QwtSplinePolynomial(3) | Qwt User's Guide | QwtSplinePolynomial(3) |

# NAME

QwtSplinePolynomial - A cubic polynomial without constant term.

# SYNOPSIS

#include <qwt_spline_polynomial.h>

## Public Member Functions

**QwtSplinePolynomial** (double **c3**=0.0, double
**c2**=0.0, double **c1**=0.0)

Constructor. bool **operator==** (const **QwtSplinePolynomial** &)
const

bool **operator!=** (const **QwtSplinePolynomial** &) const

double **valueAt** (double x) const

double **slopeAt** (double x) const

double **curvatureAt** (double x) const

## Static Public Member Functions

static **QwtSplinePolynomial** **fromSlopes** (const QPointF
&p1, double m1, const QPointF &p2, double m2)

static **QwtSplinePolynomial** **fromSlopes** (double x, double y,
double m1, double m2)

static **QwtSplinePolynomial** **fromCurvatures** (const QPointF
&p1, double cv1, const QPointF &p2, double cv2)

static **QwtSplinePolynomial** **fromCurvatures** (double dx, double dy,
double cv1, double cv2)

## Public Attributes

double **c3**

coefficient of the cubic summand double **c2**

coefficient of the quadratic summand double **c1**

coefficient of the linear summand

# Detailed Description

A cubic polynomial without constant term.

**QwtSplinePolynomial** is a 3rd degree polynomial of the form:
y = c3 * x³ + c2 * x² + c1 * x;

**QwtSplinePolynomial** 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.

**See also**

**QwtSplineC1**

Definition at line 30 of file qwt_spline_polynomial.h.

# Constructor & Destructor Documentation

## QwtSplinePolynomial::QwtSplinePolynomial (double a3 = 0.0**, double a2 = 0.0**, double a1 = 0.0**) [inline]**

Constructor.

**Parameters**

*a3*Coefficient of the cubic summand

*a2*Coefficient of the quadratic summand

*a1*Coefficient of the linear summand

Definition at line 77 of file qwt_spline_polynomial.h.

# Member Function Documentation

## double QwtSplinePolynomial::curvatureAt (double x) const [inline]

Calculate the value of the second derivate of a polynomial for a given x

**Parameters**

*x*Parameter

**Returns**

Definition at line 130 of file qwt_spline_polynomial.h.

**QwtSplinePolynomial** QwtSplinePolynomial::fromCurvatures
(const QPointF & p1, double cv1, const QPointF & p2, double cv2)
[inline]**, [static]**

Find the coefficients for the polynomial including 2 points with specific values for the 2nd derivates at these points.

**Parameters**

*p1*First point

*cv1*Value of the second derivate at p1

*p2*Second point

*cv2*Value of the second derivate at p2

**Returns**

**Note**

Definition at line 185 of file qwt_spline_polynomial.h.

**QwtSplinePolynomial** QwtSplinePolynomial::fromCurvatures
(double dx, double dy, double cv1, double cv2) [inline]**, [static]**

Find the coefficients for the polynomial from the offset between 2 points and specific values for the 2nd derivates at these points.

**Parameters**

*dx*X-offset

*dy*Y-offset

*cv1*Value of the second derivate at p1

*cv2*Value of the second derivate at p2

**Returns**

Definition at line 202 of file qwt_spline_polynomial.h.

**QwtSplinePolynomial** QwtSplinePolynomial::fromSlopes (const
QPointF & p1, double m1, const QPointF & p2, double m2) [inline]**,
[static]**

Find the coefficients for the polynomial including 2 points with specific values for the 1st derivates at these points.

**Parameters**

*p1*First point

*m1*Value of the first derivate at p1

*p2*Second point

*m2*Value of the first derivate at p2

**Returns**

**Note**

Definition at line 147 of file qwt_spline_polynomial.h.

**QwtSplinePolynomial** QwtSplinePolynomial::fromSlopes
(double dx, double dy, double m1, double m2) [inline]**, [static]**

Find the coefficients for the polynomial from the offset between 2 points and specific values for the 1st derivates at these points.

**Parameters**

*dx*X-offset

*dy*Y-offset

*m1*Value of the first derivate at p1

*m2*Value of the first derivate at p2

**Returns**

Definition at line 164 of file qwt_spline_polynomial.h.

## bool QwtSplinePolynomial::operator!= (const **QwtSplinePolynomial** & other) const [inline]

**Parameters**

*other*Other polynomial

**Returns**

Definition at line 97 of file qwt_spline_polynomial.h.

## bool QwtSplinePolynomial::operator== (const **QwtSplinePolynomial** & other) const [inline]

**Parameters**

*other*Other polynomial

**Returns**

Definition at line 88 of file qwt_spline_polynomial.h.

## double QwtSplinePolynomial::slopeAt (double x) const [inline]

Calculate the value of the first derivate of a polynomial for a given x

**Parameters**

*x*Parameter

**Returns**

Definition at line 119 of file qwt_spline_polynomial.h.

## double QwtSplinePolynomial::valueAt (double x) const [inline]

Calculate the value of a polynomial for a given x

**Parameters**

*x*Parameter

**Returns**

Definition at line 108 of file qwt_spline_polynomial.h.

# Author

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Sun Jul 18 2021 | Version 6.2.0 |