valentina/src/libs/vgeometry/vellipticalarc.cpp

/************************************************************************
 **
 **  @file   vellipticalarc.cpp
 **  @author Valentina Zhuravska <zhuravska19(at)gmail.com>
 **  @date   February 1, 2016
 **
 **  @brief
 **  @copyright
 **  This source code is part of the Valentina project, a pattern making
 **  program, whose allow create and modeling patterns of clothing.
 **  Copyright (C) 2013-2015 Valentina project
 **  <https://gitlab.com/smart-pattern/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 "vellipticalarc.h"

#include <QLineF>
#include <QPainterPath>
#include <QPoint>
#include <QtDebug>

#include "../ifc/exception/vexception.h"
#include "../ifc/ifcdef.h"
#include "../vmisc/compatibility.h"
#include "../vmisc/def.h"
#include "../vmisc/fpm/fixed.hpp"
#include "../vmisc/fpm/math.hpp"
#include "../vmisc/vabstractapplication.h"
#include "../vmisc/vmath.h"
#include "vabstractcurve.h"
#include "vellipticalarc_p.h"

namespace
{
constexpr qreal tolerance = accuracyPointOnLine / 8;

// Because of overflow we cannot generate arcs more than maxRadius
constexpr int maxRadius = 10000;

//---------------------------------------------------------------------------------------------------------------------
auto VLen(fpm::fixed_16_16 x, fpm::fixed_16_16 y) -> fpm::fixed_16_16
{
    x = fpm::abs(x);
    y = fpm::abs(y);
    if (x > y)
    {
        return x + qMax(y / 8, y / 2 - x / 8);
    }

    return y + qMax(x / 8, x / 2 - y / 8);
}

//---------------------------------------------------------------------------------------------------------------------
auto AuxRadius(fpm::fixed_16_16 xP, fpm::fixed_16_16 yP, fpm::fixed_16_16 xQ, fpm::fixed_16_16 yQ) -> fpm::fixed_16_16
{
    fpm::fixed_16_16 dP = VLen(xP, yP);
    fpm::fixed_16_16 dQ = VLen(xQ, yQ);
    fpm::fixed_16_16 dJ = VLen(xP + xQ, yP + yQ);
    fpm::fixed_16_16 dK = VLen(xP - xQ, yP - yQ);
    fpm::fixed_16_16 r1 = qMax(dP, dQ);
    fpm::fixed_16_16 r2 = qMax(dJ, dK);
    return qMax(r1 + r1 / 16, r2 - r2 / 4);
}

//---------------------------------------------------------------------------------------------------------------------
auto AngularInc(fpm::fixed_16_16 xP, fpm::fixed_16_16 yP, fpm::fixed_16_16 xQ, fpm::fixed_16_16 yQ,
                fpm::fixed_16_16 flatness) -> int
{

    fpm::fixed_16_16 r = AuxRadius(xP, yP, xQ, yQ);
    fpm::fixed_16_16 err2{r >> 3};
    // 2nd-order term
    fpm::fixed_16_16 err4{r >> 7};
    // 4th-order term
    const int kmax = qRound(0.5 * std::log2(maxSceneSize / (8. * tolerance)));
    for (int k = 0; k < kmax; ++k)
    {
        if (flatness >= err2 + err4)
        {
            return k;
        }
        err2 >>= 2;
        err4 >>= 4;
    }
    return kmax;
}

//---------------------------------------------------------------------------------------------------------------------
inline void CircleGen(fpm::fixed_16_16 &u, fpm::fixed_16_16 &v, uint k)
{
    u -= v >> k;
    v += u >> k;
}

//---------------------------------------------------------------------------------------------------------------------
auto InitialValue(fpm::fixed_16_16 u0, fpm::fixed_16_16 v0, uint k) -> fpm::fixed_16_16
{
    uint shift = 2 * k + 3;
    fpm::fixed_16_16 w{u0 >> shift};

    fpm::fixed_16_16 U0 = u0 - w + (v0 >> (k + 1));
    w >>= (shift + 1);
    U0 -= w;
    w >>= shift;
    U0 -= w;
    return U0;
}

//---------------------------------------------------------------------------------------------------------------------
auto EllipseCore(fpm::fixed_16_16 xC, fpm::fixed_16_16 yC, fpm::fixed_16_16 xP, fpm::fixed_16_16 yP,
                 fpm::fixed_16_16 xQ, fpm::fixed_16_16 yQ, fpm::fixed_16_16 sweep, fpm::fixed_16_16 flatness)
    -> QVector<QPointF>
{
    uint k = qMin(static_cast<uint>(AngularInc(xP, yP, xQ, yQ, flatness)), 16U);
    const uint count = static_cast<std::uint32_t>(sweep.raw_value()) >> (16 - k);

    QVector<QPointF> arc;
    arc.reserve(static_cast<int>(count) + 1);

    // Arc start point
    arc.append({static_cast<qreal>(xP + xC), static_cast<qreal>(yP + yC)});

    xQ = InitialValue(xQ, xP, k);
    yQ = InitialValue(yQ, yP, k);

    for (uint i = 0; i < count; ++i)
    {
        CircleGen(xQ, xP, k);
        CircleGen(yQ, yP, k);
        arc.append({static_cast<qreal>(xP + xC), static_cast<qreal>(yP + yC)});
    }

    return arc;
}

//---------------------------------------------------------------------------------------------------------------------
auto EllipticArcPoints(QPointF c, qreal radius1, qreal radius2, qreal astart, qreal asweep, qreal approximationScale)
    -> QVector<QPointF>
{
    fpm::fixed_16_16 xC{c.x()};
    fpm::fixed_16_16 yC{c.y()};

    fpm::fixed_16_16 xP{c.x() + radius1};
    fpm::fixed_16_16 yP{c.y()};

    fpm::fixed_16_16 xQ{c.x()};
    fpm::fixed_16_16 yQ{c.y() - radius2};

    xP -= xC;
    yP -= yC;
    xQ -= xC;
    yQ -= yC;

    if (not qFuzzyIsNull(astart))
    {
        // Set new conjugate diameter end points P’ and Q’
        fpm::fixed_16_16 cosa{cos(astart)};
        fpm::fixed_16_16 sina{sin(astart)};
        fpm::fixed_16_16 x{xP * cosa + xQ * sina};
        fpm::fixed_16_16 y{yP * cosa + yQ * sina};

        xQ = xQ * cosa - xP * sina;
        yQ = yQ * cosa - yP * sina;
        xP = x;
        yP = y;
    }

    // If sweep angle is negative, switch direction
    if (asweep < 0)
    {
        xQ = -xQ;
        yQ = -yQ;
        asweep = -asweep;
    }

    if (approximationScale < minCurveApproximationScale || approximationScale > maxCurveApproximationScale)
    {
        approximationScale = VAbstractApplication::VApp()->Settings()->GetCurveApproximationScale();
    }

    fpm::fixed_16_16 flatness{maxCurveApproximationScale / approximationScale * tolerance};
    fpm::fixed_16_16 swangle{asweep};
    QVector<QPointF> arc = EllipseCore(xC, yC, xP, yP, xQ, yQ, swangle, flatness);

    // Arc end point
    fpm::fixed_16_16 cosb{qCos(asweep)};
    fpm::fixed_16_16 sinb{qSin(asweep)};
    xP = xP * cosb + xQ * sinb;
    yP = yP * cosb + yQ * sinb;
    arc.append({static_cast<qreal>(xP + xC), static_cast<qreal>(yP + yC)});

    return arc;
}

//---------------------------------------------------------------------------------------------------------------------
auto JoinVectors(const QVector<QPointF> &v1, const QVector<QPointF> &v2) -> QVector<QPointF>
{
    QVector<QPointF> v;
    v.reserve(v1.size() + v2.size());

    v = v1;

    constexpr qreal accuracy = MmToPixel(0.0001);

    for (auto p : v2)
    {
        if (not VFuzzyComparePoints(v.constLast(), p, accuracy))
        {
            v.append(p);
        }
    }

    return v;
}
} // namespace

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief VEllipticalArc default constructor.
 */
VEllipticalArc::VEllipticalArc()
  : VAbstractArc(GOType::EllipticalArc),
    d(new VEllipticalArcData)
{
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief VEllipticalArc constructor.
 * @param center center point.
 * @param radius1 arc major radius.
 * @param radius2 arc minor radius.
 * @param f1 start angle (degree).
 * @param f2 end angle (degree).
 */
VEllipticalArc::VEllipticalArc(const VPointF &center, qreal radius1, qreal radius2, const QString &formulaRadius1,
                               const QString &formulaRadius2, qreal f1, const QString &formulaF1, qreal f2,
                               const QString &formulaF2, qreal rotationAngle, const QString &formulaRotationAngle,
                               quint32 idObject, Draw mode)
  : VAbstractArc(GOType::EllipticalArc, center, f1, formulaF1, f2, formulaF2, idObject, mode),
    d(new VEllipticalArcData(radius1, radius2, formulaRadius1, formulaRadius2, rotationAngle, formulaRotationAngle))
{
    CreateName();
}

//---------------------------------------------------------------------------------------------------------------------
VEllipticalArc::VEllipticalArc(const VPointF &center, qreal radius1, qreal radius2, qreal f1, qreal f2,
                               qreal rotationAngle)
  : VAbstractArc(GOType::EllipticalArc, center, f1, f2, NULL_ID, Draw::Calculation),
    d(new VEllipticalArcData(radius1, radius2, rotationAngle))
{
    CreateName();
}

//---------------------------------------------------------------------------------------------------------------------
VEllipticalArc::VEllipticalArc(qreal length, const QString &formulaLength, const VPointF &center, qreal radius1,
                               qreal radius2, const QString &formulaRadius1, const QString &formulaRadius2, qreal f1,
                               const QString &formulaF1, qreal rotationAngle, const QString &formulaRotationAngle,
                               quint32 idObject, Draw mode)
  : VAbstractArc(GOType::EllipticalArc, formulaLength, center, f1, formulaF1, idObject, mode),
    d(new VEllipticalArcData(radius1, radius2, formulaRadius1, formulaRadius2, rotationAngle, formulaRotationAngle))
{
    CreateName();
    FindF2(length);
}

//---------------------------------------------------------------------------------------------------------------------
VEllipticalArc::VEllipticalArc(qreal length, const VPointF &center, qreal radius1, qreal radius2, qreal f1,
                               qreal rotationAngle)
  : VAbstractArc(GOType::EllipticalArc, center, f1, NULL_ID, Draw::Calculation),
    d(new VEllipticalArcData(radius1, radius2, rotationAngle))
{
    CreateName();
    FindF2(length);
    SetFormulaLength(QString::number(length));
}

//---------------------------------------------------------------------------------------------------------------------
COPY_CONSTRUCTOR_IMPL_2(VEllipticalArc, VAbstractArc)

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief operator = assignment operator
 * @param arc arc
 * @return arc
 */
auto VEllipticalArc::operator=(const VEllipticalArc &arc) -> VEllipticalArc &
{
    if (&arc == this)
    {
        return *this;
    }
    VAbstractArc::operator=(arc);
    d = arc.d;
    return *this;
}

#ifdef Q_COMPILER_RVALUE_REFS
//---------------------------------------------------------------------------------------------------------------------
VEllipticalArc::VEllipticalArc(VEllipticalArc &&arc) noexcept
  : VAbstractArc(std::move(arc)),
    d(std::move(arc.d))
{
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::operator=(VEllipticalArc &&arc) noexcept -> VEllipticalArc &
{
    VAbstractArc::operator=(arc);
    std::swap(d, arc.d);
    return *this;
}
#endif

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::Rotate(QPointF originPoint, qreal degrees, const QString &prefix) const -> VEllipticalArc
{
    originPoint = d->m_transform.inverted().map(originPoint);

    QTransform t = d->m_transform;
    t.translate(originPoint.x(), originPoint.y());
    t.rotate(IsFlipped() ? degrees : -degrees);
    t.translate(-originPoint.x(), -originPoint.y());

    VEllipticalArc elArc(VAbstractArc::GetCenter(), GetRadius1(), GetRadius2(), VAbstractArc::GetStartAngle(),
                         VAbstractArc::GetEndAngle(), GetRotationAngle());
    elArc.setName(name() + prefix);

    if (not GetAliasSuffix().isEmpty())
    {
        elArc.SetAliasSuffix(GetAliasSuffix() + prefix);
    }

    elArc.SetColor(GetColor());
    elArc.SetPenStyle(GetPenStyle());
    elArc.SetFlipped(IsFlipped());
    elArc.SetTransform(t);
    elArc.SetApproximationScale(GetApproximationScale());
    return elArc;
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::Flip(const QLineF &axis, const QString &prefix) const -> VEllipticalArc
{
    VEllipticalArc elArc(VAbstractArc::GetCenter(), GetRadius1(), GetRadius2(), VAbstractArc::GetStartAngle(),
                         VAbstractArc::GetEndAngle(), GetRotationAngle());
    elArc.setName(name() + prefix);

    if (not GetAliasSuffix().isEmpty())
    {
        elArc.SetAliasSuffix(GetAliasSuffix() + prefix);
    }

    elArc.SetColor(GetColor());
    elArc.SetPenStyle(GetPenStyle());
    elArc.SetFlipped(not IsFlipped());
    elArc.SetTransform(d->m_transform * VGObject::FlippingMatrix(d->m_transform.inverted().map(axis)));
    elArc.SetApproximationScale(GetApproximationScale());
    return elArc;
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::Move(qreal length, qreal angle, const QString &prefix) const -> VEllipticalArc
{
    const VPointF oldCenter = VAbstractArc::GetCenter();
    const VPointF center = oldCenter.Move(length, angle);

    const QPointF position =
        d->m_transform.inverted().map(center.toQPointF()) - d->m_transform.inverted().map(oldCenter.toQPointF());

    QTransform t = d->m_transform;
    t.translate(position.x(), position.y());

    VEllipticalArc elArc(oldCenter, GetRadius1(), GetRadius2(), VAbstractArc::GetStartAngle(),
                         VAbstractArc::GetEndAngle(), GetRotationAngle());
    elArc.setName(name() + prefix);

    if (not GetAliasSuffix().isEmpty())
    {
        elArc.SetAliasSuffix(GetAliasSuffix() + prefix);
    }

    elArc.SetColor(GetColor());
    elArc.SetPenStyle(GetPenStyle());
    elArc.SetFlipped(IsFlipped());
    elArc.SetTransform(t);
    elArc.SetApproximationScale(GetApproximationScale());
    return elArc;
}

//---------------------------------------------------------------------------------------------------------------------
VEllipticalArc::~VEllipticalArc() = default;

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetLength return arc length.
 * @return length.
 */
auto VEllipticalArc::GetLength() const -> qreal
{
    qreal length = PathLength(GetPoints());

    if (IsFlipped())
    {
        length = length * -1;
    }

    return length;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetP1 return point associated with start angle.
 * @return point.
 */
auto VEllipticalArc::GetP1() const -> QPointF
{
    return GetTransform().map(GetP(VAbstractArc::GetStartAngle()));
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetP2 return point associated with end angle.
 * @return point.
 */
auto VEllipticalArc::GetP2() const -> QPointF
{
    return GetTransform().map(GetP(VAbstractArc::GetEndAngle()));
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::GetTransform() const -> QTransform
{
    return d->m_transform;
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::SetTransform(const QTransform &matrix, bool combine)
{
    d->m_transform = combine ? d->m_transform * matrix : matrix;
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::GetCenter() const -> VPointF
{
    VPointF center = VAbstractArc::GetCenter();
    const QPointF p = d->m_transform.map(center.toQPointF());
    center.setX(p.x());
    center.setY(p.y());
    return center;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetPoints return list of points needed for drawing arc.
 * @return list of points
 */
auto VEllipticalArc::GetPoints() const -> QVector<QPointF>
{
    const QPointF center = VAbstractArc::GetCenter().toQPointF();

    // Don't work with 0 radius. Always make it bigger than 0.
    Q_RELAXED_CONSTEXPR qreal threshold = ToPixel(0.001, Unit::Mm);
    qreal radius1 = qMax(d->radius1, threshold);
    qreal radius2 = qMax(d->radius2, threshold);
    qreal max = qMax(d->radius1, d->radius2);
    qreal scale = 1;

    if (max > maxRadius)
    {
        scale = max / maxRadius;
        radius1 /= scale;
        radius2 /= scale;
    }

    // Generate complete ellipse because angles are not correct and have to be fixed manually
    QVector<QPointF> points = EllipticArcPoints(center, radius1, radius2, 0.0, M_2PI, GetApproximationScale());
    points = ArcPoints(points);

    QTransform t = d->m_transform;
    t.translate(center.x(), center.y());
    if (not VFuzzyComparePossibleNulls(scale, 1))
    {
        // Because fixed 16.16 type has limitations it is very easy to get overflow error.
        // To avoid this we calculate an arc for scaled radiuses and then scale up to original size.
        t.scale(scale, scale);
    }
    t.rotate(-GetRotationAngle());
    t.translate(-center.x(), -center.y());

    std::transform(points.begin(), points.end(), points.begin(), [t](const QPointF &point) { return t.map(point); });

    return points;
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::GetStartAngle() const -> qreal
{
    return QLineF(GetCenter().toQPointF(), GetP1()).angle() - GetRotationAngle();
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::GetEndAngle() const -> qreal
{
    return QLineF(GetCenter().toQPointF(), GetP2()).angle() - GetRotationAngle();
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief CutArc cut arc into two arcs.
 * @param length length first arc.
 * @param arc1 first arc.
 * @param arc2 second arc.
 * @return point cutting
 */
auto VEllipticalArc::CutArc(const qreal &length, VEllipticalArc &arc1, VEllipticalArc &arc2,
                            const QString &pointName) const -> QPointF
{
    // Always need return two arcs, so we must correct wrong length.
    qreal len = 0;
    const qreal fullLength = GetLength();

    if (fullLength <= minLength)
    {
        arc1 = VEllipticalArc();
        arc2 = VEllipticalArc();

        const QString errorMsg = QObject::tr("Unable to cut curve '%1'. The curve is too short.").arg(name());
        VAbstractApplication::VApp()->IsPedantic()
            ? throw VException(errorMsg)
            : qWarning() << VAbstractApplication::warningMessageSignature + errorMsg;

        return {};
    }

    const qreal maxLength = fullLength - minLength;

    if (length < minLength)
    {
        len = minLength;

        QString errorMsg;
        if (not pointName.isEmpty())
        {
            errorMsg = QObject::tr("Curve '%1'. Length of a cut segment (%2) is too small. Optimize it to minimal "
                                   "value.")
                           .arg(name(), pointName);
        }
        else
        {
            errorMsg = QObject::tr("Curve '%1'. Length of a cut segment is too small. Optimize it to minimal value.")
                           .arg(name());
        }
        VAbstractApplication::VApp()->IsPedantic()
            ? throw VException(errorMsg)
            : qWarning() << VAbstractApplication::warningMessageSignature + errorMsg;
    }
    else if (length > maxLength)
    {
        len = maxLength;

        QString errorMsg;
        if (not pointName.isEmpty())
        {
            errorMsg = QObject::tr("Curve '%1'. Length of a cut segment (%2) is too big. Optimize it to maximal value.")
                           .arg(name(), pointName);
        }
        else
        {
            errorMsg = QObject::tr("Curve '%1'. Length of a cut segment is too big. Optimize it to maximal value.")
                           .arg(name());
        }
        VAbstractApplication::VApp()->IsPedantic()
            ? throw VException(errorMsg)
            : qWarning() << VAbstractApplication::warningMessageSignature + errorMsg;
    }
    else
    {
        len = length;
    }

    // the first arc has given length and startAngle just like in the origin arc
    arc1 = VEllipticalArc(len, QString().setNum(length), GetCenter(), d->radius1, d->radius2, d->formulaRadius1,
                          d->formulaRadius2, GetStartAngle(), GetFormulaF1(), d->rotationAngle,
                          GetFormulaRotationAngle(), getIdObject(), getMode());
    // the second arc has startAngle just like endAngle of the first arc
    // and it has endAngle just like endAngle of the origin arc
    arc2 = VEllipticalArc(GetCenter(), d->radius1, d->radius2, d->formulaRadius1, d->formulaRadius2, arc1.GetEndAngle(),
                          arc1.GetFormulaF2(), GetEndAngle(), GetFormulaF2(), d->rotationAngle,
                          GetFormulaRotationAngle(), getIdObject(), getMode());
    return arc1.GetP1();
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::CutArc(const qreal &length, const QString &pointName) const -> QPointF
{
    VEllipticalArc arc1;
    VEllipticalArc arc2;
    return this->CutArc(length, arc1, arc2, pointName);
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::CreateName()
{
    QString name = ELARC_ + QStringLiteral("%1").arg(this->GetCenter().name());
    const QString nameStr = QStringLiteral("_%1");

    if (getMode() == Draw::Modeling && getIdObject() != NULL_ID)
    {
        name += nameStr.arg(getIdObject());
    }
    else if (VAbstractCurve::id() != NULL_ID)
    {
        name += nameStr.arg(VAbstractCurve::id());
    }

    if (GetDuplicate() > 0)
    {
        name += nameStr.arg(GetDuplicate());
    }

    setName(name);
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::CreateAlias()
{
    const QString aliasSuffix = GetAliasSuffix();
    if (aliasSuffix.isEmpty())
    {
        SetAlias(QString());
        return;
    }

    SetAlias(ELARC_ + aliasSuffix);
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::FindF2(qreal length)
{
    qreal gap = 180;
    if (length < 0)
    {
        SetFlipped(true);
        gap = -gap;
    }
    while (length > MaxLength())
    {
        length = MaxLength();
    }

    // We need to calculate the second angle
    // first approximation of angle between start and end angles

    QLineF radius1(GetCenter().x(), GetCenter().y(), GetCenter().x() + d->radius1, GetCenter().y());
    radius1.setAngle(GetStartAngle());
    radius1.setAngle(radius1.angle() + gap);
    qreal endAngle = radius1.angle();

    // we need to set the end angle, because we want to use GetLength()
    SetFormulaF2(QString::number(endAngle), endAngle);

    qreal lenBez = GetLength(); // first approximation of length

    const qreal eps = ToPixel(0.001, Unit::Mm);

    while (qAbs(lenBez - length) > eps)
    {
        gap = gap / 2;
        if (gap < 0.0001)
        {
            break;
        }
        if (lenBez > length)
        { // we selected too big end angle
            radius1.setAngle(endAngle - qAbs(gap));
        }
        else
        { // we selected too little end angle
            radius1.setAngle(endAngle + qAbs(gap));
        }
        endAngle = radius1.angle();
        // we need to set d->f2, because we use it when we calculate GetLength
        SetFormulaF2(QString::number(endAngle), endAngle);
        lenBez = GetLength();
    }
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::MaxLength() const -> qreal
{
    const qreal h = qPow(d->radius1 - d->radius2, 2) / qPow(d->radius1 + d->radius2, 2);
    const qreal ellipseLength = M_PI * (d->radius1 + d->radius2) * (1 + 3 * h / (10 + qSqrt(4 - 3 * h)));
    return ellipseLength;
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::GetP(qreal angle) const -> QPointF
{
    if (qFuzzyIsNull(GetRadius1()) && qFuzzyIsNull(GetRadius2()))
    {
        return GetCenter().toQPointF();
    }

    QLineF line(0, 0, 100, 0);
    line.setAngle(angle);

    const qreal a = not qFuzzyIsNull(GetRadius1()) ? line.p2().x() / GetRadius1() : 0;
    const qreal b = not qFuzzyIsNull(GetRadius2()) ? line.p2().y() / GetRadius2() : 0;
    const qreal k = qSqrt(a * a + b * b);

    if (qFuzzyIsNull(k))
    {
        return GetCenter().toQPointF();
    }

    QPointF p(line.p2().x() / k, line.p2().y() / k);

    QLineF line2(QPointF(), p);
    SCASSERT(VFuzzyComparePossibleNulls(line2.angle(), line.angle()))

    line2.setAngle(line2.angle() + GetRotationAngle());
    return line2.p2() + VAbstractArc::GetCenter().toQPointF();
}

//---------------------------------------------------------------------------------------------------------------------
auto VEllipticalArc::ArcPoints(QVector<QPointF> points) const -> QVector<QPointF>
{
    if (points.size() < 2 || (qFuzzyIsNull(d->radius1) && qFuzzyIsNull(d->radius2)))
    {
        return points;
    }

    QPointF center = VAbstractArc::GetCenter().toQPointF();
    qreal radius = qMax(d->radius1, d->radius2) * 2;

    QLineF start(center.x(), center.y(), center.x() + radius, center.y());
    start.setAngle(VAbstractArc::GetStartAngle());

    QLineF end(center.x(), center.y(), center.x() + radius, center.y());
    end.setAngle(VAbstractArc::GetEndAngle());

    auto IsBoundedIntersection =
        [](QLineF::IntersectType type, QPointF p, const QLineF &segment1, const QLineF &segment2)
    {
        return type == QLineF::BoundedIntersection ||
               (type == QLineF::UnboundedIntersection &&
                VGObject::IsPointOnLineSegment(p, segment1.p1(), segment2.p1()) &&
                VGObject::IsPointOnLineSegment(p, segment2.p1(), segment2.p2()));
    };

    bool begin = true;

    if (start.angle() >= end.angle())
    {
        for (int i = 0; i < points.size() - 1; ++i)
        {
            QLineF edge(points.at(i), points.at(i + 1));

            QPointF p;
            QLineF::IntersectType type = Intersects(start, edge, &p);

            // QLineF::intersects not always accurate on edge cases
            if (IsBoundedIntersection(type, p, edge, start))
            {
                QVector<QPointF> head = points.mid(0, i + 1);
                QVector<QPointF> tail = points.mid(i + 1, -1);

                tail = JoinVectors({p}, tail);
                points = JoinVectors(tail, head);
                points = JoinVectors(points, {p});

                if (VFuzzyComparePossibleNulls(start.angle(), end.angle()))
                {
                    return points;
                }

                begin = false;
                break;
            }
        }
    }

    QVector<QPointF> arc;
    arc.reserve(points.size());

    for (int i = 0; i < points.size() - 1; ++i)
    {
        QLineF edge(points.at(i), points.at(i + 1));

        if (begin)
        {
            QPointF p;
            QLineF::IntersectType type = Intersects(start, edge, &p);

            // QLineF::intersects not always accurate on edge cases
            if (IsBoundedIntersection(type, p, edge, start))
            {
                arc.append(p);
                begin = false;
            }
        }
        else
        {
            QPointF p;
            QLineF::IntersectType type = Intersects(end, edge, &p);

            // QLineF::intersects not always accurate on edge cases
            if (IsBoundedIntersection(type, p, edge, end))
            {
                arc.append(points.at(i));
                arc.append(p);
                break;
            }

            arc.append(points.at(i));
        }
    }

    if (arc.isEmpty())
    {
        return points;
    }

    return arc;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetFormulaRadius1 return formula for major radius.
 * @return radius.
 */
auto VEllipticalArc::GetFormulaRadius1() const -> QString
{
    return d->formulaRadius1;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetFormulaRadius2 return formula for minor radius.
 * @return radius.
 */
auto VEllipticalArc::GetFormulaRadius2() const -> QString
{
    return d->formulaRadius2;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetFormulaRotationAngle return formula for rotation angle.
 * @return rotationAngle.
 */
auto VEllipticalArc::GetFormulaRotationAngle() const -> QString
{
    return d->formulaRotationAngle;
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::SetFormulaRadius1(const QString &formula, qreal value)
{
    d->formulaRadius1 = formula;
    d->radius1 = value;
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::SetRadius1(qreal value)
{
    d->formulaRadius1 = QString::number(value);
    d->radius1 = value;
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::SetFormulaRadius2(const QString &formula, qreal value)
{
    d->formulaRadius2 = formula;
    d->radius2 = value;
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::SetRadius2(qreal value)
{
    d->formulaRadius2 = QString::number(value);
    d->radius2 = value;
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::SetFormulaRotationAngle(const QString &formula, qreal value)
{
    d->formulaRotationAngle = formula;
    d->rotationAngle = value;
}

//---------------------------------------------------------------------------------------------------------------------
void VEllipticalArc::SetRotationAngle(qreal value)
{
    d->formulaRotationAngle = QString::number(value);
    d->rotationAngle = value;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetRadius1 return elliptical arc major radius.
 * @return string with formula.
 */
auto VEllipticalArc::GetRadius1() const -> qreal
{
    return d->radius1;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetRadius2 return elliptical arc minor radius.
 * @return string with formula.
 */
auto VEllipticalArc::GetRadius2() const -> qreal
{
    return d->radius2;
}

//---------------------------------------------------------------------------------------------------------------------
/**
 * @brief GetRotationAngle return rotation angle.
 * @return rotationAngle.
 */
auto VEllipticalArc::GetRotationAngle() const -> qreal
{
    return d->rotationAngle;
}