.TH "QwtSplineCubic" 3 "Sun Jul 18 2021" "Version 6.2.0" "Qwt User's Guide" \" -*- nroff -*-
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.SH NAME
QwtSplineCubic \- A cubic spline\&.  

.SH SYNOPSIS
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.PP
.PP
\fC#include <qwt_spline_cubic\&.h>\fP
.PP
Inherits \fBQwtSplineC2\fP\&.
.SS "Public Member Functions"

.in +1c
.ti -1c
.RI "\fBQwtSplineCubic\fP ()"
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.RI "Constructor The default setting is a non closing natural spline with no parametrization\&. "
.ti -1c
.RI "virtual \fB~QwtSplineCubic\fP ()"
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.RI "Destructor\&. "
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.RI "virtual uint \fBlocality\fP () const override"
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.ti -1c
.RI "virtual QPainterPath \fBpainterPath\fP (const QPolygonF &) const override"
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.RI "Interpolate a curve with Bezier curves\&. "
.ti -1c
.RI "virtual \fBQVector\fP< QLineF > \fBbezierControlLines\fP (const QPolygonF &points) const override"
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.RI "Interpolate a curve with Bezier curves\&. "
.ti -1c
.RI "virtual \fBQVector\fP< \fBQwtSplinePolynomial\fP > \fBpolynomials\fP (const QPolygonF &) const override"
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.RI "Calculate the interpolating polynomials for a non parametric spline\&. "
.ti -1c
.RI "virtual \fBQVector\fP< double > \fBslopes\fP (const QPolygonF &) const override"
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.RI "Find the first derivative at the control points\&. "
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.RI "virtual \fBQVector\fP< double > \fBcurvatures\fP (const QPolygonF &) const override"
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.RI "Find the second derivative at the control points\&. "
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.SS "Additional Inherited Members"
.SH "Detailed Description"
.PP 
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\&.
.PP
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\&.
.PP
Resolving the equation system is a 2 pass algorithm, requiring more CPU costs than all other implemented type of splines\&.
.PP
Definition at line 33 of file qwt_spline_cubic\&.h\&.
.SH "Member Function Documentation"
.PP 
.SS "\fBQVector\fP< QLineF > QwtSplineCubic::bezierControlLines (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"

.PP
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\&.
.PP
\fBParameters\fP
.RS 4
\fIpoints\fP Control points 
.RE
.PP
\fBReturns\fP
.RS 4
Control points of the interpolating Bezier curves
.RE
.PP
\fBNote\fP
.RS 4
The implementation simply calls \fBQwtSplineC1::bezierControlLines()\fP 
.RE
.PP

.PP
Reimplemented from \fBQwtSplineC2\fP\&.
.PP
Definition at line 1149 of file qwt_spline_cubic\&.cpp\&.
.SS "\fBQVector\fP< double > QwtSplineCubic::curvatures (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"

.PP
Find the second derivative at the control points\&. 
.PP
\fBParameters\fP
.RS 4
\fIpoints\fP Control nodes of the spline 
.RE
.PP
\fBReturns\fP
.RS 4
Vector with the values of the 2nd derivate at the control points
.RE
.PP
\fBSee also\fP
.RS 4
\fBslopes()\fP 
.RE
.PP
\fBNote\fP
.RS 4
The x coordinates need to be increasing or decreasing 
.RE
.PP

.PP
Implements \fBQwtSplineC2\fP\&.
.PP
Definition at line 1078 of file qwt_spline_cubic\&.cpp\&.
.SS "uint QwtSplineCubic::locality () const\fC [override]\fP, \fC [virtual]\fP"
A cubic spline is non local, where changing one point has em effect on all polynomials\&.
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\fBReturns\fP
.RS 4
0 
.RE
.PP

.PP
Reimplemented from \fBQwtSpline\fP\&.
.PP
Definition at line 989 of file qwt_spline_cubic\&.cpp\&.
.SS "QPainterPath QwtSplineCubic::painterPath (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"

.PP
Interpolate a curve with Bezier curves\&. Interpolates a polygon piecewise with cubic Bezier curves and returns them as QPainterPath\&.
.PP
\fBParameters\fP
.RS 4
\fIpoints\fP Control points 
.RE
.PP
\fBReturns\fP
.RS 4
Painter path, that can be rendered by QPainter
.RE
.PP
\fBNote\fP
.RS 4
The implementation simply calls \fBQwtSplineC1::painterPath()\fP 
.RE
.PP

.PP
Reimplemented from \fBQwtSplineC2\fP\&.
.PP
Definition at line 1130 of file qwt_spline_cubic\&.cpp\&.
.SS "\fBQVector\fP< \fBQwtSplinePolynomial\fP > QwtSplineCubic::polynomials (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"

.PP
Calculate the interpolating polynomials for a non parametric spline\&. 
.PP
\fBParameters\fP
.RS 4
\fIpoints\fP Control points 
.RE
.PP
\fBReturns\fP
.RS 4
Interpolating polynomials
.RE
.PP
\fBNote\fP
.RS 4
The x coordinates need to be increasing or decreasing 
.PP
The implementation simply calls \fBQwtSplineC2::polynomials()\fP, but is intended to be replaced by a one pass calculation some day\&. 
.RE
.PP

.PP
Reimplemented from \fBQwtSplineC2\fP\&.
.PP
Definition at line 1167 of file qwt_spline_cubic\&.cpp\&.
.SS "\fBQVector\fP< double > QwtSplineCubic::slopes (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"

.PP
Find the first derivative at the control points\&. In opposite to the implementation \fBQwtSplineC2::slopes\fP the first derivates are calculated directly, without calculating the second derivates first\&.
.PP
\fBParameters\fP
.RS 4
\fIpoints\fP Control nodes of the spline 
.RE
.PP
\fBReturns\fP
.RS 4
Vector with the values of the 2nd derivate at the control points
.RE
.PP
\fBSee also\fP
.RS 4
\fBcurvatures()\fP, \fBQwtSplinePolynomial::fromCurvatures()\fP 
.RE
.PP
\fBNote\fP
.RS 4
The x coordinates need to be increasing or decreasing 
.RE
.PP

.PP
Reimplemented from \fBQwtSplineC2\fP\&.
.PP
Definition at line 1006 of file qwt_spline_cubic\&.cpp\&.

.SH "Author"
.PP 
Generated automatically by Doxygen for Qwt User's Guide from the source code\&.