKernel() {
}

//========================================================================================

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VertexHandle TopologyKernel::add_vertex() {

    ++n_vertices_;

    // Create item for vertex bottom-up adjacencies
    if(v_bottom_up_) {
        outgoing_hes_per_vertex_.resize(n_vertices_);
    }

    // Resize vertex props
    resize_vprops(n_vertices_);

    // Return 0-indexed handle
    return VertexHandle((int)(n_vertices_ - 1));
}

//========================================================================================

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/// Add edge
EdgeHandle TopologyKernel::add_edge(const VertexHandle& _fromVertex,
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                                    const VertexHandle& _toVertex,
                                    bool _allowDuplicates) {
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#ifndef NDEBUG
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    if((unsigned int)_fromVertex.idx() >= n_vertices() || (unsigned int)_toVertex.idx() >= n_vertices()) {
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        std::cerr << "Vertex handle is out of bounds!" << std::endl;
        return InvalidEdgeHandle;
    }
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#endif
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    // Test if edge does not exist, yet
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    if(!_allowDuplicates) {
        for(unsigned int i = 0; i < n_edges_; ++i) {
            if(edge(EdgeHandle(i)).from_vertex() == _fromVertex && edge(EdgeHandle(i)).to_vertex() == _toVertex) {
                return EdgeHandle(i);
            } else if(edge(EdgeHandle(i)).from_vertex() == _toVertex && edge(EdgeHandle(i)).to_vertex() == _fromVertex) {
                return EdgeHandle(i);
            }
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        }
    }

    // Create edge object
    OpenVolumeMeshEdge e(_fromVertex, _toVertex);

    // Store edge locally
    edges_.push_back(e);
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    ++n_edges_;
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    // Resize props
    resize_eprops(n_edges());

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    EdgeHandle eh((int)n_edges_-1);
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    // Update vertex bottom-up adjacencies
    if(v_bottom_up_) {
        assert(outgoing_hes_per_vertex_.size() > (unsigned int)_fromVertex.idx());
        assert(outgoing_hes_per_vertex_.size() > (unsigned int)_toVertex.idx());
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        outgoing_hes_per_vertex_[_fromVertex.idx()].push_back(halfedge_handle(eh, 0));
        outgoing_hes_per_vertex_[_toVertex.idx()].push_back(halfedge_handle(eh, 1));
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    }

    // Create item for edge bottom-up adjacencies
    if(e_bottom_up_) {
        incident_hfs_per_he_.resize(n_halfedges());
    }

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    // Get handle of recently created edge
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    return eh;
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}

//========================================================================================

/// Add face via incident edges
FaceHandle TopologyKernel::add_face(const std::vector<HalfEdgeHandle>& _halfedges, bool _topologyCheck) {

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#ifndef NDEBUG
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    // Test if all edges are valid
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    for(std::vector<HalfEdgeHandle>::const_iterator it = _halfedges.begin(),
            end = _halfedges.end(); it != end; ++it) {
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        if((unsigned int)it->idx() >= n_edges_ * 2u) {
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            std::cerr << "Halfedge handle out of bounds!" << std::endl;
            return InvalidFaceHandle;
        }
    }
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#endif
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    // Perform topology check
    if(_topologyCheck) {

        /*
         * Test if halfedges are connected
         *
         * The test works as follows:
         * For every edge in the parameter vector
         * put all incident vertices into a
         * set of either "from"-vertices or "to"-vertices,
         * respectively.
         * If and only if all edges are connected,
         * then both sets are identical.
         */

        std::set<VertexHandle> fromVertices;
        std::set<VertexHandle> toVertices;

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        for(std::vector<HalfEdgeHandle>::const_iterator it = _halfedges.begin(),
            end = _halfedges.end(); it != end; ++it) {
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            fromVertices.insert(halfedge(*it).from_vertex());
            toVertices.insert(halfedge(*it).to_vertex());
        }

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        for(std::set<VertexHandle>::const_iterator v_it = fromVertices.begin(),
                v_end = fromVertices.end(); v_it != v_end; ++v_it) {
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            if(toVertices.count(*v_it) != 1) {
                std::cerr << "The specified halfedges are not connected!" << std::endl;
                return InvalidFaceHandle;
            }
        }

        // The halfedges are now guaranteed to be connected
    }

    // Create face
    OpenVolumeMeshFace face(_halfedges);

    faces_.push_back(face);
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    ++n_faces_;
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    // Get added face's handle
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    FaceHandle fh(n_faces_ - 1);
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    // Resize props
    resize_fprops(n_faces());

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    // Update edge bottom-up adjacencies
    if(e_bottom_up_) {

        for(std::vector<HalfEdgeHandle>::const_iterator it = _halfedges.begin(),
            end = _halfedges.end(); it != end; ++it) {
            assert(incident_hfs_per_he_.size() > (unsigned int)it->idx());
            assert(incident_hfs_per_he_.size() > (unsigned int)opposite_halfedge_handle(*it).idx());
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            incident_hfs_per_he_[it->idx()].push_back(halfface_handle(fh, 0));
            incident_hfs_per_he_[opposite_halfedge_handle(*it).idx()].push_back(halfface_handle(fh, 1));
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        }
    }

    // Create item for face bottom-up adjacencies
    if(f_bottom_up_) {
        incident_cell_per_hf_.resize(n_halffaces(), InvalidCellHandle);
    }

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    // Return handle of recently created face
    return fh;
}

//========================================================================================

/// Add face via incident vertices
/// Define the _vertices in counter-clockwise order (from the "outside")
FaceHandle TopologyKernel::add_face(const std::vector<VertexHandle>& _vertices) {

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#ifndef NDEBUG
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    // Test if all vertices exist
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    for(std::vector<VertexHandle>::const_iterator it = _vertices.begin(),
            end = _vertices.end(); it != end; ++it) {
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        if((unsigned int)it->idx() >= n_vertices()) {
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            std::cerr << "Vertex handle out of bounds!" << std::endl;
            return InvalidFaceHandle;
        }
    }
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#endif
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    // Add edge for each pair of vertices
    std::vector<HalfEdgeHandle> halfedges;
    std::vector<VertexHandle>::const_iterator it = _vertices.begin();
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    std::vector<VertexHandle>::const_iterator end = _vertices.end();
    for(; (it+1) != end; ++it) {
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        EdgeHandle e_idx = add_edge(*it, *(it+1));

        // Swap halfedge if edge already existed and
        // has been initially defined in reverse orientation
        int swap = 0;
        if(edge(e_idx).to_vertex() == *it) swap = 1;

        halfedges.push_back(halfedge_handle(e_idx, swap));
    }
    EdgeHandle e_idx = add_edge(*it, *_vertices.begin());
    int swap = 0;
    if(edge(e_idx).to_vertex() == *it) swap = 1;
    halfedges.push_back(halfedge_handle(e_idx, swap));

    // Add face
#ifndef NDEBUG
    return add_face(halfedges, true);
#else
    return add_face(halfedges, false);
#endif
}

//========================================================================================

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void TopologyKernel::reorder_incident_halffaces(const EdgeHandle& _eh) {

    /* Put halffaces in clockwise order via the
     * same cell property which now exists.
     * Note, this only works for manifold configurations though.
     * Proceed as follows: Pick one starting halfface. Assuming
     * that all halfface normals point into the incident cell,
     * we find the adjacent halfface within the incident cell
     * along the considered halfedge. We set the found halfface
     * to be the one to be processed next. If we reach an outside
     * region, we try to go back from the starting halfface in reverse
     * order. If the complex is properly connected (the pairwise
     * intersection of two adjacent 3-dimensional cells is always
     * a 2-dimensional entity, namely a facet), such an ordering
     * always exists and will be found. If not, a correct order
     * can not be given and, as a result, the related iterators
     * will address the related entities in an arbitrary fashion.
     */

    for(unsigned char s = 0; s <= 1; s++) {

        HalfEdgeHandle cur_he = halfedge_handle(_eh, s);
        std::vector<HalfFaceHandle> new_halffaces;
        HalfFaceHandle start_hf = InvalidHalfFaceHandle;
        HalfFaceHandle cur_hf = InvalidHalfFaceHandle;

        // Start with one incident halfface and go
        // into the first direction
        assert(incident_hfs_per_he_.size() > (unsigned int)cur_he.idx());

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        if(incident_hfs_per_he_[cur_he.idx()].size() != 0) {
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            // Get start halfface
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            cur_hf = *incident_hfs_per_he_[cur_he.idx()].begin();
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            start_hf = cur_hf;

            while(cur_hf != InvalidHalfFaceHandle) {

                // Add halfface
                new_halffaces.push_back(cur_hf);

                // Go to next halfface
                cur_hf = adjacent_halfface_in_cell(cur_hf, cur_he);

                if(cur_hf != InvalidHalfFaceHandle)
                    cur_hf = opposite_halfface_handle(cur_hf);

                // End when we're through
                if(cur_hf == start_hf) break;
            }

            // First direction has terminated
            // If new_halffaces has the same size as old (unordered)
            // vector of incident halffaces, we are done here
            // If not, try the other way round
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            if(new_halffaces.size() != incident_hfs_per_he_[cur_he.idx()].size()) {
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                // Get opposite of start halfface
                cur_hf = start_hf;

                 while(cur_hf != InvalidHalfFaceHandle) {

                     cur_hf = opposite_halfface_handle(cur_hf);
                     cur_hf = adjacent_halfface_in_cell(cur_hf, cur_he);

                     if(cur_hf == start_hf) break;

                     if(cur_hf != InvalidHalfFaceHandle)
                         new_halffaces.insert(new_halffaces.begin(), cur_hf);
                     else break;
                }
            }

            // Everything worked just fine, set the new ordered vector
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            if(new_halffaces.size() == incident_hfs_per_he_[cur_he.idx()].size()) {
                incident_hfs_per_he_[cur_he.idx()] = new_halffaces;
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            }
        }
    }
}

//========================================================================================

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/// Add cell via incident halffaces
CellHandle TopologyKernel::add_cell(const std::vector<HalfFaceHandle>& _halffaces, bool _topologyCheck) {

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#ifndef NDEBUG
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    // Test if halffaces have valid indices
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    for(std::vector<HalfFaceHandle>::const_iterator it = _halffaces.begin(),
            end = _halffaces.end(); it != end; ++it) {
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        if((unsigned int)it->idx() >= n_faces_ * 2u) {
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            std::cerr << "HalfFace handle is out of bounds!" << std::endl;
            return InvalidCellHandle;
        }
    }
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#endif
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    // Perform topology check
    if(_topologyCheck) {

        /*
         * Test if all halffaces are connected and form a two-manifold
         * => Cell is closed
         *
         * This test is simple: The number of involved half-edges has to be
         * exactly twice the number of involved edges.
         */

        std::set<HalfEdgeHandle> incidentHalfedges;
        std::set<EdgeHandle>     incidentEdges;

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        for(std::vector<HalfFaceHandle>::const_iterator it = _halffaces.begin(),
                end = _halffaces.end(); it != end; ++it) {
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            OpenVolumeMeshFace hface = halfface(*it);
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            for(std::vector<HalfEdgeHandle>::const_iterator he_it = hface.halfedges().begin(),
                    he_end = hface.halfedges().end(); he_it != he_end; ++he_it) {
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                incidentHalfedges.insert(*he_it);
                incidentEdges.insert(edge_handle(*he_it));
            }
        }

        if(incidentHalfedges.size() != (incidentEdges.size() * 2u)) {
            std::cerr << "The specified halffaces are not connected!" << std::endl;
            return InvalidCellHandle;
        }

        // The halffaces are now guaranteed to form a two-manifold
    }

    // Create new cell
    OpenVolumeMeshCell cell(_halffaces);

    cells_.push_back(cell);
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    ++n_cells_;
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    // Resize props
    resize_cprops(n_cells());

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    CellHandle ch((int)n_cells_-1);
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    // Update face bottom-up adjacencies
    if(f_bottom_up_) {

        std::set<EdgeHandle> cell_edges;
        for(std::vector<HalfFaceHandle>::const_iterator it = _halffaces.begin(),
                end = _halffaces.end(); it != end; ++it) {
            assert(incident_cell_per_hf_.size() > (unsigned int)it->idx());
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            if(_topologyCheck) {
                assert(incident_cell_per_hf_[it->idx()] == InvalidCellHandle);
                if(incident_cell_per_hf_[it->idx()] != InvalidCellHandle) {
                    std::cerr << "Warning: One of the specified half-face is already incident to another cell!" << std::endl;
                }
            }

            // Overwrite incident cell for current half-face
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            incident_cell_per_hf_[it->idx()] = ch;
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            // Collect all edges of cell
            const std::vector<HalfEdgeHandle> hes = halfface(*it).halfedges();
            for(std::vector<HalfEdgeHandle>::const_iterator he_it = hes.begin(),
                    he_end = hes.end(); he_it != he_end; ++he_it) {
                cell_edges.insert(edge_handle(*he_it));
            }
        }

        if(e_bottom_up_) {

            // Try to reorder all half-faces w.r.t.
            // their incident half-edges such that all
            // half-faces are in cyclic order around
            // a half-edge
            for(std::set<EdgeHandle>::const_iterator e_it = cell_edges.begin(),
                    e_end = cell_edges.end(); e_it != e_end; ++e_it) {
                reorder_incident_halffaces(*e_it);
            }
        }
    }

    return ch;
}

//========================================================================================

/**
 * \brief Delete vertex from mesh
 *
 * After performing this operation, all vertices
 * following vertex _h in the array will be accessible
 * through their old handle decreased by one.
 * This function directly fixes the vertex links
 * in all edges. These steps are performed:
 *
 * 1) Search all incident half-edges HE_v +
 *    Decrease all vertex handles in incident edges
 *    with index > v by 1
 * 2) Delete entry in BU: V -> HF
 * 3) Delete vertex itself (not necessary here since
 *    a vertex is only represented by a number)
 * 4) Delete property entry
 * 5) Delete incident edges
 *
 * @param _h A vertex handle
 */
VertexIter TopologyKernel::delete_vertex(const VertexHandle& _h) {

    assert(_h.idx() < (int)n_vertices());

    // 1)
    std::priority_queue<EdgeHandle> incident_edges;
    if(v_bottom_up_) {

        // Speed-up, because we know the incident edges
        // Get incident edges
        assert(outgoing_hes_per_vertex_.size() > (unsigned int)_h.idx());
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        const std::vector<HalfEdgeHandle>& inc_hes = outgoing_hes_per_vertex_[_h.idx()];
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        for(std::vector<HalfEdgeHandle>::const_iterator he_it = inc_hes.begin(),
                he_end = inc_hes.end(); he_it != he_end; ++he_it) {
            incident_edges.push(edge_handle(*he_it));
        }
        // Decrease all vertex handles that are greater than _h in all edge definitions
        for(std::vector<std::vector<HalfEdgeHandle> >::iterator he_it = (outgoing_hes_per_vertex_.begin() + _h.idx() + 1),
                he_end = outgoing_hes_per_vertex_.end(); he_it != he_end; ++he_it) {
            for(std::vector<HalfEdgeHandle>::const_iterator it = he_it->begin(),
                    end = he_it->end(); it != end; ++it) {

                if(it->idx() % 2 == 0) {
                    VertexHandle vh = edge(edge_handle(*it)).from_vertex();
                    if(vh.is_valid())
                        edge(edge_handle(*it)).set_from_vertex(VertexHandle(vh.idx() - 1));
                } else {
                    VertexHandle vh = edge(edge_handle(*it)).to_vertex();
                    if(vh.is_valid())
                        edge(edge_handle(*it)).set_to_vertex(VertexHandle(vh.idx() - 1));
                }
            }
        }
    } else {

        // Iterate over all edges
        for(EdgeIter e_it = edges_begin(), e_end = edges_end();
                e_it != e_end; ++e_it) {

            // Get incident edges
            if(edge(*e_it).from_vertex() == _h ||
                    edge(*e_it).to_vertex() == _h) {
                incident_edges.push(*e_it);
                continue;
            }

            // Decrease all vertex handles in edge definitions that are greater than _h
            if(edge(*e_it).from_vertex() > _h) {
                edge(*e_it).set_from_vertex(VertexHandle(edge(*e_it).from_vertex().idx() - 1));
            }
            if(edge(*e_it).to_vertex() > _h) {
                edge(*e_it).set_to_vertex(VertexHandle(edge(*e_it).to_vertex().idx() - 1));
            }
        }
    }

    // 2)
    if(v_bottom_up_) {
        assert(outgoing_hes_per_vertex_.size() > (unsigned int)_h.idx());
        outgoing_hes_per_vertex_.erase(outgoing_hes_per_vertex_.begin() + _h.idx());
    }

    // 3)
    --n_vertices_;

    // 4)
    vertex_deleted(_h);

    // 5)
    while(!incident_edges.empty()) {
        delete_edge(incident_edges.top());
        incident_edges.pop();
    }

    // Iterator to next element in vertex list
    return (vertices_begin() + _h.idx());
}

//========================================================================================

/**
 * \brief Delete edge from mesh
 *
 * After performing this operation, all edges
 * following edge _h in the array will be accessible
 * through their old handle decreased by one.
 * This function directly fixes the edge links
 * in all faces. These steps are performed:
 *
 * 1) Delete links in BU: V -> HE
 * 2) Search all incident faces +
 *    decrease all half-edge handles > he
 *    in all incident faces
 * 3) Delete item in BU: HE -> HF
 * 4) Decrease all entries > he in BU: V -> HE
 * 5) Delete edge from storage array
 * 6) Delete property item
 * 7) Delete incident faces
 *
 * @param _h An edge handle
 */
EdgeIter TopologyKernel::delete_edge(const EdgeHandle& _h) {

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    assert(_h.idx() < (int)n_edges_);
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    // 1)
    if(v_bottom_up_) {

        VertexHandle v0 = edge(_h).from_vertex();
        VertexHandle v1 = edge(_h).to_vertex();
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        assert(outgoing_hes_per_vertex_.size() > (unsigned int)std::max(v0.idx(), v1.idx()));
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        outgoing_hes_per_vertex_[v0.idx()].erase(
                std::remove(outgoing_hes_per_vertex_[v0.idx()].begin(),
                            outgoing_hes_per_vertex_[v0.idx()].end(),
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                            halfedge_handle(_h, 0)),
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                            outgoing_hes_per_vertex_[v0.idx()].end());
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        outgoing_hes_per_vertex_[v1.idx()].erase(
                std::remove(outgoing_hes_per_vertex_[v1.idx()].begin(),
                            outgoing_hes_per_vertex_[v1.idx()].end(),
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                            halfedge_handle(_h, 1)),
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                            outgoing_hes_per_vertex_[v1.idx()].end());
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    }

    // 2)
    std::priority_queue<FaceHandle> incident_faces;
    if(e_bottom_up_) {

        // Speed-up, because we already know all incident faces
        // Get incident faces
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        assert(incident_hfs_per_he_.size() > (unsigned int)halfedge_handle(_h, 0).idx());
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        const std::vector<HalfFaceHandle>& inc_hfs = incident_hfs_per_he_[halfedge_handle(_h, 0).idx()];
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        for(std::vector<HalfFaceHandle>::const_iterator hf_it = inc_hfs.begin(),
                hf_end = inc_hfs.end(); hf_it != hf_end; ++hf_it) {
            incident_faces.push(face_handle(*hf_it));
        }

        // Decrease all half-edge handles > he in face definitions
        // Get all faces that need updates
        std::set<FaceHandle> update_faces;
        for(std::vector<std::vector<HalfFaceHandle> >::const_iterator iit =
                (incident_hfs_per_he_.begin() + halfedge_handle(_h, 1).idx() + 1),
                iit_end = incident_hfs_per_he_.end(); iit != iit_end; ++iit) {
            for(std::vector<HalfFaceHandle>::const_iterator it = iit->begin(),
                    end = iit->end(); it != end; ++it) {
                update_faces.insert(face_handle(*it));
            }
        }
        // Update respective handles
        HEHandleCorrection cor(halfedge_handle(_h, 1));
        for(std::set<FaceHandle>::iterator f_it = update_faces.begin(),
                f_end = update_faces.end(); f_it != f_end; ++f_it) {

            std::vector<HalfEdgeHandle> hes = face(*f_it).halfedges();

            // Delete current half-edge from face's half-edge list
            hes.erase(std::remove(hes.begin(), hes.end(), halfedge_handle(_h, 0)), hes.end());
            hes.erase(std::remove(hes.begin(), hes.end(), halfedge_handle(_h, 1)), hes.end());

            std::for_each(hes.begin(), hes.end(),
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                          fun::bind(&HEHandleCorrection::correctValue, &cor, fun::placeholders::_1));
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            face(*f_it).set_halfedges(hes);
        }
    } else {

        // Iterate over all faces
        for(FaceIter f_it = faces_begin(), f_end = faces_end();
                f_it != f_end; ++f_it) {

            std::vector<HalfEdgeHandle> hes = face(*f_it).halfedges();
            if(std::find(hes.begin(), hes.end(), halfedge_handle(_h, 0)) != hes.end() ||
                    std::find(hes.begin(), hes.end(), halfedge_handle(_h, 1)) != hes.end()) {
                // Face is incident to current edge
                incident_faces.push(*f_it);
                continue;
            }

            // Delete current half-edge from face's half-edge list
            hes.erase(std::remove(hes.begin(), hes.end(), halfedge_handle(_h, 0)), hes.end());
            hes.erase(std::remove(hes.begin(), hes.end(), halfedge_handle(_h, 1)), hes.end());

            // Decrease all half-edge handles greater than _h in face
            HEHandleCorrection cor(halfedge_handle(_h, 1));
            std::for_each(hes.begin(), hes.end(),
666
                          fun::bind(&HEHandleCorrection::correctValue, &cor, fun::placeholders::_1));
667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682
            face(*f_it).set_halfedges(hes);
        }
    }

    // 3)
    if(e_bottom_up_) {
        assert(incident_hfs_per_he_.size() > (unsigned int)halfedge_handle(_h, 1).idx());
        incident_hfs_per_he_.erase(incident_hfs_per_he_.begin() + halfedge_handle(_h, 1).idx());
        incident_hfs_per_he_.erase(incident_hfs_per_he_.begin() + halfedge_handle(_h, 0).idx());
    }

    // 4)
    if(v_bottom_up_) {
        HEHandleCorrection cor(halfedge_handle(_h, 1));
        std::for_each(outgoing_hes_per_vertex_.begin(),
                      outgoing_hes_per_vertex_.end(),
683
                      fun::bind(&HEHandleCorrection::correctVecValue, &cor, fun::placeholders::_1));
684 685 686 687
    }

    // 5)
    edges_.erase(edges_.begin() + _h.idx());
688
    --n_edges_;
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    // 6)
    edge_deleted(_h);

    // 7)
    while(!incident_faces.empty()) {
        delete_face(incident_faces.top());
        incident_faces.pop();
    }

    // Return iterator to next element in list
    return (edges_begin() + _h.idx());
}

//========================================================================================

/**
 * \brief Delete face from mesh
 *
 * After performing this operation, all faces
 * following face _h in the array will be accessible
 * through their old handle decreased by one.
 * This function directly fixes the face links
 * in all cells. These steps are performed:
 *
 * 1) Delete links in BU: HE -> HF
 * 2) Search all incident cells +
 *    decrease all half-face handles > hf
 *    in all incident cells
 * 3) Delete item in BU: HF -> C
 * 4) Decrease all entries > hf in BU: HE -> HF
 * 5) Delete face from storage array
 * 6) Delete property item
 * 7) Delete incident cells
 *
 * @param _h A face handle
 */
FaceIter TopologyKernel::delete_face(const FaceHandle& _h) {

728
    assert(_h.idx() < (int)n_faces_);
729 730 731 732 733 734 735 736

    // 1)
    if(e_bottom_up_) {

        const std::vector<HalfEdgeHandle>& hes = face(_h).halfedges();
        for(std::vector<HalfEdgeHandle>::const_iterator he_it = hes.begin(),
                he_end = hes.end(); he_it != he_end; ++he_it) {

737
            assert(incident_hfs_per_he_.size() > (unsigned int)std::max(he_it->idx(), opposite_halfedge_handle(*he_it).idx()));
738

739 740 741 742
            incident_hfs_per_he_[he_it->idx()].erase(
                    std::remove(incident_hfs_per_he_[he_it->idx()].begin(),
                                incident_hfs_per_he_[he_it->idx()].end(),
                                halfface_handle(_h, 0)), incident_hfs_per_he_[he_it->idx()].end());
743 744


745 746 747 748
            incident_hfs_per_he_[opposite_halfedge_handle(*he_it).idx()].erase(
                    std::remove(incident_hfs_per_he_[opposite_halfedge_handle(*he_it).idx()].begin(),
                                incident_hfs_per_he_[opposite_halfedge_handle(*he_it).idx()].end(),
                                halfface_handle(_h, 1)), incident_hfs_per_he_[opposite_halfedge_handle(*he_it).idx()].end());
749 750 751 752 753 754 755 756 757
        }
    }

    // 2)
    std::priority_queue<CellHandle> incident_cells;
    if(f_bottom_up_) {

        // Speed-up, since we already know all incident cells
        // Get incident cells for deletion
758
        assert(incident_cell_per_hf_.size() > (unsigned int)halfface_handle(_h, 1).idx());
759 760
        if(incident_cell_per_hf_[halfface_handle(_h, 0).idx()].is_valid()) {
            incident_cells.push(incident_cell_per_hf_[halfface_handle(_h, 0).idx()]);
761
        }
762 763
        if(incident_cell_per_hf_[halfface_handle(_h, 1).idx()].is_valid()) {
            incident_cells.push(incident_cell_per_hf_[halfface_handle(_h, 1).idx()]);
764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783
        }

        // Decrease all half-face handles > _h in all cells
        std::set<CellHandle> update_cells;
        for(std::vector<CellHandle>::const_iterator c_it = (incident_cell_per_hf_.begin() + halfface_handle(_h, 1).idx() + 1),
                c_end = incident_cell_per_hf_.end(); c_it != c_end; ++c_it) {
            if(!c_it->is_valid()) continue;
            update_cells.insert(*c_it);
        }
        for(std::set<CellHandle>::const_iterator c_it = update_cells.begin(),
                c_end = update_cells.end(); c_it != c_end; ++c_it) {

            std::vector<HalfFaceHandle> hfs = cell(*c_it).halffaces();

            // Delete current half-faces from cell's half-face list
            hfs.erase(std::remove(hfs.begin(), hfs.end(), halfface_handle(_h, 0)), hfs.end());
            hfs.erase(std::remove(hfs.begin(), hfs.end(), halfface_handle(_h, 1)), hfs.end());

            HFHandleCorrection cor(halfface_handle(_h, 1));
            std::for_each(hfs.begin(), hfs.end(),
784
                          fun::bind(&HFHandleCorrection::correctValue, &cor, fun::placeholders::_1));
785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805
            cell(*c_it).set_halffaces(hfs);
        }

    } else {

        // Iterate over all cells
        for(CellIter c_it = cells_begin(), c_end = cells_end(); c_it != c_end; ++c_it) {

            std::vector<HalfFaceHandle> hfs = cell(*c_it).halffaces();
            if(std::find(hfs.begin(), hfs.end(), halfface_handle(_h, 0)) != hfs.end() ||
                    std::find(hfs.begin(), hfs.end(), halfface_handle(_h, 1)) != hfs.end()) {
                // Delete cell
                incident_cells.push(*c_it);
                continue;
            }
            // Delete current half-faces from cell's half-face list
            hfs.erase(std::remove(hfs.begin(), hfs.end(), halfface_handle(_h, 0)), hfs.end());
            hfs.erase(std::remove(hfs.begin(), hfs.end(), halfface_handle(_h, 1)), hfs.end());

            HFHandleCorrection cor(halfface_handle(_h, 1));
            std::for_each(hfs.begin(), hfs.end(),
806
                          fun::bind(&HFHandleCorrection::correctValue, &cor, fun::placeholders::_1));
807 808 809 810 811 812
            cell(*c_it).set_halffaces(hfs);
        }
    }

    // 3)
    if(f_bottom_up_) {
813
        assert(incident_cell_per_hf_.size() > (unsigned int)halfface_handle(_h, 1).idx());
814 815 816 817 818 819 820 821 822
        incident_cell_per_hf_.erase(incident_cell_per_hf_.begin() + halfface_handle(_h, 1).idx());
        incident_cell_per_hf_.erase(incident_cell_per_hf_.begin() + halfface_handle(_h, 0).idx());
    }

    // 4)
    if(e_bottom_up_) {
        HFHandleCorrection cor(halfface_handle(_h, 1));
        std::for_each(incident_hfs_per_he_.begin(),
                      incident_hfs_per_he_.end(),
823
                      fun::bind(&HFHandleCorrection::correctVecValue, &cor, fun::placeholders::_1));
824 825 826 827
    }

    // 5)
    faces_.erase(faces_.begin() + _h.idx());
828
    --n_faces_;
829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861

    // 6)
    face_deleted(_h);

    // 7)
    while(!incident_cells.empty()) {
        delete_cell(incident_cells.top());
        incident_cells.pop();
    }

    // Return iterator to next element in list
    return (faces_begin() + _h.idx());
}

//========================================================================================

/**
 * \brief Delete cell from mesh
 *
 * After performing this operation, all cells
 * following cell _h in the array will be accessible
 * through their old handle decreased by one.
 * These steps are performed:
 *
 * 1) Delete links in BU: HF -> C
 * 2) Decrease all entries > c in BU: HF -> C
 * 3) Delete cell from storage array
 * 4) Delete property item
 *
 * @param _h A cell handle
 */
CellIter TopologyKernel::delete_cell(const CellHandle& _h) {

862
    assert(_h.idx() < (int)n_cells_);
863 864 865 866 867 868 869 870

    // 1)
    if(f_bottom_up_) {
        const std::vector<HalfFaceHandle>& hfs = cell(_h).halffaces();
        for(std::vector<HalfFaceHandle>::const_iterator hf_it = hfs.begin(),
                hf_end = hfs.end(); hf_it != hf_end; ++hf_it) {
            assert(incident_cell_per_hf_.size() > (unsigned int)hf_it->idx());

871
            incident_cell_per_hf_[hf_it->idx()] = InvalidCellHandle;
872 873 874 875 876 877 878 879
        }
    }

    // 2)
    if(f_bottom_up_) {
        CHandleCorrection cor(_h);
        std::for_each(incident_cell_per_hf_.begin(),
                      incident_cell_per_hf_.end(),
880
                      fun::bind(&CHandleCorrection::correctValue, &cor, fun::placeholders::_1));
881 882 883 884
    }

    // 3)
    cells_.erase(cells_.begin() + _h.idx());
885
    --n_cells_;
886 887 888 889 890

    // 4)
    cell_deleted(_h);

    return (cells_begin() + _h.idx());
891 892 893 894 895 896 897 898
}

//========================================================================================

/// Get edge with handle _edgeHandle
const OpenVolumeMeshEdge& TopologyKernel::edge(const EdgeHandle& _edgeHandle) const {

    // Test if edge is valid
899 900
    assert((unsigned int)_edgeHandle.idx() < n_edges_);
    assert(_edgeHandle.idx() >= 0);
901

902
    return edges_[_edgeHandle.idx()];
903 904 905 906 907 908 909 910
}

//========================================================================================

/// Get face with handle _faceHandle
const OpenVolumeMeshFace& TopologyKernel::face(const FaceHandle& _faceHandle) const {

    // Test if face is valid
911 912
    assert((unsigned int)_faceHandle.idx() < n_faces_);
    assert(_faceHandle.idx() >= 0);
913

914
    return faces_[_faceHandle.idx()];
915 916 917 918 919 920 921 922
}

//========================================================================================

/// Get cell with handle _cellHandle
const OpenVolumeMeshCell& TopologyKernel::cell(const CellHandle& _cellHandle) const {

    // Test if cell is valid
923 924
    assert((unsigned int)_cellHandle.idx() < n_cells_);
    assert(_cellHandle.idx() >= 0);
925

926
    return cells_[_cellHandle.idx()];
927 928 929 930 931 932 933 934
}

//========================================================================================

/// Get edge with handle _edgeHandle
OpenVolumeMeshEdge& TopologyKernel::edge(const EdgeHandle& _edgeHandle) {

    // Test if edge is valid
935 936
    assert((unsigned int)_edgeHandle.idx() < n_edges_);
    assert(_edgeHandle.idx() >= 0);
937

938
    return edges_[_edgeHandle.idx()];
939 940 941 942 943 944 945 946
}

//========================================================================================

/// Get face with handle _faceHandle
OpenVolumeMeshFace& TopologyKernel::face(const FaceHandle& _faceHandle) {

    // Test if face is valid
947 948
    assert((unsigned int)_faceHandle.idx() < n_faces_);
    assert(_faceHandle.idx() >= 0);
949

950
    return faces_[_faceHandle.idx()];
951 952 953 954 955 956 957 958
}

//========================================================================================

/// Get cell with handle _cellHandle
OpenVolumeMeshCell& TopologyKernel::cell(const CellHandle& _cellHandle) {

    // Test if cell is valid
959 960
    assert((unsigned int)_cellHandle.idx() < n_cells_);
    assert(_cellHandle.idx() >= 0);
961

962
    return cells_[_cellHandle.idx()];
963 964 965 966 967 968 969 970
}

//========================================================================================

/// Get edge that corresponds to halfedge with handle _halfEdgeHandle
const OpenVolumeMeshEdge TopologyKernel::halfedge(const HalfEdgeHandle& _halfEdgeHandle) const {

    // Is handle in range?
971 972
    assert((unsigned int)_halfEdgeHandle.idx() < (n_edges_ * 2));
    assert(_halfEdgeHandle.idx() >= 0);
973 974 975

    // In case the handle is even, just return the corresponding edge
    /// Otherwise return the opposite halfedge via opposite()
976 977
    if(_halfEdgeHandle.idx() % 2 == 0)
        return edges_[(int)(_halfEdgeHandle.idx() / 2)];
978
    else
979
        return opposite_halfedge(edges_[(int)(_halfEdgeHandle.idx() / 2)]);
980 981 982 983 984 985 986 987
}

//========================================================================================

/// Get face that corresponds to halfface with handle _halfFaceHandle
const OpenVolumeMeshFace TopologyKernel::halfface(const HalfFaceHandle& _halfFaceHandle) const {

    // Is handle in range?
988 989
    assert((unsigned int)_halfFaceHandle.idx() < (n_faces_ * 2));
    assert(_halfFaceHandle.idx() >= 0);
990 991 992

    // In case the handle is not even, just return the corresponding face
    // Otherwise return the opposite halfface via opposite()
993 994
    if(_halfFaceHandle.idx() % 2 == 0)
        return faces_[(int)(_halfFaceHandle.idx() / 2)];
995
    else
996
        return opposite_halfface(faces_[(int)(_halfFaceHandle.idx() / 2)]);
997 998 999 1000 1001 1002 1003 1004
}

//========================================================================================

/// Get opposite halfedge that corresponds to halfedge with handle _halfEdgeHandle
const OpenVolumeMeshEdge TopologyKernel::opposite_halfedge(const HalfEdgeHandle& _halfEdgeHandle) const {

    // Is handle in range?
1005 1006
    assert(_halfEdgeHandle.idx() >= 0);
    assert((unsigned int)_halfEdgeHandle.idx() < (n_edges_ * 2));
1007 1008 1009

    // In case the handle is not even, just return the corresponding edge
    // Otherwise return the opposite halfedge via opposite()
1010 1011
    if(_halfEdgeHandle.idx() % 2 != 0)
        return edges_[(int)(_halfEdgeHandle.idx() / 2)];
1012
    else
1013
        return opposite_halfedge(edges_[(int)(_halfEdgeHandle.idx() / 2)]);
1014 1015 1016 1017 1018 1019 1020 1021
}

//========================================================================================

/// Get opposite halfface that corresponds to halfface with handle _halfFaceHandle
const OpenVolumeMeshFace TopologyKernel::opposite_halfface(const HalfFaceHandle& _halfFaceHandle) const {

    // Is handle in range?
1022 1023
    assert(_halfFaceHandle.idx() >= 0);
    assert((unsigned int)_halfFaceHandle.idx() < (n_faces_ * 2));
1024 1025 1026

    // In case the handle is not even, just return the corresponding face
    // Otherwise return the opposite via the first face's opposite() function
1027 1028
    if(_halfFaceHandle.idx() % 2 != 0)
        return faces_[(int)(_halfFaceHandle.idx() / 2)];
1029
    else
1030
        return opposite_halfface(faces_[(int)(_halfFaceHandle.idx() / 2)]);
1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050
}

//========================================================================================

const HalfEdgeHandle TopologyKernel::halfedge(const VertexHandle& _vh1, const VertexHandle& _vh2) const {

    assert(_vh1.idx() < (int)n_vertices());
    assert(_vh2.idx() < (int)n_vertices());

    for(VertexOHalfEdgeIter voh_it = voh_iter(_vh1); voh_it.valid(); ++voh_it) {
        if(halfedge(*voh_it).to_vertex() == _vh2) {
            return *voh_it;
        }
    }

    return InvalidHalfEdgeHandle;
}

//========================================================================================

1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093
const HalfFaceHandle TopologyKernel::halfface(const std::vector<VertexHandle>& _vs) const {

    assert(_vs.size() > 2);

    VertexHandle v0 = _vs[0], v1 = _vs[1], v2 = _vs[2];

    assert(v0.is_valid() && v1.is_valid() && v2.is_valid());

    HalfEdgeHandle he0 = halfedge(v0, v1);
    if(!he0.is_valid()) return InvalidHalfFaceHandle;
    HalfEdgeHandle he1 = halfedge(v1, v2);
    if(!he1.is_valid()) return InvalidHalfFaceHandle;

    std::vector<HalfEdgeHandle> hes;
    hes.push_back(he0);
    hes.push_back(he1);

    return halfface(hes);
}

//========================================================================================

const HalfFaceHandle TopologyKernel::halfface(const std::vector<HalfEdgeHandle>& _hes) const {

    assert(_hes.size() >= 2);

    HalfEdgeHandle he0 = _hes[0], he1 = _hes[1];

    assert(he0.is_valid() && he1.is_valid());

    for(HalfEdgeHalfFaceIter hehf_it = hehf_iter(he0); hehf_it.valid(); ++hehf_it) {

        std::vector<HalfEdgeHandle> hes = halfface(*hehf_it).halfedges();
        if(std::find(hes.begin(), hes.end(), he1) != hes.end()) {
            return *hehf_it;
        }
    }

    return InvalidHalfFaceHandle;
}

//========================================================================================

1094 1095
const HalfEdgeHandle TopologyKernel::next_halfedge_in_halfface(const HalfEdgeHandle& _heh, const HalfFaceHandle& _hfh) const {

1096 1097
    assert((unsigned int)_hfh.idx() < n_faces_ * 2u);
    assert((unsigned int)_heh.idx() < n_edges_ * 2u);
1098 1099 1100

    std::vector<HalfEdgeHandle> hes = halfface(_hfh).halfedges();

1101
    for(std::vector<HalfEdgeHandle>::const_iterator it = hes.begin();
1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115
            it != hes.end(); ++it) {
        if(*it == _heh) {
            if((it + 1) != hes.end()) return *(it + 1);
            else return *hes.begin();
        }
    }

    return InvalidHalfEdgeHandle;
}

//========================================================================================

const HalfEdgeHandle TopologyKernel::prev_halfedge_in_halfface(const HalfEdgeHandle& _heh, const HalfFaceHandle& _hfh) const {

1116 1117
    assert((unsigned int)_hfh.idx() < n_faces_ * 2u);
    assert((unsigned int)_heh.idx() < n_edges_ * 2u);
1118 1119 1120

    std::vector<HalfEdgeHandle> hes = halfface(_hfh).halfedges();

1121
    for(std::vector<HalfEdgeHandle>::const_iterator it = hes.begin();
1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133
            it != hes.end(); ++it) {
        if(*it == _heh) {
            if(it != hes.begin()) return *(it - 1);
            else return *(hes.end() - 1);
        }
    }

    return InvalidHalfEdgeHandle;
}

//========================================================================================

1134 1135
HalfFaceHandle
TopologyKernel::adjacent_halfface_in_cell(const HalfFaceHandle& _halfFaceHandle, const HalfEdgeHandle& _halfEdgeHandle) const {
1136

1137
#ifndef NDEBUG
1138
    if((unsigned int)_halfFaceHandle.idx() >= incident_cell_per_hf_.size() || _halfFaceHandle.idx() < 0) {
1139 1140
        return InvalidHalfFaceHandle;
    }
1141
#endif
1142 1143 1144
    if(!has_face_bottom_up_adjacencies()) {
        return InvalidHalfFaceHandle;
    }
1145
    if(incident_cell_per_hf_[_halfFaceHandle.idx()] == InvalidCellHandle) {
1146 1147 1148
        // Specified halfface is on the outside of the complex
        return InvalidHalfFaceHandle;
    }
1149

1150
    OpenVolumeMeshCell c = cell(incident_cell_per_hf_[_halfFaceHandle.idx()]);
1151

1152 1153 1154 1155 1156 1157
    // Make sure that _halfFaceHandle is incident to _halfEdgeHandle
    bool skipped = false;
    bool found = false;
    HalfFaceHandle idx = InvalidHalfFaceHandle;
    for(std::vector<HalfFaceHandle>::const_iterator hf_it = c.halffaces().begin();
            hf_it != c.halffaces().end(); ++hf_it) {
1158

1159 1160 1161 1162
        if(*hf_it == _halfFaceHandle) {
            skipped = true;
            continue;
        }
1163

1164 1165 1166
        OpenVolumeMeshFace hf = halfface(*hf_it);
        for(std::vector<HalfEdgeHandle>::const_iterator he_it = hf.halfedges().begin();
            he_it != hf.halfedges().end(); ++he_it) {
1167

1168 1169 1170 1171 1172 1173 1174 1175 1176 1177
            if(edge_handle(*he_it) == edge_handle(_halfEdgeHandle)) {
                found = true;
                idx = *hf_it;
            }
            if(skipped && found) break;
        }
        if(skipped && found) break;
    }
    return ((skipped && found) ? idx : InvalidHalfFaceHandle);
}
1178

1179
//========================================================================================
1180

1181
CellHandle TopologyKernel::incident_cell(const HalfFaceHandle& _halfFaceHandle) const {
1182

1183 1184 1185
    if(!has_face_bottom_up_adjacencies()) {
        return InvalidCellHandle;
    }
1186
    if((unsigned int)_halfFaceHandle.idx() >= incident_cell_per_hf_.size() || _halfFaceHandle.idx() < 0) {
1187
        return InvalidCellHandle;
1188
    }
1189

1190
    return incident_cell_per_hf_[_halfFaceHandle.idx()];
1191 1192 1193 1194
}

//========================================================================================

1195
void TopologyKernel::compute_vertex_bottom_up_adjacencies() {
1196 1197 1198 1199 1200 1201

    // Clear adjacencies
    outgoing_hes_per_vertex_.clear();
    outgoing_hes_per_vertex_.resize(n_vertices());

    // Store outgoing halfedges per vertex
1202
    unsigned int n_vertices = n_edges_;
1203 1204 1205
    for(unsigned int i = 0; i < n_vertices; ++i) {

        VertexHandle from = edges_[i].from_vertex();
1206
        if((unsigned int)from.idx() >= outgoing_hes_per_vertex_.size()) {
1207 1208 1209
            std::cerr << "update_adjacencies(): Vertex handle is out of bounds!" << std::endl;
            return;
        }
1210
        outgoing_hes_per_vertex_[from.idx()].push_back(halfedge_handle(EdgeHandle(i), 0));
1211 1212

        VertexHandle to = edges_[i].to_vertex();
1213
        if((unsigned int)to.idx() >= outgoing_hes_per_vertex_.size()) {
1214 1215 1216 1217
            std::cerr << "update_adjacencies(): Vertex handle is out of bounds!" << std::endl;
            return;
        }
        // Store opposite halfedge handle
1218
        outgoing_hes_per_vertex_[to.idx()].push_back(halfedge_handle(EdgeHandle(i), 1));
1219 1220 1221 1222 1223
    }
}

//========================================================================================

1224
void TopologyKernel::compute_edge_bottom_up_adjacencies() {
1225 1226 1227

    // Clear
    incident_hfs_per_he_.clear();
1228
    incident_hfs_per_he_.resize(n_edges_ * 2u);
1229 1230

    // Store incident halffaces per halfedge
1231
    unsigned int n_faces = n_faces_;
1232 1233