QwtSplineC2 - Base class for spline interpolations providing a second order parametric continuity ( C2 ) between adjoining curves.
NAME SYNOPSIS Public Types Public Member Functions Detailed Description Member Enumeration Documentation enum QwtSplineC2::BoundaryConditionC2 Constructor & Destructor Documentation QwtSplineC2::QwtSplineC2 () QwtSplineC2::˜QwtSplineC2 () [virtual] Member Function Documentation QVector< QLineF > QwtSplineC2::bezierControlLines (const QPolygonF &points) const [override], [virtual] virtual QVector< double > QwtSplineC2::curvatures (const QPolygonF &points) const [pure virtual] QPolygonF QwtSplineC2::equidistantPolygon (const QPolygonF & points, doubledistance, bool withNodes) const [override], [virtual] QPainterPath QwtSplineC2::painterPath (const QPolygonF & points) const[override], [virtual] QVector< QwtSplinePolynomial > QwtSplineC2::polynomials (const QPolygonF &points) const [override], [virtual] QVector< double > QwtSplineC2::slopes (const QPolygonF & points) const[override], [virtual] AuthorNAME
QwtSplineC2 − Base class for spline interpolations providing a second order parametric continuity ( C2 ) between adjoining curves.
SYNOPSIS
#include <qwt_spline.h>
Inherits QwtSplineC1.
Inherited by QwtSplineCubic.
Public Types
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.
Public Member Functions
QwtSplineC2
()
Constructor.
virtual ˜QwtSplineC2 ()
Destructor.
virtual QPainterPath painterPath (const QPolygonF
&) const override
Interpolate a curve with Bezier curves.
virtual QVector< QLineF >
bezierControlLines (const QPolygonF &) const
override
Interpolate a curve with Bezier curves.
virtual QPolygonF equidistantPolygon (const QPolygonF
&, double distance, bool withNodes) const override
Find an interpolated polygon with
equidistant"points.
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 =0
Find the second derivative at the control 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.
virtual uint locality () const
Detailed Description
Base class for spline interpolations providing a second order parametric continuity ( C2 ) between adjoining curves.
All interpolations with C2 continuity are based on rules for finding the 2. derivate at some control points.
In case of non parametric splines those points are the curve points, while for parametric splines the calculation is done twice using a parameter value t.
See also
QwtSplineParametrization
Definition at line 267 of file qwt_spline.h.
Member Enumeration Documentation
enum QwtSplineC2::BoundaryConditionC2
Boundary condition that requires C2 continuity
See also
QwtSpline::boundaryCondition, QwtSpline::BoundaryCondition
Enumerator
CubicRunout
The second derivate at the endpoint is related to the second derivatives at the 2 neighbours: cv[0] := 2.0 * cv[1] - cv[2].
Note
boundaryValue() is ignored
NotAKnot
The 3rd derivate at the endpoint matches the 3rd derivate at its neighbours. Or in other words: the first/last curve segment extents the polynomial of its neighboured polynomial
Note
boundaryValue() is ignored
Definition at line 275 of file qwt_spline.h.
Constructor & Destructor Documentation
QwtSplineC2::QwtSplineC2 ()
Constructor. The default setting is a non closing spline with no parametrization ( QwtSplineParametrization::ParameterX ).
See also
QwtSpline::setParametrization(), QwtSpline::setBoundaryType()
Definition at line 1228 of file qwt_spline.cpp.
QwtSplineC2::˜QwtSplineC2 () [virtual]
Destructor.
Definition at line 1233 of file qwt_spline.cpp.
Member Function Documentation
QVector< QLineF > QwtSplineC2::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(), but is intended to be replaced by a more efficient implementation that builds the polynomials by the curvatures some day.
Reimplemented from QwtSplineC1.
Reimplemented in QwtSplineCubic.
Definition at line 1270 of file qwt_spline.cpp.
virtual QVector< double > QwtSplineC2::curvatures (const QPolygonF &points) const [pure 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
Implemented in QwtSplineCubic.
QPolygonF QwtSplineC2::equidistantPolygon (const QPolygonF & points, doubledistance, bool withNodes) const [override], [virtual]
Find an interpolated polygon with "equidistant" points. The implementation is optimzed for non parametric curves ( QwtSplineParametrization::ParameterX ) and falls back to QwtSpline::equidistantPolygon() otherwise.
Parameters
points Control nodes of
the spline
distance Distance between 2 points according to the
parametrization
withNodes When true, also add the control nodes ( even
if not being equidistant )
Returns
Interpolating polygon
See also
QwtSpline::equidistantPolygon()
Reimplemented from QwtSplineC1.
Definition at line 1295 of file qwt_spline.cpp.
QPainterPath QwtSplineC2::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(), but is intended to be replaced by a one pass calculation some day.
Reimplemented from QwtSplineC1.
Reimplemented in QwtSplineCubic.
Definition at line 1249 of file qwt_spline.cpp.
QVector< QwtSplinePolynomial > QwtSplineC2::polynomials (const QPolygonF &points) const [override], [virtual]
Calculate the interpolating polynomials for a non parametric spline. C2 spline interpolations are based on finding values for the second derivates of f at the control points. The interpolating polynomials can be calculated from the the second derivates using QwtSplinePolynomial::fromCurvatures.
The default implementation is a 2 pass calculation. In derived classes it might be overloaded by a one pass implementation.
Parameters
points Control points
Returns
Interpolating polynomials
Note
The x coordinates need to be increasing or decreasing
Reimplemented from QwtSplineC1.
Reimplemented in QwtSplineCubic.
Definition at line 1381 of file qwt_spline.cpp.
QVector< double > QwtSplineC2::slopes (const QPolygonF & points) const[override], [virtual]
Find the first derivative at the control points. An implementation calculating the 2nd derivatives and then building the slopes in a 2nd loop. QwtSplineCubic overloads it with a more performant implementation doing it in one loop.
Parameters
points Control nodes of the spline
Returns
Vector with the values of the 1nd derivate at the control points
See also
curvatures()
Note
The x coordinates need to be increasing or decreasing
Implements QwtSplineC1.
Reimplemented in QwtSplineCubic.
Definition at line 1339 of file qwt_spline.cpp.
Author
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