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 *
       x^3 + c2 * x^2 + 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
           Curvature at x

       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
           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.

   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
           Coefficients of the polynomials

       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
           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.

   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
           Coefficients of the polynomials

       Definition at line 164 of file qwt_spline_polynomial.h.

   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.

   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.

   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.

   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.


Author
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Version 6.2.0                   Sun Jul 18 2021         QwtSplinePolynomial(3)