878 lines
28 KiB
C++
878 lines
28 KiB
C++
/************************************************************************
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**
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** @file vspline.cpp
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** @author Roman Telezhynskyi <dismine(at)gmail.com>
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** @date November 15, 2013
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**
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** @brief
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** @copyright
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** This source code is part of the Valentine project, a pattern making
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** program, whose allow create and modeling patterns of clothing.
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** Copyright (C) 2013-2015 Valentina project
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** <https://bitbucket.org/dismine/valentina> All Rights Reserved.
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**
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** Valentina is free software: you can redistribute it and/or modify
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** it under the terms of the GNU General Public License as published by
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** the Free Software Foundation, either version 3 of the License, or
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** (at your option) any later version.
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**
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** Valentina is distributed in the hope that it will be useful,
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** but WITHOUT ANY WARRANTY; without even the implied warranty of
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** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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** GNU General Public License for more details.
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**
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** You should have received a copy of the GNU General Public License
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** along with Valentina. If not, see <http://www.gnu.org/licenses/>.
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**
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*************************************************************************/
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#include "vspline.h"
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#include "vspline_p.h"
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#include <QDebug>
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#include <QPainterPath>
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#include <QtCore/qmath.h>
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief VSpline default constructor
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*/
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VSpline::VSpline()
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:VAbstractCurve(GOType::Spline), d(new VSplineData)
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{}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief VSpline constructor.
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* @param spline spline from which the copy.
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*/
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VSpline::VSpline ( const VSpline & spline )
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:VAbstractCurve(spline), d(spline.d)
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{}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief VSpline constructor.
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* @param p1 first point spline.
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* @param p4 last point spline.
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* @param angle1 angle from first point to first control point.
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* @param angle2 angle from second point to second control point.
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* @param kCurve coefficient of curvature spline.
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* @param kAsm1 coefficient of length first control line.
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* @param kAsm2 coefficient of length second control line.
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*/
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VSpline::VSpline (VPointF p1, VPointF p4, qreal angle1, qreal angle2, qreal kAsm1, qreal kAsm2, qreal kCurve,
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quint32 idObject, Draw mode)
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:VAbstractCurve(GOType::Spline, idObject, mode), d(new VSplineData(p1, p4, angle1, angle2, kAsm1, kAsm2, kCurve))
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{
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CreateName();
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief VSpline constructor.
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* @param p1 first point spline.
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* @param p2 first control point.
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* @param p3 second control point.
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* @param p4 second point spline.
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*/
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VSpline::VSpline (VPointF p1, QPointF p2, QPointF p3, VPointF p4, qreal kCurve, quint32 idObject, Draw mode)
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:VAbstractCurve(GOType::Spline, idObject, mode), d(new VSplineData(p1, p2, p3, p4, kCurve))
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{
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CreateName();
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}
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//---------------------------------------------------------------------------------------------------------------------
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VSpline::~VSpline()
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{}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief GetLength return length of spline.
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* @return length.
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*/
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qreal VSpline::GetLength () const
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{
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return LengthBezier ( GetP1().toQPointF(), d->p2, d->p3, GetP4().toQPointF());
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}
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//---------------------------------------------------------------------------------------------------------------------
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qreal VSpline::LengthT(qreal t) const
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{
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if (t < 0 || t > 1)
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{
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qDebug()<<"Wrong value t.";
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return 0;
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}
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QLineF seg1_2 ( GetP1 ().toQPointF(), GetP2 () );
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seg1_2.setLength(seg1_2.length () * t);
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QPointF p12 = seg1_2.p2();
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QLineF seg2_3 ( GetP2 (), GetP3 () );
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seg2_3.setLength(seg2_3.length () * t);
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QPointF p23 = seg2_3.p2();
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QLineF seg12_23 ( p12, p23 );
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seg12_23.setLength(seg12_23.length () * t);
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QPointF p123 = seg12_23.p2();
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QLineF seg3_4 ( GetP3 (), GetP4 ().toQPointF() );
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seg3_4.setLength(seg3_4.length () * t);
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QPointF p34 = seg3_4.p2();
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QLineF seg23_34 ( p23, p34 );
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seg23_34.setLength(seg23_34.length () * t);
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QPointF p234 = seg23_34.p2();
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QLineF seg123_234 ( p123, p234 );
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seg123_234.setLength(seg123_234.length () * t);
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QPointF p1234 = seg123_234.p2();
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return LengthBezier ( GetP1().toQPointF(), p12, p123, p1234);
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief CutSpline cut spline. GetPointP1() of base spline will return first point for first spline, GetPointP4()
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* of base spline will return forth point of second spline.
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* @param length length first spline
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* @param spl1p2 second point of first spline
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* @param spl1p3 third point of first spline
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* @param spl2p2 second point of second spline
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* @param spl2p3 third point of second spline
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* @return point of cutting. This point is forth point of first spline and first point of second spline.
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*/
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QPointF VSpline::CutSpline ( qreal length, QPointF &spl1p2, QPointF &spl1p3, QPointF &spl2p2, QPointF &spl2p3 ) const
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{
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//Always need return two splines, so we must correct wrong length.
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if (length < GetLength()*0.02)
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{
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length = GetLength()*0.02;
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}
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else if ( length > GetLength()*0.98)
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{
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length = GetLength()*0.98;
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}
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// Very stupid way find correct value of t.
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// Better first compare with t = 0.5. Find length of spline.
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// If length larger, take t = 0.75 and so on.
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// If length less, take t = 0.25 and so on.
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qreal parT = 0;
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qreal step = 0.001;
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while (1)
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{
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parT = parT + step;
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qreal splLength = LengthT(parT);
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if (splLength >= length || parT > 1)
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{
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break;
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}
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}
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QLineF seg1_2 ( GetP1 ().toQPointF(), GetP2 () );
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seg1_2.setLength(seg1_2.length () * parT);
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QPointF p12 = seg1_2.p2();
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QLineF seg2_3 ( GetP2 (), GetP3 () );
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seg2_3.setLength(seg2_3.length () * parT);
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QPointF p23 = seg2_3.p2();
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QLineF seg12_23 ( p12, p23 );
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seg12_23.setLength(seg12_23.length () * parT);
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QPointF p123 = seg12_23.p2();
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QLineF seg3_4 ( GetP3 (), GetP4 ().toQPointF() );
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seg3_4.setLength(seg3_4.length () * parT);
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QPointF p34 = seg3_4.p2();
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QLineF seg23_34 ( p23, p34 );
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seg23_34.setLength(seg23_34.length () * parT);
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QPointF p234 = seg23_34.p2();
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QLineF seg123_234 ( p123, p234 );
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seg123_234.setLength(seg123_234.length () * parT);
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QPointF p1234 = seg123_234.p2();
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spl1p2 = p12;
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spl1p3 = p123;
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spl2p2 = p234;
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spl2p3 = p34;
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return p1234;
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}
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//---------------------------------------------------------------------------------------------------------------------
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QPointF VSpline::CutSpline(qreal length, VSpline &spl1, VSpline &spl2) const
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{
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QPointF spl1p2;
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QPointF spl1p3;
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QPointF spl2p2;
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QPointF spl2p3;
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QPointF cutPoint = CutSpline (length, spl1p2, spl1p3, spl2p2, spl2p3 );
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spl1 = VSpline(GetP1(), spl1p2, spl1p3, cutPoint, GetKcurve());
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spl2 = VSpline(cutPoint, spl2p2, spl2p3, GetP4(), GetKcurve());
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return cutPoint;
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief GetPoints return list with spline points.
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* @return list of points.
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*/
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QVector<QPointF> VSpline::GetPoints () const
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{
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return GetPoints(GetP1().toQPointF(), d->p2, d->p3, GetP4().toQPointF());
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief GetPoints return list with spline points.
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* @param p1 first spline point.
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* @param p2 first control point.
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* @param p3 second control point.
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* @param p4 last spline point.
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* @return list of points.
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*/
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QVector<QPointF> VSpline::GetPoints (const QPointF &p1, const QPointF &p2, const QPointF &p3, const QPointF &p4)
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{
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QVector<QPointF> pvector;
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QVector<qreal> x;
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QVector<qreal> y;
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QVector<qreal>& wx = x;
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QVector<qreal>& wy = y;
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x.append ( p1.x () );
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y.append ( p1.y () );
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PointBezier_r ( p1.x (), p1.y (), p2.x (), p2.y (),
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p3.x (), p3.y (), p4.x (), p4.y (), 0, wx, wy );
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x.append ( p4.x () );
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y.append ( p4.y () );
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for ( qint32 i = 0; i < x.count(); ++i )
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{
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pvector.append( QPointF ( x.at(i), y.at(i)) );
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}
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return pvector;
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief LengthBezier return spline length using 4 spline point.
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* @param p1 first spline point
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* @param p2 first control point.
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* @param p3 second control point.
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* @param p4 last spline point.
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* @return length.
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*/
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qreal VSpline::LengthBezier ( const QPointF &p1, const QPointF &p2, const QPointF &p3, const QPointF &p4 )
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{
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QPainterPath splinePath;
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QVector<QPointF> points = GetPoints (p1, p2, p3, p4);
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splinePath.moveTo(points.at(0));
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for (qint32 i = 1; i < points.count(); ++i)
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{
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splinePath.lineTo(points.at(i));
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}
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return splinePath.length();
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}
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//---------------------------------------------------------------------------------------------------------------------
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/**
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* @brief PointBezier_r find spline point using four point of spline.
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* @param x1 х coordinate first point.
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* @param y1 у coordinate first point.
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* @param x2 х coordinate first control point.
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* @param y2 у coordinate first control point.
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* @param x3 х coordinate second control point.
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* @param y3 у coordinate second control point.
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* @param x4 х coordinate last point.
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* @param y4 у coordinate last point.
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* @param level level of recursion. In the begin 0.
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* @param px list х coordinat spline points.
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* @param py list у coordinat spline points.
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*/
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void VSpline::PointBezier_r ( qreal x1, qreal y1, qreal x2, qreal y2,
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qreal x3, qreal y3, qreal x4, qreal y4,
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qint16 level, QVector<qreal> &px, QVector<qreal> &py)
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{
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if (px.size() >= 2)
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{
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for (int i=1; i < px.size(); ++i)
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{
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if (QPointF(px.at(i-1), py.at(i-1)) == QPointF(px.at(i), py.at(i)))
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{
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qCritical("All neighbors points in path must be unique.");
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}
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}
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}
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const double curve_collinearity_epsilon = 1e-30;
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const double curve_angle_tolerance_epsilon = 0.01;
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const double m_angle_tolerance = 0.0;
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enum curve_recursion_limit_e { curve_recursion_limit = 32 };
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const double m_cusp_limit = 0.0;
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double m_approximation_scale = 1.0;
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double m_distance_tolerance_square;
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m_distance_tolerance_square = 0.5 / m_approximation_scale;
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m_distance_tolerance_square *= m_distance_tolerance_square;
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if (level > curve_recursion_limit)
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{
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return;
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}
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// Calculate all the mid-points of the line segments
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//----------------------
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const double x12 = (x1 + x2) / 2;
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const double y12 = (y1 + y2) / 2;
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const double x23 = (x2 + x3) / 2;
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const double y23 = (y2 + y3) / 2;
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const double x34 = (x3 + x4) / 2;
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const double y34 = (y3 + y4) / 2;
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const double x123 = (x12 + x23) / 2;
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const double y123 = (y12 + y23) / 2;
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const double x234 = (x23 + x34) / 2;
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const double y234 = (y23 + y34) / 2;
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const double x1234 = (x123 + x234) / 2;
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const double y1234 = (y123 + y234) / 2;
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// Try to approximate the full cubic curve by a single straight line
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//------------------
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const double dx = x4-x1;
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const double dy = y4-y1;
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double d2 = fabs((x2 - x4) * dy - (y2 - y4) * dx);
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double d3 = fabs((x3 - x4) * dy - (y3 - y4) * dx);
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switch ((static_cast<int>(d2 > curve_collinearity_epsilon) << 1) +
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static_cast<int>(d3 > curve_collinearity_epsilon))
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{
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case 0:
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{
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// All collinear OR p1==p4
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//----------------------
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double k = dx*dx + dy*dy;
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if (k < 0.000000001)
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{
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d2 = CalcSqDistance(x1, y1, x2, y2);
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d3 = CalcSqDistance(x4, y4, x3, y3);
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}
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else
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{
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k = 1 / k;
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{
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const double da1 = x2 - x1;
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const double da2 = y2 - y1;
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d2 = k * (da1*dx + da2*dy);
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}
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{
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const double da1 = x3 - x1;
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const double da2 = y3 - y1;
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d3 = k * (da1*dx + da2*dy);
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}
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// cppcheck-suppress incorrectLogicOperator
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if (d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1)
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{
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// Simple collinear case, 1---2---3---4
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// We can leave just two endpoints
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return;
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}
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if (d2 <= 0)
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{
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d2 = CalcSqDistance(x2, y2, x1, y1);
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}
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else if (d2 >= 1)
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{
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d2 = CalcSqDistance(x2, y2, x4, y4);
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}
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else
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{
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d2 = CalcSqDistance(x2, y2, x1 + d2*dx, y1 + d2*dy);
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}
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if (d3 <= 0)
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{
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d3 = CalcSqDistance(x3, y3, x1, y1);
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}
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else if (d3 >= 1)
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{
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d3 = CalcSqDistance(x3, y3, x4, y4);
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}
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else
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{
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d3 = CalcSqDistance(x3, y3, x1 + d3*dx, y1 + d3*dy);
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}
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}
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if (d2 > d3)
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{
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if (d2 < m_distance_tolerance_square)
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{
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px.append(x2);
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py.append(y2);
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return;
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}
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}
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else
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{
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if (d3 < m_distance_tolerance_square)
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{
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px.append(x3);
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py.append(y3);
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return;
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}
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}
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break;
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}
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case 1:
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{
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// p1,p2,p4 are collinear, p3 is significant
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//----------------------
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if (d3 * d3 <= m_distance_tolerance_square * (dx*dx + dy*dy))
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{
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if (m_angle_tolerance < curve_angle_tolerance_epsilon)
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{
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px.append(x23);
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py.append(y23);
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return;
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}
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// Angle Condition
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//----------------------
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double da1 = fabs(atan2(y4 - y3, x4 - x3) - atan2(y3 - y2, x3 - x2));
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if (da1 >= M_PI)
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{
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da1 = 2*M_PI - da1;
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}
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if (da1 < m_angle_tolerance)
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{
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px.append(x2);
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py.append(y2);
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px.append(x3);
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py.append(y3);
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return;
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}
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if (m_cusp_limit > 0.0 || m_cusp_limit < 0.0)
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{
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if (da1 > m_cusp_limit)
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{
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px.append(x3);
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py.append(y3);
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return;
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}
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}
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}
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break;
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}
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case 2:
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{
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// p1,p3,p4 are collinear, p2 is significant
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//----------------------
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if (d2 * d2 <= m_distance_tolerance_square * (dx*dx + dy*dy))
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{
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if (m_angle_tolerance < curve_angle_tolerance_epsilon)
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{
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px.append(x23);
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py.append(y23);
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return;
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}
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// Angle Condition
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//----------------------
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double da1 = fabs(atan2(y3 - y2, x3 - x2) - atan2(y2 - y1, x2 - x1));
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if (da1 >= M_PI)
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{
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da1 = 2*M_PI - da1;
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}
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if (da1 < m_angle_tolerance)
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{
|
||
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 = 2*M_PI - da1;
|
||
}
|
||
if (da2 >= M_PI)
|
||
{
|
||
da2 = 2*M_PI - 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 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 VSpline::CalcSqDistance (qreal x1, qreal y1, qreal x2, qreal y2)
|
||
{
|
||
qreal dx = x2 - x1;
|
||
qreal dy = y2 - y1;
|
||
return dx * dx + dy * dy;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief CreateName create spline name.
|
||
*/
|
||
void VSpline::CreateName()
|
||
{
|
||
setName(QString(spl_+"%1_%2").arg(this->GetP1().name(), this->GetP4().name()));
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @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.
|
||
*/
|
||
// cppcheck-suppress unusedFunction
|
||
QVector<QPointF> VSpline::SplinePoints(const QPointF &p1, const QPointF &p4, qreal angle1, qreal angle2, qreal kAsm1,
|
||
qreal kAsm2, qreal kCurve)
|
||
{
|
||
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 / 180.0 / 4 );
|
||
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 GetPoints(p1, p2, p3, p4);
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
VSpline &VSpline::operator =(const VSpline &spline)
|
||
{
|
||
if ( &spline == this )
|
||
{
|
||
return *this;
|
||
}
|
||
VAbstractCurve::operator=(spline);
|
||
d = spline.d;
|
||
return *this;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief GetP1 return first spline point.
|
||
* @return first point.
|
||
*/
|
||
VPointF VSpline::GetP1() const
|
||
{
|
||
return d->p1;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief GetP2 return first control point.
|
||
* @return first control point.
|
||
*/
|
||
QPointF VSpline::GetP2() const
|
||
{
|
||
return d->p2;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief GetP3 return second control point.
|
||
* @return second control point.
|
||
*/
|
||
QPointF VSpline::GetP3() const
|
||
{
|
||
return d->p3;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief GetP4 return last spline point.
|
||
* @return остання точка сплайну.
|
||
*/
|
||
VPointF VSpline::GetP4() const
|
||
{
|
||
return d->p4;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief GetAngle1 return first angle control line.
|
||
* @return angle.
|
||
*/
|
||
qreal VSpline::GetAngle1() const
|
||
{
|
||
return d->angle1;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief GetAngle2 return second angle control line.
|
||
* @return angle.
|
||
*/
|
||
qreal VSpline::GetAngle2() const
|
||
{
|
||
return d->angle2;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief GetKasm1 return coefficient of length first control line.
|
||
* @return coefficient.
|
||
*/
|
||
qreal VSpline::GetKasm1() const
|
||
{
|
||
return d->kAsm1;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief GetKasm2 return coefficient of length second control line.
|
||
* @return coefficient.
|
||
*/
|
||
qreal VSpline::GetKasm2() const
|
||
{
|
||
return d->kAsm2;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
/**
|
||
* @brief GetKcurve return coefficient of curvature spline.
|
||
* @return coefficient
|
||
*/
|
||
qreal VSpline::GetKcurve() const
|
||
{
|
||
return d->kCurve;
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
void VSpline::SetKcurve(qreal factor)
|
||
{
|
||
if (factor > 0)
|
||
{
|
||
d->kCurve = factor;
|
||
}
|
||
}
|
||
|
||
//---------------------------------------------------------------------------------------------------------------------
|
||
int VSpline::Sign(long double ld)
|
||
{
|
||
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).
|
||
*/
|
||
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 (qFuzzyCompare(x.at(2) + 1, 0. + 1))
|
||
{
|
||
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().toQPointF().x(), d->p2.x(), d->p3.x(), GetP4().toQPointF().x(), pBt.x());
|
||
ts += CalcT (GetP1().toQPointF().y(), d->p2.y(), d->p3.y(), GetP4().toQPointF().y(), pBt.y());
|
||
|
||
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().toQPointF();
|
||
const QPointF p1 = d->p2;
|
||
const QPointF p2 = d->p3;
|
||
const QPointF p3 = GetP4().toQPointF();
|
||
//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;
|
||
}
|