This package provides an implementation of algorithmes to do the conversion between equivalent geometric entities from package Geom2d. It gives the possibility : . to obtain the B-spline representation of bounded curves. . to split a B-spline curve into several B-spline curves with some constraints of continuity, . to convert a B-spline curve into several Bezier curves or surfaces. All the geometric entities used in this package are bounded. References : . Generating the Bezier Points of B-spline curves and surfaces (Wolfgang Bohm) CAGD volume 13 number 6 november 1981 . On NURBS: A Survey (Leslie Piegl) IEEE Computer Graphics and Application January 1991 . Curve and surface construction using rational B-splines (Leslie Piegl and Wayne Tiller) CAD Volume 19 number 9 november 1987 . A survey of curve and surface methods in CAGD (Wolfgang BOHM) CAGD 1 1984. More...

#include <Geom2dConvert.hxx>

Static Public Member Functions
static Handle< Geom2d_BSplineCurve >	SplitBSplineCurve (const Handle< Geom2d_BSplineCurve > &C, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Boolean SameOrientation=Standard_True)
	– Convert a curve to BSpline by Approximation More...

static Handle< Geom2d_BSplineCurve >	SplitBSplineCurve (const Handle< Geom2d_BSplineCurve > &C, const Standard_Real FromU1, const Standard_Real ToU2, const Standard_Real ParametricTolerance, const Standard_Boolean SameOrientation=Standard_True)
	This function computes the segment of B-spline curve between the parametric values FromU1, ToU2. If C is periodic the arc has the same orientation as C if SameOrientation = True. If C is not periodic SameOrientation is not used for the computation and C is oriented fromU1 toU2. If U1 and U2 and two parametric values we consider that U1 = U2 if Abs (U1 - U2) <= ParametricTolerance and ParametricTolerance must be greater or equal to Resolution from package gp. More...

static Handle< Geom2d_BSplineCurve >	CurveToBSplineCurve (const Handle< Geom2d_Curve > &C, const Convert_ParameterisationType Parameterisation=Convert_TgtThetaOver2)
	This function converts a non infinite curve from Geom into a B-spline curve. C must be an ellipse or a circle or a trimmed conic or a trimmed line or a Bezier curve or a trimmed Bezier curve or a BSpline curve or a trimmed BSpline curve or an Offset curve or a trimmed Offset curve. The returned B-spline is not periodic except if C is a Circle or an Ellipse. ParameterisationType applies only if the curve is a Circle or an ellipse : TgtThetaOver2, TgtThetaOver2_1, TgtThetaOver2_2, TgtThetaOver2_3, TgtThetaOver2_4, Purpose: this is the classical rational parameterisation 2 1 - t cos(theta) = ---— 2 1 + t. More...

static void	ConcatG1 (TColGeom2d_Array1OfBSplineCurve &ArrayOfCurves, const TColStd_Array1OfReal &ArrayOfToler, Handle< TColGeom2d_HArray1OfBSplineCurve > &ArrayOfConcatenated, const Standard_Boolean ClosedFlag, const Standard_Real ClosedTolerance)
	This Method concatenates G1 the ArrayOfCurves as far as it is possible. ArrayOfCurves[0..N-1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N-2] ClosedTolerance indicates if the ArrayOfCurves is closed. In this case ClosedTolerance contains the biggest tolerance of the two points which are at the closure. Otherwise its value is 0.0. More...

static void	ConcatC1 (TColGeom2d_Array1OfBSplineCurve &ArrayOfCurves, const TColStd_Array1OfReal &ArrayOfToler, Handle< TColStd_HArray1OfInteger > &ArrayOfIndices, Handle< TColGeom2d_HArray1OfBSplineCurve > &ArrayOfConcatenated, const Standard_Boolean ClosedFlag, const Standard_Real ClosedTolerance)
	This Method concatenates C1 the ArrayOfCurves as far as it is possible. ArrayOfCurves[0..N-1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N-2] ClosedTolerance indicates if the ArrayOfCurves is closed. In this case ClosedTolerance contains the biggest tolerance of the two points which are at the closure. Otherwise its value is 0.0. More...

static void	ConcatC1 (TColGeom2d_Array1OfBSplineCurve &ArrayOfCurves, const TColStd_Array1OfReal &ArrayOfToler, Handle< TColStd_HArray1OfInteger > &ArrayOfIndices, Handle< TColGeom2d_HArray1OfBSplineCurve > &ArrayOfConcatenated, const Standard_Boolean ClosedFlag, const Standard_Real ClosedTolerance, const Standard_Real AngularTolerance)
	This Method concatenates C1 the ArrayOfCurves as far as it is possible. ArrayOfCurves[0..N-1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N-2] ClosedTolerance indicates if the ArrayOfCurves is closed. In this case ClosedTolerance contains the biggest tolerance of the two points which are at the closure. Otherwise its value is 0.0. More...

static void	C0BSplineToC1BSplineCurve (Handle< Geom2d_BSplineCurve > &BS, const Standard_Real Tolerance)
	This Method reduces as far as it is possible the multiplicities of the knots of the BSpline BS.(keeping the geometry). It returns a new BSpline which could still be C0. tolerance is a geometrical tolerance. More...

static void	C0BSplineToArrayOfC1BSplineCurve (const Handle< Geom2d_BSplineCurve > &BS, Handle< TColGeom2d_HArray1OfBSplineCurve > &tabBS, const Standard_Real Tolerance)
	This Method reduces as far as it is possible the multiplicities of the knots of the BSpline BS.(keeping the geometry). It returns an array of BSpline C1. Tolerance is a geometrical tolerance. More...

static void	C0BSplineToArrayOfC1BSplineCurve (const Handle< Geom2d_BSplineCurve > &BS, Handle< TColGeom2d_HArray1OfBSplineCurve > &tabBS, const Standard_Real AngularTolerance, const Standard_Real Tolerance)
	This Method reduces as far as it is possible the multiplicities of the knots of the BSpline BS.(keeping the geometry). It returns an array of BSpline C1. tolerance is a geometrical tolerance. More...

Detailed Description

This package provides an implementation of algorithmes to do the conversion between equivalent geometric entities from package Geom2d. It gives the possibility : . to obtain the B-spline representation of bounded curves. . to split a B-spline curve into several B-spline curves with some constraints of continuity, . to convert a B-spline curve into several Bezier curves or surfaces. All the geometric entities used in this package are bounded. References : . Generating the Bezier Points of B-spline curves and surfaces (Wolfgang Bohm) CAGD volume 13 number 6 november 1981 . On NURBS: A Survey (Leslie Piegl) IEEE Computer Graphics and Application January 1991 . Curve and surface construction using rational B-splines (Leslie Piegl and Wayne Tiller) CAD Volume 19 number 9 november 1987 . A survey of curve and surface methods in CAGD (Wolfgang BOHM) CAGD 1 1984.

Member Function Documentation

static void Geom2dConvert::C0BSplineToArrayOfC1BSplineCurve	(	const Handle< Geom2d_BSplineCurve > &	BS,
		Handle< TColGeom2d_HArray1OfBSplineCurve > &	tabBS,
		const Standard_Real	Tolerance
	)

static

This Method reduces as far as it is possible the multiplicities of the knots of the BSpline BS.(keeping the geometry). It returns an array of BSpline C1. Tolerance is a geometrical tolerance.

static void Geom2dConvert::C0BSplineToArrayOfC1BSplineCurve	(	const Handle< Geom2d_BSplineCurve > &	BS,
		Handle< TColGeom2d_HArray1OfBSplineCurve > &	tabBS,
		const Standard_Real	AngularTolerance,
		const Standard_Real	Tolerance
	)

static

This Method reduces as far as it is possible the multiplicities of the knots of the BSpline BS.(keeping the geometry). It returns an array of BSpline C1. tolerance is a geometrical tolerance.

static void Geom2dConvert::C0BSplineToC1BSplineCurve	(	Handle< Geom2d_BSplineCurve > &	BS,
		const Standard_Real	Tolerance
	)

static

This Method reduces as far as it is possible the multiplicities of the knots of the BSpline BS.(keeping the geometry). It returns a new BSpline which could still be C0. tolerance is a geometrical tolerance.

static void Geom2dConvert::ConcatC1	(	TColGeom2d_Array1OfBSplineCurve &	ArrayOfCurves,
		const TColStd_Array1OfReal &	ArrayOfToler,
		Handle< TColStd_HArray1OfInteger > &	ArrayOfIndices,
		Handle< TColGeom2d_HArray1OfBSplineCurve > &	ArrayOfConcatenated,
		const Standard_Boolean	ClosedFlag,
		const Standard_Real	ClosedTolerance
	)

static

This Method concatenates C1 the ArrayOfCurves as far as it is possible. ArrayOfCurves[0..N-1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N-2] ClosedTolerance indicates if the ArrayOfCurves is closed. In this case ClosedTolerance contains the biggest tolerance of the two points which are at the closure. Otherwise its value is 0.0.

static void Geom2dConvert::ConcatC1	(	TColGeom2d_Array1OfBSplineCurve &	ArrayOfCurves,
		const TColStd_Array1OfReal &	ArrayOfToler,
		Handle< TColStd_HArray1OfInteger > &	ArrayOfIndices,
		Handle< TColGeom2d_HArray1OfBSplineCurve > &	ArrayOfConcatenated,
		const Standard_Boolean	ClosedFlag,
		const Standard_Real	ClosedTolerance,
		const Standard_Real	AngularTolerance
	)

static

This Method concatenates C1 the ArrayOfCurves as far as it is possible. ArrayOfCurves[0..N-1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N-2] ClosedTolerance indicates if the ArrayOfCurves is closed. In this case ClosedTolerance contains the biggest tolerance of the two points which are at the closure. Otherwise its value is 0.0.

static void Geom2dConvert::ConcatG1	(	TColGeom2d_Array1OfBSplineCurve &	ArrayOfCurves,
		const TColStd_Array1OfReal &	ArrayOfToler,
		Handle< TColGeom2d_HArray1OfBSplineCurve > &	ArrayOfConcatenated,
		const Standard_Boolean	ClosedFlag,
		const Standard_Real	ClosedTolerance
	)

static

This Method concatenates G1 the ArrayOfCurves as far as it is possible. ArrayOfCurves[0..N-1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N-2] ClosedTolerance indicates if the ArrayOfCurves is closed. In this case ClosedTolerance contains the biggest tolerance of the two points which are at the closure. Otherwise its value is 0.0.

static Handle< Geom2d_BSplineCurve > Geom2dConvert::CurveToBSplineCurve	(	const Handle< Geom2d_Curve > &	C,
		const Convert_ParameterisationType	Parameterisation = `Convert_TgtThetaOver2`
	)

static

This function converts a non infinite curve from Geom into a B-spline curve. C must be an ellipse or a circle or a trimmed conic or a trimmed line or a Bezier curve or a trimmed Bezier curve or a BSpline curve or a trimmed BSpline curve or an Offset curve or a trimmed Offset curve. The returned B-spline is not periodic except if C is a Circle or an Ellipse. ParameterisationType applies only if the curve is a Circle or an ellipse : TgtThetaOver2, TgtThetaOver2_1, TgtThetaOver2_2, TgtThetaOver2_3, TgtThetaOver2_4, Purpose: this is the classical rational parameterisation 2 1 - t cos(theta) = ---— 2 1 + t.

2t sin(theta) = ---— 2 1 + t

t = tan (theta/2)

with TgtThetaOver2 the routine will compute the number of spans using the rule num_spans = [ (ULast - UFirst) / 1.2 ] + 1 with TgtThetaOver2_N, N spans will be forced: an error will be raized if (ULast - UFirst) >= PI and N = 1, ULast - UFirst >= 2 PI and N = 2

QuasiAngular, here t is a rational function that approximates theta -—> tan(theta/2). Neverthless the composing with above function yields exact functions whose square sum up to 1 RationalC1 ; t is replaced by a polynomial function of u so as to grant C1 contiuity across knots. Exceptions Standard_DomainError if the curve C is infinite. Standard_ConstructionError:

if C is a complete circle or ellipse, and if Parameterisation is not equal to Convert_TgtThetaOver2 or to Convert_RationalC1, or
if C is a trimmed circle or ellipse and if Parameterisation is equal to Convert_TgtThetaOver2_1 and if U2 - U1 > 0.9999 * Pi where U1 and U2 are respectively the first and the last parameters of the trimmed curve (this method of parameterization cannot be used to convert a half-circle or a half-ellipse, for example), or
if C is a trimmed circle or ellipse and Parameterisation is equal to Convert_TgtThetaOver2_2 and U2 - U1 > 1.9999 * Pi where U1 and U2 are respectively the first and the last parameters of the trimmed curve (this method of parameterization cannot be used to convert a quasi-complete circle or ellipse).

static Handle< Geom2d_BSplineCurve > Geom2dConvert::SplitBSplineCurve	(	const Handle< Geom2d_BSplineCurve > &	C,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		const Standard_Boolean	SameOrientation = `Standard_True`
	)

static

– Convert a curve to BSpline by Approximation

This method computes the arc of B-spline curve between the two knots FromK1 and ToK2. If C is periodic the arc has the same orientation as C if SameOrientation = Standard_True. If C is not periodic SameOrientation is not used for the computation and C is oriented from the knot fromK1 to the knot toK2. We just keep the local definition of C between the knots FromK1 and ToK2. The returned B-spline curve has its first and last knots with a multiplicity equal to degree + 1, where degree is the polynomial degree of C. The indexes of the knots FromK1 and ToK2 doesn't include the repetition of multiple knots in their definition.

Raised if FromK1 or ToK2 are out of the bounds [FirstUKnotIndex, LastUKnotIndex] Raised if FromK1 = ToK2

static Handle< Geom2d_BSplineCurve > Geom2dConvert::SplitBSplineCurve	(	const Handle< Geom2d_BSplineCurve > &	C,
		const Standard_Real	FromU1,
		const Standard_Real	ToU2,
		const Standard_Real	ParametricTolerance,
		const Standard_Boolean	SameOrientation = `Standard_True`
	)

static

This function computes the segment of B-spline curve between the parametric values FromU1, ToU2. If C is periodic the arc has the same orientation as C if SameOrientation = True. If C is not periodic SameOrientation is not used for the computation and C is oriented fromU1 toU2. If U1 and U2 and two parametric values we consider that U1 = U2 if Abs (U1 - U2) <= ParametricTolerance and ParametricTolerance must be greater or equal to Resolution from package gp.

Raised if FromU1 or ToU2 are out of the parametric bounds of the curve (The tolerance criterion is ParametricTolerance). Raised if Abs (FromU1 - ToU2) <= ParametricTolerance Raised if ParametricTolerance < Resolution from gp.

The documentation for this class was generated from the following file:

Geom2dConvert.hxx

Static Public Member Functions

Detailed Description

Member Function Documentation