meshtools.cpp

#include "mesh.h"
#include <cstdlib>

HalfEdge* vertOnBoundary(Vertex* currentVertex) {

    unsigned short n = currentVertex->val;
    HalfEdge* currentEdge = currentVertex->out;

    for (unsigned int k = 0; k < n; k++) {
        if (!currentEdge->polygon) {
            return currentEdge;
        }
        currentEdge = currentEdge->prev->twin;
    }

    return nullptr;
}


void Mesh::subdivideCatmullClark(Mesh& mesh) {
    QVector<Vertex>& newVertices = mesh.getVertices();
    QVector<HalfEdge>& newHalfEdges = mesh.getHalfEdges();
    QVector<Face>& newFaces = mesh.getFaces();

    unsigned int numVerts, numHalfEdges, numFaces, sumFaceValences;
    unsigned int k, m, s, t;
    unsigned int vIndex, hIndex, fIndex;
    unsigned short n;
    HalfEdge* currentEdge;

    qDebug() << ":: Creating new Catmull-Clark mesh";

    numVerts = vertices.size();
    numHalfEdges = halfEdges.size();
    numFaces = faces.size();

    // Reserve memory
    newVertices.reserve(numFaces + numVerts + numHalfEdges/2);

    sumFaceValences = 0;
    for (k=0; k<numFaces; k++) {
        sumFaceValences += faces[k].val;
    }

    newHalfEdges.reserve(2*numHalfEdges + 2*sumFaceValences);
    newFaces.reserve(sumFaceValences);

    // Create face points
    for (k=0; k<numFaces; k++) {
        n = faces[k].val;
        // Coords (x,y,z), Out, Valence, Index
        newVertices.append( Vertex(facePoint(&faces[k]),
                                   nullptr,
                                   n,
                                   k) );
    }

    qDebug() << " * Created face points";

    vIndex = numFaces;

    // Create vertex points
    for (k=0; k<numVerts; k++) {
        n = vertices[k].val;
        // Coords (x,y,z), Out, Valence, Index
        newVertices.append( Vertex(vertexPoint(vertices[k].out, newVertices),
                                   nullptr,
                                   n,
                                   vIndex) );
        vIndex++;
    }

    qDebug() << " * Created vertex points";

    // Create edge points
    for (k=0; k<numHalfEdges; k++) {
        currentEdge = &halfEdges[k];

        if (k < currentEdge->twin->index) {
            m = (!currentEdge->polygon || !currentEdge->twin->polygon) ? 3 : 4;
            // Coords (x,y,z), Out, Valence, Index
            newVertices.append( Vertex(edgePoint(currentEdge, newVertices),
                                       nullptr,
                                       m,
                                       vIndex) );
            vIndex++;
        }
    }

    qDebug() << " * Created edge points";

    // Split halfedges
    splitHalfEdges(newVertices, newHalfEdges);

    qDebug() << " * Split halfedges";

    hIndex = 2*numHalfEdges;
    fIndex = 0;

    // Create faces and remaining halfedges
    for (k=0; k<numFaces; k++) {
        currentEdge = faces[k].side;
        n = faces[k].val;

        for (m=0; m<n; m++) {

            s = currentEdge->prev->index;
            t = currentEdge->index;

            // Side, Val, Index
            newFaces.append(Face(nullptr,
                                 4,
                                 fIndex));

            newFaces[fIndex].side = &newHalfEdges[ 2*t ];

            // Target, Next, Prev, Twin, Poly, Index
            newHalfEdges.append(HalfEdge( &newVertices[k],
                                          nullptr,
                                          &newHalfEdges[ 2*t ],
                                nullptr,
                                &newFaces[fIndex],
                                hIndex ));

            newHalfEdges.append(HalfEdge( nullptr,
                                          &newHalfEdges[2*s+1],
                                &newHalfEdges[hIndex],
                                nullptr,
                                &newFaces[fIndex],
                                hIndex+1 ));

            newHalfEdges[hIndex].next = &newHalfEdges[hIndex+1];
            newHalfEdges[hIndex+1].target = newHalfEdges[hIndex+1].next->twin->target;

            newHalfEdges[2*s+1].next = &newHalfEdges[2*t];
            newHalfEdges[2*s+1].prev = &newHalfEdges[hIndex+1];
            newHalfEdges[2*s+1].polygon = &newFaces[fIndex];

            newHalfEdges[2*t].next = &newHalfEdges[hIndex];
            newHalfEdges[2*t].prev = &newHalfEdges[2*s+1];
            newHalfEdges[2*t].polygon = &newFaces[fIndex];

            if (m > 0) {
                // Twins
                newHalfEdges[hIndex+1].twin = &newHalfEdges[hIndex-2];
                newHalfEdges[hIndex-2].twin = &newHalfEdges[hIndex+1];
            }

            // For edge points
            newHalfEdges[2*t].target->out = &newHalfEdges[hIndex];

            hIndex += 2;
            fIndex++;
            currentEdge = currentEdge->next;
        }

        newHalfEdges[hIndex-2*n+1].twin = &newHalfEdges[hIndex-2];
        newHalfEdges[hIndex-2].twin = &newHalfEdges[hIndex-2*n+1];

        // For face points
        newVertices[k].out = &newHalfEdges[hIndex-1];

    }

    qDebug() << " * Created faces and remaining halfedges";

    // For vertex points
    for (k=0; k<numVerts; k++) {
        newVertices[numFaces + k].out = &newHalfEdges[ 2*vertices[k].out->index ];
    }

    qDebug() << " * Completed!";
    qDebug() << "   # Vertices:" << newVertices.size();
    qDebug() << "   # HalfEdges:" << newHalfEdges.size();
    qDebug() << "   # Faces:" << newFaces.size();
    computeLimitMesh(mesh);
    computeQuadPatches(mesh);
}


// ---

QVector3D Mesh::vertexPoint(HalfEdge* firstEdge, QVector<Vertex>& newVertices) {
    unsigned short k;
    QVector3D sumStarPts, sumFacePts;
    QVector3D vertexPt;

    Vertex* currentVertex = firstEdge->twin->target;
    unsigned int n = currentVertex->val;

    sumStarPts = QVector3D();
    sumFacePts = QVector3D();
    HalfEdge* currentEdge = firstEdge;

    // Catmull-Clark (also supporting initial meshes containing n-gons)
    if (HalfEdge* boundaryEdge = vertOnBoundary(currentVertex)) {
        if (boundaryEdge->twin->target->val == 2) {
            // Interpolate corners
            vertexPt = boundaryEdge->twin->target->coords;
        }
        else {
            vertexPt  = 1.0 * boundaryEdge->target->coords;
            vertexPt += 6.0 * boundaryEdge->twin->target->coords;
            vertexPt += 1.0 * boundaryEdge->prev->twin->target->coords;
            vertexPt /= 8.0;
        }
    }
    else {
        for (k = 0; k < n; k++) {
            sumStarPts += currentEdge->target->coords;
            sumFacePts += newVertices[currentEdge->polygon->index].coords;
            currentEdge = currentEdge->prev->twin;
        }

        vertexPt = ((n-2)*currentVertex->coords + sumStarPts/n + sumFacePts/n)/n;
    }

    return vertexPt;

}

QVector3D Mesh::edgePoint(HalfEdge* firstEdge, QVector<Vertex>& newVertices) {
    QVector3D EdgePt = QVector3D();
    HalfEdge* currentEdge = firstEdge;

    // Catmull-Clark (also supporting initial meshes containing n-gons)
    if (!currentEdge->polygon || !currentEdge->twin->polygon) {
        EdgePt  = 4.0 * currentEdge->target->coords;
        EdgePt += 4.0 * currentEdge->twin->target->coords;
        EdgePt /= 8.0;
    }
    else {
        EdgePt  = currentEdge->target->coords;
        EdgePt += currentEdge->twin->target->coords;
        EdgePt += newVertices[currentEdge->polygon->index].coords;
        EdgePt += newVertices[currentEdge->twin->polygon->index].coords;
        EdgePt /= 4.0;
    }

    return EdgePt;

}

QVector3D Mesh::facePoint(Face* f) {
    QVector3D facePt;
    HalfEdge* currentEdge = f->side;

    for (unsigned int k = 0; k < f->val; k++) {
        // General approach
        facePt += 1.0f/float(f->val) * currentEdge->target->coords;
        currentEdge = currentEdge->next;
    }

    return facePt;

}


// For Bilinear, Catmull-Clark and Loop
void Mesh::splitHalfEdges(QVector<Vertex>& newVertices, QVector<HalfEdge>& newHalfEdges) {
    unsigned int k, m;
    unsigned int vIndex;
    HalfEdge* currentEdge;

    vIndex = vertices.size() + faces.size();

    for (k = 0; k < static_cast<unsigned int>(halfEdges.size()); k++) {
        currentEdge = &halfEdges[k];
        m = currentEdge->twin->index;

        // Target, Next, Prev, Twin, Poly, Index
        newHalfEdges.append(HalfEdge(nullptr,
                                     nullptr,
                                     nullptr,
                                     nullptr,
                                     nullptr,
                                     2*k));

        newHalfEdges.append(HalfEdge(nullptr,
                                     nullptr,
                                     nullptr,
                                     nullptr,
                                     nullptr,
                                     2*k+1));

        if (k < m) {
            newHalfEdges[2*k].target = &newVertices[ vIndex ];
            newHalfEdges[2*k+1].target = &newVertices[ faces.size() + currentEdge->target->index ];
            vIndex++;
        }
        else {
            newHalfEdges[2*k].target = newHalfEdges[2*m].target;
            newHalfEdges[2*k+1].target = &newVertices[ faces.size() + currentEdge->target->index ];

            // Assign Twins
            newHalfEdges[2*k].twin = &newHalfEdges[2*m+1];
            newHalfEdges[2*k+1].twin = &newHalfEdges[2*m];
            newHalfEdges[2*m].twin = &newHalfEdges[2*k+1];
            newHalfEdges[2*m+1].twin = &newHalfEdges[2*k];

            // Boundary edges are added last when importing a mesh, so their index will always be higher than their twins.
            if (!currentEdge->polygon) {
                newHalfEdges[2*k].next = &newHalfEdges[2*k+1];
                newHalfEdges[2*k+1].prev = &newHalfEdges[2*k];

                if (currentEdge > currentEdge->next) {
                    m = currentEdge->next->index;
                    newHalfEdges[2*k+1].next = &newHalfEdges[2*m];
                    newHalfEdges[2*m].prev = &newHalfEdges[2*k+1];
                }

                if (currentEdge > currentEdge->prev) {
                    m = currentEdge->prev->index;
                    newHalfEdges[2*k].prev = &newHalfEdges[2*m+1];
                    newHalfEdges[2*m+1].next = &newHalfEdges[2*k];
                }
            }
        }
    }

    // Note that Next, Prev and Poly are not yet assigned at this point.

}

// Computes the midpoint of a given (half)edge.
QVector3D computeHalfEdgeMidpoint(HalfEdge* edge) {
    auto target = edge->target;
    auto prevTarget = edge->twin->target;

    return (target->coords + prevTarget->coords) / 2.0;
}

// Computes the midpoint of a face.
QVector3D computeFaceMidpoint(Face* face) {
    HalfEdge* initialSide = face->side;
    QVector3D coords = QVector3D();
    HalfEdge* currentSide = initialSide->next;
    coords += currentSide->target->coords;
    while (currentSide != initialSide) {
        currentSide = currentSide->next;
        coords += currentSide->target->coords;
    }
    return coords / face->val;
}

// Computes wether the vertex is on a boundary or not.
bool isOnBoundary(Vertex* vertex) {
    HalfEdge* initialEdge = vertex->out;
    int outgoingEdgeCounter = 1;
    HalfEdge* currentEdge = initialEdge->prev->twin;

    for(;outgoingEdgeCounter < vertex->val; ++outgoingEdgeCounter) {
        if (currentEdge->polygon == nullptr) {
            return true;
        }
        currentEdge = currentEdge->prev->twin;
    }
    return false;
}

// Computes the sumparts of the p0 equation.
QVector<QVector3D> getOutgoingEdgeSumParts(Vertex* vertex) {
    QVector<QVector3D> sumParts;
    HalfEdge* initialEdge = vertex->out;
    int outgoingEdgeCounter = 0;
    HalfEdge* currentEdge = initialEdge;
    for(;outgoingEdgeCounter < vertex->val; ++outgoingEdgeCounter) {
        QVector3D mi = computeHalfEdgeMidpoint(currentEdge);
        QVector3D ci = computeFaceMidpoint(currentEdge->polygon);
        sumParts.push_back(mi + ci);
        currentEdge = currentEdge->prev->twin;
    }
    return sumParts;
}

void Mesh::computeLimitMesh(Mesh &mesh) {
    for(int i = 0; i < mesh.vertices.size(); ++i) {
        Vertex& sourceVertex = mesh.vertices[i];
        QVector3D vertexLimitPt = QVector3D();

        // Check for boundary vertex.
        if (HalfEdge* boundaryEdge = vertOnBoundary(&sourceVertex)) {
            if (boundaryEdge->twin->target->val == 2) {
                // Interpolate corners
                vertexLimitPt = boundaryEdge->twin->target->coords;
            } else {
                // Apply 1 4 1 limit mask.
                vertexLimitPt  = 1.0 * boundaryEdge->target->coords;
                vertexLimitPt += 4.0 * boundaryEdge->twin->target->coords;
                vertexLimitPt += 1.0 * boundaryEdge->prev->twin->target->coords;
                vertexLimitPt /= 6.0;
            }
        } else {
            // Apply equation from the paper to compute p0.
            auto sumParts = getOutgoingEdgeSumParts(&sourceVertex);
            float n = sourceVertex.val;

            float firstPart = (n - 3.0) / (n + 5.0);
            float secondPart = (4.0 / (n * (n + 5.0)));

            QVector3D p0 = firstPart * sourceVertex.coords;
            QVector3D sumResult = QVector3D();
            for(auto& k : sumParts) {
                sumResult += k;
            }
            p0 +=  secondPart * sumResult;
            vertexLimitPt = p0;
        }
        mesh.vertices[i].limitCoords = vertexLimitPt;
    }
    mesh.extractAttributes();
}

QuadPatch extractQuadPatch(Face& face) {
    QuadPatch patch;

    // F marks the face. s marks the side edge of F.
    //  p12 - p13 - p14 - p15
    //  |     |     |     |
    //  p8 -  p9 - p10 - p11
    //  |     |  F  |     |
    //  p4 -  p5 s  p6 - p7
    //  |     |     |     |
    // p0  -  p1 -  p2 - p3

    // NOTE: The orientation of the patch is based on the orientation of the side s.

    auto p5p6 = face.side;
    auto p6p10 = face.side->next;
    auto p10p9 = face.side->next->next;
    auto p9p5 = face.side->prev;

    // Bottom middle edge points
    auto p1 = p5p6->twin->next->target->index;
    auto p2 = p5p6->twin->prev->twin->target->index;

    // Top middle edge points
    auto p14 = p10p9->twin->next->target->index;
    auto p13 = p10p9->twin->prev->twin->target->index;

    // Right middle edge points
    auto p7  = p6p10->twin->next->target->index;
    auto p11 = p6p10->twin->prev->twin->target->index;

    // Left middle edge points
    auto p8  = p9p5->twin->next->target->index;
    auto p4  = p9p5->twin->prev->twin->target->index;

    // Corner points
    auto p0 = p9p5->twin->prev->twin->next->target->index;
    //auto p0 = p9p5->twin->prev->twin->next->target->index;
    auto p3 = p5p6->twin->prev->twin->next->target->index;

    auto p12 = p10p9->twin->prev->twin->next->target->index;
    auto p15 = p6p10->twin->prev->twin->next->target->index;

    // Bottom left vertex of face
    auto p5 = face.side->twin->target->index;

    // Bottom right vertex of face
    auto p6 = face.side->target->index;

    // Top left vertex of face
    auto p9 = face.side->prev->twin->target->index;

    // Top right vertex of face
    auto p10 = face.side->next->target->index;

    patch.vertIndices = {
        p0, p1, p2, p3,
        p4, p5, p6, p7,

        p8,  p9,  p10, p11,
        p12, p13, p14, p15,
    };

    return patch;
}

// Checks if a face is regular or not.
// Basically walks the neighbourhood of the current face and checks if the neighbouring ones are quads as well.
bool isRegularFace(Face& face) {
    if (face.val != 4) {
        return false;
    }
    HalfEdge* currentSide = face.side;

    do {
        if (currentSide->twin->polygon == nullptr || currentSide->twin->polygon->val != 4)
            return false;
        if (currentSide->twin->next->twin->polygon == nullptr || currentSide->twin->next->twin->polygon->val != 4)
            return false;
        if (currentSide->target->val != 4)
            return false;
        currentSide = currentSide->next;
    } while (face.side != currentSide);

    return true;
}

// Grabs all the quad patches for tesselated drawing
void Mesh::computeQuadPatches(Mesh &mesh) {

    mesh.tessPatches.clear();
    mesh.tessPatches.reserve(mesh.faces.size());

    for(int k = 0; k < mesh.faces.size(); ++k) {
        auto face = mesh.faces[k];
        if (isRegularFace(face))
            mesh.tessPatches.push_back(extractQuadPatch(face));
    }
}