.TH "QwtSplineC1" 3 "Sun Jul 18 2021" "Version 6.2.0" "Qwt User's Guide" \" -*- nroff -*-
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.SH NAME
QwtSplineC1 \- Base class for spline interpolations providing a first order parametric continuity ( C1 ) between adjoining curves\&.  

.SH SYNOPSIS
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.PP
.PP
\fC#include <qwt_spline\&.h>\fP
.PP
Inherits \fBQwtSplineG1\fP\&.
.PP
Inherited by \fBQwtSplineC2\fP, and \fBQwtSplineLocal\fP\&.
.SS "Public Member Functions"

.in +1c
.ti -1c
.RI "\fBQwtSplineC1\fP ()"
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.RI "Constructor\&. "
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.RI "virtual \fB~QwtSplineC1\fP ()"
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.RI "Destructor\&. "
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.RI "virtual QPainterPath \fBpainterPath\fP (const QPolygonF &) const override"
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.RI "Calculate an interpolated painter path\&. "
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.RI "virtual \fBQVector\fP< QLineF > \fBbezierControlLines\fP (const QPolygonF &) const override"
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.RI "Interpolate a curve with Bezier curves\&. "
.ti -1c
.RI "virtual QPolygonF \fBequidistantPolygon\fP (const QPolygonF &, double distance, bool withNodes) const override"
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.RI "Find an interpolated polygon with 'equidistant' points\&. "
.ti -1c
.RI "virtual \fBQVector\fP< \fBQwtSplinePolynomial\fP > \fBpolynomials\fP (const QPolygonF &) const"
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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 =0"
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.RI "Find the first derivative at the control points\&. "
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.RI "virtual double \fBslopeAtBeginning\fP (const QPolygonF &, double slopeNext) const"
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.RI "virtual double \fBslopeAtEnd\fP (const QPolygonF &, double slopeBefore) const"
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.SS "Additional Inherited Members"
.SH "Detailed Description"
.PP 
Base class for spline interpolations providing a first order parametric continuity ( C1 ) between adjoining curves\&. 

All interpolations with C1 continuity are based on rules for finding the 1\&. derivate at some control points\&.
.PP
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\&.
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\fBSee also\fP
.RS 4
\fBQwtSplineParametrization\fP 
.RE
.PP

.PP
Definition at line 235 of file qwt_spline\&.h\&.
.SH "Constructor & Destructor Documentation"
.PP 
.SS "QwtSplineC1::QwtSplineC1 ()"

.PP
Constructor\&. The default setting is a non closing spline with no parametrization ( \fBQwtSplineParametrization::ParameterX\fP )\&.
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\fBSee also\fP
.RS 4
\fBQwtSpline::setParametrization()\fP, \fBQwtSpline::setBoundaryType()\fP 
.RE
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.PP
Definition at line 962 of file qwt_spline\&.cpp\&.
.SH "Member Function Documentation"
.PP 
.SS "\fBQVector\fP< QLineF > QwtSplineC1::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\&.
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\fBParameters\fP
.RS 4
\fIpoints\fP Control points 
.RE
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\fBReturns\fP
.RS 4
Control points of the interpolating Bezier curves 
.RE
.PP

.PP
Implements \fBQwtSplineInterpolating\fP\&.
.PP
Reimplemented in \fBQwtSplineCubic\fP, \fBQwtSplineLocal\fP, and \fBQwtSplineC2\fP\&.
.PP
Definition at line 1101 of file qwt_spline\&.cpp\&.
.SS "QPolygonF QwtSplineC1::equidistantPolygon (const QPolygonF & points, double distance, bool withNodes) const\fC [override]\fP, \fC [virtual]\fP"

.PP
Find an interpolated polygon with 'equidistant' points\&. The implementation is optimzed for non parametric curves ( \fBQwtSplineParametrization::ParameterX\fP ) and falls back to QwtSpline::equidistantPolygon() otherwise\&.
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\fBParameters\fP
.RS 4
\fIpoints\fP Control nodes of the spline 
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\fIdistance\fP Distance between 2 points according to the parametrization 
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\fIwithNodes\fP When true, also add the control nodes ( even if not being equidistant )
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\fBReturns\fP
.RS 4
Interpolating polygon
.RE
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\fBSee also\fP
.RS 4
QwtSpline::equidistantPolygon() 
.RE
.PP

.PP
Reimplemented from \fBQwtSplineInterpolating\fP\&.
.PP
Reimplemented in \fBQwtSplineC2\fP\&.
.PP
Definition at line 1167 of file qwt_spline\&.cpp\&.
.SS "QPainterPath QwtSplineC1::painterPath (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"

.PP
Calculate an interpolated painter path\&. Interpolates a polygon piecewise into cubic Bezier curves and returns them as QPainterPath\&.
.PP
The implementation calculates the slopes at the control points and converts them into painter path elements in an additional loop\&.
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\fBParameters\fP
.RS 4
\fIpoints\fP Control points 
.RE
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\fBReturns\fP
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QPainterPath Painter path, that can be rendered by QPainter
.RE
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\fBNote\fP
.RS 4
Derived spline classes might overload \fBpainterPath()\fP to avoid the extra loops for converting results into a QPainterPath 
.RE
.PP

.PP
Reimplemented from \fBQwtSplineInterpolating\fP\&.
.PP
Reimplemented in \fBQwtSplineLocal\fP, \fBQwtSplineCubic\fP, and \fBQwtSplineC2\fP\&.
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Definition at line 1043 of file qwt_spline\&.cpp\&.
.SS "\fBQVector\fP< \fBQwtSplinePolynomial\fP > QwtSplineC1::polynomials (const QPolygonF & points) const\fC [virtual]\fP"

.PP
Calculate the interpolating polynomials for a non parametric spline\&. C1 spline interpolations are based on finding values for the first derivates at the control points\&. The interpolating polynomials can be calculated from the the first derivates using \fBQwtSplinePolynomial::fromSlopes()\fP\&.
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The default implementation is a two pass calculation\&. In derived classes it might be overloaded by a one pass implementation\&.
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\fBParameters\fP
.RS 4
\fIpoints\fP Control points 
.RE
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\fBReturns\fP
.RS 4
Interpolating polynomials
.RE
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\fBNote\fP
.RS 4
The x coordinates need to be increasing or decreasing 
.RE
.PP

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Reimplemented in \fBQwtSplineLocal\fP, \fBQwtSplineCubic\fP, and \fBQwtSplineC2\fP\&.
.PP
Definition at line 1201 of file qwt_spline\&.cpp\&.
.SS "double QwtSplineC1::slopeAtBeginning (const QPolygonF & points, double slopeNext) const\fC [virtual]\fP"

.PP
\fBParameters\fP
.RS 4
\fIpoints\fP Control points 
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\fIslopeNext\fP Value of the first derivative at the second point
.RE
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\fBReturns\fP
.RS 4
value of the first derivative at the first point 
.RE
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\fBSee also\fP
.RS 4
\fBslopeAtEnd()\fP, \fBQwtSpline::boundaryCondition()\fP, \fBQwtSpline::boundaryValue()\fP 
.RE
.PP

.PP
Definition at line 979 of file qwt_spline\&.cpp\&.
.SS "double QwtSplineC1::slopeAtEnd (const QPolygonF & points, double slopeBefore) const\fC [virtual]\fP"

.PP
\fBParameters\fP
.RS 4
\fIpoints\fP Control points 
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\fIslopeBefore\fP Value of the first derivative at the point before the last one
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\fBReturns\fP
.RS 4
value of the first derivative at the last point 
.RE
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\fBSee also\fP
.RS 4
\fBslopeAtBeginning()\fP, \fBQwtSpline::boundaryCondition()\fP, \fBQwtSpline::boundaryValue()\fP 
.RE
.PP

.PP
Definition at line 997 of file qwt_spline\&.cpp\&.
.SS "\fBQVector\fP< double > QwtSplineC1::slopes (const QPolygonF & points) const\fC [pure virtual]\fP"

.PP
Find the first 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
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\fBNote\fP
.RS 4
The x coordinates need to be increasing or decreasing 
.RE
.PP

.PP
Implemented in \fBQwtSplineLocal\fP, \fBQwtSplineCubic\fP, and \fBQwtSplineC2\fP\&.

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