286 lines
6.6 KiB
Groff
286 lines
6.6 KiB
Groff
.TH "QwtSplinePolynomial" 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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QwtSplinePolynomial \- A cubic polynomial without constant term\&.
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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_polynomial\&.h>\fP
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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 "\fBQwtSplinePolynomial\fP (double \fBc3\fP=0\&.0, double \fBc2\fP=0\&.0, double \fBc1\fP=0\&.0)"
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.br
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.RI "Constructor\&. "
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.ti -1c
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.RI "bool \fBoperator==\fP (const \fBQwtSplinePolynomial\fP &) const"
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.br
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.ti -1c
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.RI "bool \fBoperator!=\fP (const \fBQwtSplinePolynomial\fP &) const"
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.br
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.ti -1c
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.RI "double \fBvalueAt\fP (double x) const"
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.br
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.ti -1c
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.RI "double \fBslopeAt\fP (double x) const"
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.br
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.ti -1c
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.RI "double \fBcurvatureAt\fP (double x) const"
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.br
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.in -1c
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.SS "Static Public Member Functions"
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.in +1c
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.ti -1c
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.RI "static \fBQwtSplinePolynomial\fP \fBfromSlopes\fP (const QPointF &p1, double m1, const QPointF &p2, double m2)"
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.br
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.ti -1c
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.RI "static \fBQwtSplinePolynomial\fP \fBfromSlopes\fP (double x, double y, double m1, double m2)"
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.br
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.ti -1c
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.RI "static \fBQwtSplinePolynomial\fP \fBfromCurvatures\fP (const QPointF &p1, double cv1, const QPointF &p2, double cv2)"
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.br
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.ti -1c
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.RI "static \fBQwtSplinePolynomial\fP \fBfromCurvatures\fP (double dx, double dy, double cv1, double cv2)"
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.br
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.in -1c
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.SS "Public Attributes"
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.in +1c
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.ti -1c
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.RI "double \fBc3\fP"
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.br
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.RI "coefficient of the cubic summand "
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.ti -1c
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.RI "double \fBc2\fP"
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.br
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.RI "coefficient of the quadratic summand "
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.ti -1c
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.RI "double \fBc1\fP"
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.br
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.RI "coefficient of the linear summand "
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.in -1c
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.SH "Detailed Description"
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.PP
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A cubic polynomial without constant term\&.
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\fBQwtSplinePolynomial\fP is a 3rd degree polynomial of the form: y = c3 * x³ + c2 * x² + c1 * x;
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.PP
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\fBQwtSplinePolynomial\fP is usually used in combination with polygon interpolation, where it is not necessary to store a constant term ( c0 ), as the translation is known from the corresponding polygon points\&.
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.PP
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\fBSee also\fP
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.RS 4
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\fBQwtSplineC1\fP
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.RE
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.PP
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.PP
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Definition at line 30 of file qwt_spline_polynomial\&.h\&.
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.SH "Constructor & Destructor Documentation"
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.PP
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.SS "QwtSplinePolynomial::QwtSplinePolynomial (double a3 = \fC0\&.0\fP, double a2 = \fC0\&.0\fP, double a1 = \fC0\&.0\fP)\fC [inline]\fP"
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.PP
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Constructor\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIa3\fP Coefficient of the cubic summand
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.br
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\fIa2\fP Coefficient of the quadratic summand
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.br
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\fIa1\fP Coefficient of the linear summand
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.RE
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.PP
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.PP
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Definition at line 77 of file qwt_spline_polynomial\&.h\&.
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.SH "Member Function Documentation"
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.PP
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.SS "double QwtSplinePolynomial::curvatureAt (double x) const\fC [inline]\fP"
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Calculate the value of the second derivate of a polynomial for a given x
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.PP
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\fBParameters\fP
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.RS 4
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\fIx\fP Parameter
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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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Curvature at x
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.RE
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.PP
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.PP
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Definition at line 130 of file qwt_spline_polynomial\&.h\&.
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.SS "\fBQwtSplinePolynomial\fP QwtSplinePolynomial::fromCurvatures (const QPointF & p1, double cv1, const QPointF & p2, double cv2)\fC [inline]\fP, \fC [static]\fP"
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Find the coefficients for the polynomial including 2 points with specific values for the 2nd derivates at these points\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIp1\fP First point
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.br
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\fIcv1\fP Value of the second derivate at p1
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.br
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\fIp2\fP Second point
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.br
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\fIcv2\fP Value of the second derivate at p2
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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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Coefficients of the 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 missing constant term of the polynomial is p1\&.y()
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.RE
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.PP
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.PP
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Definition at line 185 of file qwt_spline_polynomial\&.h\&.
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.SS "\fBQwtSplinePolynomial\fP QwtSplinePolynomial::fromCurvatures (double dx, double dy, double cv1, double cv2)\fC [inline]\fP, \fC [static]\fP"
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Find the coefficients for the polynomial from the offset between 2 points and specific values for the 2nd derivates at these points\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIdx\fP X-offset
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.br
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\fIdy\fP Y-offset
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.br
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\fIcv1\fP Value of the second derivate at p1
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.br
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\fIcv2\fP Value of the second derivate at p2
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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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Coefficients of the polynomials
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.RE
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.PP
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.PP
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Definition at line 202 of file qwt_spline_polynomial\&.h\&.
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.SS "\fBQwtSplinePolynomial\fP QwtSplinePolynomial::fromSlopes (const QPointF & p1, double m1, const QPointF & p2, double m2)\fC [inline]\fP, \fC [static]\fP"
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Find the coefficients for the polynomial including 2 points with specific values for the 1st derivates at these points\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIp1\fP First point
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.br
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\fIm1\fP Value of the first derivate at p1
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.br
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\fIp2\fP Second point
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.br
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\fIm2\fP Value of the first derivate at p2
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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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Coefficients of the 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 missing constant term of the polynomial is p1\&.y()
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.RE
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.PP
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.PP
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Definition at line 147 of file qwt_spline_polynomial\&.h\&.
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.SS "\fBQwtSplinePolynomial\fP QwtSplinePolynomial::fromSlopes (double dx, double dy, double m1, double m2)\fC [inline]\fP, \fC [static]\fP"
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Find the coefficients for the polynomial from the offset between 2 points and specific values for the 1st derivates at these points\&.
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.PP
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\fBParameters\fP
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.RS 4
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\fIdx\fP X-offset
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.br
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\fIdy\fP Y-offset
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.br
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\fIm1\fP Value of the first derivate at p1
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.br
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\fIm2\fP Value of the first derivate at p2
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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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Coefficients of the polynomials
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.RE
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.PP
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.PP
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Definition at line 164 of file qwt_spline_polynomial\&.h\&.
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.SS "bool QwtSplinePolynomial::operator!= (const \fBQwtSplinePolynomial\fP & other) const\fC [inline]\fP"
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.PP
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\fBParameters\fP
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.RS 4
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\fIother\fP Other polynomial
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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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true, when the polynomials have different coefficients
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.RE
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.PP
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.PP
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Definition at line 97 of file qwt_spline_polynomial\&.h\&.
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.SS "bool QwtSplinePolynomial::operator== (const \fBQwtSplinePolynomial\fP & other) const\fC [inline]\fP"
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.PP
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\fBParameters\fP
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.RS 4
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\fIother\fP Other polynomial
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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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true, when both polynomials have the same coefficients
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.RE
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.PP
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.PP
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Definition at line 88 of file qwt_spline_polynomial\&.h\&.
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.SS "double QwtSplinePolynomial::slopeAt (double x) const\fC [inline]\fP"
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Calculate the value of the first derivate of a polynomial for a given x
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.PP
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\fBParameters\fP
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.RS 4
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\fIx\fP Parameter
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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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Slope at x
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.RE
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.PP
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.PP
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Definition at line 119 of file qwt_spline_polynomial\&.h\&.
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.SS "double QwtSplinePolynomial::valueAt (double x) const\fC [inline]\fP"
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Calculate the value of a polynomial for a given x
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.PP
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\fBParameters\fP
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.RS 4
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\fIx\fP Parameter
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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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Value at x
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.RE
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.PP
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.PP
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Definition at line 108 of file qwt_spline_polynomial\&.h\&.
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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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