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.