QwtSplinePolynomial(3)

📦
version 6.3.0 · 2 versions
, in alpine 3.24

💅 NAME

QwtSplinePolynomial — a cubic polynomial with no constant term, bestie. That's the whole vibe. It's a 3rd-degree situation that starts at the origin and goes places. ✨

So okay, this is from the Qwt library, and honestly? The header of this page says QwtSplinePolynomial(3) and it lives in the Library Functions Manual — so yeah, you're in the right place, pull up a chair. 🎀

✨ 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 (the dramatic one, the x³ energy)
  • double c2 — coefficient of the quadratic summand (the x² supporting actress)
  • double c1 — coefficient of the linear summand (the humble little x)

🌈 Detailed Description

A cubic polynomial without constant term. Yes, again, because it's that iconic. 👑

QwtSplinePolynomial is a 3rd degree polynomial of the form:

y = c3 * x³ + c2 * x² + c1 * x;

So like — where's the c0, you ask? Not here, babes. 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. Basically the offset is already handled elsewhere so this struct doesn't need to carry it around. Lowkey efficient, highkey elegant. 💅

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. Your main character moment — build a polynomial from scratch. 🫶

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. That's the curvature, the bend, the how-much-is-this-curving of it all. 😭

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. Two points, two curvatures, one polynomial. Slay. ✨

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. Same energy as above but you're feeding it offsets instead of 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. Slope girlies rise up. 📈

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]

The "are we not the same" check.

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]

The "are we literally twins" check. 💖

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. Just plug the x in and see what y comes out — the classic. 🌟

Parameters

  • x — Parameter

Returns Value at x

Definition at line 108 of file qwt_spline_polynomial.h.

🍓 Member Data Documentation

double QwtSplinePolynomial::c1

coefficient of the linear summand

Definition at line 64 of file qwt_spline_polynomial.h.

double QwtSplinePolynomial::c2

coefficient of the quadratic summand

Definition at line 61 of file qwt_spline_polynomial.h.

double QwtSplinePolynomial::c3

coefficient of the cubic summand

Definition at line 58 of file qwt_spline_polynomial.h.

🧚 Author

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And that's the whole page, bestie — no cap. 💀 This little beauty came to you courtesy of Doxygen, auto-generated for the Qwt User's Guide straight from the source code, and it's filed under QwtSplinePolynomial(3). Go forth and interpolate those polygons. 🫶✨

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