304 lines
8.0 KiB
Groff
304 lines
8.0 KiB
Groff
.TH "QwtSplineC2" 3 "Sun Jul 18 2021" "Version 6.2.0" "Qwt User's Guide" \" -*- nroff -*-
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.ad l
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.nh
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.SH NAME
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QwtSplineC2 \- Base class for spline interpolations providing a second order parametric continuity ( C2 ) between adjoining curves\&.
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.SH SYNOPSIS
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.br
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.PP
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.PP
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\fC#include <qwt_spline\&.h>\fP
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.PP
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Inherits \fBQwtSplineC1\fP\&.
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.PP
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Inherited by \fBQwtSplineCubic\fP\&.
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.SS "Public Types"
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.in +1c
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.ti -1c
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.RI "enum \fBBoundaryConditionC2\fP { \fBCubicRunout\fP = LinearRunout + 1, \fBNotAKnot\fP }"
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.br
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.in -1c
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.SS "Public Member Functions"
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.in +1c
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.ti -1c
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.RI "\fBQwtSplineC2\fP ()"
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.br
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.RI "Constructor\&. "
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.ti -1c
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.RI "virtual \fB~QwtSplineC2\fP ()"
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.br
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.RI "Destructor\&. "
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.ti -1c
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.RI "virtual QPainterPath \fBpainterPath\fP (const QPolygonF &) const override"
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.br
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.RI "Interpolate a curve with Bezier curves\&. "
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.ti -1c
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.RI "virtual \fBQVector\fP< QLineF > \fBbezierControlLines\fP (const QPolygonF &) const override"
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.br
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.RI "Interpolate a curve with Bezier curves\&. "
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.ti -1c
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.RI "virtual QPolygonF \fBequidistantPolygon\fP (const QPolygonF &, double distance, bool withNodes) const override"
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.br
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.RI "Find an interpolated polygon with 'equidistant' points\&. "
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.ti -1c
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.RI "virtual \fBQVector\fP< \fBQwtSplinePolynomial\fP > \fBpolynomials\fP (const QPolygonF &) const override"
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.br
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.RI "Calculate the interpolating polynomials for a non parametric spline\&. "
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.ti -1c
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.RI "virtual \fBQVector\fP< double > \fBslopes\fP (const QPolygonF &) const override"
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.br
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.RI "Find the first derivative at the control points\&. "
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.ti -1c
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.RI "virtual \fBQVector\fP< double > \fBcurvatures\fP (const QPolygonF &) const =0"
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.br
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.RI "Find the second derivative at the control points\&. "
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.in -1c
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.SH "Detailed Description"
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.PP
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Base class for spline interpolations providing a second order parametric continuity ( C2 ) between adjoining curves\&.
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All interpolations with C2 continuity are based on rules for finding the 2\&. derivate at some control points\&.
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.PP
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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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.PP
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\fBSee also\fP
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.RS 4
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\fBQwtSplineParametrization\fP
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.RE
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.PP
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.PP
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Definition at line 267 of file qwt_spline\&.h\&.
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.SH "Member Enumeration Documentation"
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.PP
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.SS "enum \fBQwtSplineC2::BoundaryConditionC2\fP"
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Boundary condition that requires C2 continuity
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.PP
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\fBSee also\fP
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.RS 4
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\fBQwtSpline::boundaryCondition\fP, \fBQwtSpline::BoundaryCondition\fP
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.RE
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.PP
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.PP
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\fBEnumerator\fP
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.in +1c
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.TP
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\fB\fICubicRunout \fP\fP
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The second derivate at the endpoint is related to the second derivatives at the 2 neighbours: cv[0] := 2\&.0 * cv[1] - cv[2]\&.
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.PP
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\fBNote\fP
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.RS 4
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\fBboundaryValue()\fP is ignored
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.RE
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.PP
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.TP
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\fB\fINotAKnot \fP\fP
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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
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.PP
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\fBNote\fP
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.RS 4
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\fBboundaryValue()\fP is ignored
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.RE
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.PP
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.PP
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Definition at line 275 of file qwt_spline\&.h\&.
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.SH "Constructor & Destructor Documentation"
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.PP
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.SS "QwtSplineC2::QwtSplineC2 ()"
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.PP
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Constructor\&. The default setting is a non closing spline with no parametrization ( \fBQwtSplineParametrization::ParameterX\fP )\&.
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.PP
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\fBSee also\fP
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.RS 4
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\fBQwtSpline::setParametrization()\fP, \fBQwtSpline::setBoundaryType()\fP
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.RE
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.PP
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.PP
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Definition at line 1228 of file qwt_spline\&.cpp\&.
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.SH "Member Function Documentation"
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.PP
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.SS "\fBQVector\fP< QLineF > QwtSplineC2::bezierControlLines (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"
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.PP
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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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.PP
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\fBParameters\fP
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.RS 4
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\fIpoints\fP Control points
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.RE
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.PP
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\fBReturns\fP
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.RS 4
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Control points of the interpolating Bezier curves
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.RE
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.PP
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\fBNote\fP
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.RS 4
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The implementation simply calls \fBQwtSplineC1::bezierControlLines()\fP, but is intended to be replaced by a more efficient implementation that builds the polynomials by the curvatures some day\&.
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.RE
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.PP
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.PP
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Reimplemented from \fBQwtSplineC1\fP\&.
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.PP
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Reimplemented in \fBQwtSplineCubic\fP\&.
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.PP
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Definition at line 1270 of file qwt_spline\&.cpp\&.
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.SS "\fBQVector\fP< double > QwtSplineC2::curvatures (const QPolygonF & points) const\fC [pure virtual]\fP"
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.PP
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Find the second derivative at the control points\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIpoints\fP Control nodes of the spline
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.RE
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.PP
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\fBReturns\fP
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.RS 4
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Vector with the values of the 2nd derivate at the control points
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.RE
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.PP
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\fBSee also\fP
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.RS 4
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\fBslopes()\fP
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.RE
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.PP
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\fBNote\fP
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.RS 4
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The x coordinates need to be increasing or decreasing
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.RE
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.PP
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.PP
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Implemented in \fBQwtSplineCubic\fP\&.
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.SS "QPolygonF QwtSplineC2::equidistantPolygon (const QPolygonF & points, double distance, bool withNodes) const\fC [override]\fP, \fC [virtual]\fP"
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.PP
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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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.PP
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\fBParameters\fP
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.RS 4
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\fIpoints\fP Control nodes of the spline
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.br
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\fIdistance\fP Distance between 2 points according to the parametrization
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.br
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\fIwithNodes\fP When true, also add the control nodes ( even if not being equidistant )
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.RE
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.PP
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\fBReturns\fP
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.RS 4
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Interpolating polygon
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.RE
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.PP
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\fBSee also\fP
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.RS 4
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QwtSpline::equidistantPolygon()
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.RE
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.PP
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.PP
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Reimplemented from \fBQwtSplineC1\fP\&.
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.PP
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Definition at line 1295 of file qwt_spline\&.cpp\&.
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.SS "QPainterPath QwtSplineC2::painterPath (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"
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.PP
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Interpolate a curve with Bezier curves\&. Interpolates a polygon piecewise with cubic Bezier curves and returns them as QPainterPath\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIpoints\fP Control points
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.RE
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.PP
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\fBReturns\fP
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.RS 4
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Painter path, that can be rendered by QPainter
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.RE
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.PP
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\fBNote\fP
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.RS 4
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The implementation simply calls \fBQwtSplineC1::painterPath()\fP, but is intended to be replaced by a one pass calculation some day\&.
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.RE
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.PP
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.PP
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Reimplemented from \fBQwtSplineC1\fP\&.
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.PP
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Reimplemented in \fBQwtSplineCubic\fP\&.
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.PP
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Definition at line 1249 of file qwt_spline\&.cpp\&.
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.SS "\fBQVector\fP< \fBQwtSplinePolynomial\fP > QwtSplineC2::polynomials (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"
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.PP
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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 \fBQwtSplinePolynomial::fromCurvatures\fP\&.
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.PP
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The default implementation is a 2 pass calculation\&. In derived classes it might be overloaded by a one pass implementation\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIpoints\fP Control points
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.RE
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.PP
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\fBReturns\fP
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.RS 4
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Interpolating polynomials
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.RE
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.PP
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\fBNote\fP
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.RS 4
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The x coordinates need to be increasing or decreasing
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.RE
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.PP
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.PP
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Reimplemented from \fBQwtSplineC1\fP\&.
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.PP
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Reimplemented in \fBQwtSplineCubic\fP\&.
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.PP
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Definition at line 1381 of file qwt_spline\&.cpp\&.
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.SS "\fBQVector\fP< double > QwtSplineC2::slopes (const QPolygonF & points) const\fC [override]\fP, \fC [virtual]\fP"
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.PP
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Find the first derivative at the control points\&. An implementation calculating the 2nd derivatives and then building the slopes in a 2nd loop\&. \fBQwtSplineCubic\fP overloads it with a more performant implementation doing it in one loop\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIpoints\fP Control nodes of the spline
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.RE
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.PP
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\fBReturns\fP
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.RS 4
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Vector with the values of the 1nd derivate at the control points
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.RE
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.PP
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\fBSee also\fP
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.RS 4
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\fBcurvatures()\fP
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.RE
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.PP
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\fBNote\fP
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.RS 4
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The x coordinates need to be increasing or decreasing
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.RE
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.PP
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.PP
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Implements \fBQwtSplineC1\fP\&.
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.PP
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Reimplemented in \fBQwtSplineCubic\fP\&.
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.PP
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Definition at line 1339 of file qwt_spline\&.cpp\&.
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.SH "Author"
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.PP
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Generated automatically by Doxygen for Qwt User's Guide from the source code\&.
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