798 lines
26 KiB
C++
798 lines
26 KiB
C++
#define _USE_MATH_DEFINES
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#include <cmath>
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#include "vspline.h"
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#include <QDebug>
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VSpline::VSpline():p1(0), p2(QPointF()), p3(QPointF()), p4(0), angle1(0), angle2(0), kAsm1(1), kAsm2(1),
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kCurve(1), points(0), _referens(0), mode(Draw::Calculation), idObject(0){
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}
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VSpline::VSpline ( const VSpline & spline ):p1(spline.GetP1 ()), p2(spline.GetP2 ()), p3(spline.GetP3 ()),
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p4(spline.GetP4 ()), angle1(spline.GetAngle1 ()), angle2(spline.GetAngle2 ()), kAsm1(spline.GetKasm1()),
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kAsm2(spline.GetKasm2()), kCurve(spline.GetKcurve()), points(spline.GetDataPoints()), _referens(0),
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mode(spline.getMode()), idObject(spline.getIdObject()){
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}
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VSpline::VSpline (const QMap<qint64, VPointF> *points, qint64 p1, qint64 p4, qreal angle1, qreal angle2,
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qreal kAsm1, qreal kAsm2 , qreal kCurve, Draw::Mode mode, qint64 idObject):p1(p1), p2(QPointF()), p3(QPointF()),
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p4(p4), angle1(angle1), angle2(angle2), kAsm1(kAsm1), kAsm2(kAsm2), kCurve(kCurve), points(points),
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_referens(0), mode(mode), idObject(idObject){
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ModifiSpl ( p1, p4, angle1, angle2, kAsm1, kAsm2, kCurve );
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}
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VSpline::VSpline (const QMap<qint64, VPointF> *points, qint64 p1, QPointF p2, QPointF p3, qint64 p4,
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qreal kCurve, Draw::Mode mode, qint64 idObject):p1(p1), p2(p2), p3(p3), p4(p4), angle1(0), angle2(0), kAsm1(1), kAsm2(1),
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kCurve(1), points(points), _referens(0), mode(mode), idObject(idObject){
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ModifiSpl ( p1, p2, p3, p4, kCurve);
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}
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void VSpline::ModifiSpl ( qint64 p1, qint64 p4, qreal angle1, qreal angle2,
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qreal kAsm1, qreal kAsm2, qreal kCurve){
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this->p1 = p1;
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this->p4 = p4;
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this->angle1 = angle1;
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this->angle2 = angle2;
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this->kAsm1 = kAsm1;
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this->kAsm2 = kAsm2;
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this->kCurve = kCurve;
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QLineF p1pX(GetPointP1().x(), GetPointP1().y(), GetPointP1().x() + 100, GetPointP1().y());
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p1pX.setAngle( angle1 );
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qreal L = 0, radius = 0, angle = 90;
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// angle = QLineF(GetPointP1(), p1pX.p2()).angleTo(QLineF(GetPointP1(), GetPointP4()));
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// if ( angle > 180 ){
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// angle = 360 - angle;
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// }
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QPointF point1 = GetPointP1().toQPointF();
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QPointF point4 = GetPointP4().toQPointF();
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radius = QLineF(QPointF(point1.x(), point4.y()),point4).length();
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// radius = QLineF(GetPointP1(), GetPointP4()).length() / 2 / sin( angle * M_PI / 180.0 );
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L = kCurve * radius * 4 / 3 * tan( angle * M_PI / 180.0 / 4 );
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QLineF p1p2(GetPointP1().x(), GetPointP1().y(), GetPointP1().x() + L * kAsm1, GetPointP1().y());
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p1p2.setAngle(angle1);
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QLineF p4p3(GetPointP4().x(), GetPointP4().y(), GetPointP4().x() + L * kAsm2, GetPointP4().y());
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p4p3.setAngle(angle2);
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this->p2 = p1p2.p2();
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this->p3 = p4p3.p2();
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}
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void VSpline::ModifiSpl (qint64 p1, QPointF p2, QPointF p3, qint64 p4, qreal kCurve){
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this->p1 = p1;
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this->p2 = p2;
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this->p3 = p3;
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this->p4 = p4;
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this->angle1 = QLineF ( GetPointP1().toQPointF(), p2 ).angle();
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this->angle2 = QLineF ( GetPointP4().toQPointF(), p3 ).angle();
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QLineF p1pX(GetPointP1().x(), GetPointP1().y(), GetPointP1().x() + 100, GetPointP1().y());
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p1pX.setAngle( angle1 );
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qreal L = 0, radius = 0, angle = 90;
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// angle = QLineF(GetPointP1(), p1pX.p2()).angleTo(QLineF(GetPointP1(), GetPointP4()));
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// if ( angle >= 180 ){
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// angle = 360 - angle;
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// }
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QPointF point1 = GetPointP1().toQPointF();
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QPointF point4 = GetPointP4().toQPointF();
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radius = QLineF(QPointF(point1.x(), point4.y()),point4).length();
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// radius = QLineF(GetPointP1(), GetPointP4()).length() / 2 / sin( angle * M_PI / 180.0 );
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L = kCurve * radius * 4 / 3 * tan( angle * M_PI / 180.0 / 4 );
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this->kCurve = kCurve;
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this->kAsm1 = QLineF ( GetPointP1().toQPointF(), p2 ).length()/L;
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this->kAsm2 = QLineF ( GetPointP4().toQPointF(), p3 ).length()/L;
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}
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//void VSpline::RotationSpl (QPointF pRotate, qreal angle ){
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// QLineF pRotateP1 (pRotate, p1);
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// pRotateP1.setAngle(angle);
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// p1 = pRotateP1.p2();
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// QLineF pRotateP2 (pRotate, p2);
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// pRotateP2.setAngle(angle);
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// p2 = pRotateP2.p2();
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// QLineF pRotateP3 (pRotate, p3);
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// pRotateP3.setAngle(angle);
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// p3 = pRotateP3.p2();
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// QLineF pRotateP4 (pRotate, p4);
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// pRotateP4.setAngle(angle);
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// p4 = pRotateP4.p2();
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// angle1 = QLineF(p1, p2).angle();
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// angle2 = QLineF(p4, p2).angle();
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//}
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//void VSpline::BiasSpl ( qreal mx, qreal my ){
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// p1 = QPointF(p1.x()+mx, p1.y()+my);
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// p2 = QPointF(p2.x()+mx, p2.y()+my);
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// p3 = QPointF(p3.x()+mx, p3.y()+my);
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// p4 = QPointF(p4.x()+mx, p4.y()+my);
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//}
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qint64 VSpline::GetP1 () const{
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return p1;
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}
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VPointF VSpline::GetPointP1() const{
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if(points->contains(p1)){
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return points->value(p1);
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} else {
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qCritical()<<"Не можу знайти id = "<<p1<<" в таблиці.";
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throw"Не можу знайти точку за id.";
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}
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return VPointF();
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}
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QPointF VSpline::GetP2 () const{
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return p2;
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}
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QPointF VSpline::GetP3 () const{
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return p3;
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}
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qint64 VSpline::GetP4() const{
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return p4;
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}
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VPointF VSpline::GetPointP4() const{
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if(points->contains(p4)){
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return points->value(p4);
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} else {
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qCritical()<<"Не можу знайти id = "<<p4<<" в таблиці.";
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throw"Не можу знайти точку за id.";
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}
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return VPointF();
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}
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qreal VSpline::GetAngle1() const{
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return angle1;
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}
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qreal VSpline::GetAngle2 () const{
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return angle2;
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}
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qreal VSpline::GetLength () const{
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return LengthBezier ( GetPointP1().toQPointF(), this->p2, this->p3, GetPointP4().toQPointF());
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}
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QString VSpline::GetName() const{
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VPointF first = GetPointP1();
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VPointF second = GetPointP4();
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return QString("Spl_%1_%2").arg(first.name(), second.name());
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}
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qreal VSpline::GetKasm1() const{
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return kAsm1;
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}
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qreal VSpline::GetKasm2() const{
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return kAsm2;
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}
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qreal VSpline::GetKcurve() const{
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return kCurve;
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}
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const QMap<qint64, VPointF> *VSpline::GetDataPoints() const{
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return points;
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}
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QLineF::IntersectType VSpline::CrossingSplLine ( const QLineF &line, QPointF *intersectionPoint ) const{
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QVector<qreal> px;
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QVector<qreal> py;
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px.append ( GetPointP1 ().x () );
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py.append ( GetPointP1 ().y () );
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QVector<qreal>& wpx = px;
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QVector<qreal>& wpy = py;
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PointBezier_r ( GetPointP1 ().x (), GetPointP1 ().y (), GetP2 ().x (), GetP2 ().y (),
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GetP3 ().x (), GetP3 ().y (), GetPointP4 ().x (), GetPointP4 ().y (),
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0, wpx, wpy);
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px.append ( GetPointP4 ().x () );
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py.append ( GetPointP4 ().y () );
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qint32 i = 0;
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QPointF crosPoint;
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QLineF::IntersectType type = QLineF::NoIntersection;
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for ( i = 0; i < px.count()-1; ++i ){
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type = line.intersect(QLineF ( QPointF ( px[i], py[i] ),
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QPointF ( px[i+1], py[i+1] )), &crosPoint);
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if ( type == QLineF::BoundedIntersection ){
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*intersectionPoint = crosPoint;
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return type;
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}
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}
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throw "Не можу знайти точку перетину сплайну з лінією.";
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}
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//void VSpline::CutSpline ( qreal length, VSpline* curFir, VSpline* curSec ) const{
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// if ( length > GetLength()){
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// throw"Не правильна довжина нового сплайну\n";
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// }
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// qreal parT = length / GetLength();
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// QLineF seg1_2 ( GetPointP1 (), 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 (), GetPointP4 () );
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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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// curFir->ModifiSpl ( GetPointP1 (), p12, p123, p1234 );
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// curSec->ModifiSpl ( p1234, p234, p34, GetPointP4 () );
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//}
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//void VSpline::CutSpline ( QPointF point, VSpline* curFir, VSpline* curSec ) const{
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// qreal t = param_t (point);
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// qreal length = t*this->GetLength();
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// CutSpline ( length, curFir, curSec );
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//}
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//void VSpline::PutAlongSpl (QPointF &moveP, qreal move ) const{
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// if ( GetLength () < move ){
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// qDebug()<<"Довжина більше довжини сплайну.";
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// qDebug()<<GetLength()<<"<"<<move;
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// throw "Довжина більше довжини сплайну.";
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// }
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// if ( move <= 0 ){
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// qDebug()<<"Довжина менше дорівнює нулю.";
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// throw "Довжина менше дорівнює нулю.";
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// }
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// qreal t = 0;
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// if ( move == 0 ){
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// t = 0;
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// } else {
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// t = move / GetLength ();
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// moveP.setX ( pow ( 1 - t, 3 ) * GetPointP1 ().x () + 3 * t * pow ( 1 - t, 2 ) *
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// GetP2 ().x () + 3 * t * t * ( 1 - t ) * GetP3 ().x () +
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// pow ( t, 3 ) * GetPointP4 ().x () );
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// moveP.setY ( pow ( 1 - t, 3 ) * GetPointP1 ().y () + 3 * t * pow ( 1 - t, 2 ) *
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// GetP2 ().y () + 3 * t * t * ( 1 - t ) * GetP3 ().y () +
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// pow ( t, 3 ) * GetPointP4 ().y () );
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// }
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//}
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QVector<QPointF> VSpline::GetPoints () const{
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return GetPoints(GetPointP1().toQPointF(), p2, p3, GetPointP4().toQPointF());
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// QLineF line1(points.at(0).toPoint(), points.at(1).toPoint());
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// line1.setLength(500);
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// QLineF line2 = line1;
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// line2.setAngle(line2.angle()+90);
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// qreal xk1 = line1.p2().x();
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// qreal xk0 = line1.p1().x();
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// qreal y = line2.p2().y();
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// qreal yk0 = line1.p1().y();
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// qreal yk1 = line1.p2().y();
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// qreal x = line2.p2().x();
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// qreal check = (xk1 - xk0) * (y - yk0) - (yk1 - yk0) * (x - xk0);
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// if(check > 0){
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// return points;
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// } else {
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// QVector<QPointF> reversePoints;
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// for (qint32 i = points.size() - 1; i >= 0; --i) {
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// reversePoints.append(points.at(i));
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// }
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// return reversePoints;
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// }
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}
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QVector<QPointF> VSpline::GetPoints (QPointF p1, QPointF p2, QPointF p3, QPointF p4){
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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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pvector.append( QPointF ( x[i], y[i] ) );
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}
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return pvector;
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}
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qreal VSpline::LengthBezier ( QPointF p1, QPointF p2, QPointF p3, QPointF p4 ) const{
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/*QVector<qreal> px;
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QVector<qreal> py;
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QVector<qreal>& wpx = px;
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QVector<qreal>& wpy = py;
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px.append ( p1.x () );
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py.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, wpx, wpy);
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px.append ( p4.x () );
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py.append ( p4.y () );
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qint32 i = 0;
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qreal length = 0.0;
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*
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* Наприклад маємо 10 точок. Від 0 до 9 і останню точку не опрацьовуємо.
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* Тому від 0 до 8(<10-1).
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*
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for ( i = 0; i < px.count() - 1; ++i ){
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length += QLineF ( QPointF ( px[i], py[i] ), QPointF ( px[i+1], py[i+1] ) ).length ();
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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[0]);
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for (qint32 i = 1; i < points.count(); ++i){
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splinePath.lineTo(points[i]);
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}
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return splinePath.length();
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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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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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double x12 = (x1 + x2) / 2;
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double y12 = (y1 + y2) / 2;
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double x23 = (x2 + x3) / 2;
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double y23 = (y2 + y3) / 2;
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double x34 = (x3 + x4) / 2;
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double y34 = (y3 + y4) / 2;
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double x123 = (x12 + x23) / 2;
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double y123 = (y12 + y23) / 2;
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double x234 = (x23 + x34) / 2;
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double y234 = (y23 + y34) / 2;
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double x1234 = (x123 + x234) / 2;
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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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double dx = x4-x1;
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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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double da1, da2, k;
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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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// All collinear OR p1==p4
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//----------------------
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k = dx*dx + dy*dy;
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if(k == 0)
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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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da1 = x2 - x1;
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da2 = y2 - y1;
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d2 = k * (da1*dx + da2*dy);
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da1 = x3 - x1;
|
||
da2 = y3 - y1;
|
||
d3 = k * (da1*dx + da2*dy);
|
||
if(d2 > 0 && d2 < 1 && d3 > 0 && d3 < 1)
|
||
{
|
||
// Simple collinear case, 1---2---3---4
|
||
// We can leave just two endpoints
|
||
return;
|
||
}
|
||
if(d2 <= 0)
|
||
d2 = CalcSqDistance(x2, y2, x1, y1);
|
||
else if(d2 >= 1)
|
||
d2 = CalcSqDistance(x2, y2, x4, y4);
|
||
else
|
||
d2 = CalcSqDistance(x2, y2, x1 + d2*dx, y1 + d2*dy);
|
||
|
||
if(d3 <= 0)
|
||
d3 = CalcSqDistance(x3, y3, x1, y1);
|
||
else if(d3 >= 1)
|
||
d3 = CalcSqDistance(x3, y3, x4, y4);
|
||
else
|
||
d3 = CalcSqDistance(x3, y3, x1 + d3*dx, y1 + d3*dy);
|
||
}
|
||
if(d2 > d3)
|
||
{
|
||
if(d2 < m_distance_tolerance_square)
|
||
{
|
||
|
||
px.append(x2);
|
||
py.append(y2);
|
||
//m_points.add(point_d(x2, y2));
|
||
return;
|
||
}
|
||
}
|
||
else
|
||
{
|
||
if(d3 < m_distance_tolerance_square)
|
||
{
|
||
|
||
px.append(x3);
|
||
py.append(y3);
|
||
//m_points.add(point_d(x3, y3));
|
||
return;
|
||
}
|
||
}
|
||
break;
|
||
case 1:
|
||
// p1,p2,p4 are collinear, p3 is significant
|
||
//----------------------
|
||
if(d3 * d3 <= m_distance_tolerance_square * (dx*dx + dy*dy))
|
||
{
|
||
if(m_angle_tolerance < curve_angle_tolerance_epsilon)
|
||
{
|
||
|
||
px.append(x23);
|
||
py.append(y23);
|
||
//m_points.add(point_d(x23, y23));
|
||
return;
|
||
}
|
||
|
||
// Angle Condition
|
||
//----------------------
|
||
da1 = fabs(atan2(y4 - y3, x4 - x3) - atan2(y3 - y2, x3 - x2));
|
||
if(da1 >= M_PI)
|
||
da1 = 2*M_PI - da1;
|
||
|
||
if(da1 < m_angle_tolerance)
|
||
{
|
||
|
||
px.append(x2);
|
||
py.append(y2);
|
||
|
||
px.append(x3);
|
||
py.append(y3);
|
||
//m_points.add(point_d(x2, y2));
|
||
//m_points.add(point_d(x3, y3));
|
||
return;
|
||
}
|
||
|
||
if(m_cusp_limit != 0.0)
|
||
{
|
||
if(da1 > m_cusp_limit)
|
||
{
|
||
|
||
px.append(x3);
|
||
py.append(y3);
|
||
//m_points.add(point_d(x3, y3));
|
||
return;
|
||
}
|
||
}
|
||
}
|
||
break;
|
||
|
||
case 2:
|
||
// p1,p3,p4 are collinear, p2 is significant
|
||
//----------------------
|
||
if(d2 * d2 <= m_distance_tolerance_square * (dx*dx + dy*dy))
|
||
{
|
||
if(m_angle_tolerance < curve_angle_tolerance_epsilon)
|
||
{
|
||
|
||
px.append(x23);
|
||
py.append(y23);
|
||
//m_points.add(point_d(x23, y23));
|
||
return;
|
||
}
|
||
|
||
// Angle Condition
|
||
//----------------------
|
||
da1 = fabs(atan2(y3 - y2, x3 - x2) - atan2(y2 - y1, x2 - x1));
|
||
if(da1 >= M_PI) da1 = 2*M_PI - da1;
|
||
|
||
if(da1 < m_angle_tolerance)
|
||
{
|
||
|
||
px.append(x2);
|
||
py.append(y2);
|
||
|
||
px.append(x3);
|
||
py.append(y3);
|
||
//m_points.add(point_d(x2, y2));
|
||
//m_points.add(point_d(x3, y3));
|
||
return;
|
||
}
|
||
|
||
if(m_cusp_limit != 0.0)
|
||
{
|
||
if(da1 > m_cusp_limit)
|
||
{
|
||
px.append(x2);
|
||
py.append(y2);
|
||
|
||
//m_points.add(point_d(x2, 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);
|
||
//m_points.add(point_d(x23, y23));
|
||
return;
|
||
}
|
||
|
||
// Angle & Cusp Condition
|
||
//----------------------
|
||
k = atan2(y3 - y2, x3 - x2);
|
||
da1 = fabs(k - atan2(y2 - y1, x2 - x1));
|
||
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);
|
||
//m_points.add(point_d(x23, y23));
|
||
return;
|
||
}
|
||
|
||
if(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;
|
||
}
|
||
|
||
// 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);
|
||
}
|
||
|
||
qreal VSpline::CalcSqDistance (qreal x1, qreal y1, qreal x2, qreal y2){
|
||
qreal dx = x2 - x1;
|
||
qreal dy = y2 - y1;
|
||
return dx * dx + dy * dy;
|
||
}
|
||
|
||
QPainterPath VSpline::GetPath() const{
|
||
QPainterPath splinePath;
|
||
QVector<QPointF> points = GetPoints ();
|
||
splinePath.moveTo(points[0]);
|
||
for (qint32 i = 1; i < points.count(); ++i){
|
||
splinePath.lineTo(points[i]);
|
||
}
|
||
return splinePath;
|
||
}
|
||
|
||
qint32 VSpline::referens() const{
|
||
return _referens;
|
||
}
|
||
|
||
void VSpline::incrementReferens(){
|
||
++_referens;
|
||
}
|
||
|
||
void VSpline::decrementReferens(){
|
||
if(_referens > 0){
|
||
--_referens;
|
||
}
|
||
}
|
||
|
||
/* Cubic equation solution. Real coefficients case.
|
||
|
||
int Cubic(double *x,double a,double b,double c);
|
||
Parameters:
|
||
x - solution array (size 3). On 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.
|
||
a, b, c - coefficients, as described
|
||
Returns: 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(qreal *x, qreal a, qreal b, qreal c){
|
||
qreal q,r,r2,q3;
|
||
|
||
q = (a*a - 3.*b)/9.;
|
||
r = (a*(2.*a*a - 9.*b) + 27.*c)/54.;
|
||
r2 = r*r;
|
||
q3 = pow(q,3);
|
||
if(r2<q3) {
|
||
qreal t = acos(r/sqrt(q3));
|
||
a/=3.;
|
||
q = -2.*sqrt(q);
|
||
x[0] = q*cos(t/3.)-a;
|
||
x[1] = q*cos((t + M_2PI)/3.) - a;
|
||
x[2] = q*cos((t - M_2PI)/3.) - a;
|
||
return(3);
|
||
} else {
|
||
qreal aa,bb;
|
||
if(r<=0.){
|
||
r=-r;
|
||
}
|
||
aa = -pow(r + sqrt(r2-q3),1./3.);
|
||
if(aa!=0.){
|
||
bb=q/aa;
|
||
} else {
|
||
bb=0.;
|
||
}
|
||
a/=3.;
|
||
q = aa+bb;
|
||
r = aa-bb;
|
||
x[0] = q-a;
|
||
x[1] = (-0.5)*q-a;
|
||
x[2] = (sqrt(3.)*0.5)*fabs(r);
|
||
if(x[2]==0.){
|
||
return(2);
|
||
}
|
||
return(1);
|
||
}
|
||
}
|
||
|
||
//qreal VSpline::calc_t (qreal curve_coord1, qreal curve_coord2, qreal curve_coord3,
|
||
// qreal curve_coord4, qreal point_coord) const{
|
||
// qreal P1, P2, P3, P4, Bt;
|
||
// qreal a, b, c, d, ret_t;
|
||
|
||
// qreal *t = static_cast<qreal *>(malloc(3*sizeof(qreal)));
|
||
// P1 = curve_coord1;
|
||
// P2 = curve_coord2;
|
||
// P3 = curve_coord3;
|
||
// P4 = curve_coord4;
|
||
// Bt = point_coord;
|
||
|
||
// a = -P1 + 3*P2 - 3*P3 + P4;
|
||
// b = 3*P1 - 6*P2 + 3*P3;
|
||
// c = -3*P1 + 3*P2;
|
||
// d = -Bt + P1;
|
||
|
||
// if(Cubic(t, b/a, c/a, d/a) == 3){
|
||
// ret_t = t[2];
|
||
// } else {
|
||
// ret_t = t[0];
|
||
// }
|
||
// /*
|
||
// * Повертається три значення, але експереминтально знайдено що шукане
|
||
// * значення знаходиться в третьому.
|
||
// */
|
||
|
||
// free(t);
|
||
// if(ret_t<0 || ret_t>1){
|
||
// qDebug()<<"Неправильне значення параметра. фунція calc_t";
|
||
// throw"Неправильне значення параметра. фунція calc_t";
|
||
// }
|
||
// return ret_t;
|
||
//}
|
||
/*
|
||
* Функція знаходить підходяще значення параметна t якому відповідає точка на сплайні.
|
||
*/
|
||
//qreal VSpline::param_t (QPointF pBt)const{
|
||
// qreal t_x, t_y;
|
||
// t_x = calc_t (GetPointP1().x(), p2.x(), p3.x(), GetPointP4().x(), pBt.x());
|
||
// t_y = calc_t (GetPointP1().y(), p2.y(), p3.y(), GetPointP4().y(), pBt.y());
|
||
// /*
|
||
// * Порівнюємо значення по х і по у і визначаємо найбільше. Це значення і
|
||
// * буде шуканим.
|
||
// */
|
||
// if(t_x>t_y)
|
||
// return t_x;
|
||
// else
|
||
// return t_y;
|
||
//}
|
||
|
||
//void VSpline::Mirror(const QPointF Pmirror){
|
||
// QPointF P1 = p1;
|
||
// P1 = QPointF(P1.x() - Pmirror.x(), P1.y() - Pmirror.y());
|
||
// P1 = QPointF(P1.x() * -1.0, P1.y() * 1.0);
|
||
// P1 = QPointF(P1.x() + Pmirror.x(), P1.y() + Pmirror.y());
|
||
// QPointF P2 = p2;
|
||
// P2 = QPointF(P2.x() - Pmirror.x(), P2.y() - Pmirror.y());
|
||
// P2 = QPointF(P2.x() * -1.0, P2.y() * 1.0);
|
||
// P2 = QPointF(P2.x() + Pmirror.x(), P2.y() + Pmirror.y());
|
||
// QPointF P3 = p3;
|
||
// P3 = QPointF(P3.x() - Pmirror.x(), P3.y() - Pmirror.y());
|
||
// P3 = QPointF(P3.x() * -1.0, P3.y() * 1.0);
|
||
// P3 = QPointF(P3.x() + Pmirror.x(), P3.y() + Pmirror.y());
|
||
// QPointF P4 = p4;
|
||
// P4 = QPointF(P4.x() - Pmirror.x(), P4.y() - Pmirror.y());
|
||
// P4 = QPointF(P4.x() * -1.0, P4.y() * 1.0);
|
||
// P4 = QPointF(P4.x() + Pmirror.x(), P4.y() + Pmirror.y());
|
||
// this->ModifiSpl(P1, P2, P3, P4);
|
||
//}
|
||
|
||
Draw::Mode VSpline::getMode() const{
|
||
return mode;
|
||
}
|
||
|
||
void VSpline::setMode(const Draw::Mode &value){
|
||
mode = value;
|
||
}
|
||
|
||
QVector<QPointF> VSpline::SplinePoints(QPointF p1, 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);
|
||
}
|
||
|
||
qint64 VSpline::getIdObject() const{
|
||
return idObject;
|
||
}
|
||
|
||
void VSpline::setIdObject(const qint64 &value){
|
||
idObject = value;
|
||
}
|
||
|
||
VSpline &VSpline::operator =(const VSpline &spline){
|
||
this->p1 = spline.GetP1 ();
|
||
this->p2 = spline.GetP2 ();
|
||
this->p3 = spline.GetP3 ();
|
||
this->p4 = spline.GetP4 ();
|
||
this->angle1 = spline.GetAngle1 ();
|
||
this->angle2 = spline.GetAngle2 ();
|
||
this->kAsm1 = spline.GetKasm1();
|
||
this->kAsm2 = spline.GetKasm2();
|
||
this->kCurve = spline.GetKcurve();
|
||
this->points = spline.GetDataPoints();
|
||
this->_referens = 0;
|
||
this->mode = spline.getMode();
|
||
this->idObject = spline.getIdObject();
|
||
return *this;
|
||
}
|