valentina/src/libs/vgeometry/vabstractcubicbezier.cpp

/************************************************************************
 **
 **  @file   vabstractcubicbezier.cpp
 **  @author Roman Telezhynskyi <dismine(at)gmail.com>
 **  @date   8 3, 2016
 **
 **  @brief
 **  @copyright
 **  This source code is part of the Valentine project, a pattern making
 **  program, whose allow create and modeling patterns of clothing.
 **  Copyright (C) 2016 Valentina project
 **  <https://bitbucket.org/dismine/valentina> All Rights Reserved.
 **
 **  Valentina is free software: you can redistribute it and/or modify
 **  it under the terms of the GNU General Public License as published by
 **  the Free Software Foundation, either version 3 of the License, or
 **  (at your option) any later version.
 **
 **  Valentina 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 General Public License for more details.
 **
 **  You should have received a copy of the GNU General Public License
 **  along with Valentina.  If not, see <http://www.gnu.org/licenses/>.
 **
 *************************************************************************/

#include "vabstractcubicbezier.h"
#include "../vgeometry/vpointf.h"

#include <QPainterPath>
#include <QDebug>

//---------------------------------------------------------------------------------------------------------------------
VAbstractCubicBezier::VAbstractCubicBezier(const GOType &type, const quint32 &idObject, const Draw &mode)
    : VAbstractCurve(type, idObject, mode)
{
}

//---------------------------------------------------------------------------------------------------------------------
VAbstractCubicBezier::VAbstractCubicBezier(const VAbstractCubicBezier &curve)
    : VAbstractCurve(curve)
{
}

//---------------------------------------------------------------------------------------------------------------------
VAbstractCubicBezier &VAbstractCubicBezier::operator=(const VAbstractCubicBezier &curve)
{
    if ( &curve == this )
    {
        return *this;
    }
    VAbstractCurve::operator=(curve);
    return *this;
}

//---------------------------------------------------------------------------------------------------------------------
VAbstractCubicBezier::~VAbstractCubicBezier()
{
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief CutSpline cut spline.
 * @param length length first spline
 * @param spl1p2 second point of first spline
 * @param spl1p3 third point of first spline
 * @param spl2p2 second point of second spline
 * @param spl2p3 third point of second spline
 * @return point of cutting. This point is forth point of first spline and first point of second spline.
 */
QPointF VAbstractCubicBezier::CutSpline(qreal length, QPointF &spl1p2, QPointF &spl1p3, QPointF &spl2p2,
                                        QPointF &spl2p3) const
{
    //Always need return two splines, so we must correct wrong length.
    const qreal minLength = ToPixel(1, Unit::Mm);
    const qreal fullLength = GetLength();

    if (fullLength <= minLength)
    {
        spl1p2 = spl1p3 = spl2p2 = spl2p3 = QPointF();
        return QPointF();
    }

    const qreal maxLength = fullLength - minLength;

    if (length < minLength)
    {
        length = minLength;
    }
    else if (length > maxLength)
    {
        length = maxLength;
    }

    const qreal parT = GetParmT(length);

    QLineF seg1_2 ( GetP1 ().toQPointF(), GetControlPoint1 () );
    seg1_2.setLength(seg1_2.length () * parT);
    const QPointF p12 = seg1_2.p2();

    QLineF seg2_3 ( GetControlPoint1(), GetControlPoint2 () );
    seg2_3.setLength(seg2_3.length () * parT);
    const QPointF p23 = seg2_3.p2();

    QLineF seg12_23 ( p12, p23 );
    seg12_23.setLength(seg12_23.length () * parT);
    const QPointF p123 = seg12_23.p2();

    QLineF seg3_4 ( GetControlPoint2 (), GetP4 ().toQPointF() );
    seg3_4.setLength(seg3_4.length () * parT);
    const QPointF p34 = seg3_4.p2();

    QLineF seg23_34 ( p23, p34 );
    seg23_34.setLength(seg23_34.length () * parT);
    const QPointF p234 = seg23_34.p2();

    QLineF seg123_234 ( p123, p234 );
    seg123_234.setLength(seg123_234.length () * parT);
    const QPointF p1234 = seg123_234.p2();

    spl1p2 = p12;
    spl1p3 = p123;
    spl2p2 = p234;
    spl2p3 = p34;
    return p1234;
}

//---------------------------------------------------------------------------------------------------------------------
QString VAbstractCubicBezier::NameForHistory(const QString &toolName) const
{
    QString name = toolName + QString(" %1_%2").arg(GetP1().name()).arg(GetP4().name());
    if (GetDuplicate() > 0)
    {
        name += QString("_%1").arg(GetDuplicate());
    }
    return name;
}

//---------------------------------------------------------------------------------------------------------------------
qreal VAbstractCubicBezier::GetParmT(qreal length) const
{
    if (length < 0)
    {
        return 0;
    }
    else if (length > GetLength())
    {
        length = GetLength();
    }

    const qreal eps = 0.001 * length;
    qreal parT = 0.5;
    qreal step = parT;
    qreal splLength = LengthT(parT);

    while (qAbs(splLength - length) > eps)
    {
        step /= 2.0;
        splLength > length ? parT -= step : parT += step;
        splLength = LengthT(parT);
    }
    return parT;
}

//---------------------------------------------------------------------------------------------------------------------
void VAbstractCubicBezier::CreateName()
{
    QString name = SPL_ + QString("%1_%2").arg(GetP1().name()).arg(GetP4().name());
    if (GetDuplicate() > 0)
    {
        name += QString("_%1").arg(GetDuplicate());
    }

    setName(name);
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief CalcSqDistance calculate squared distance.
 * @param x1 х coordinate first point.
 * @param y1 у coordinate first point.
 * @param x2 х coordinate second point.
 * @param y2 у coordinate second point.
 * @return squared length.
 */
qreal VAbstractCubicBezier::CalcSqDistance(qreal x1, qreal y1, qreal x2, qreal y2)
{
    const qreal dx = x2 - x1;
    const qreal dy = y2 - y1;
    return dx * dx + dy * dy;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief PointBezier_r find spline point using four point of spline.
 * @param x1 х coordinate first point.
 * @param y1 у coordinate first point.
 * @param x2 х coordinate first control point.
 * @param y2 у coordinate first control point.
 * @param x3 х coordinate second control point.
 * @param y3 у coordinate second control point.
 * @param x4 х coordinate last point.
 * @param y4 у coordinate last point.
 * @param level level of recursion. In the begin 0.
 * @param px list х coordinat spline points.
 * @param py list у coordinat spline points.
 */
void VAbstractCubicBezier::PointBezier_r(qreal x1, qreal y1, qreal x2, qreal y2, qreal x3, qreal y3, qreal x4, qreal y4,
                                         qint16 level, QVector<qreal> &px, QVector<qreal> &py)
{
    if (px.size() >= 2)
    {
        for (int i=1; i < px.size(); ++i)
        {
            if (QPointF(px.at(i-1), py.at(i-1)) == QPointF(px.at(i), py.at(i)))
            {
                qDebug("All neighbors points in path must be unique.");
            }
        }
    }

    const double curve_collinearity_epsilon                 = 1e-30;
    const double curve_angle_tolerance_epsilon              = 0.01;
    const double m_angle_tolerance = 0.0;
    enum curve_recursion_limit_e { curve_recursion_limit = 32 };
    const double m_cusp_limit = 0.0;
    double m_approximation_scale = 1.0;
    double m_distance_tolerance_square;

    m_distance_tolerance_square = 0.5 / m_approximation_scale;
    m_distance_tolerance_square *= m_distance_tolerance_square;

    if (level > curve_recursion_limit)
    {
        return;
    }

    // Calculate all the mid-points of the line segments
    //----------------------
    const double x12   = (x1 + x2) / 2;
    const double y12   = (y1 + y2) / 2;
    const double x23   = (x2 + x3) / 2;
    const double y23   = (y2 + y3) / 2;
    const double x34   = (x3 + x4) / 2;
    const double y34   = (y3 + y4) / 2;
    const double x123  = (x12 + x23) / 2;
    const double y123  = (y12 + y23) / 2;
    const double x234  = (x23 + x34) / 2;
    const double y234  = (y23 + y34) / 2;
    const double x1234 = (x123 + x234) / 2;
    const double y1234 = (y123 + y234) / 2;


    // Try to approximate the full cubic curve by a single straight line
    //------------------
    const double dx = x4-x1;
    const double dy = y4-y1;

    double d2 = fabs((x2 - x4) * dy - (y2 - y4) * dx);
    double d3 = fabs((x3 - x4) * dy - (y3 - y4) * dx);

    switch ((static_cast<int>(d2 > curve_collinearity_epsilon) << 1) +
             static_cast<int>(d3 > curve_collinearity_epsilon))
    {
        case 0:
        {
            // All collinear OR p1==p4
            //----------------------
            double k = dx*dx + dy*dy;
            if (k < 0.000000001)
            {
                d2 = CalcSqDistance(x1, y1, x2, y2);
                d3 = CalcSqDistance(x4, y4, x3, y3);
            }
            else
            {
                k   = 1 / k;
                {
                    const double da1 = x2 - x1;
                    const double da2 = y2 - y1;
                    d2  = k * (da1*dx + da2*dy);
                }
                {
                    const double da1 = x3 - x1;
                    const double da2 = y3 - y1;
                    d3  = k * (da1*dx + da2*dy);
                }
                if (d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1)
                {
                    // Simple collinear case, 1---2---3---4
                    // We can leave just two endpoints
                    return;
                }
                if (d2 <= 0)
                {
                    d2 = CalcSqDistance(x2, y2, x1, y1);
                }
                else if (d2 >= 1)
                {
                    d2 = CalcSqDistance(x2, y2, x4, y4);
                }
                else
                {
                    d2 = CalcSqDistance(x2, y2, x1 + d2*dx, y1 + d2*dy);
                }

                if (d3 <= 0)
                {
                    d3 = CalcSqDistance(x3, y3, x1, y1);
                }
                else if (d3 >= 1)
                {
                    d3 = CalcSqDistance(x3, y3, x4, y4);
                }
                else
                {
                    d3 = CalcSqDistance(x3, y3, x1 + d3*dx, y1 + d3*dy);
                }
            }
            if (d2 > d3)
            {
                if (d2 < m_distance_tolerance_square)
                {
                    px.append(x2);
                    py.append(y2);
                    return;
                }
            }
            else
            {
                if (d3 < m_distance_tolerance_square)
                {
                    px.append(x3);
                    py.append(y3);
                    return;
                }
            }
            break;
        }
        case 1:
        {
            // p1,p2,p4 are collinear, p3 is significant
            //----------------------
            if (d3 * d3 <= m_distance_tolerance_square * (dx*dx + dy*dy))
            {
                if (m_angle_tolerance < curve_angle_tolerance_epsilon)
                {
                    px.append(x23);
                    py.append(y23);
                    return;
                }

                // Angle Condition
                //----------------------
                double da1 = fabs(atan2(y4 - y3, x4 - x3) - atan2(y3 - y2, x3 - x2));
                if (da1 >= M_PI)
                {
                    da1 = M_2PI - da1;
                }

                if (da1 < m_angle_tolerance)
                {
                    px.append(x2);
                    py.append(y2);

                    px.append(x3);
                    py.append(y3);
                    return;
                }

                if (m_cusp_limit > 0.0 || m_cusp_limit < 0.0)
                {
                    if (da1 > m_cusp_limit)
                    {
                        px.append(x3);
                        py.append(y3);
                        return;
                    }
                }
            }
            break;
        }
        case 2:
        {
            // p1,p3,p4 are collinear, p2 is significant
            //----------------------
            if (d2 * d2 <= m_distance_tolerance_square * (dx*dx + dy*dy))
            {
                if (m_angle_tolerance < curve_angle_tolerance_epsilon)
                {
                    px.append(x23);
                    py.append(y23);
                    return;
                }

                // Angle Condition
                //----------------------
                double da1 = fabs(atan2(y3 - y2, x3 - x2) - atan2(y2 - y1, x2 - x1));
                if (da1 >= M_PI)
                {
                    da1 = M_2PI - da1;
                }

                if (da1 < m_angle_tolerance)
                {
                    px.append(x2);
                    py.append(y2);

                    px.append(x3);
                    py.append(y3);
                    return;
                }

                if (m_cusp_limit > 0.0 || m_cusp_limit < 0.0)
                {
                    if (da1 > m_cusp_limit)
                    {
                        px.append(x2);
                        py.append(y2);
                        return;
                    }
                }
            }
            break;
        }
        case 3:
        {
            // Regular case
            //-----------------
            if ((d2 + d3)*(d2 + d3) <= m_distance_tolerance_square * (dx*dx + dy*dy))
            {
                // If the curvature doesn't exceed the distance_tolerance value
                // we tend to finish subdivisions.
                //----------------------
                if (m_angle_tolerance < curve_angle_tolerance_epsilon)
                {
                    px.append(x23);
                    py.append(y23);
                    return;
                }

                // Angle & Cusp Condition
                //----------------------
                const double k   = atan2(y3 - y2, x3 - x2);
                double da1 = fabs(k - atan2(y2 - y1, x2 - x1));
                double da2 = fabs(atan2(y4 - y3, x4 - x3) - k);
                if (da1 >= M_PI)
                {
                    da1 = M_2PI - da1;
                }
                if (da2 >= M_PI)
                {
                    da2 = M_2PI - da2;
                }

                if (da1 + da2 < m_angle_tolerance)
                {
                    // Finally we can stop the recursion
                    //----------------------

                    px.append(x23);
                    py.append(y23);
                    return;
                }

                if (m_cusp_limit > 0.0 || m_cusp_limit < 0.0)
                {
                    if (da1 > m_cusp_limit)
                    {
                        px.append(x2);
                        py.append(y2);
                        return;
                    }

                    if (da2 > m_cusp_limit)
                    {
                        px.append(x3);
                        py.append(y3);
                        return;
                    }
                }
            }
            break;
        }
        default:
            break;
    }

    // Continue subdivision
    //----------------------
    PointBezier_r(x1, y1, x12, y12, x123, y123, x1234, y1234, static_cast<qint16>(level + 1), px, py);
    PointBezier_r(x1234, y1234, x234, y234, x34, y34, x4, y4, static_cast<qint16>(level + 1), px, py);
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetCubicBezierPoints return list with cubic bezier curve points.
 * @param p1 first spline point.
 * @param p2 first control point.
 * @param p3 second control point.
 * @param p4 last spline point.
 * @return list of points.
 */
QVector<QPointF> VAbstractCubicBezier::GetCubicBezierPoints(const QPointF &p1, const QPointF &p2, const QPointF &p3,
                                                            const QPointF &p4)
{
    QVector<QPointF> pvector;
    QVector<qreal> x;
    QVector<qreal> y;
    QVector<qreal>& wx = x;
    QVector<qreal>& wy = y;
    x.append ( p1.x () );
    y.append ( p1.y () );
    PointBezier_r ( p1.x (), p1.y (), p2.x (), p2.y (),
                    p3.x (), p3.y (), p4.x (), p4.y (), 0, wx, wy );
    x.append ( p4.x () );
    y.append ( p4.y () );
    for ( qint32 i = 0; i < x.count(); ++i )
    {
        pvector.append( QPointF ( x.at(i), y.at(i)) );
    }
    return pvector;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief LengthBezier return spline length using 4 spline point.
 * @param p1 first spline point
 * @param p2 first control point.
 * @param p3 second control point.
 * @param p4 last spline point.
 * @return length.
 */
qreal VAbstractCubicBezier::LengthBezier(const QPointF &p1, const QPointF &p2, const QPointF &p3, const QPointF &p4)
{
    return PathLength(GetCubicBezierPoints(p1, p2, p3, p4));
}

//---------------------------------------------------------------------------------------------------------------------
qreal VAbstractCubicBezier::LengthT(qreal t) const
{
    if (t < 0 || t > 1)
    {
        qDebug()<<"Wrong value t.";
        return 0;
    }
    QLineF seg1_2 ( GetP1 ().toQPointF(), GetControlPoint1 () );
    seg1_2.setLength(seg1_2.length () * t);
    const QPointF p12 = seg1_2.p2();

    QLineF seg2_3 ( GetControlPoint1 (), GetControlPoint2 () );
    seg2_3.setLength(seg2_3.length () * t);
    const QPointF p23 = seg2_3.p2();

    QLineF seg12_23 ( p12, p23 );
    seg12_23.setLength(seg12_23.length () * t);
    const QPointF p123 = seg12_23.p2();

    QLineF seg3_4 ( GetControlPoint2 (), GetP4 ().toQPointF() );
    seg3_4.setLength(seg3_4.length () * t);
    const QPointF p34 = seg3_4.p2();

    QLineF seg23_34 ( p23, p34 );
    seg23_34.setLength(seg23_34.length () * t);
    const QPointF p234 = seg23_34.p2();

    QLineF seg123_234 ( p123, p234 );
    seg123_234.setLength(seg123_234.length () * t);
    const QPointF p1234 = seg123_234.p2();

    return LengthBezier ( GetP1().toQPointF(), p12, p123, p1234);
}