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589
tests/splinetest/main.cpp
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589
tests/splinetest/main.cpp
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/*****************************************************************************
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* Qwt Examples - Copyright (C) 2002 Uwe Rathmann
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* This file may be used under the terms of the 3-clause BSD License
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*****************************************************************************/
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#include <QwtSplineCubic>
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#include <QwtSplineLocal>
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#include <QwtSplineParametrization>
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#include <QwtSplinePolynomial>
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#include <QwtMath>
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#include <QPolygon>
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#include <QPainterPath>
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#include <QDebug>
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#define DEBUG_ERRORS 1
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static inline bool fuzzyCompare( double a, double b )
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{
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return ( qFuzzyIsNull(a) && qFuzzyIsNull(b) ) || qFuzzyCompare(a, b);
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}
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static QwtSplinePolynomial polynomialAt( int index,
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const QPolygonF& points, const QVector< double >& m )
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{
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return QwtSplinePolynomial::fromSlopes(
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points[index], m[index], points[index + 1], m[index + 1] );
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}
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class CubicSpline : public QwtSplineCubic
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{
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public:
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CubicSpline( const QString& name )
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: d_name( name )
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{
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}
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void setBoundaryConditions( int condition, double valueBegin, double valueEnd )
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{
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const QwtSpline::BoundaryCondition c =
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static_cast< QwtSpline::BoundaryCondition >( condition );
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setBoundaryCondition( QwtSpline::AtBeginning, c );
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setBoundaryValue( QwtSpline::AtEnd, valueBegin );
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setBoundaryCondition( QwtSpline::AtEnd, c );
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setBoundaryValue( QwtSpline::AtEnd, valueEnd );
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}
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QString name() const
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{
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return d_name;
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}
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private:
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const QString d_name;
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};
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class LocalSpline : public QwtSplineLocal
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{
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public:
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LocalSpline( QwtSplineLocal::Type type, const QString& name )
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: QwtSplineLocal( type ),
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d_name( name )
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{
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}
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void setBoundaryConditions( int condition, double valueBegin, double valueEnd )
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{
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const QwtSpline::BoundaryCondition c =
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static_cast< QwtSpline::BoundaryCondition >( condition );
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setBoundaryCondition( QwtSpline::AtBeginning, c );
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setBoundaryValue( QwtSpline::AtEnd, valueBegin );
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setBoundaryCondition( QwtSpline::AtEnd, c );
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setBoundaryValue( QwtSpline::AtEnd, valueEnd );
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}
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QString name() const
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{
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return d_name;
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}
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private:
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const QString d_name;
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};
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class SplineTester
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{
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public:
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enum Type
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{
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Cardinal,
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Akima,
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Cubic
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};
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void testSplineC1( const LocalSpline* spline, const QPolygonF& points ) const;
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void testSplineC2( const CubicSpline* spline, const QPolygonF& points ) const;
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private:
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bool verifyBoundary( const QwtSpline*, QwtSpline::BoundaryPosition,
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const QPolygonF& points, const QVector< double >& m ) const;
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int verifyNodesCV( const QPolygonF& p, const QVector< double >& cv ) const;
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int verifyNodesM( const QPolygonF& p, const QVector< double >& m ) const;
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};
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void SplineTester::testSplineC1( const LocalSpline* spline, const QPolygonF& points ) const
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{
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const QVector< double > m = spline->slopes( points );
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if ( m.size() != points.size() )
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{
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qDebug() << qPrintable( spline->name() ) << "("
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<< points.size() << "):" << "not implemented";
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return;
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}
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const bool okStart = verifyBoundary( spline, QwtSpline::AtBeginning, points, m );
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const bool okEnd = verifyBoundary( spline, QwtSpline::AtEnd, points, m );
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if ( !okStart || !okEnd )
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{
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qDebug() << qPrintable( spline->name() ) << "("
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<< points.size() << "):" << false;
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#if DEBUG_ERRORS > 0
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if ( !okStart )
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qDebug() << " invalid start condition";
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if ( !okEnd )
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qDebug() << " invalid end condition";
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#endif
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}
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}
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void SplineTester::testSplineC2( const CubicSpline* spline, const QPolygonF& points ) const
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{
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const QVector< double > m = spline->slopes( points );
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const QVector< double > cv = spline->curvatures( points );
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if ( m.size() != points.size() )
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{
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qDebug() << qPrintable( spline->name() ) << "("
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<< points.size() << "):" << "not implemented";
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return;
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}
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const bool okStart = verifyBoundary( spline, QwtSpline::AtBeginning, points, m );
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const int numErrorsM = verifyNodesM( points, m );
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const int numErrorsCV = verifyNodesCV( points, cv );
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const bool okEnd = verifyBoundary( spline, QwtSpline::AtEnd, points, m );
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if ( !okStart || numErrorsM > 0 || numErrorsCV > 0 || !okEnd )
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{
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qDebug() << qPrintable( spline->name() ) << "("
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<< points.size() << "):" << false;
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#if DEBUG_ERRORS > 0
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if ( !okStart )
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qDebug() << " invalid start condition";
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if ( numErrorsM > 0 )
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qDebug() << " invalid node conditions ( slope )" << numErrorsM;
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if ( numErrorsCV > 0 )
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qDebug() << " invalid node conditions ( curvature )" << numErrorsCV;
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if ( !okEnd )
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qDebug() << " invalid end condition";
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#endif
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}
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}
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bool SplineTester::verifyBoundary( const QwtSpline* spline, QwtSpline::BoundaryPosition pos,
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const QPolygonF& points, const QVector< double >& m ) const
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{
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const bool isC2 = dynamic_cast< const QwtSplineC2* >( spline );
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const int n = points.size();
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const QwtSplinePolynomial polynomBegin = polynomialAt( 0, points, m );
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const QwtSplinePolynomial polynomEnd = polynomialAt( n - 2, points, m );
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bool ok = false;
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if ( spline->boundaryType() != QwtSpline::ConditionalBoundaries )
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{
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// periodic or closed
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const double dx = points[n - 1].x() - points[n - 2].x();
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ok = fuzzyCompare( polynomEnd.slopeAt( dx ),
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polynomBegin.slopeAt( 0.0 ) );
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if ( ok && isC2 )
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{
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ok = fuzzyCompare( polynomEnd.curvatureAt( dx ),
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polynomBegin.curvatureAt( 0.0 ) );
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}
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return ok;
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}
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switch( spline->boundaryCondition( pos ) )
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{
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case QwtSpline::Clamped1:
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{
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const double mt = ( pos == QwtSpline::AtBeginning ) ? m.first() : m.last();
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ok = fuzzyCompare( mt, spline->boundaryValue( pos ) );
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break;
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}
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case QwtSpline::Clamped2:
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{
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double cv;
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if ( pos == QwtSpline::AtBeginning )
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{
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cv = polynomBegin.curvatureAt( 0.0 );
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}
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else
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{
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const double dx = points[n - 1].x() - points[n - 2].x();
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cv = polynomEnd.curvatureAt( dx );
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}
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ok = fuzzyCompare( cv, spline->boundaryValue( pos ) );
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break;
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}
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case QwtSpline::Clamped3:
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{
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double c3;
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if ( pos == QwtSpline::AtBeginning )
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c3 = polynomBegin.c3;
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else
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c3 = polynomEnd.c3;
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ok = fuzzyCompare( 6.0 * c3, spline->boundaryValue( pos ) );
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break;
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}
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case QwtSpline::LinearRunout:
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{
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const double ratio = spline->boundaryValue( pos );
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if ( pos == QwtSpline::AtBeginning )
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{
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const double s = ( points[1].y() - points[0].y() ) /
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( points[1].x() - points[0].x() );
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ok = fuzzyCompare( m[0], s - ratio * ( s - m[1] ) );
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}
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else
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{
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const double s = ( points[n - 1].y() - points[n - 2].y() ) /
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( points[n - 1].x() - points[n - 2].x() );
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ok = fuzzyCompare( m[n - 1], s - ratio * ( s - m[n - 2] ) );
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}
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break;
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}
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case QwtSplineC2::CubicRunout:
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{
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if ( pos == QwtSpline::AtBeginning )
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{
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const QwtSplinePolynomial polynomBegin2 = polynomialAt( 1, points, m );
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const double cv0 = polynomBegin.curvatureAt( 0.0 );
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const double cv1 = polynomBegin2.curvatureAt( 0.0 );
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const double cv2 = polynomBegin2.curvatureAt( points[2].x() - points[1].x() );
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ok = fuzzyCompare( cv0, 2 * cv1 - cv2 );
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}
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else
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{
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const QwtSplinePolynomial polynomEnd2 = polynomialAt( n - 3, points, m );
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const double cv0 = polynomEnd.curvatureAt( points[n - 1].x() - points[n - 2].x() );
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const double cv1 = polynomEnd.curvatureAt( 0.0 );
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const double cv2 = polynomEnd2.curvatureAt( 0.0 );
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ok = fuzzyCompare( cv0, 2 * cv1 - cv2 );
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}
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break;
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}
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case QwtSplineC2::NotAKnot:
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{
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if ( pos == QwtSpline::AtBeginning )
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{
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const QwtSplinePolynomial polynomBegin2 = polynomialAt( 1, points, m );
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ok = fuzzyCompare( polynomBegin.c3, polynomBegin2.c3 );
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}
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else
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{
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const QwtSplinePolynomial polynomEnd2 = polynomialAt( n - 3, points, m );
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ok = fuzzyCompare( polynomEnd.c3, polynomEnd2.c3 );
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}
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break;
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}
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}
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return ok;
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}
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int SplineTester::verifyNodesCV( const QPolygonF& points, const QVector< double >& cv ) const
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{
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const int n = points.size();
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int numErrors = 0;
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double h1 = points[1].x() - points[0].x();
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double s1 = ( points[1].y() - points[0].y() ) / h1;
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for ( int i = 1; i < n - 2; i++ )
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{
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const double h2 = points[i + 1].x() - points[i].x();
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const double s2 = ( points[i + 1].y() - points[i].y() ) / h2;
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const double v = ( h1 + h2 ) * cv[i] + 0.5 * ( h1 * cv[i - 1] + h2 * cv[i + 1] );
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if ( !fuzzyCompare( v, 3 * ( s2 - s1 ) ) )
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{
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#if DEBUG_ERRORS > 1
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qDebug() << "invalid node condition (cv)" << i
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<< cv[i - 1] << cv[i] << cv[i + 1]
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<< v - 3 * ( s2 - s1 );
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#endif
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numErrors++;
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}
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h1 = h2;
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s1 = s2;
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}
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return numErrors;
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}
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int SplineTester::verifyNodesM( const QPolygonF& points, const QVector< double >& m ) const
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{
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const int n = points.size();
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int numErrors = 0;
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double dx1 = points[1].x() - points[0].x();
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QwtSplinePolynomial polynomial1 = QwtSplinePolynomial::fromSlopes(
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dx1, points[1].y() - points[0].y(), m[0], m[1] );
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for ( int i = 1; i < n - 1; i++ )
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{
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const double dx2 = points[i + 1].x() - points[i].x();
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const double dy2 = points[i + 1].y() - points[i].y();
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const QwtSplinePolynomial polynomial2 =
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QwtSplinePolynomial::fromSlopes( dx2, dy2, m[i], m[i + 1] );
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const double cv1 = polynomial1.curvatureAt( dx1 );
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const double cv2 = polynomial2.curvatureAt( 0.0 );
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if ( !fuzzyCompare( cv1, cv2 ) )
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{
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#if DEBUG_ERRORS > 1
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qDebug() << "invalid node condition (m)" << i <<
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cv1 << cv1 << cv2 - cv1;
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#endif
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numErrors++;
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}
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dx1 = dx2;
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polynomial1 = polynomial2;
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}
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return numErrors;
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}
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static void testSplines( SplineTester::Type splineType, const QPolygonF& points )
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{
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struct Condition
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{
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const char* name;
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int condition;
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double valueBegin;
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double valueEnd;
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} conditions[] =
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{
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{ "Periodic", -1, 0.0, 0.0 },
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{ "Clamped1", QwtSpline::Clamped1, 0.5, 1.0 },
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{ "Clamped2", QwtSpline::Clamped2, 0.4, -0.8 },
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{ "Clamped3", QwtSpline::Clamped3, 0.03, 0.01 },
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{ "Linear Runout", QwtSpline::LinearRunout, 0.3, 0.7 },
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{ "Cubic Runout", QwtSplineC2::CubicRunout, 0.0, 0.0 },
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{ "Not A Knot", QwtSplineC2::NotAKnot, 0.0, 0.0 }
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};
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for ( uint i = 0; i < sizeof( conditions ) / sizeof( conditions[0] ); i++ )
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{
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const Condition& c = conditions[i];
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if ( conditions[i].condition == QwtSplineC2::NotAKnot && points.size() < 4 )
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continue;
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if ( splineType != SplineTester::Cubic )
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{
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LocalSpline* spline;
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if ( splineType == SplineTester::Cardinal )
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{
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const QString name = QString( c.name ) + " Spline Cardinal";
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spline = new LocalSpline( QwtSplineLocal::Cardinal, name );
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}
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else
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{
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const QString name = QString( c.name ) + " Spline Akima";
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spline = new LocalSpline( QwtSplineLocal::Akima, name );
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}
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if ( c.condition < 0 )
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{
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spline->setBoundaryType( QwtSpline::PeriodicPolygon );
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}
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else
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||||
{
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if ( c.condition == QwtSplineC2::NotAKnot
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|| c.condition == QwtSplineC2::CubicRunout )
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||||
{
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// requires C2 continuity
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continue;
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||||
}
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spline->setBoundaryType( QwtSpline::ConditionalBoundaries );
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spline->setBoundaryConditions( c.condition,
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conditions[i].valueBegin, c.valueEnd );
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}
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SplineTester tester;
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tester.testSplineC1( spline, points );
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delete spline;
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||||
}
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||||
else
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||||
{
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||||
const QString name = QString( c.name ) + " Spline Cubic";
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CubicSpline spline( name );
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if ( conditions[i].condition < 0 )
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{
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spline.setBoundaryType( QwtSpline::PeriodicPolygon );
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}
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else
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||||
{
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spline.setBoundaryType( QwtSpline::ConditionalBoundaries );
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spline.setBoundaryConditions( conditions[i].condition,
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conditions[i].valueBegin, conditions[i].valueEnd );
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||||
}
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||||
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SplineTester tester;
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tester.testSplineC2( &spline, points );
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||||
}
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||||
}
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||||
}
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||||
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||||
static void testSplines( const QPolygonF& points )
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||||
{
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testSplines( SplineTester::Cardinal, points );
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testSplines( SplineTester::Akima, points );
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testSplines( SplineTester::Cubic, points );
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}
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||||
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||||
static void testSplines()
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||||
{
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QPolygonF points;
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||||
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// 3 points
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||||
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||||
points << QPointF( 10, 50 ) << QPointF( 60, 30 ) << QPointF( 82, 50 );
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||||
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||||
testSplines( points );
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||||
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||||
// 4 points
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||||
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||||
points.clear();
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||||
points << QPointF( 10, 50 ) << QPointF( 60, 30 )
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||||
<< QPointF( 70, 5 ) << QPointF( 82, 50 );
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||||
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||||
testSplines( points );
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||||
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||||
// 5 points
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||||
points.clear();
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||||
points << QPointF( 10, 50 ) << QPointF( 20, 20 ) << QPointF( 60, 30 )
|
||||
<< QPointF( 70, 5 ) << QPointF( 82, 50 );
|
||||
|
||||
testSplines( points );
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||||
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||||
// 12 points
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||||
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||||
points.clear();
|
||||
points << QPointF( 10, 50 ) << QPointF( 20, 90 ) << QPointF( 25, 60 )
|
||||
<< QPointF( 35, 38 ) << QPointF( 42, 40 ) << QPointF( 55, 60 )
|
||||
<< QPointF( 60, 50 ) << QPointF( 65, 80 ) << QPointF( 73, 30 )
|
||||
<< QPointF( 82, 30 ) << QPointF( 87, 40 ) << QPointF( 95, 50 );
|
||||
|
||||
testSplines( points );
|
||||
|
||||
// many points
|
||||
points.clear();
|
||||
|
||||
const double x1 = 10.0;
|
||||
const double x2 = 1000.0;
|
||||
const double y1 = -10000.0;
|
||||
const double y2 = 10000.0;
|
||||
|
||||
points += QPointF( x1, y1 );
|
||||
|
||||
const int n = 100;
|
||||
const double dx = ( x2 - x1 ) / n;
|
||||
const int mod = y2 - y1;
|
||||
for ( int i = 1; i < n - 1; i++ )
|
||||
{
|
||||
const double r = qwtRand() % mod;
|
||||
points += QPointF( x1 + i * dx, y1 + r );
|
||||
}
|
||||
points += QPointF( x2, y1 );
|
||||
|
||||
testSplines( points );
|
||||
}
|
||||
|
||||
static void testPaths( const char* prompt, const QwtSpline& spline,
|
||||
const QPolygonF& points1, const QPolygonF& points2 )
|
||||
{
|
||||
const QPainterPath path1 = spline.painterPath( points1 );
|
||||
const QPainterPath path2 = spline.painterPath( points2 );
|
||||
|
||||
if ( path1 != path2 )
|
||||
{
|
||||
QString txt( "Parametric Spline" );
|
||||
if ( spline.boundaryType() != QwtSpline::ConditionalBoundaries )
|
||||
txt += "(closed)";
|
||||
txt += ": ";
|
||||
txt += prompt;
|
||||
txt += " => failed.";
|
||||
|
||||
qDebug() << qPrintable( txt );
|
||||
}
|
||||
}
|
||||
|
||||
static void testDuplicates()
|
||||
{
|
||||
QwtSplineLocal spline( QwtSplineLocal::Cardinal );
|
||||
spline.setParametrization( QwtSplineParametrization::ParameterChordal );
|
||||
|
||||
QPolygonF points;
|
||||
points += QPointF( 1, 6 );
|
||||
points += QPointF( 2, 7 );
|
||||
points += QPointF( 3, 5);
|
||||
points += QPointF( 2, 4 );
|
||||
points += QPointF( 0, 3 );
|
||||
|
||||
// inserting duplicates
|
||||
|
||||
QPolygonF points1;
|
||||
for ( int i = 0; i < points.size(); i++ )
|
||||
{
|
||||
points1 += points[i];
|
||||
points1 += points[i];
|
||||
}
|
||||
|
||||
testPaths( "Duplicates", spline, points, points1 );
|
||||
|
||||
spline.setBoundaryType( QwtSpline::ClosedPolygon );
|
||||
|
||||
testPaths( "Duplicates", spline, points, points1 );
|
||||
|
||||
QPolygonF points2 = points;
|
||||
points2.append( points[0] );
|
||||
testPaths( "First point also at End", spline, points, points2 );
|
||||
|
||||
QPolygonF points3 = points;
|
||||
points3.prepend( points.first() );
|
||||
testPaths( "First point twice", spline, points, points3 );
|
||||
|
||||
QPolygonF points4 = points;
|
||||
points4.append( points.last() );
|
||||
testPaths( "Last point twice", spline, points, points4 );
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
testSplines();
|
||||
testDuplicates();
|
||||
}
|
||||
18
tests/splinetest/splinetest.pro
Normal file
18
tests/splinetest/splinetest.pro
Normal file
@@ -0,0 +1,18 @@
|
||||
################################################################
|
||||
# Qwt Widget Library
|
||||
# Copyright (C) 1997 Josef Wilgen
|
||||
# Copyright (C) 2002 Uwe Rathmann
|
||||
#
|
||||
# This library is free software; you can redistribute it and/or
|
||||
# modify it under the terms of the Qwt License, Version 1.0
|
||||
################################################################
|
||||
|
||||
include( $${PWD}/../tests.pri )
|
||||
|
||||
CONFIG -= gui
|
||||
|
||||
TARGET = splinetest
|
||||
|
||||
SOURCES = \
|
||||
main.cpp
|
||||
|
||||
Reference in New Issue
Block a user