QwtSplineCubic(3)

📦
version 6.3.0 · 2 versions
, in alpine 3.24

🌸 NAME 🌸

okay so bestie, this is the QwtSplineCubic(3) page from the Library Functions Manual, and it is literally all about 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.

🦋 Public Member Functions inherited from QwtSplineC2 🦋

  • QwtSplineC2 () — Constructor.
  • virtual ~QwtSplineC2 () — Destructor.
  • virtual QPolygonF equidistantPolygon (const QPolygonF &, double distance, bool withNodes) const override — Find an interpolated polygon with equidistant"points.

🦋 Public Member Functions inherited from QwtSplineC1 🦋

  • QwtSplineC1 () — Constructor.
  • virtual ~QwtSplineC1 () — Destructor.
  • virtual double slopeAtBeginning (const QPolygonF &, double slopeNext) const
  • virtual double slopeAtEnd (const QPolygonF &, double slopeBefore) const

🦋 Public Member Functions inherited from QwtSplineG1 🦋

  • QwtSplineG1 () — Constructor.
  • virtual ~QwtSplineG1 () — Destructor.

🦋 Public Member Functions inherited from QwtSplineInterpolating 🦋

  • QwtSplineInterpolating () — Constructor.
  • virtual ~QwtSplineInterpolating () — Destructor.
  • virtual QPolygonF polygon (const QPolygonF &, double tolerance) const override — Interpolate a curve by a polygon.

🦋 Public Member Functions inherited from QwtSpline 🦋

  • QwtSpline () — Constructor.
  • virtual ~QwtSpline () — Destructor.
  • void setParametrization (int type)
  • void setParametrization (QwtSplineParametrization *)
  • const QwtSplineParametrization * parametrization () const
  • void setBoundaryType (BoundaryType)
  • BoundaryType boundaryType () const
  • void setBoundaryValue (BoundaryPosition, double value) — Define the boundary value.
  • double boundaryValue (BoundaryPosition) const
  • void setBoundaryCondition (BoundaryPosition, int condition) — Define the condition for an endpoint of the spline.
  • int boundaryCondition (BoundaryPosition) const
  • void setBoundaryConditions (int condition, double valueBegin=0.0, double valueEnd=0.0) — Define the condition at the endpoints of a spline.

🌈 Additional Inherited Members 🌈

🍓 Public Types inherited from QwtSplineC2 🍓

enum BoundaryConditionC2 { CubicRunout = LinearRunout + 1, NotAKnot }

🍓 Public Types inherited from QwtSpline 🍓

enum BoundaryType { ConditionalBoundaries, PeriodicPolygon, ClosedPolygon }
enum BoundaryPosition { AtBeginning, AtEnd }
enum BoundaryCondition { Clamped1, Clamped2, Clamped3, LinearRunout }

Boundary condition.

💫 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.

🎀 Constructor & Destructor Documentation 🎀

🧚 QwtSplineCubic::QwtSplineCubic ()

Constructor The default setting is a non closing natural spline with no parametrization.

Definition at line 966 of file qwt_spline_cubic.cpp.

🧚 QwtSplineCubic::~QwtSplineCubic () [virtual]

Destructor.

Definition at line 979 of file qwt_spline_cubic.cpp.

👑 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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okay that is the whole vibe, bestie: source/version is Qwt User's Guide, the page is QwtSplineCubic(3), and the footer date is not printed on this page, so I am not inventing one — periodt 💜✨

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