Open CASCADE Technology
7.3.0

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 Bspline representation of bounded curves. . to split a Bspline curve into several Bspline curves with some constraints of continuity, . to convert a Bspline curve into several Bezier curves or surfaces. All the geometric entities used in this package are bounded. References : . Generating the Bezier Points of Bspline 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 Bsplines (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 Bspline 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 Bspline 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 Bspline 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..N1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N2] 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..N1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N2] 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..N1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N2] 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...  
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 Bspline representation of bounded curves. . to split a Bspline curve into several Bspline curves with some constraints of continuity, . to convert a Bspline curve into several Bezier curves or surfaces. All the geometric entities used in this package are bounded. References : . Generating the Bezier Points of Bspline 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 Bsplines (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.

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 
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 
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 
This Method concatenates C1 the ArrayOfCurves as far as it is possible. ArrayOfCurves[0..N1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N2] 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 
This Method concatenates C1 the ArrayOfCurves as far as it is possible. ArrayOfCurves[0..N1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N2] 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 
This Method concatenates G1 the ArrayOfCurves as far as it is possible. ArrayOfCurves[0..N1] ArrayOfToler contains the biggest tolerance of the two points shared by two consecutives curves. Its dimension: [0..N2] 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 
This function converts a non infinite curve from Geom into a Bspline 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 Bspline 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:

static 
– Convert a curve to BSpline by Approximation
This method computes the arc of Bspline 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 Bspline 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 
This function computes the segment of Bspline 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.