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QwtSplinePolynomial Class Reference

A cubic polynomial without constant term. More...

`#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::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

## curvatureAt()

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
  Curvature at x

Definition at line 130 of file qwt_spline_polynomial.h.

## fromCurvatures() [1/2]

QwtSplinePolynomial QwtSplinePolynomial::fromCurvatures | ( | const QPointF & | p1,
|  | double | cv1,
|  | const QPointF & | p2,
|  | double | cv2 )

inlinestatic

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
  Coefficients of the polynomials

Note
  The missing constant term of the polynomial is p1.y()

Definition at line 185 of file qwt_spline_polynomial.h.

## fromCurvatures() [2/2]

QwtSplinePolynomial QwtSplinePolynomial::fromCurvatures | ( | double | dx,
|  | double | dy,
|  | double | cv1,
|  | double | cv2 )

inlinestatic

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
  Coefficients of the polynomials

Definition at line 202 of file qwt_spline_polynomial.h.

## fromSlopes() [1/2]

QwtSplinePolynomial QwtSplinePolynomial::fromSlopes | ( | const QPointF & | p1,
|  | double | m1,
|  | const QPointF & | p2,
|  | double | m2 )

inlinestatic

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
  Coefficients of the polynomials

Note
  The missing constant term of the polynomial is p1.y()

Definition at line 147 of file qwt_spline_polynomial.h.

## fromSlopes() [2/2]

QwtSplinePolynomial QwtSplinePolynomial::fromSlopes | ( | double | dx,
|  | double | dy,
|  | double | m1,
|  | double | m2 )

inlinestatic

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
  Coefficients of the polynomials

Definition at line 164 of file qwt_spline_polynomial.h.

## operator!=()

bool QwtSplinePolynomial::operator!= | ( | const QwtSplinePolynomial & | other | ) | const

inline

Parameters

  other | Other polynomial

Returns
  true, when the polynomials have different coefficients

Definition at line 97 of file qwt_spline_polynomial.h.

## operator==()

bool QwtSplinePolynomial::operator== | ( | const QwtSplinePolynomial & | other | ) | const

inline

Parameters

  other | Other polynomial

Returns
  true, when both polynomials have the same coefficients

Definition at line 88 of file qwt_spline_polynomial.h.

## slopeAt()

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
  Slope at x

Definition at line 119 of file qwt_spline_polynomial.h.

## valueAt()

double QwtSplinePolynomial::valueAt | ( | double | x | ) | const

inline

Calculate the value of a polynomial for a given x

Parameters

  x | Parameter

Returns
  Value at x

Definition at line 108 of file qwt_spline_polynomial.h.

## Member Data Documentation

## c1

double QwtSplinePolynomial::c1

coefficient of the linear summand

Definition at line 64 of file qwt_spline_polynomial.h.

## c2

double QwtSplinePolynomial::c2

coefficient of the quadratic summand

Definition at line 61 of file qwt_spline_polynomial.h.

## c3

double QwtSplinePolynomial::c3

coefficient of the cubic summand

Definition at line 58 of file qwt_spline_polynomial.h.