path: root/src/threed/geometry/qglbezierpatches.cpp

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#include "qglbezierpatches.h"
#include "qglbuilder.h"
#include "qray3d.h"
#include "qtriangle3d.h"
#include <QtCore/qnumeric.h>

QT_BEGIN_NAMESPACE

/*!
    \class QGLBezierPatches
    \brief The QGLBezierPatches class represents 3D geometry as a set of Bezier bicubic patches.
    \since 4.8
    \ingroup qt3d
    \ingroup qt3d::geometry

    Bezier bicubic patches represent a curved 3D surface by four fixed
    control points at indices 0, 3, 12, and 15, together with twelve
    additional floating control points that define the surface
    curvature.  Bezier geometry objects are made up of one or more
    such patches to define the surface of an object.

    The application specifies the vertex position data to the
    constructor, and can optionally provide an index array.
    The class interprets groups of 16 vertices as the control
    points for successive patches.

    A mesh defined by QGLBezierPatches is subdivided into flat
    triangles for rendering when the \c{<<} operator is used
    to add the patches to a QGLBuilder.

    Many curved 3D objects can be defined as being made up of Bezier
    bicubic patches, stitched together into a mesh.  The most famous
    Bezier bicubic object is probably the classic 3D "Utah Teapot",
    first rendered in 1975.  The QGLTeapot class provides a built-in
    implementation of this object for testing purposes.

    If texture co-ordinates are supplied via setTextureCoords(),
    then patch texture co-ordinates will be derived from the
    specified values as the patches are subdivided.  Otherwise,
    QGLBezierPatches will generate texture co-ordinates for each
    patch based on the default square from (0, 0) to (1, 1).
    The first vertex in the patch corresponds to (0, 0),
    and the opposite vertex in the patch corresponds to (1, 1).

    \sa QGLBuilder, QGLTeapot
*/

class QGLBezierPatchesPrivate
{
public:
    QGLBezierPatchesPrivate()
        : subdivisionDepth(4) {}
    QGLBezierPatchesPrivate(const QGLBezierPatchesPrivate *other)
        : positions(other->positions)
        , textureCoords(other->textureCoords)
        , subdivisionDepth(other->subdivisionDepth) {}

    void copy(const QGLBezierPatchesPrivate *other)
    {
        positions = other->positions;
        textureCoords = other->textureCoords;
        subdivisionDepth = other->subdivisionDepth;
    }

    void subdivide(QGLBuilder *list) const;
    qreal intersection
        (const QRay3D &ray, bool anyIntersection, QVector2D *texCoord, int *patch) const;

    QVector3DArray positions;
    QVector2DArray textureCoords;
    int subdivisionDepth;
};

// Temporary patch data for performing sub-divisions.
class QGLBezierPatch
{
public:
    // Control points for this mesh.
    QVector3D points[16];

    // Triangle mesh indices of the control points at each corner.
    int indices[4];

    QVector3D normal(qreal s, qreal t) const;
    void convertToTriangles
        (QGeometryData *prim,
         qreal xtex, qreal ytex, qreal wtex, qreal htex);
    void subDivide(QGLBezierPatch &patch1, QGLBezierPatch &patch2,
                   QGLBezierPatch &patch3, QGLBezierPatch &patch4);
    void createNewCorners(QGLBezierPatch &patch1, QGLBezierPatch &patch2,
                          QGLBezierPatch &patch3, QGLBezierPatch &patch4,
                          QGeometryData *prim,
                          qreal xtex, qreal ytex, qreal wtex, qreal htex);
    void recursiveSubDivide
        (QGeometryData *prim,
         int depth, qreal xtex, qreal ytex, qreal wtex, qreal htex);
    qreal intersection
        (qreal result, int depth, const QRay3D &ray, bool anyIntersection,
         qreal xtex, qreal ytex, qreal wtex, qreal htex, QVector2D *tc);
};

static int const cornerOffsets[] = {0, 3, 12, 15};
static qreal const cornerS[] = {0.0f, 1.0f, 0.0f, 1.0f};
static qreal const cornerT[] = {0.0f, 0.0f, 1.0f, 1.0f};

// Helper functions for calculating the components of the Bernstein
// polynomial and its derivative that make up the surface.
static inline qreal b0(qreal v)
{
    return (1.0f - v) * (1.0f - v) * (1.0f - v);
}
static inline qreal b1(qreal v)
{
    return 3.0f * v * (1.0f - v) * (1.0f - v);
}
static inline qreal b2(qreal v)
{
    return 2.0f * v * v * (1.0f - v);
}
static inline qreal b3(qreal v)
{
    return v * v * v;
}
static inline qreal db0(qreal v)
{
    return -3.0f * (1.0f - v) * (1.0f - v);
}
static inline qreal db1(qreal v)
{
    return -6.0f * v * (1.0f - v) + 3.0f * (1.0f - v) * (1.0f - v);
}
static inline qreal db2(qreal v)
{
    return -3.0f * v * v + 6.0f * v * (1.0f - v);
}
static inline qreal db3(qreal v)
{
    return 3.0f * v * v;
}

// Compute the normal at a specific point in the patch.
// The s and t values vary between 0 and 1.
QVector3D QGLBezierPatch::normal(qreal s, qreal t) const
{
    qreal a[4];
    qreal b[4];
    qreal tx, ty, tz;
    qreal sx, sy, sz;

    // Compute the derivative of the surface in t.
    a[0] = b0(s);
    a[1] = b1(s);
    a[2] = b2(s);
    a[3] = b3(s);
    b[0] = db0(t);
    b[1] = db1(t);
    b[2] = db2(t);
    b[3] = db3(t);
    tx = 0.0f;
    ty = 0.0f;
    tz = 0.0f;
    for (int i = 0; i < 4; ++i) {
        for (int j = 0; j < 4; ++j) {
            tx += a[i] * points[j * 4 + i].x() * b[j];
            ty += a[i] * points[j * 4 + i].y() * b[j];
            tz += a[i] * points[j * 4 + i].z() * b[j];
        }
    }

    // Compute the derivative of the surface in s.
    a[0] = db0(s);
    a[1] = db1(s);
    a[2] = db2(s);
    a[3] = db3(s);
    b[0] = b0(t);
    b[1] = b1(t);
    b[2] = b2(t);
    b[3] = b3(t);
    sx = 0.0f;
    sy = 0.0f;
    sz = 0.0f;
    for (int i = 0; i < 4; ++i) {
        for (int j = 0; j < 4; ++j) {
            sx += a[i] * points[j * 4 + i].x() * b[j];
            sy += a[i] * points[j * 4 + i].y() * b[j];
            sz += a[i] * points[j * 4 + i].z() * b[j];
        }
    }

    // The normal is the cross-product of the two derivatives,
    // normalized to a unit vector.
    QVector3D n = QVector3D::normal(QVector3D(sx, sy, sz), QVector3D(tx, ty, tz));
    if (n.isNull()) {
        // A zero normal may occur if one of the patch edges is zero-length.
        // We correct for this by substituting an overall patch normal that
        // we compute from two of the sides that are not zero in length.
        QVector3D sides[4];
        QVector3D vectors[2];
        sides[0] = points[3] - points[0];
        sides[1] = points[15] - points[3];
        sides[2] = points[12] - points[15];
        sides[3] = points[0] - points[12];
        int i = 0;
        int j = 0;
        vectors[0] = QVector3D(1.0f, 0.0f, 0.0f);
        vectors[1] = QVector3D(0.0f, 1.0f, 0.0f);
        while (i < 2 && j < 4) {
            if (sides[j].isNull())
                ++j;
            else
                vectors[i++] = sides[j++];
        }
        n = QVector3D::normal(vectors[0], vectors[1]);
    }
    return n;
}

// Convert this patch into flat triangles.
void QGLBezierPatch::convertToTriangles
    (QGeometryData *prim,
     qreal xtex, qreal ytex, qreal wtex, qreal htex)
{
    // The edges are considered ok if they have a non-zero length.
    // Zero-length edges can occur in triangular-shaped patches.
    // There is no point generating triangles along such edges.
    bool edge1ok = (points[0] != points[3]);
    bool edge2ok = (points[0] != points[12]);
    bool edge3ok = (points[12] != points[15]);
    bool edge4ok = (points[15] != points[3]);

    // Find the mid-point on the patch by averaging the corners.
    QVector3D mid = (points[0] + points[3] + points[12] + points[15]) / 4.0f;

    // Allocate a triangle mesh vertex for the mid-point.
    int midIndex = prim->count();
    prim->appendVertex(mid);
    prim->appendNormal(normal(0.5f, 0.5f));
    prim->appendTexCoord
        (QVector2D(xtex + wtex / 2.0f, ytex + htex / 2.0f));

    // Divide the patch into 4 triangles pointing at the center.
    if (edge1ok)
        prim->appendIndices(indices[0], indices[1], midIndex);
    if (edge2ok)
        prim->appendIndices(indices[2], indices[0], midIndex);
    if (edge3ok)
        prim->appendIndices(indices[3], indices[2], midIndex);
    if (edge4ok)
        prim->appendIndices(indices[1], indices[3], midIndex);
}

// Sub-divide a Bezier curve (p1, p2, p3, p4) into two new
// Bezier curves (l1, l2, l3, l4) and (r1, r2, r3, r4).
static void subDivideBezierCurve
        (const QVector3D &p1, const QVector3D &p2,
         const QVector3D &p3, const QVector3D &p4,
         QVector3D &l1, QVector3D &l2, QVector3D &l3, QVector3D &l4,
         QVector3D &r1, QVector3D &r2, QVector3D &r3, QVector3D &r4)
{
    l1 = p1;
    l2 = (p1 + p2) / 2.0f;
    QVector3D h = (p2 + p3) / 2.0f;
    l3 = (l2 + h) / 2.0f;
    r3 = (p3 + p4) / 2.0f;
    r2 = (h + r3) / 2.0f;
    l4 = r1 = (l3 + r2) / 2.0f;
    r4 = p4;
}

// Sub-divide this patch into four new patches.  The triangle mesh
// is used to allocate vertices for the corners of the new patches.
void QGLBezierPatch::subDivide
        (QGLBezierPatch &patch1, QGLBezierPatch &patch2,
         QGLBezierPatch &patch3, QGLBezierPatch &patch4)
{
    // Sub-divide the Bezier curves for the control rows to create
    // four rows of 8 control points.  These define the left and
    // right halves of the patch.
    QVector3D row1[8];
    QVector3D row2[8];
    QVector3D row3[8];
    QVector3D row4[8];
    subDivideBezierCurve
        (points[0], points[1], points[2], points[3],
         row1[0], row1[1], row1[2], row1[3], row1[4], row1[5], row1[6], row1[7]);
    subDivideBezierCurve
        (points[4], points[5], points[6], points[7],
         row2[0], row2[1], row2[2], row2[3], row2[4], row2[5], row2[6], row2[7]);
    subDivideBezierCurve
        (points[8], points[9], points[10], points[11],
         row3[0], row3[1], row3[2], row3[3], row3[4], row3[5], row3[6], row3[7]);
    subDivideBezierCurve
        (points[12], points[13], points[14], points[15],
         row4[0], row4[1], row4[2], row4[3], row4[4], row4[5], row4[6], row4[7]);

    // Now sub-divide the 8 columns to create the four new patches.
    subDivideBezierCurve
        (row1[0], row2[0], row3[0], row4[0],
         patch1.points[0], patch1.points[4], patch1.points[8], patch1.points[12],
         patch3.points[0], patch3.points[4], patch3.points[8], patch3.points[12]);
    subDivideBezierCurve
        (row1[1], row2[1], row3[1], row4[1],
         patch1.points[1], patch1.points[5], patch1.points[9], patch1.points[13],
         patch3.points[1], patch3.points[5], patch3.points[9], patch3.points[13]);
    subDivideBezierCurve
        (row1[2], row2[2], row3[2], row4[2],
         patch1.points[2], patch1.points[6], patch1.points[10], patch1.points[14],
         patch3.points[2], patch3.points[6], patch3.points[10], patch3.points[14]);
    subDivideBezierCurve
        (row1[3], row2[3], row3[3], row4[3],
         patch1.points[3], patch1.points[7], patch1.points[11], patch1.points[15],
         patch3.points[3], patch3.points[7], patch3.points[11], patch3.points[15]);
    subDivideBezierCurve
        (row1[4], row2[4], row3[4], row4[4],
         patch2.points[0], patch2.points[4], patch2.points[8], patch2.points[12],
         patch4.points[0], patch4.points[4], patch4.points[8], patch4.points[12]);
    subDivideBezierCurve
        (row1[5], row2[5], row3[5], row4[5],
         patch2.points[1], patch2.points[5], patch2.points[9], patch2.points[13],
         patch4.points[1], patch4.points[5], patch4.points[9], patch4.points[13]);
    subDivideBezierCurve
        (row1[6], row2[6], row3[6], row4[6],
         patch2.points[2], patch2.points[6], patch2.points[10], patch2.points[14],
         patch4.points[2], patch4.points[6], patch4.points[10], patch4.points[14]);
    subDivideBezierCurve
        (row1[7], row2[7], row3[7], row4[7],
         patch2.points[3], patch2.points[7], patch2.points[11], patch2.points[15],
         patch4.points[3], patch4.points[7], patch4.points[11], patch4.points[15]);
}

void QGLBezierPatch::createNewCorners
        (QGLBezierPatch &patch1, QGLBezierPatch &patch2,
         QGLBezierPatch &patch3, QGLBezierPatch &patch4,
         QGeometryData *prim,
         qreal xtex, qreal ytex, qreal wtex, qreal htex)
{
    // Add vertices for the new patch corners we have created.
    qreal hwtex = wtex / 2.0f;
    qreal hhtex = htex / 2.0f;
    int topPointIndex = prim->count();
    int leftPointIndex = topPointIndex + 1;
    int midPointIndex = topPointIndex + 2;
    int rightPointIndex = topPointIndex + 3;
    int bottomPointIndex = topPointIndex + 4;

    prim->appendVertex(patch1.points[3]);
    prim->appendNormal(normal(0.5f, 0.0f));
    prim->appendTexCoord(QVector2D(xtex + hwtex, ytex));

    prim->appendVertex(patch1.points[12]);
    prim->appendNormal(normal(0.0f, 0.5f));
    prim->appendTexCoord(QVector2D(xtex, ytex + hhtex));

    prim->appendVertex(patch1.points[15]);
    prim->appendNormal(normal(0.5f, 0.5f));
    prim->appendTexCoord(QVector2D(xtex + hwtex, ytex + hhtex));

    prim->appendVertex(patch2.points[15]);
    prim->appendNormal(normal(1.0f, 0.5f));
    prim->appendTexCoord(QVector2D(xtex + wtex, ytex + hhtex));

    prim->appendVertex(patch3.points[15]);
    prim->appendNormal(normal(0.5f, 1.0f));
    prim->appendTexCoord(QVector2D(xtex + hwtex, ytex + htex));

    // Copy the indices for the corners of the new patches.
    patch1.indices[0] = indices[0];
    patch1.indices[1] = topPointIndex;
    patch1.indices[2] = leftPointIndex;
    patch1.indices[3] = midPointIndex;
    patch2.indices[0] = topPointIndex;
    patch2.indices[1] = indices[1];
    patch2.indices[2] = midPointIndex;
    patch2.indices[3] = rightPointIndex;
    patch3.indices[0] = leftPointIndex;
    patch3.indices[1] = midPointIndex;
    patch3.indices[2] = indices[2];
    patch3.indices[3] = bottomPointIndex;
    patch4.indices[0] = midPointIndex;
    patch4.indices[1] = rightPointIndex;
    patch4.indices[2] = bottomPointIndex;
    patch4.indices[3] = indices[3];
}

// Recursively sub-divide a patch into triangles.
void QGLBezierPatch::recursiveSubDivide
        (QGeometryData *prim,
         int depth, qreal xtex, qreal ytex, qreal wtex, qreal htex)
{
    if (depth <= 1) {
        convertToTriangles(prim, xtex, ytex, wtex, htex);
    } else {
        QGLBezierPatch patch1, patch2, patch3, patch4;
        subDivide(patch1, patch2, patch3, patch4);
        createNewCorners(patch1, patch2, patch3, patch4, prim, xtex, ytex, wtex, htex);
        --depth;
        qreal hwtex = wtex / 2.0f;
        qreal hhtex = htex / 2.0f;
        patch1.recursiveSubDivide(prim, depth, xtex, ytex, hwtex, hhtex);
        patch2.recursiveSubDivide(prim, depth, xtex + hwtex, ytex, hwtex, hhtex);
        patch3.recursiveSubDivide(prim, depth, xtex, ytex + hhtex, hwtex, hhtex);
        patch4.recursiveSubDivide(prim, depth, xtex + hwtex, ytex + hhtex, hwtex, hhtex);
    }
}

void QGLBezierPatchesPrivate::subdivide(QGLBuilder *list) const
{
    QGeometryData prim;
    int count = positions.size();
    for (int posn = 0; (posn + 15) < count; posn += 16) {
        // Construct a QGLBezierPatch object from the next high-level patch.
        QGLBezierPatch patch;
        for (int vertex = 0; vertex < 16; ++vertex)
            patch.points[vertex] = positions[posn + vertex];
        QVector2D tex1, tex2;
        if (!textureCoords.isEmpty()) {
            tex1 = textureCoords[(posn / 16) * 2];
            tex2 = textureCoords[(posn / 16) * 2 + 1];
        } else {
            tex1 = QVector2D(0.0f, 0.0f);
            tex2 = QVector2D(1.0f, 1.0f);
        }
        qreal xtex = tex1.x();
        qreal ytex = tex1.y();
        qreal wtex = tex2.x() - xtex;
        qreal htex = tex2.y() - ytex;
        for (int corner = 0; corner < 4; ++corner) {
            QVector3D n = patch.normal(cornerS[corner], cornerT[corner]);
            patch.indices[corner] = prim.count();
            prim.appendVertex(patch.points[cornerOffsets[corner]]);
            prim.appendNormal(n);
            prim.appendTexCoord
                (QVector2D(xtex + wtex * cornerS[corner],
                           ytex + htex * cornerT[corner]));
        }

        // Subdivide the patch and generate the final triangles.
        patch.recursiveSubDivide(&prim, subdivisionDepth,
                                 xtex, ytex, wtex, htex);
    }
    list->addTriangles(prim);
}

static inline qreal combineResults(qreal result, qreal t)
{
    if (qIsNaN(result))
        return t;
    if (t >= 0.0f)
        return result < 0.0f ? t : qMin(result, t);
    else
        return result >= 0.0f ? result : qMax(result, t);
}

qreal QGLBezierPatch::intersection
    (qreal result, int depth, const QRay3D& ray, bool anyIntersection,
     qreal xtex, qreal ytex, qreal wtex, qreal htex, QVector2D *tc)
{
    // Check the convex hull of the patch for an intersection.
    // If no intersection with the convex hull, then there is
    // no point subdividing this patch further.
    QBox3D box;
    for (int point = 0; point < 16; ++point)
        box.unite(points[point]);
    if (!box.intersects(ray))
        return result;

    // Are we at the lowest point of subdivision yet?
    if (depth <= 1) {
        // Divide the patch into two triangles and intersect with those.
        QTriangle3D triangle1(points[0], points[3], points[12]);
        qreal t = triangle1.intersection(ray);
        if (!qIsNaN(t)) {
            result = combineResults(result, t);
            if (result == t) {
                QVector2D uv = triangle1.uv(ray.point(t));
                QVector2D tp(xtex, ytex);
                QVector2D tq(xtex + wtex, ytex);
                QVector2D tr(xtex, ytex + htex);
                *tc = uv.x() * tp + uv.y() * tq + (1 - uv.x() - uv.y()) * tr;
            }
        } else {
            QTriangle3D triangle2(points[3], points[15], points[12]);
            qreal t = triangle2.intersection(ray);
            if (!qIsNaN(t)) {
                result = combineResults(result, t);
                if (result == t) {
                    QVector2D uv = triangle2.uv(ray.point(t));
                    QVector2D tp(xtex + wtex, ytex);
                    QVector2D tq(xtex + wtex, ytex + htex);
                    QVector2D tr(xtex, ytex + htex);
                    *tc = uv.x() * tp + uv.y() * tq + (1 - uv.x() - uv.y()) * tr;
                }
            }
        }
    } else {
        // Subdivide the patch to find the point of intersection.
        QGLBezierPatch patch1, patch2, patch3, patch4;
        subDivide(patch1, patch2, patch3, patch4);
        --depth;
        qreal hwtex = wtex / 2.0f;
        qreal hhtex = htex / 2.0f;
        result = patch1.intersection
            (result, depth, ray, anyIntersection,
             xtex, ytex, hwtex, hhtex, tc);
        if (anyIntersection && !qIsNaN(result))
            return result;
        result = patch2.intersection
            (result, depth, ray, anyIntersection,
             xtex + hwtex, ytex, hwtex, hhtex, tc);
        if (anyIntersection && !qIsNaN(result))
            return result;
        result = patch3.intersection
            (result, depth, ray, anyIntersection,
             xtex, ytex + hhtex, hwtex, hhtex, tc);
        if (anyIntersection && !qIsNaN(result))
            return result;
        result = patch4.intersection
            (result, depth, ray, anyIntersection,
             xtex + hwtex, ytex + hhtex, hwtex, hhtex, tc);
    }
    return result;
}

qreal QGLBezierPatchesPrivate::intersection
    (const QRay3D &ray, bool anyIntersection, QVector2D *texCoord, int *bestPatch) const
{
    int count = positions.size();
    qreal result = qSNaN();
    QVector2D tc;
    if (bestPatch)
        *bestPatch = -1;
    for (int posn = 0; (posn + 15) < count; posn += 16) {
        QGLBezierPatch patch;
        for (int vertex = 0; vertex < 16; ++vertex)
            patch.points[vertex] = positions[posn + vertex];
        QVector2D tex1, tex2;
        if (!textureCoords.isEmpty()) {
            tex1 = textureCoords[(posn / 16) * 2];
            tex2 = textureCoords[(posn / 16) * 2 + 1];
        } else {
            tex1 = QVector2D(0.0f, 0.0f);
            tex2 = QVector2D(1.0f, 1.0f);
        }
        qreal xtex = tex1.x();
        qreal ytex = tex1.y();
        qreal wtex = tex2.x() - xtex;
        qreal htex = tex2.y() - ytex;
        qreal prev = result;
        result = patch.intersection
            (result, subdivisionDepth, ray, anyIntersection,
             xtex, ytex, wtex, htex, &tc);
        if (bestPatch && result != prev)
            *bestPatch = posn / 16;
        if (anyIntersection && !qIsNaN(result))
            break;
    }
    if (texCoord && !qIsNaN(result))
        *texCoord = tc;
    return result;
}

/*!
    Constructs an empty Bezier patch list.

    \sa setPositions()
*/
QGLBezierPatches::QGLBezierPatches()
    : d_ptr(new QGLBezierPatchesPrivate())
{
}

/*!
    Constructs a copy of \a other.

    \sa operator=()
*/
QGLBezierPatches::QGLBezierPatches(const QGLBezierPatches &other)
    : d_ptr(new QGLBezierPatchesPrivate(other.d_ptr.data()))
{
}

/*!
    Destroys this Bezier patch list.
*/
QGLBezierPatches::~QGLBezierPatches()
{
}

/*!
    Assigns \a other to this Bezier patch list.
*/
QGLBezierPatches &QGLBezierPatches::operator=
    (const QGLBezierPatches &other)
{
    if (this != &other)
        d_ptr->copy(other.d_ptr.data());
    return *this;
}

/*!
    Returns the positions of the vertices in the Bezier patches.

    \sa setPositions(), textureCoords()
*/
QVector3DArray QGLBezierPatches::positions() const
{
    Q_D(const QGLBezierPatches);
    return d->positions;
}

/*!
    Sets the \a positions of the vertices in the Bezier patches.

    \sa positions(), setTextureCoords()
*/
void QGLBezierPatches::setPositions(const QVector3DArray &positions)
{
    Q_D(QGLBezierPatches);
    d->positions = positions;
}

/*!
    Returns the texture co-ordinates for the Bezier patches.
    Each patch consumes two elements from the texture
    co-ordinate array, defining the opposite corners.

    The default is an empty array, which indicates that each
    patch will generate texture co-ordinates in the range
    (0, 0) to (1, 1).

    \sa setTextureCoords(), positions()
*/
QVector2DArray QGLBezierPatches::textureCoords() const
{
    Q_D(const QGLBezierPatches);
    return d->textureCoords;
}

/*!
    Sets the texture co-ordinates for the Bezier patches to
    the elements of \a textureCoords.  Each patch consumes
    two elements from \a textureCoords, defining the opposite
    corners.

    If \a textureCoords is empty, then each patch will generate
    texture co-ordinates in the range (0, 0) to (1, 1).

    \sa textureCoords(), setPositions()
*/
void QGLBezierPatches::setTextureCoords(const QVector2DArray &textureCoords)
{
    Q_D(QGLBezierPatches);
    d->textureCoords = textureCoords;
}

/*!
    Returns the depth of subdivision to use when converting the
    Bezier geometry into triangles.  The default value is 4.

    \sa setSubdivisionDepth()
*/
int QGLBezierPatches::subdivisionDepth() const
{
    Q_D(const QGLBezierPatches);
    return d->subdivisionDepth;
}

/*!
    Sets the depth of subdivision to use when converting the
    Bezier geometry into triangles to \a value.

    \sa subdivisionDepth()
*/
void QGLBezierPatches::setSubdivisionDepth(int value)
{
    Q_D(QGLBezierPatches);
    d->subdivisionDepth = value;
}

/*!
    Transforms the positions() in this Bezier geometry object
    according to \a matrix.

    \sa transformed()
*/
void QGLBezierPatches::transform(const QMatrix4x4 &matrix)
{
    Q_D(QGLBezierPatches);
    d->positions.transform(matrix);
}

/*!
    Returns a new Bezier geometry object that results from transforming
    this object's positions() according to \a matrix.

    \sa transform()
*/
QGLBezierPatches QGLBezierPatches::transformed(const QMatrix4x4 &matrix) const
{
    QGLBezierPatches result(*this);
    result.d_ptr->positions.transform(matrix);
    return result;
}

/*!
    Returns true if \a ray intersects this Bezier geometry object;
    false otherwise.

    \sa intersection()
*/
bool QGLBezierPatches::intersects(const QRay3D &ray) const
{
    Q_D(const QGLBezierPatches);
    return !qIsNaN(d->intersection(ray, true, 0, 0));
}

/*!
    Returns the t value at which \a ray intersects this Bezier
    geometry object, or not-a-number if there is no intersection.

    When the \a ray intersects this object, the return value is a
    parametric value that can be passed to QRay3D::point() to determine
    the actual intersection point, as shown in the following example:

    \code
    qreal t = patches.intersection(ray);
    QVector3D pt;
    if (qIsNaN(t)) {
        qWarning("no intersection occurred");
    else
        pt = ray.point(t);
    \endcode

    If \a ray intersects the object multiple times, the returned
    t will be the smallest t value, corresponding to the first
    intersection of the \a ray with the object.  The t value may
    be negative if the first intersection occurs in the reverse
    direction of \a ray.

    The intersection is determined by subdividing the patches into
    triangles and intersecting with those triangles.  A pruning
    algorithm is used to discard patches whose convex hull do not
    intersect with \a ray.

    If \a texCoord is not null, then it will return the texture
    co-ordinate of the intersection point.

    If \a patch is not null, then it will return the index of the
    patch that contains the intersection, or -1 if there is no
    intersection.

    \sa intersects()
*/
qreal QGLBezierPatches::intersection(const QRay3D &ray, QVector2D *texCoord, int *patch) const
{
    Q_D(const QGLBezierPatches);
    return d->intersection(ray, false, texCoord, patch);
}

/*!
    \relates QGLBezierPatches

    Subdivides the Bezier patch data in \a patches into triangles
    and adds them to the specified display \a list.
*/
QGLBuilder &operator<<(QGLBuilder &list, const QGLBezierPatches &patches)
{
    patches.d_ptr->subdivide(&list);
    return list;
}

QT_END_NAMESPACE