QwtSplineParametrization(3) Qwt User's Guide QwtSplineParametrization(3)

NAME

QwtSplineParametrization - Curve parametrization used for a spline interpolation.

SYNOPSIS

#include <qwt_spline_parametrization.h>

Public Types

enum Type { ParameterX, ParameterY, ParameterUniform, ParameterChordal, ParameterCentripetal, ParameterManhattan }
Parametrization type.

Public Member Functions

QwtSplineParametrization (int type)
virtual ~QwtSplineParametrization ()
Destructor. int type () const
virtual double valueIncrement (const QPointF &, const QPointF &) const
Calculate the parameter value increment for 2 points.

Static Public Member Functions

static double valueIncrementX (const QPointF &, const QPointF &)
Calculate the ParameterX value increment for 2 points. static double valueIncrementY (const QPointF &, const QPointF &)
Calculate the ParameterY value increment for 2 points. static double valueIncrementUniform (const QPointF &, const QPointF &)
Calculate the ParameterUniform value increment. static double valueIncrementChordal (const QPointF &, const QPointF &)
Calculate the ParameterChordal value increment for 2 points. static double valueIncrementCentripetal (const QPointF &, const QPointF &)
Calculate the ParameterCentripetal value increment for 2 points. static double valueIncrementManhattan (const QPointF &, const QPointF &)
Calculate the ParameterManhattan value increment for 2 points.

Detailed Description

Curve parametrization used for a spline interpolation.

Parametrization is the process of finding a parameter value for each curve point - usually related to some physical quantity ( distance, time ... ).

Often accumulating the curve length is the intended way of parametrization, but as the interpolated curve is not known in advance an approximation needs to be used.

The values are calculated by cumulating increments, that are provided by QwtSplineParametrization. As the curve parameters need to be montonically increasing, each increment need to be positive.

• t[0] = 0;
• t[i] = t[i-1] + valueIncrement( point[i-1], p[i] );

QwtSplineParametrization provides the most common used type of parametrizations and offers an interface to inject custom implementations.

Note

The most relevant types of parametrization are trying to provide an approximation of the curve length.

QwtSpline::setParametrization()

Definition at line 44 of file qwt_spline_parametrization.h.

Member Enumeration Documentation

enum QwtSplineParametrization::Type

Parametrization type.

Enumerator

No parametrization: t[i] = x[i]

valueIncrementX()
No parametrization: t[i] = y[i]

valueIncrementY()
Uniform parametrization: t[i] = i;

A very fast parametrization, with good results, when the geometry of the control points is somehow 'equidistant'. F.e. when recording the position of a body, that is moving with constant speed every n seconds.

valueIncrementUniform()
Parametrization using the chordal length between two control points

The chordal length is the most commonly used approximation for the curve length.

valueIncrementChordal()
Centripetal parametrization

Based on the square root of the chordal length.

Its name stems from the physical observations regarding the centripetal force, of a body moving along the curve.

valueIncrementCentripetal()
Parametrization using the manhattan length between two control points

Approximating the curve length by the manhattan length is faster than the chordal length, but usually gives worse results.

valueIncrementManhattan()

Definition at line 48 of file qwt_spline_parametrization.h.

Constructor & Destructor Documentation

QwtSplineParametrization::QwtSplineParametrization (int type) [explicit]

Constructor

Parameters

type Parametrization type

type()

Definition at line 17 of file qwt_spline_parametrization.cpp.

Member Function Documentation

int QwtSplineParametrization::type () const

Returns

Parametrization type

Definition at line 72 of file qwt_spline_parametrization.cpp.

double QwtSplineParametrization::valueIncrement (const QPointF & point1, const QPointF & point2) const [virtual]

Calculate the parameter value increment for 2 points.

Parameters

point1 First point
point2 Second point

Returns

Value increment

Definition at line 35 of file qwt_spline_parametrization.cpp.

double QwtSplineParametrization::valueIncrementCentripetal (const QPointF & point1, const QPointF & point2) [inline], [static]

Calculate the ParameterCentripetal value increment for 2 points.

Parameters

point1 First point
point2 Second point

Returns

The square root of a chordal increment

Definition at line 196 of file qwt_spline_parametrization.h.

double QwtSplineParametrization::valueIncrementChordal (const QPointF & point1, const QPointF & point2) [inline], [static]

Calculate the ParameterChordal value increment for 2 points.

Parameters

point1 First point
point2 Second point

Returns

qSqrt( dx * dx + dy * dy );

Definition at line 179 of file qwt_spline_parametrization.h.

double QwtSplineParametrization::valueIncrementManhattan (const QPointF & point1, const QPointF & point2) [inline], [static]

Calculate the ParameterManhattan value increment for 2 points.

Parameters

point1 First point
point2 Second point

Returns

| point2.x() - point1.x() | + | point2.y() - point1.y() |

Definition at line 210 of file qwt_spline_parametrization.h.

double QwtSplineParametrization::valueIncrementUniform (const QPointF & point1, const QPointF & point2) [inline], [static]

Calculate the ParameterUniform value increment.

Parameters

point1 First point
point2 Second point

Returns

1.0

Definition at line 162 of file qwt_spline_parametrization.h.

double QwtSplineParametrization::valueIncrementX (const QPointF & point1, const QPointF & point2) [inline], [static]

Calculate the ParameterX value increment for 2 points.

Parameters

point1 First point
point2 Second point

Returns

point2.x() - point1.x();

Definition at line 134 of file qwt_spline_parametrization.h.

double QwtSplineParametrization::valueIncrementY (const QPointF & point1, const QPointF & point2) [inline], [static]

Calculate the ParameterY value increment for 2 points.

Parameters

point1 First point
point2 Second point

Returns

point2.y() - point1.y();

Definition at line 148 of file qwt_spline_parametrization.h.

Author

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