path: root/thirdparty/vhacd/src/vhacdICHull.cpp

/* Copyright (c) 2011 Khaled Mamou (kmamou at gmail dot com)
 All rights reserved.
 
 
 Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
 
 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
 
 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
 
 3. The names of the contributors may not be used to endorse or promote products derived from this software without specific prior written permission.
 
 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
#include "vhacdICHull.h"
#include <limits>

#ifdef _MSC_VER
#pragma warning(disable:4456 4706)
#endif


namespace VHACD {
const double ICHull::sc_eps = 1.0e-15;
const int32_t ICHull::sc_dummyIndex = std::numeric_limits<int32_t>::max();
ICHull::ICHull()
{
    m_isFlat = false;
}
bool ICHull::AddPoints(const Vec3<double>* points, size_t nPoints)
{
    if (!points) {
        return false;
    }
    CircularListElement<TMMVertex>* vertex = NULL;
    for (size_t i = 0; i < nPoints; i++) {
        vertex = m_mesh.AddVertex();
        vertex->GetData().m_pos.X() = points[i].X();
        vertex->GetData().m_pos.Y() = points[i].Y();
        vertex->GetData().m_pos.Z() = points[i].Z();
        vertex->GetData().m_name = static_cast<int32_t>(i);
    }
    return true;
}
bool ICHull::AddPoint(const Vec3<double>& point, int32_t id)
{
    if (AddPoints(&point, 1)) {
        m_mesh.m_vertices.GetData().m_name = id;
        return true;
    }
    return false;
}

ICHullError ICHull::Process()
{
    uint32_t addedPoints = 0;
    if (m_mesh.GetNVertices() < 3) {
        return ICHullErrorNotEnoughPoints;
    }
    if (m_mesh.GetNVertices() == 3) {
        m_isFlat = true;
        CircularListElement<TMMTriangle>* t1 = m_mesh.AddTriangle();
        CircularListElement<TMMTriangle>* t2 = m_mesh.AddTriangle();
        CircularListElement<TMMVertex>* v0 = m_mesh.m_vertices.GetHead();
        CircularListElement<TMMVertex>* v1 = v0->GetNext();
        CircularListElement<TMMVertex>* v2 = v1->GetNext();
        // Compute the normal to the plane
        Vec3<double> p0 = v0->GetData().m_pos;
        Vec3<double> p1 = v1->GetData().m_pos;
        Vec3<double> p2 = v2->GetData().m_pos;
        m_normal = (p1 - p0) ^ (p2 - p0);
        m_normal.Normalize();
        t1->GetData().m_vertices[0] = v0;
        t1->GetData().m_vertices[1] = v1;
        t1->GetData().m_vertices[2] = v2;
        t2->GetData().m_vertices[0] = v1;
        t2->GetData().m_vertices[1] = v2;
        t2->GetData().m_vertices[2] = v2;
        return ICHullErrorOK;
    }
    if (m_isFlat) {
        m_mesh.m_edges.Clear();
        m_mesh.m_triangles.Clear();
        m_isFlat = false;
    }
    if (m_mesh.GetNTriangles() == 0) // we have to create the first polyhedron
    {
        ICHullError res = DoubleTriangle();
        if (res != ICHullErrorOK) {
            return res;
        }
        else {
            addedPoints += 3;
        }
    }
    CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
    // go to the first added and not processed vertex
    while (!(vertices.GetHead()->GetPrev()->GetData().m_tag)) {
        vertices.Prev();
    }
    while (!vertices.GetData().m_tag) // not processed
    {
        vertices.GetData().m_tag = true;
        if (ProcessPoint()) {
            addedPoints++;
            CleanUp(addedPoints);
            vertices.Next();
            if (!GetMesh().CheckConsistancy()) {
                size_t nV = m_mesh.GetNVertices();
                CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
                for (size_t v = 0; v < nV; ++v) {
                    if (vertices.GetData().m_name == sc_dummyIndex) {
                        vertices.Delete();
                        break;
                    }
                    vertices.Next();
                }
                return ICHullErrorInconsistent;
            }
        }
    }
    if (m_isFlat) {
        SArray<CircularListElement<TMMTriangle>*> trianglesToDuplicate;
        size_t nT = m_mesh.GetNTriangles();
        for (size_t f = 0; f < nT; f++) {
            TMMTriangle& currentTriangle = m_mesh.m_triangles.GetHead()->GetData();
            if (currentTriangle.m_vertices[0]->GetData().m_name == sc_dummyIndex || currentTriangle.m_vertices[1]->GetData().m_name == sc_dummyIndex || currentTriangle.m_vertices[2]->GetData().m_name == sc_dummyIndex) {
                m_trianglesToDelete.PushBack(m_mesh.m_triangles.GetHead());
                for (int32_t k = 0; k < 3; k++) {
                    for (int32_t h = 0; h < 2; h++) {
                        if (currentTriangle.m_edges[k]->GetData().m_triangles[h] == m_mesh.m_triangles.GetHead()) {
                            currentTriangle.m_edges[k]->GetData().m_triangles[h] = 0;
                            break;
                        }
                    }
                }
            }
            else {
                trianglesToDuplicate.PushBack(m_mesh.m_triangles.GetHead());
            }
            m_mesh.m_triangles.Next();
        }
        size_t nE = m_mesh.GetNEdges();
        for (size_t e = 0; e < nE; e++) {
            TMMEdge& currentEdge = m_mesh.m_edges.GetHead()->GetData();
            if (currentEdge.m_triangles[0] == 0 && currentEdge.m_triangles[1] == 0) {
                m_edgesToDelete.PushBack(m_mesh.m_edges.GetHead());
            }
            m_mesh.m_edges.Next();
        }
        size_t nV = m_mesh.GetNVertices();
        CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
        for (size_t v = 0; v < nV; ++v) {
            if (vertices.GetData().m_name == sc_dummyIndex) {
                vertices.Delete();
            }
            else {
                vertices.GetData().m_tag = false;
                vertices.Next();
            }
        }
        CleanEdges();
        CleanTriangles();
        CircularListElement<TMMTriangle>* newTriangle;
        for (size_t t = 0; t < trianglesToDuplicate.Size(); t++) {
            newTriangle = m_mesh.AddTriangle();
            newTriangle->GetData().m_vertices[0] = trianglesToDuplicate[t]->GetData().m_vertices[1];
            newTriangle->GetData().m_vertices[1] = trianglesToDuplicate[t]->GetData().m_vertices[0];
            newTriangle->GetData().m_vertices[2] = trianglesToDuplicate[t]->GetData().m_vertices[2];
        }
    }
    return ICHullErrorOK;
}
ICHullError ICHull::Process(const uint32_t nPointsCH,
    const double minVolume)
{
    uint32_t addedPoints = 0;
    if (nPointsCH < 3 || m_mesh.GetNVertices() < 3) {
        return ICHullErrorNotEnoughPoints;
    }
    if (m_mesh.GetNVertices() == 3) {
        m_isFlat = true;
        CircularListElement<TMMTriangle>* t1 = m_mesh.AddTriangle();
        CircularListElement<TMMTriangle>* t2 = m_mesh.AddTriangle();
        CircularListElement<TMMVertex>* v0 = m_mesh.m_vertices.GetHead();
        CircularListElement<TMMVertex>* v1 = v0->GetNext();
        CircularListElement<TMMVertex>* v2 = v1->GetNext();
        // Compute the normal to the plane
        Vec3<double> p0 = v0->GetData().m_pos;
        Vec3<double> p1 = v1->GetData().m_pos;
        Vec3<double> p2 = v2->GetData().m_pos;
        m_normal = (p1 - p0) ^ (p2 - p0);
        m_normal.Normalize();
        t1->GetData().m_vertices[0] = v0;
        t1->GetData().m_vertices[1] = v1;
        t1->GetData().m_vertices[2] = v2;
        t2->GetData().m_vertices[0] = v1;
        t2->GetData().m_vertices[1] = v0;
        t2->GetData().m_vertices[2] = v2;
        return ICHullErrorOK;
    }

    if (m_isFlat) {
        m_mesh.m_triangles.Clear();
        m_mesh.m_edges.Clear();
        m_isFlat = false;
    }

    if (m_mesh.GetNTriangles() == 0) // we have to create the first polyhedron
    {
        ICHullError res = DoubleTriangle();
        if (res != ICHullErrorOK) {
            return res;
        }
        else {
            addedPoints += 3;
        }
    }
    CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
    while (!vertices.GetData().m_tag && addedPoints < nPointsCH) // not processed
    {
        if (!FindMaxVolumePoint((addedPoints > 4) ? minVolume : 0.0)) {
            break;
        }
        vertices.GetData().m_tag = true;
        if (ProcessPoint()) {
            addedPoints++;
            CleanUp(addedPoints);
            if (!GetMesh().CheckConsistancy()) {
                size_t nV = m_mesh.GetNVertices();
                CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
                for (size_t v = 0; v < nV; ++v) {
                    if (vertices.GetData().m_name == sc_dummyIndex) {
                        vertices.Delete();
                        break;
                    }
                    vertices.Next();
                }
                return ICHullErrorInconsistent;
            }
            vertices.Next();
        }
    }
    // delete remaining points
    while (!vertices.GetData().m_tag) {
        vertices.Delete();
    }
    if (m_isFlat) {
        SArray<CircularListElement<TMMTriangle>*> trianglesToDuplicate;
        size_t nT = m_mesh.GetNTriangles();
        for (size_t f = 0; f < nT; f++) {
            TMMTriangle& currentTriangle = m_mesh.m_triangles.GetHead()->GetData();
            if (currentTriangle.m_vertices[0]->GetData().m_name == sc_dummyIndex || currentTriangle.m_vertices[1]->GetData().m_name == sc_dummyIndex || currentTriangle.m_vertices[2]->GetData().m_name == sc_dummyIndex) {
                m_trianglesToDelete.PushBack(m_mesh.m_triangles.GetHead());
                for (int32_t k = 0; k < 3; k++) {
                    for (int32_t h = 0; h < 2; h++) {
                        if (currentTriangle.m_edges[k]->GetData().m_triangles[h] == m_mesh.m_triangles.GetHead()) {
                            currentTriangle.m_edges[k]->GetData().m_triangles[h] = 0;
                            break;
                        }
                    }
                }
            }
            else {
                trianglesToDuplicate.PushBack(m_mesh.m_triangles.GetHead());
            }
            m_mesh.m_triangles.Next();
        }
        size_t nE = m_mesh.GetNEdges();
        for (size_t e = 0; e < nE; e++) {
            TMMEdge& currentEdge = m_mesh.m_edges.GetHead()->GetData();
            if (currentEdge.m_triangles[0] == 0 && currentEdge.m_triangles[1] == 0) {
                m_edgesToDelete.PushBack(m_mesh.m_edges.GetHead());
            }
            m_mesh.m_edges.Next();
        }
        size_t nV = m_mesh.GetNVertices();
        CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
        for (size_t v = 0; v < nV; ++v) {
            if (vertices.GetData().m_name == sc_dummyIndex) {
                vertices.Delete();
            }
            else {
                vertices.GetData().m_tag = false;
                vertices.Next();
            }
        }
        CleanEdges();
        CleanTriangles();
        CircularListElement<TMMTriangle>* newTriangle;
        for (size_t t = 0; t < trianglesToDuplicate.Size(); t++) {
            newTriangle = m_mesh.AddTriangle();
            newTriangle->GetData().m_vertices[0] = trianglesToDuplicate[t]->GetData().m_vertices[1];
            newTriangle->GetData().m_vertices[1] = trianglesToDuplicate[t]->GetData().m_vertices[0];
            newTriangle->GetData().m_vertices[2] = trianglesToDuplicate[t]->GetData().m_vertices[2];
        }
    }
    return ICHullErrorOK;
}
bool ICHull::FindMaxVolumePoint(const double minVolume)
{
    CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
    CircularListElement<TMMVertex>* vMaxVolume = 0;
    CircularListElement<TMMVertex>* vHeadPrev = vertices.GetHead()->GetPrev();

    double maxVolume = minVolume;
    double volume = 0.0;
    while (!vertices.GetData().m_tag) // not processed
    {
        if (ComputePointVolume(volume, false)) {
            if (maxVolume < volume) {
                maxVolume = volume;
                vMaxVolume = vertices.GetHead();
            }
            vertices.Next();
        }
    }
    CircularListElement<TMMVertex>* vHead = vHeadPrev->GetNext();
    vertices.GetHead() = vHead;
    if (!vMaxVolume) {
        return false;
    }
    if (vMaxVolume != vHead) {
        Vec3<double> pos = vHead->GetData().m_pos;
        int32_t id = vHead->GetData().m_name;
        vHead->GetData().m_pos = vMaxVolume->GetData().m_pos;
        vHead->GetData().m_name = vMaxVolume->GetData().m_name;
        vMaxVolume->GetData().m_pos = pos;
        vHead->GetData().m_name = id;
    }
    return true;
}
ICHullError ICHull::DoubleTriangle()
{
    // find three non colinear points
    m_isFlat = false;
    CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
    CircularListElement<TMMVertex>* v0 = vertices.GetHead();
    while (Colinear(v0->GetData().m_pos,
        v0->GetNext()->GetData().m_pos,
        v0->GetNext()->GetNext()->GetData().m_pos)) {
        if ((v0 = v0->GetNext()) == vertices.GetHead()) {
            return ICHullErrorCoplanarPoints;
        }
    }
    CircularListElement<TMMVertex>* v1 = v0->GetNext();
    CircularListElement<TMMVertex>* v2 = v1->GetNext();
    // mark points as processed
    v0->GetData().m_tag = v1->GetData().m_tag = v2->GetData().m_tag = true;

    // create two triangles
    CircularListElement<TMMTriangle>* f0 = MakeFace(v0, v1, v2, 0);
    MakeFace(v2, v1, v0, f0);

    // find a fourth non-coplanar point to form tetrahedron
    CircularListElement<TMMVertex>* v3 = v2->GetNext();
    vertices.GetHead() = v3;

    double vol = ComputeVolume4(v0->GetData().m_pos, v1->GetData().m_pos, v2->GetData().m_pos, v3->GetData().m_pos);
    while (fabs(vol) < sc_eps && !v3->GetNext()->GetData().m_tag) {
        v3 = v3->GetNext();
        vol = ComputeVolume4(v0->GetData().m_pos, v1->GetData().m_pos, v2->GetData().m_pos, v3->GetData().m_pos);
    }
    if (fabs(vol) < sc_eps) {
        // compute the barycenter
        Vec3<double> bary(0.0, 0.0, 0.0);
        CircularListElement<TMMVertex>* vBary = v0;
        do {
            bary += vBary->GetData().m_pos;
        } while ((vBary = vBary->GetNext()) != v0);
        bary /= static_cast<double>(vertices.GetSize());

        // Compute the normal to the plane
        Vec3<double> p0 = v0->GetData().m_pos;
        Vec3<double> p1 = v1->GetData().m_pos;
        Vec3<double> p2 = v2->GetData().m_pos;
        m_normal = (p1 - p0) ^ (p2 - p0);
        m_normal.Normalize();
        // add dummy vertex placed at (bary + normal)
        vertices.GetHead() = v2;
        Vec3<double> newPt = bary + m_normal;
        AddPoint(newPt, sc_dummyIndex);
        m_isFlat = true;
        return ICHullErrorOK;
    }
    else if (v3 != vertices.GetHead()) {
        TMMVertex temp;
        temp.m_name = v3->GetData().m_name;
        temp.m_pos = v3->GetData().m_pos;
        v3->GetData().m_name = vertices.GetHead()->GetData().m_name;
        v3->GetData().m_pos = vertices.GetHead()->GetData().m_pos;
        vertices.GetHead()->GetData().m_name = temp.m_name;
        vertices.GetHead()->GetData().m_pos = temp.m_pos;
    }
    return ICHullErrorOK;
}
CircularListElement<TMMTriangle>* ICHull::MakeFace(CircularListElement<TMMVertex>* v0,
    CircularListElement<TMMVertex>* v1,
    CircularListElement<TMMVertex>* v2,
    CircularListElement<TMMTriangle>* fold)
{
    CircularListElement<TMMEdge>* e0;
    CircularListElement<TMMEdge>* e1;
    CircularListElement<TMMEdge>* e2;
    int32_t index = 0;
    if (!fold) // if first face to be created
    {
        e0 = m_mesh.AddEdge(); // create the three edges
        e1 = m_mesh.AddEdge();
        e2 = m_mesh.AddEdge();
    }
    else // otherwise re-use existing edges (in reverse order)
    {
        e0 = fold->GetData().m_edges[2];
        e1 = fold->GetData().m_edges[1];
        e2 = fold->GetData().m_edges[0];
        index = 1;
    }
    e0->GetData().m_vertices[0] = v0;
    e0->GetData().m_vertices[1] = v1;
    e1->GetData().m_vertices[0] = v1;
    e1->GetData().m_vertices[1] = v2;
    e2->GetData().m_vertices[0] = v2;
    e2->GetData().m_vertices[1] = v0;
    // create the new face
    CircularListElement<TMMTriangle>* f = m_mesh.AddTriangle();
    f->GetData().m_edges[0] = e0;
    f->GetData().m_edges[1] = e1;
    f->GetData().m_edges[2] = e2;
    f->GetData().m_vertices[0] = v0;
    f->GetData().m_vertices[1] = v1;
    f->GetData().m_vertices[2] = v2;
    // link edges to face f
    e0->GetData().m_triangles[index] = e1->GetData().m_triangles[index] = e2->GetData().m_triangles[index] = f;
    return f;
}
CircularListElement<TMMTriangle>* ICHull::MakeConeFace(CircularListElement<TMMEdge>* e, CircularListElement<TMMVertex>* p)
{
    // create two new edges if they don't already exist
    CircularListElement<TMMEdge>* newEdges[2];
    for (int32_t i = 0; i < 2; ++i) {
        if (!(newEdges[i] = e->GetData().m_vertices[i]->GetData().m_duplicate)) { // if the edge doesn't exits add it and mark the vertex as duplicated
            newEdges[i] = m_mesh.AddEdge();
            newEdges[i]->GetData().m_vertices[0] = e->GetData().m_vertices[i];
            newEdges[i]->GetData().m_vertices[1] = p;
            e->GetData().m_vertices[i]->GetData().m_duplicate = newEdges[i];
        }
    }
    // make the new face
    CircularListElement<TMMTriangle>* newFace = m_mesh.AddTriangle();
    newFace->GetData().m_edges[0] = e;
    newFace->GetData().m_edges[1] = newEdges[0];
    newFace->GetData().m_edges[2] = newEdges[1];
    MakeCCW(newFace, e, p);
    for (int32_t i = 0; i < 2; ++i) {
        for (int32_t j = 0; j < 2; ++j) {
            if (!newEdges[i]->GetData().m_triangles[j]) {
                newEdges[i]->GetData().m_triangles[j] = newFace;
                break;
            }
        }
    }
    return newFace;
}
bool ICHull::ComputePointVolume(double& totalVolume, bool markVisibleFaces)
{
    // mark visible faces
    CircularListElement<TMMTriangle>* fHead = m_mesh.GetTriangles().GetHead();
    CircularListElement<TMMTriangle>* f = fHead;
    CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
    CircularListElement<TMMVertex>* vertex0 = vertices.GetHead();
    bool visible = false;
    Vec3<double> pos0 = Vec3<double>(vertex0->GetData().m_pos.X(),
        vertex0->GetData().m_pos.Y(),
        vertex0->GetData().m_pos.Z());
    double vol = 0.0;
    totalVolume = 0.0;
    Vec3<double> ver0, ver1, ver2;
    do {
        ver0.X() = f->GetData().m_vertices[0]->GetData().m_pos.X();
        ver0.Y() = f->GetData().m_vertices[0]->GetData().m_pos.Y();
        ver0.Z() = f->GetData().m_vertices[0]->GetData().m_pos.Z();
        ver1.X() = f->GetData().m_vertices[1]->GetData().m_pos.X();
        ver1.Y() = f->GetData().m_vertices[1]->GetData().m_pos.Y();
        ver1.Z() = f->GetData().m_vertices[1]->GetData().m_pos.Z();
        ver2.X() = f->GetData().m_vertices[2]->GetData().m_pos.X();
        ver2.Y() = f->GetData().m_vertices[2]->GetData().m_pos.Y();
        ver2.Z() = f->GetData().m_vertices[2]->GetData().m_pos.Z();
        vol = ComputeVolume4(ver0, ver1, ver2, pos0);
        if (vol < -sc_eps) {
            vol = fabs(vol);
            totalVolume += vol;
            if (markVisibleFaces) {
                f->GetData().m_visible = true;
                m_trianglesToDelete.PushBack(f);
            }
            visible = true;
        }
        f = f->GetNext();
    } while (f != fHead);

    if (m_trianglesToDelete.Size() == m_mesh.m_triangles.GetSize()) {
        for (size_t i = 0; i < m_trianglesToDelete.Size(); i++) {
            m_trianglesToDelete[i]->GetData().m_visible = false;
        }
        visible = false;
    }
    // if no faces visible from p then p is inside the hull
    if (!visible && markVisibleFaces) {
        vertices.Delete();
        m_trianglesToDelete.Resize(0);
        return false;
    }
    return true;
}
bool ICHull::ProcessPoint()
{
    double totalVolume = 0.0;
    if (!ComputePointVolume(totalVolume, true)) {
        return false;
    }
    // Mark edges in interior of visible region for deletion.
    // Create a new face based on each border edge
    CircularListElement<TMMVertex>* v0 = m_mesh.GetVertices().GetHead();
    CircularListElement<TMMEdge>* eHead = m_mesh.GetEdges().GetHead();
    CircularListElement<TMMEdge>* e = eHead;
    CircularListElement<TMMEdge>* tmp = 0;
    int32_t nvisible = 0;
    m_edgesToDelete.Resize(0);
    m_edgesToUpdate.Resize(0);
    do {
        tmp = e->GetNext();
        nvisible = 0;
        for (int32_t k = 0; k < 2; k++) {
            if (e->GetData().m_triangles[k]->GetData().m_visible) {
                nvisible++;
            }
        }
        if (nvisible == 2) {
            m_edgesToDelete.PushBack(e);
        }
        else if (nvisible == 1) {
            e->GetData().m_newFace = MakeConeFace(e, v0);
            m_edgesToUpdate.PushBack(e);
        }
        e = tmp;
    } while (e != eHead);
    return true;
}
bool ICHull::MakeCCW(CircularListElement<TMMTriangle>* f,
    CircularListElement<TMMEdge>* e,
    CircularListElement<TMMVertex>* v)
{
    // the visible face adjacent to e
    CircularListElement<TMMTriangle>* fv;
    if (e->GetData().m_triangles[0]->GetData().m_visible) {
        fv = e->GetData().m_triangles[0];
    }
    else {
        fv = e->GetData().m_triangles[1];
    }

    //  set vertex[0] and vertex[1] to have the same orientation as the corresponding vertices of fv.
    int32_t i; // index of e->m_vertices[0] in fv
    CircularListElement<TMMVertex>* v0 = e->GetData().m_vertices[0];
    CircularListElement<TMMVertex>* v1 = e->GetData().m_vertices[1];
    for (i = 0; fv->GetData().m_vertices[i] != v0; i++)
        ;

    if (fv->GetData().m_vertices[(i + 1) % 3] != e->GetData().m_vertices[1]) {
        f->GetData().m_vertices[0] = v1;
        f->GetData().m_vertices[1] = v0;
    }
    else {
        f->GetData().m_vertices[0] = v0;
        f->GetData().m_vertices[1] = v1;
        // swap edges
        CircularListElement<TMMEdge>* tmp = f->GetData().m_edges[0];
        f->GetData().m_edges[0] = f->GetData().m_edges[1];
        f->GetData().m_edges[1] = tmp;
    }
    f->GetData().m_vertices[2] = v;
    return true;
}
bool ICHull::CleanUp(uint32_t& addedPoints)
{
    bool r0 = CleanEdges();
    bool r1 = CleanTriangles();
    bool r2 = CleanVertices(addedPoints);
    return r0 && r1 && r2;
}
bool ICHull::CleanEdges()
{
    // integrate the new faces into the data structure
    CircularListElement<TMMEdge>* e;
    const size_t ne_update = m_edgesToUpdate.Size();
    for (size_t i = 0; i < ne_update; ++i) {
        e = m_edgesToUpdate[i];
        if (e->GetData().m_newFace) {
            if (e->GetData().m_triangles[0]->GetData().m_visible) {
                e->GetData().m_triangles[0] = e->GetData().m_newFace;
            }
            else {
                e->GetData().m_triangles[1] = e->GetData().m_newFace;
            }
            e->GetData().m_newFace = 0;
        }
    }
    // delete edges maked for deletion
    CircularList<TMMEdge>& edges = m_mesh.GetEdges();
    const size_t ne_delete = m_edgesToDelete.Size();
    for (size_t i = 0; i < ne_delete; ++i) {
        edges.Delete(m_edgesToDelete[i]);
    }
    m_edgesToDelete.Resize(0);
    m_edgesToUpdate.Resize(0);
    return true;
}
bool ICHull::CleanTriangles()
{
    CircularList<TMMTriangle>& triangles = m_mesh.GetTriangles();
    const size_t nt_delete = m_trianglesToDelete.Size();
    for (size_t i = 0; i < nt_delete; ++i) {
        triangles.Delete(m_trianglesToDelete[i]);
    }
    m_trianglesToDelete.Resize(0);
    return true;
}
bool ICHull::CleanVertices(uint32_t& addedPoints)
{
    // mark all vertices incident to some undeleted edge as on the hull
    CircularList<TMMEdge>& edges = m_mesh.GetEdges();
    CircularListElement<TMMEdge>* e = edges.GetHead();
    size_t nE = edges.GetSize();
    for (size_t i = 0; i < nE; i++) {
        e->GetData().m_vertices[0]->GetData().m_onHull = true;
        e->GetData().m_vertices[1]->GetData().m_onHull = true;
        e = e->GetNext();
    }
    // delete all the vertices that have been processed but are not on the hull
    CircularList<TMMVertex>& vertices = m_mesh.GetVertices();
    CircularListElement<TMMVertex>* vHead = vertices.GetHead();
    CircularListElement<TMMVertex>* v = vHead;
    v = v->GetPrev();
    do {
        if (v->GetData().m_tag && !v->GetData().m_onHull) {
            CircularListElement<TMMVertex>* tmp = v->GetPrev();
            vertices.Delete(v);
            v = tmp;
            addedPoints--;
        }
        else {
            v->GetData().m_duplicate = 0;
            v->GetData().m_onHull = false;
            v = v->GetPrev();
        }
    } while (v->GetData().m_tag && v != vHead);
    return true;
}
void ICHull::Clear()
{
    m_mesh.Clear();
    m_edgesToDelete.Resize(0);
    m_edgesToUpdate.Resize(0);
    m_trianglesToDelete.Resize(0);
    m_isFlat = false;
}
const ICHull& ICHull::operator=(ICHull& rhs)
{
    if (&rhs != this) {
        m_mesh.Copy(rhs.m_mesh);
        m_edgesToDelete = rhs.m_edgesToDelete;
        m_edgesToUpdate = rhs.m_edgesToUpdate;
        m_trianglesToDelete = rhs.m_trianglesToDelete;
        m_isFlat = rhs.m_isFlat;
    }
    return (*this);
}
bool ICHull::IsInside(const Vec3<double>& pt0, const double eps)
{
    const Vec3<double> pt(pt0.X(), pt0.Y(), pt0.Z());
    if (m_isFlat) {
        size_t nT = m_mesh.m_triangles.GetSize();
        Vec3<double> ver0, ver1, ver2, a, b, c;
        double u, v;
        for (size_t t = 0; t < nT; t++) {
            ver0.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.X();
            ver0.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.Y();
            ver0.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.Z();
            ver1.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.X();
            ver1.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.Y();
            ver1.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.Z();
            ver2.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.X();
            ver2.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.Y();
            ver2.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.Z();
            a = ver1 - ver0;
            b = ver2 - ver0;
            c = pt - ver0;
            u = c * a;
            v = c * b;
            if (u >= 0.0 && u <= 1.0 && v >= 0.0 && u + v <= 1.0) {
                return true;
            }
            m_mesh.m_triangles.Next();
        }
        return false;
    }
    else {
        size_t nT = m_mesh.m_triangles.GetSize();
        Vec3<double> ver0, ver1, ver2;
        double vol;
        for (size_t t = 0; t < nT; t++) {
            ver0.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.X();
            ver0.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.Y();
            ver0.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[0]->GetData().m_pos.Z();
            ver1.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.X();
            ver1.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.Y();
            ver1.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[1]->GetData().m_pos.Z();
            ver2.X() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.X();
            ver2.Y() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.Y();
            ver2.Z() = m_mesh.m_triangles.GetHead()->GetData().m_vertices[2]->GetData().m_pos.Z();
            vol = ComputeVolume4(ver0, ver1, ver2, pt);
            if (vol < eps) {
                return false;
            }
            m_mesh.m_triangles.Next();
        }
        return true;
    }
}
}