valentina/src/libs/vgeometry/vspline.cpp

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/************************************************************************
**
** @file vspline.cpp
** @author Roman Telezhynskyi <dismine(at)gmail.com>
** @date November 15, 2013
**
** @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) 2013-2015 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/>.
**
*************************************************************************/
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#include "vspline.h"
#include <QLineF>
#include "vabstractcurve.h"
#include "vspline_p.h"
#include "../vmisc/vmath.h"
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief VSpline default constructor
*/
VSpline::VSpline()
:VAbstractCubicBezier(GOType::Spline), d(new VSplineData)
{}
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//---------------------------------------------------------------------------------------------------------------------
/**
* @brief VSpline constructor.
* @param spline spline from which the copy.
*/
VSpline::VSpline ( const VSpline & spline )
:VAbstractCubicBezier(spline), d(spline.d)
{}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief VSpline constructor.
* @param p1 first point spline.
* @param p4 last point spline.
* @param angle1 angle from first point to first control point.
* @param angle2 angle from second point to second control point.
* @param kCurve coefficient of curvature spline.
* @param kAsm1 coefficient of length first control line.
* @param kAsm2 coefficient of length second control line.
*/
VSpline::VSpline (const VPointF &p1, const VPointF &p4, qreal angle1, qreal angle2, qreal kAsm1, qreal kAsm2,
qreal kCurve, quint32 idObject, Draw mode)
: VAbstractCubicBezier(GOType::Spline, idObject, mode),
d(new VSplineData(p1, p4, angle1, angle2, kAsm1, kAsm2, kCurve))
{
CreateName();
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}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief VSpline constructor.
* @param p1 first point spline.
* @param p2 first control point.
* @param p3 second control point.
* @param p4 second point spline.
*/
VSpline::VSpline (const VPointF &p1, const QPointF &p2, const QPointF &p3, const VPointF &p4, quint32 idObject,
Draw mode)
:VAbstractCubicBezier(GOType::Spline, idObject, mode), d(new VSplineData(p1, p2, p3, p4))
{
CreateName();
}
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//---------------------------------------------------------------------------------------------------------------------
/**
* @brief VSpline constructor
* @param p1 first point spline.
* @param p4 first control point.
* @param angle1 angle from first point to first control point.
* @param angle1Formula formula angle from first point to first control point.
* @param angle2 angle from second point to second control point.
* @param angle2Formula formula angle from second point to second control point.
* @param c1Length length from first point to first control point.
* @param c1LengthFormula formula length from first point to first control point.
* @param c2Length length from second point to first control point.
* @param c2LengthFormula formula length from second point to first control point.
*/
VSpline::VSpline(const VPointF &p1, const VPointF &p4, qreal angle1, const QString &angle1Formula, qreal angle2,
const QString &angle2Formula, qreal c1Length, const QString &c1LengthFormula, qreal c2Length,
const QString &c2LengthFormula, quint32 idObject, Draw mode)
: VAbstractCubicBezier(GOType::Spline, idObject, mode),
d(new VSplineData(p1, p4, angle1, angle1Formula, angle2, angle2Formula, c1Length, c1LengthFormula, c2Length,
c2LengthFormula))
{
CreateName();
}
//---------------------------------------------------------------------------------------------------------------------
VSpline VSpline::Rotate(const QPointF &originPoint, qreal degrees, const QString &prefix) const
{
const VPointF p1 = GetP1().Rotate(originPoint, degrees);
const VPointF p4 = GetP4().Rotate(originPoint, degrees);
const QPointF p2 = VPointF::RotatePF(originPoint, GetP2(), degrees);
const QPointF p3 = VPointF::RotatePF(originPoint, GetP3(), degrees);
VSpline spl(p1, p2, p3, p4);
spl.setName(name() + prefix);
return spl;
}
//---------------------------------------------------------------------------------------------------------------------
VSpline VSpline::Flip(const QLineF &axis, const QString &prefix) const
{
const VPointF p1 = GetP1().Flip(axis);
const VPointF p4 = GetP4().Flip(axis);
const QPointF p2 = VPointF::FlipPF(axis, GetP2());
const QPointF p3 = VPointF::FlipPF(axis, GetP3());
VSpline spl(p1, p2, p3, p4);
spl.setName(name() + prefix);
return spl;
}
//---------------------------------------------------------------------------------------------------------------------
VSpline VSpline::Move(qreal length, qreal angle, const QString &prefix) const
{
const VPointF p1 = GetP1().Move(length, angle);
const VPointF p4 = GetP4().Move(length, angle);
const QPointF p2 = VPointF::MovePF(GetP2(), length, angle);
const QPointF p3 = VPointF::MovePF(GetP3(), length, angle);
VSpline spl(p1, p2, p3, p4);
spl.setName(name() + prefix);
return spl;
}
//---------------------------------------------------------------------------------------------------------------------
VSpline::~VSpline()
{}
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//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetLength return length of spline.
* @return length.
*/
qreal VSpline::GetLength () const
{
return LengthBezier ( GetP1(), GetP2(), GetP3(), GetP4());
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}
//---------------------------------------------------------------------------------------------------------------------
QPointF VSpline::CutSpline(qreal length, VSpline &spl1, VSpline &spl2) const
{
QPointF spl1p2;
QPointF spl1p3;
QPointF spl2p2;
QPointF spl2p3;
const QPointF cutPoint = CutSpline (length, spl1p2, spl1p3, spl2p2, spl2p3 );
spl1 = VSpline(GetP1(), spl1p2, spl1p3, cutPoint);
spl2 = VSpline(cutPoint, spl2p2, spl2p3, GetP4());
return cutPoint;
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetPoints return list with spline points.
* @return list of points.
*/
QVector<QPointF> VSpline::GetPoints () const
{
return GetCubicBezierPoints(GetP1(), GetP2(), GetP3(), GetP4());
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief SplinePoints return list with spline points.
* @param p1 first spline point.
* @param p4 last spline point.
* @param angle1 angle from first point to first control point.
* @param angle2 angle from second point to second control point.
* @param kAsm1 coefficient of length first control line.
* @param kAsm2 coefficient of length second control line.
* @param kCurve coefficient of curvature spline.
* @return list with spline points.
*/
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// cppcheck-suppress unusedFunction
QVector<QPointF> VSpline::SplinePoints(const QPointF &p1, const QPointF &p4, qreal angle1, qreal angle2, qreal kAsm1,
qreal kAsm2, qreal kCurve)
{
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QLineF p1pX(p1.x(), p1.y(), p1.x() + 100, p1.y());
p1pX.setAngle( angle1 );
qreal L = 0, radius = 0, angle = 90;
radius = QLineF(QPointF(p1.x(), p4.y()), p4).length();
L = kCurve * radius * 4 / 3 * tan( angle * M_PI_4 / 180.0 );
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QLineF p1p2(p1.x(), p1.y(), p1.x() + L * kAsm1, p1.y());
p1p2.setAngle(angle1);
QLineF p4p3(p4.x(), p4.y(), p4.x() + L * kAsm2, p4.y());
p4p3.setAngle(angle2);
QPointF p2 = p1p2.p2();
QPointF p3 = p4p3.p2();
return GetCubicBezierPoints(p1, p2, p3, p4);
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}
//---------------------------------------------------------------------------------------------------------------------
VSpline &VSpline::operator =(const VSpline &spline)
{
if ( &spline == this )
{
return *this;
}
VAbstractCubicBezier::operator=(spline);
d = spline.d;
return *this;
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetP1 return first spline point.
* @return first point.
*/
VPointF VSpline::GetP1() const
{
return d->p1;
}
//---------------------------------------------------------------------------------------------------------------------
void VSpline::SetP1(const VPointF &p)
{
d->p1 = p;
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetP2 return first control point.
* @return first control point.
*/
VPointF VSpline::GetP2() const
{
QLineF p1p2(d->p1.x(), d->p1.y(), d->p1.x() + d->c1Length, d->p1.y());
p1p2.setAngle(d->angle1);
return VPointF(p1p2.p2());
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetP3 return second control point.
* @return second control point.
*/
VPointF VSpline::GetP3() const
{
QLineF p4p3(d->p4.x(), d->p4.y(), d->p4.x() + d->c2Length, d->p4.y());
p4p3.setAngle(d->angle2);
return VPointF(p4p3.p2());
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetP4 return last spline point.
* @return остання точка сплайну.
*/
VPointF VSpline::GetP4() const
{
return d->p4;
}
//---------------------------------------------------------------------------------------------------------------------
void VSpline::SetP4(const VPointF &p)
{
d->p4 = p;
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetAngle1 return first angle control line.
* @return angle.
*/
qreal VSpline::GetStartAngle() const
{
return d->angle1;
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetAngle2 return second angle control line.
* @return angle.
*/
qreal VSpline::GetEndAngle() const
{
return d->angle2;
}
//---------------------------------------------------------------------------------------------------------------------
QString VSpline::GetStartAngleFormula() const
{
return d->angle1F;
}
//---------------------------------------------------------------------------------------------------------------------
QString VSpline::GetEndAngleFormula() const
{
return d->angle2F;
}
//---------------------------------------------------------------------------------------------------------------------
void VSpline::SetStartAngle(qreal angle, const QString &formula)
{
d->angle1 = angle;
d->angle1F = formula;
}
//---------------------------------------------------------------------------------------------------------------------
void VSpline::SetEndAngle(qreal angle, const QString &formula)
{
d->angle2 = angle;
d->angle2F = formula;
}
//---------------------------------------------------------------------------------------------------------------------
qreal VSpline::GetC1Length() const
{
return d->c1Length;
}
//---------------------------------------------------------------------------------------------------------------------
qreal VSpline::GetC2Length() const
{
return d->c2Length;
}
//---------------------------------------------------------------------------------------------------------------------
QString VSpline::GetC1LengthFormula() const
{
return d->c1LengthF;
}
//---------------------------------------------------------------------------------------------------------------------
QString VSpline::GetC2LengthFormula() const
{
return d->c2LengthF;
}
//---------------------------------------------------------------------------------------------------------------------
void VSpline::SetC1Length(qreal length, const QString &formula)
{
d->c1Length = length;
d->c1LengthF = formula;
}
//---------------------------------------------------------------------------------------------------------------------
void VSpline::SetC2Length(qreal length, const QString &formula)
{
d->c2Length = length;
d->c2LengthF = formula;
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetKasm1 return coefficient of length first control line.
* @return coefficient.
*/
qreal VSpline::GetKasm1() const
{
return QLineF(d->p1, GetP2()).length() / VSplineData::GetL(d->p1, d->p4,
d->kCurve);
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetKasm2 return coefficient of length second control line.
* @return coefficient.
*/
qreal VSpline::GetKasm2() const
{
return QLineF(d->p4, GetP3()).length() / VSplineData::GetL(d->p1, d->p4,
d->kCurve);
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief GetKcurve return coefficient of curvature spline.
* @return coefficient
*/
qreal VSpline::GetKcurve() const
{
return d->kCurve;
}
//---------------------------------------------------------------------------------------------------------------------
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int VSpline::Sign(long double ld)
{
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if (qAbs(ld)<0.00000000001)
{
return 0;
}
return (ld>0) ? 1 : -1;
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief Cubic Cubic equation solution. Real coefficients case.
*
* This method use method Vieta-Cardano for eval cubic equations.
* Cubic equation write in form x3+a*x2+b*x+c=0.
*
* Output:
* 3 real roots -> then x is filled with them;
* 1 real + 2 complex -> x[0] is real, x[1] is real part of complex roots, x[2] - non-negative imaginary part.
*
* @param x solution array (size 3).
* @param a coefficient
* @param b coefficient
* @param c coefficient
* @return 3 - 3 real roots;
* 1 - 1 real root + 2 complex;
* 2 - 1 real root + complex roots imaginary part is zero (i.e. 2 real roots).
*/
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qint32 VSpline::Cubic(QVector<qreal> &x, qreal a, qreal b, qreal c)
{
//To find cubic equation roots in the case of real coefficients, calculated at the beginning
const qreal q = (pow(a, 2) - 3*b)/9.;
const qreal r = (2*pow(a, 3) - 9*a*b + 27.*c)/54.;
if (pow(r, 2) < pow(q, 3))
{ // equation has three real roots, use formula Vieta
const qreal t = acos(r/sqrt(pow(q, 3)))/3.;
x.insert(0, -2.*sqrt(q)*cos(t)-a/3);
x.insert(1, -2.*sqrt(q)*cos(t + (2*M_2PI/3.)) - a/3.);
x.insert(2, -2.*sqrt(q)*cos(t - (2*M_2PI/3.)) - a/3.);
return(3);
}
else
{ // 1 real root + 2 complex
//Formula Cardano
const qreal aa = -Sign(r)*pow(fabs(r)+sqrt(pow(r, 2)-pow(q, 3)), 1./3.);
const qreal bb = Sign(aa) == 0 ? 0 : q/aa;
x.insert(0, aa+bb-a/3.); // Real root
x.insert(1, (-0.5)*(aa+bb)-a/3.); //Complex root
x.insert(2, (sqrt(3.)*0.5)*fabs(aa-bb)); // Complex root
if (qFuzzyIsNull(x.at(2)))
{
return(2);
}
return(1);
}
}
//---------------------------------------------------------------------------------------------------------------------
QVector<qreal> VSpline::CalcT (qreal curveCoord1, qreal curveCoord2, qreal curveCoord3,
qreal curveCoord4, qreal pointCoord) const
{
const qreal a = -curveCoord1 + 3*curveCoord2 - 3*curveCoord3 + curveCoord4;
const qreal b = 3*curveCoord1 - 6*curveCoord2 + 3*curveCoord3;
const qreal c = -3*curveCoord1 + 3*curveCoord2;
const qreal d = -pointCoord + curveCoord1;
QVector<qreal> t = QVector<qreal>(3, -1);
Cubic(t, b/a, c/a, d/a);
QVector<qreal> retT;
for (int i=0; i < t.size(); ++i)
{
if ( t.at(i) >= 0 && t.at(i) <= 1 )
{
retT.append(t.at(i));
}
}
return retT;
}
//---------------------------------------------------------------------------------------------------------------------
/**
* @brief VSpline::ParamT calculate t coeffient that reprezent point on curve.
*
* Each point that belongs to Cubic Bézier curve can be shown by coefficient in interval [0; 1].
*
* @param pBt point on curve
* @return t coeffient that reprezent this point on curve. Return -1 if point doesn't belongs to curve.
*/
qreal VSpline::ParamT (const QPointF &pBt) const
{
QVector<qreal> ts;
// Calculate t coefficient for each axis
ts += CalcT (GetP1().x(), GetP2().x(), GetP3().x(), GetP4().x(), pBt.x());
ts += CalcT (GetP1().y(), GetP2().y(), GetP3().y(), GetP4().y(), pBt.y());
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if (ts.isEmpty())
{
return -1; // We don't have candidates
}
qreal tx = -1;
qreal eps = 3; // Error calculation
// In morst case we will have 6 result in interval [0; 1].
// Here we try find closest to our point.
for (int i=0; i< ts.size(); ++i)
{
const qreal t = ts.at(i);
const QPointF p0 = GetP1();
const QPointF p1 = GetP2();
const QPointF p2 = GetP3();
const QPointF p3 = GetP4();
//The explicit form of the Cubic Bézier curve
const qreal pointX = pow(1-t, 3)*p0.x() + 3*pow(1-t, 2)*t*p1.x() + 3*(1-t)*pow(t, 2)*p2.x() + pow(t, 3)*p3.x();
const qreal pointY = pow(1-t, 3)*p0.y() + 3*pow(1-t, 2)*t*p1.y() + 3*(1-t)*pow(t, 2)*p2.y() + pow(t, 3)*p3.y();
const QLineF line(pBt, QPointF(pointX, pointY));
if (line.length() <= eps)
{
tx = t;
eps = line.length(); //Next point should be even closest
}
}
return tx;
}
//---------------------------------------------------------------------------------------------------------------------
QPointF VSpline::GetControlPoint1() const
{
return GetP2 ();
}
//---------------------------------------------------------------------------------------------------------------------
QPointF VSpline::GetControlPoint2() const
{
return GetP3 ();
}