QwtSplineCubic(3)              Qwt User's Guide              QwtSplineCubic(3)

NAME
       QwtSplineCubic - A cubic spline.


SYNOPSIS
       #include <qwt_spline_cubic.h>

       Inherits QwtSplineC2.

   Public Member Functions
       QwtSplineCubic ()
           Constructor The default setting is a non closing natural spline
           with no parametrization.
       virtual ~QwtSplineCubic ()
           Destructor.
       virtual uint locality () const override
       virtual QPainterPath painterPath (const QPolygonF &) const override
           Interpolate a curve with Bezier curves.
       virtual QVector< QLineF > bezierControlLines (const QPolygonF &points)
           const override
           Interpolate a curve with Bezier curves.
       virtual QVector< QwtSplinePolynomial > polynomials (const QPolygonF &)
           const override
           Calculate the interpolating polynomials for a non parametric
           spline.
       virtual QVector< double > slopes (const QPolygonF &) const override
           Find the first derivative at the control points.
       virtual QVector< double > curvatures (const QPolygonF &) const override
           Find the second derivative at the control points.

   Additional Inherited Members

Detailed Description
       A cubic spline.

       A cubic spline is a spline with C2 continuity at all control points. It
       is a non local spline, what means that all polynomials are changing
       when one control point has changed.

       The implementation is based on the fact, that the continuity condition
       means an equation with 3 unknowns for 3 adjacent points. The equation
       system can be resolved by defining start/end conditions, that allow
       substituting of one of the unknowns for the start/end equations.

       Resolving the equation system is a 2 pass algorithm, requiring more CPU
       costs than all other implemented type of splines.

       Definition at line 33 of file qwt_spline_cubic.h.

Member Function Documentation
   QVector< QLineF > QwtSplineCubic::bezierControlLines (const QPolygonF &
       points) const [override],  [virtual]
       Interpolate a curve with Bezier curves. Interpolates a polygon
       piecewise with cubic Bezier curves and returns the 2 control points of
       each curve as QLineF.

       Parameters
           points Control points

       Returns
           Control points of the interpolating Bezier curves

       Note
           The implementation simply calls QwtSplineC1::bezierControlLines()

       Reimplemented from QwtSplineC2.

       Definition at line 1149 of file qwt_spline_cubic.cpp.

   QVector< double > QwtSplineCubic::curvatures (const QPolygonF & points)
       const [override],  [virtual]
       Find the second derivative at the control points.

       Parameters
           points Control nodes of the spline

       Returns
           Vector with the values of the 2nd derivate at the control points

       See also
           slopes()

       Note
           The x coordinates need to be increasing or decreasing

       Implements QwtSplineC2.

       Definition at line 1078 of file qwt_spline_cubic.cpp.

   uint QwtSplineCubic::locality () const [override],  [virtual]
       A cubic spline is non local, where changing one point has em effect on
       all polynomials.

       Returns
           0

       Reimplemented from QwtSpline.

       Definition at line 989 of file qwt_spline_cubic.cpp.

   QPainterPath QwtSplineCubic::painterPath (const QPolygonF & points) const
       [override],  [virtual]
       Interpolate a curve with Bezier curves. Interpolates a polygon
       piecewise with cubic Bezier curves and returns them as QPainterPath.

       Parameters
           points Control points

       Returns
           Painter path, that can be rendered by QPainter

       Note
           The implementation simply calls QwtSplineC1::painterPath()

       Reimplemented from QwtSplineC2.

       Definition at line 1130 of file qwt_spline_cubic.cpp.

   QVector< QwtSplinePolynomial > QwtSplineCubic::polynomials (const QPolygonF
       & points) const [override],  [virtual]
       Calculate the interpolating polynomials for a non parametric spline.

       Parameters
           points Control points

       Returns
           Interpolating polynomials

       Note
           The x coordinates need to be increasing or decreasing

           The implementation simply calls QwtSplineC2::polynomials(), but is
           intended to be replaced by a one pass calculation some day.

       Reimplemented from QwtSplineC2.

       Definition at line 1167 of file qwt_spline_cubic.cpp.

   QVector< double > QwtSplineCubic::slopes (const QPolygonF & points) const
       [override],  [virtual]
       Find the first derivative at the control points. In opposite to the
       implementation QwtSplineC2::slopes the first derivates are calculated
       directly, without calculating the second derivates first.

       Parameters
           points Control nodes of the spline

       Returns
           Vector with the values of the 2nd derivate at the control points

       See also
           curvatures(), QwtSplinePolynomial::fromCurvatures()

       Note
           The x coordinates need to be increasing or decreasing

       Reimplemented from QwtSplineC2.

       Definition at line 1006 of file qwt_spline_cubic.cpp.


Author
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Version 6.2.0                   Sun Jul 18 2021              QwtSplineCubic(3)