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Static Public Member Functions
Geom2dConvert Class Reference

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 <br>


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
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.
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.
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 <br>

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:
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 <br>

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 <br>

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 <br>

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 <br>

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 <br>

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 <br>

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 <br>

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 <br>

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 <br>

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 <br>


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:
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