QwtSpline(3) Qwt User's Guide QwtSpline(3) NAME QwtSpline - Base class for all splines. SYNOPSIS #include Inherited by QwtSplineBasis, and QwtSplineInterpolating. Public Types enum BoundaryType { ConditionalBoundaries, PeriodicPolygon, ClosedPolygon } enum BoundaryPosition { AtBeginning, AtEnd } enum BoundaryCondition { Clamped1, Clamped2, Clamped3, LinearRunout } Boundary condition. Public Member Functions QwtSpline () Constructor. virtual ~QwtSpline () Destructor. void setParametrization (int type) void setParametrization (QwtSplineParametrization *) const QwtSplineParametrization * parametrization () const void setBoundaryType (BoundaryType) BoundaryType boundaryType () const void setBoundaryValue (BoundaryPosition, double value) Define the boundary value. double boundaryValue (BoundaryPosition) const void setBoundaryCondition (BoundaryPosition, int condition) Define the condition for an endpoint of the spline. int boundaryCondition (BoundaryPosition) const void setBoundaryConditions (int condition, double valueBegin=0.0, double valueEnd=0.0) Define the condition at the endpoints of a spline. virtual QPolygonF polygon (const QPolygonF &, double tolerance) const Interpolate a curve by a polygon. virtual QPainterPath painterPath (const QPolygonF &) const =0 virtual uint locality () const Detailed Description Base class for all splines. A spline is a curve represented by a sequence of polynomials. Spline approximation is the process of finding polynomials for a given set of points. When the algorithm preserves the initial points it is called interpolating. Splines can be classified according to conditions of the polynomials that are met at the start/endpoints of the pieces: o Geometric Continuity o G0: polynomials are joined o G1: first derivatives are proportional at the join point The curve tangents thus have the same direction, but not necessarily the same magnitude. i.e., C1'(1) = (a,b,c) and C2'(0) = (k*a, k*b, k*c). o G2: first and second derivatives are proportional at join point o Parametric Continuity o C0: curves are joined o C1: first derivatives equal o C2: first and second derivatives are equal Geometric continuity requires the geometry to be continuous, while parametric continuity requires that the underlying parameterization be continuous as well. Parametric continuity of order n implies geometric continuity of order n, but not vice-versa. QwtSpline is the base class for spline approximations of any continuity. Definition at line 57 of file qwt_spline.h. Member Enumeration Documentation enum QwtSpline::BoundaryCondition Boundary condition. A spline algorithm calculates polynomials by looking a couple of points back/ahead ( locality() ). At the ends additional rules are necessary to compensate the missing points. See also boundaryCondition(), boundaryValue() QwtSplineC2::BoundaryConditionC2 Enumerator Clamped1 The first derivative at the end point is given See also boundaryValue() Clamped2 The second derivative at the end point is given See also boundaryValue() Note a condition having a second derivative of 0 is also called 'natural'. Clamped3 The third derivative at the end point is given See also boundaryValue() Note a condition having a third derivative of 0 is also called 'parabolic runout'. LinearRunout The first derivate at the endpoint is related to the first derivative at its neighbour by the boundary value. F,e when the boundary value at the end is 1.0 then the slope at the last 2 points is the same. See also boundaryValue(). Definition at line 119 of file qwt_spline.h. enum QwtSpline::BoundaryPosition position of a boundary condition See also boundaryCondition(), boundaryValue() Enumerator AtBeginning the condition is at the beginning of the polynomial AtEnd the condition is at the end of the polynomial Definition at line 99 of file qwt_spline.h. enum QwtSpline::BoundaryType Boundary type specifying the spline at its endpoints See also setBoundaryType(), boundaryType() Enumerator ConditionalBoundaries The polynomials at the start/endpoint depend on specific conditions See also QwtSpline::BoundaryCondition PeriodicPolygon The polynomials at the start/endpoint are found by using imaginary additional points. Additional points at the end are found by translating points from the beginning or v.v. ClosedPolygon ClosedPolygon is similar to PeriodicPolygon beside, that the interpolation includes the connection between the last and the first control point. Note Only works for parametrizations, where the parameter increment for the the final closing line is positive. This excludes QwtSplineParametrization::ParameterX and QwtSplineParametrization::ParameterY Definition at line 65 of file qwt_spline.h. Constructor & Destructor Documentation QwtSpline::QwtSpline () Constructor. The default setting is a non closing spline with chordal parametrization See also setParametrization(), setBoundaryType() Definition at line 540 of file qwt_spline.cpp. Member Function Documentation int QwtSpline::boundaryCondition (BoundaryPosition position) const Returns Condition for an endpoint of the spline Parameters position At the beginning or the end of the spline See also setBoundaryCondition(), boundaryValue(), setBoundaryConditions() Definition at line 651 of file qwt_spline.cpp. QwtSpline::BoundaryType QwtSpline::boundaryType () const Returns Boundary type See also setBoundaryType() Definition at line 626 of file qwt_spline.cpp. double QwtSpline::boundaryValue (BoundaryPosition position) const Returns Boundary value Parameters position At the beginning or the end of the spline See also setBoundaryValue(), boundaryCondition() Definition at line 682 of file qwt_spline.cpp. uint QwtSpline::locality () const [virtual] The locality of an spline interpolation identifies how many adjacent polynomials are affected, when changing the position of one point. A locality of 'n' means, that changing the coordinates of a point has an effect on 'n' leading and 'n' following polynomials. Those polynomials can be calculated from a local subpolygon. A value of 0 means, that the interpolation is not local and any modification of the polygon requires to recalculate all polynomials ( f.e cubic splines ). Returns Order of locality Reimplemented in QwtSplinePleasing, QwtSplineLocal, QwtSplineCubic, and QwtSplineBasis. Definition at line 564 of file qwt_spline.cpp. QPainterPath QwtSpline::painterPath (const QPolygonF & points) const [pure virtual] Approximates a polygon piecewise with cubic Bezier curves and returns them as QPainterPath. Parameters points Control points Returns Painter path, that can be rendered by QPainter See also polygon(), QwtBezier Implemented in QwtSplinePleasing, QwtSplineLocal, QwtSplineCubic, QwtSplineBasis, QwtSplineC2, QwtSplineC1, and QwtSplineInterpolating. const QwtSplineParametrization * QwtSpline::parametrization () const Returns parametrization See also setParametrization() Definition at line 605 of file qwt_spline.cpp. QPolygonF QwtSpline::polygon (const QPolygonF & points, double tolerance) const [virtual] Interpolate a curve by a polygon. Interpolates a polygon piecewise with Bezier curves interpolating them in a 2nd pass by polygons. The interpolation is based on 'Piecewise Linear Approximation of Bezier Curves' by Roger Willcocks ( http://www.rops.org ) Parameters points Control points tolerance Maximum for the accepted error of the approximation Returns polygon approximating the interpolating polynomials See also bezierControlLines(), QwtBezier Reimplemented in QwtSplineInterpolating. Definition at line 496 of file qwt_spline.cpp. void QwtSpline::setBoundaryCondition (BoundaryPosition position, int condition) Define the condition for an endpoint of the spline. Parameters position At the beginning or the end of the spline condition Condition See also BoundaryCondition, QwtSplineC2::BoundaryCondition, boundaryCondition() Definition at line 639 of file qwt_spline.cpp. void QwtSpline::setBoundaryConditions (int condition, double valueBegin = 0.0, double valueEnd = 0.0) Define the condition at the endpoints of a spline. Parameters condition Condition valueBegin Used for the condition at the beginning of te spline valueEnd Used for the condition at the end of te spline See also BoundaryCondition, QwtSplineC2::BoundaryCondition, testBoundaryCondition(), setBoundaryValue() Definition at line 700 of file qwt_spline.cpp. void QwtSpline::setBoundaryType (BoundaryType boundaryType) Define the boundary type for the endpoints of the approximating spline. Parameters boundaryType Boundary type See also boundaryType() Definition at line 617 of file qwt_spline.cpp. void QwtSpline::setBoundaryValue (BoundaryPosition position, double value) Define the boundary value. The boundary value is an parameter used in combination with the boundary condition. Its meaning depends on the condition. Parameters position At the beginning or the end of the spline value Value used for the condition at the end point See also boundaryValue(), setBoundaryCondition() Definition at line 670 of file qwt_spline.cpp. void QwtSpline::setParametrization (int type) Define the parametrization for a parametric spline approximation The default setting is a chordal parametrization. Parameters type Type of parametrization, usually one of QwtSplineParametrization::Type See also parametrization() Definition at line 576 of file qwt_spline.cpp. void QwtSpline::setParametrization (QwtSplineParametrization * parametrization) Define the parametrization for a parametric spline approximation The default setting is a chordal parametrization. Parameters parametrization Parametrization See also parametrization() Definition at line 592 of file qwt_spline.cpp. Author Generated automatically by Doxygen for Qwt User's Guide from the source code. Version 6.2.0 Sun Jul 18 2021 QwtSpline(3)