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Geom_BSplineSurface Class Reference

Describes a BSpline surface.
In each parametric direction, a BSpline surface can be:
More...

#include <Geom_BSplineSurface.hxx>

Inheritance diagram for Geom_BSplineSurface:
Inheritance graph
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Public Member Functions

 Geom_BSplineSurface (const TColgp_Array2OfPnt &Poles, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean UPeriodic=Standard_False, const Standard_Boolean VPeriodic=Standard_False)
 Creates a non-rational b-spline surface (weights
default value is 1.).
//! The following conditions must be verified.
0 < UDegree <= MaxDegree.
UKnots.Length() == UMults.Length() >= 2
UKnots(i) < UKnots(i+1) (Knots are increasing)
1 <= UMults(i) <= UDegree
On a non uperiodic surface the first and last
umultiplicities may be UDegree+1 (this is even
recommanded if you want the curve to start and finish on
the first and last pole).
On a uperiodic surface the first and the last
umultiplicities must be the same.
on non-uperiodic surfaces
Poles.ColLength() == Sum(UMults(i)) - UDegree - 1 >= 2
on uperiodic surfaces
Poles.ColLength() == Sum(UMults(i)) except the first or last
The previous conditions for U holds also for V, with the
RowLength of the poles.

 Geom_BSplineSurface (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean UPeriodic=Standard_False, const Standard_Boolean VPeriodic=Standard_False)
 Creates a non-rational b-spline surface (weights
default value is 1.).

//! The following conditions must be verified.
0 < UDegree <= MaxDegree.

UKnots.Length() == UMults.Length() >= 2

UKnots(i) < UKnots(i+1) (Knots are increasing)
1 <= UMults(i) <= UDegree

On a non uperiodic surface the first and last
umultiplicities may be UDegree+1 (this is even
recommanded if you want the curve to start and finish on
the first and last pole).

On a uperiodic surface the first and the last
umultiplicities must be the same.

on non-uperiodic surfaces

Poles.ColLength() == Sum(UMults(i)) - UDegree - 1 >= 2

on uperiodic surfaces

Poles.ColLength() == Sum(UMults(i)) except the first or
last


The previous conditions for U holds also for V, with the
RowLength of the poles.

void ExchangeUV ()
 Exchanges the u and v parametric directions on
this BSpline surface.
As a consequence:

void SetUPeriodic ()
 Sets the surface U periodic.

void SetVPeriodic ()
 Modifies this surface to be periodic in the u (or v)
parametric direction.
To become periodic in a given parametric direction a
surface must be closed in that parametric direction,
and the knot sequence relative to that direction must be periodic.
To generate this periodic sequence of knots, the
functions FirstUKnotIndex and LastUKnotIndex (or
FirstVKnotIndex and LastVKnotIndex) are used to
compute I1 and I2. These are the indexes, in the
knot array associated with the given parametric
direction, of the knots that correspond to the first and
last parameters of this BSpline surface in the given
parametric direction. Hence the period is:
Knots(I1) - Knots(I2)
As a result, the knots and poles tables are modified.
Exceptions
Standard_ConstructionError if the surface is not
closed in the given parametric direction.

void PeriodicNormalization (Standard_Real &U, Standard_Real &V) const
 returns the parameter normalized within
the period if the surface is periodic : otherwise
does not do anything

void SetUOrigin (const Standard_Integer Index)
 Assigns the knot of index Index in the knots table in
the corresponding parametric direction to be the
origin of this periodic BSpline surface. As a
consequence, the knots and poles tables are modified.
Exceptions
Standard_NoSuchObject if this BSpline surface is
not periodic in the given parametric direction.
Standard_DomainError if Index is outside the
bounds of the knots table in the given parametric direction.

void SetVOrigin (const Standard_Integer Index)
 Assigns the knot of index Index in the knots table in
the corresponding parametric direction to be the
origin of this periodic BSpline surface. As a
consequence, the knots and poles tables are modified.
Exceptions
Standard_NoSuchObject if this BSpline surface is
not periodic in the given parametric direction.
Standard_DomainError if Index is outside the
bounds of the knots table in the given parametric direction.

void SetUNotPeriodic ()
void SetVNotPeriodic ()
 Modifies this surface to be periodic in the u (or v) parametric direction.
To become periodic in a given parametric direction a
surface must be closed in that parametric direction,
and the knot sequence relative to that direction must be periodic.
To generate this periodic sequence of knots, the
functions FirstUKnotIndex and LastUKnotIndex (or
FirstVKnotIndex and LastVKnotIndex) are used to
compute I1 and I2. These are the indexes, in the
knot array associated with the given parametric
direction, of the knots that correspond to the first and
last parameters of this BSpline surface in the given
parametric direction. Hence the period is:
Knots(I1) - Knots(I2)
As a result, the knots and poles tables are modified.
Exceptions
Standard_ConstructionError if the surface is not
closed in the given parametric direction.

void UReverse ()
 Reverses the U direction of parametrization of <me>.
The bounds of the surface are not modified.

void VReverse ()
 Changes the orientation of this BSpline surface in the
u (or v) parametric direction. The bounds of the
surface are not changed but the given parametric
direction is reversed. Hence the orientation of the
surface is reversed.
The knots and poles tables are modified.

Standard_Real UReversedParameter (const Standard_Real U) const
 Returns the parameter on the Ureversed surface for
the point of parameter U on <me>.

me->UReversed()->Value(me->UReversedParameter(U),V)

is the same point as

me->Value(U,V)

Standard_Real VReversedParameter (const Standard_Real V) const
 Computes the u (or v) parameter on the modified
surface, produced by reversing its u (or v) parametric
direction, for the point of u parameter U, (or of v
parameter V) on this BSpline surface.
For a BSpline surface, these functions return respectively:

void IncreaseDegree (const Standard_Integer UDegree, const Standard_Integer VDegree)
 Increases the degrees of this BSpline surface to
UDegree and VDegree in the u and v parametric
directions respectively. As a result, the tables of poles,
weights and multiplicities are modified. The tables of
knots is not changed.
Note: Nothing is done if the given degree is less than
or equal to the current degree in the corresponding
parametric direction.
Exceptions
Standard_ConstructionError if UDegree or
VDegree is greater than
Geom_BSplineSurface::MaxDegree().

void InsertUKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_True)
void InsertVKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_True)
 Inserts into the knots table for the corresponding
parametric direction of this BSpline surface:

Standard_Boolean RemoveUKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance)
Standard_Boolean RemoveVKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance)
 Reduces to M the multiplicity of the knot of index
Index in the given parametric direction. If M is 0, the knot is removed.
With a modification of this type, the table of poles is also modified.
Two different algorithms are used systematically to
compute the new poles of the surface. For each
pole, the distance between the pole calculated
using the first algorithm and the same pole
calculated using the second algorithm, is checked. If
this distance is less than Tolerance it ensures that
the surface is not modified by more than Tolerance.
Under these conditions, the function returns true;
otherwise, it returns false.
A low tolerance prevents modification of the
surface. A high tolerance "smoothes" the surface.
Exceptions
Standard_OutOfRange if Index is outside the
bounds of the knots table of this BSpline surface.

void IncreaseUMultiplicity (const Standard_Integer UIndex, const Standard_Integer M)
 Increases the multiplicity of the knot of range UIndex
in the UKnots sequence.
M is the new multiplicity. M must be greater than the
previous multiplicity and lower or equal to the degree
of the surface in the U parametric direction.
//! Raised if M is not in the range [1, UDegree]
Raised if UIndex is not in the range [FirstUKnotIndex,
LastUKnotIndex] given by the methods with the same name.

void IncreaseUMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer M)
 Increases until order M the multiplicity of the set of knots
FromI1,...., ToI2 in the U direction. This method can be used
to make a B_spline surface into a PiecewiseBezier B_spline
surface.
If <me> was uniform, it can become non uniform.
Raised if FromI1 or ToI2 is out of the range [FirstUKnotIndex,
LastUKnotIndex].
M should be greater than the previous multiplicity of the
all the knots FromI1,..., ToI2 and lower or equal to the
Degree of the surface in the U parametric direction.

void IncrementUMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer Step)
 Increments the multiplicity of the consecutives uknots FromI1..ToI2
by step. The multiplicity of each knot FromI1,.....,ToI2 must be
lower or equal to the UDegree of the B_spline.
Raised if FromI1 or ToI2 is not in the range
[FirstUKnotIndex, LastUKnotIndex]
Raised if one knot has a multiplicity greater than UDegree.

void IncreaseVMultiplicity (const Standard_Integer VIndex, const Standard_Integer M)
 Increases the multiplicity of a knot in the V direction.
M is the new multiplicity.
M should be greater than the previous multiplicity and lower
than the degree of the surface in the V parametric direction.
Raised if VIndex is not in the range [FirstVKnotIndex,
LastVKnotIndex] given by the methods with the same name.

void IncreaseVMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer M)
 Increases until order M the multiplicity of the set of knots
FromI1,...., ToI2 in the V direction. This method can be used to
make a BSplineSurface into a PiecewiseBezier B_spline
surface. If <me> was uniform, it can become non-uniform.
Raised if FromI1 or ToI2 is out of the range [FirstVKnotIndex,
LastVKnotIndex] given by the methods with the same name.
M should be greater than the previous multiplicity of the
all the knots FromI1,..., ToI2 and lower or equal to the
Degree of the surface in the V parametric direction.

void IncrementVMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer Step)
 Increments the multiplicity of the consecutives vknots FromI1..ToI2
by step. The multiplicity of each knot FromI1,.....,ToI2 must be
lower or equal to the VDegree of the B_spline.
Raised if FromI1 or ToI2 is not in the range
[FirstVKnotIndex, LastVKnotIndex]
Raised if one knot has a multiplicity greater than VDegree.

void InsertUKnot (const Standard_Real U, const Standard_Integer M, const Standard_Real ParametricTolerance, const Standard_Boolean Add=Standard_True)
 Inserts a knot value in the sequence of UKnots. If U is a knot
value this method increases the multiplicity of the knot if the
previous multiplicity was lower than M else it does nothing. The
tolerance criterion is ParametricTolerance. ParametricTolerance
should be greater or equal than Resolution from package gp.
Raised if U is out of the bounds [U1, U2] given by the methods
Bounds, the criterion ParametricTolerance is used.
Raised if M is not in the range [1, UDegree].

void InsertVKnot (const Standard_Real V, const Standard_Integer M, const Standard_Real ParametricTolerance, const Standard_Boolean Add=Standard_True)
 Inserts a knot value in the sequence of VKnots. If V is a knot
value this method increases the multiplicity of the knot if the
previous multiplicity was lower than M otherwise it does nothing.
The tolerance criterion is ParametricTolerance.
ParametricTolerance should be greater or equal than Resolution
from package gp.
raises if V is out of the Bounds [V1, V2] given by the methods
Bounds, the criterion ParametricTolerance is used.
raises if M is not in the range [1, VDegree].

void Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2)
 Segments the surface between U1 and U2 in the U-Direction.
between V1 and V2 in the V-Direction.
The control points are modified, the first and the last point
are not the same.
Warnings :
Even if <me> is not closed it can become closed after the
segmentation for example if U1 or U2 are out of the bounds
of the surface <me> or if the surface makes loop.
//! raises if U2 < U1 or V2 < V1

void CheckAndSegment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2)
 Segments the surface between U1 and U2 in the U-Direction.
between V1 and V2 in the V-Direction.

same as Segment but do nothing if U1 and U2 (resp. V1 and V2) are
equal to the bounds in U (resp. in V) of <me>.
For example, if <me> is periodic in V, it will be always periodic
in V after the segmentation if the bounds in V are unchanged

Warnings :
Even if <me> is not closed it can become closed after the
segmentation for example if U1 or U2 are out of the bounds
of the surface <me> or if the surface makes loop.
//! raises if U2 < U1 or V2 < V1

void SetUKnot (const Standard_Integer UIndex, const Standard_Real K)
 Substitutes the UKnots of range UIndex with K.
Raised if UIndex < 1 or UIndex > NbUKnots
Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex-1)

void SetUKnots (const TColStd_Array1OfReal &UK)
 Changes all the U-knots of the surface.
The multiplicity of the knots are not modified.
Raised if there is an index such that UK (Index+1) <= UK (Index).
Raised if UK.Lower() < 1 or UK.Upper() > NbUKnots

void SetUKnot (const Standard_Integer UIndex, const Standard_Real K, const Standard_Integer M)
 Changes the value of the UKnots of range UIndex and
increases its multiplicity.
Raised if UIndex is not in the range [FirstUKnotIndex,
LastUKnotIndex] given by the methods with the same name.
Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex-1)
M must be lower than UDegree and greater than the previous
multiplicity of the knot of range UIndex.

void SetVKnot (const Standard_Integer VIndex, const Standard_Real K)
 Substitutes the VKnots of range VIndex with K.
Raised if VIndex < 1 or VIndex > NbVKnots
Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex-1)

void SetVKnots (const TColStd_Array1OfReal &VK)
 Changes all the V-knots of the surface.
The multiplicity of the knots are not modified.
Raised if there is an index such that VK (Index+1) <= VK (Index).
Raised if VK.Lower() < 1 or VK.Upper() > NbVKnots

void SetVKnot (const Standard_Integer VIndex, const Standard_Real K, const Standard_Integer M)
 Changes the value of the VKnots of range VIndex and increases
its multiplicity.
Raised if VIndex is not in the range [FirstVKnotIndex,
LastVKnotIndex] given by the methods with the same name.
Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex-1)
M must be lower than VDegree and greater than the previous
multiplicity of the knot of range VIndex.

void LocateU (const Standard_Real U, const Standard_Real ParametricTolerance, Standard_Integer &I1, Standard_Integer &I2, const Standard_Boolean WithKnotRepetition=Standard_False) const
 Locates the parametric value U in the sequence of UKnots.
If "WithKnotRepetition" is True we consider the knot's
representation with repetition of multiple knot value,
otherwise we consider the knot's representation with
no repetition of multiple knot values.
UKnots (I1) <= U <= UKnots (I2)
. if I1 = I2 U is a knot value (the tolerance criterion
ParametricTolerance is used).
. if I1 < 1 => U < UKnots(1) - Abs(ParametricTolerance)
. if I2 > NbUKnots => U > UKnots(NbUKnots)+Abs(ParametricTolerance)

void LocateV (const Standard_Real V, const Standard_Real ParametricTolerance, Standard_Integer &I1, Standard_Integer &I2, const Standard_Boolean WithKnotRepetition=Standard_False) const
 Locates the parametric value U in the sequence of knots.
If "WithKnotRepetition" is True we consider the knot's
representation with repetition of multiple knot value,
otherwise we consider the knot's representation with
no repetition of multiple knot values.
VKnots (I1) <= V <= VKnots (I2)
. if I1 = I2 V is a knot value (the tolerance criterion
ParametricTolerance is used).
. if I1 < 1 => V < VKnots(1) - Abs(ParametricTolerance)
. if I2 > NbVKnots => V > VKnots(NbVKnots)+Abs(ParametricTolerance)
//! poles insertion and removing
The following methods are available only if the surface
is Uniform or QuasiUniform in the considered direction
The knot repartition is modified.

void SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt &P)
 Substitutes the pole of range (UIndex, VIndex) with P.
If the surface is rational the weight of range (UIndex, VIndex)
is not modified.
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
VIndex > NbVPoles.

void SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt &P, const Standard_Real Weight)
 Substitutes the pole and the weight of range (UIndex, VIndex)
with P and W.
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
VIndex > NbVPoles.
//! Raised if Weight <= Resolution from package gp.

void SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles)
 Changes a column of poles or a part of this column.
//! Raised if Vindex < 1 or VIndex > NbVPoles.
Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles.

void SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights)
 Changes a column of poles or a part of this column with the
corresponding weights. If the surface was rational it can
become non rational. If the surface was non rational it can
become rational.
//! Raised if Vindex < 1 or VIndex > NbVPoles.
Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles
Raised if the bounds of CPoleWeights are not the same as the
bounds of CPoles.
Raised if one of the weight value of CPoleWeights is lower or
equal to Resolution from package gp.

void SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights)
 Changes a row of poles or a part of this row with the
corresponding weights. If the surface was rational it can
become non rational. If the surface was non rational it can
become rational.
//! Raised if Uindex < 1 or UIndex > NbUPoles.
Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles
raises if the bounds of CPoleWeights are not the same as the
bounds of CPoles.
Raised if one of the weight value of CPoleWeights is lower or
equal to Resolution from package gp.

void SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles)
 Changes a row of poles or a part of this row.
//! Raised if Uindex < 1 or UIndex > NbUPoles.
Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles.

void SetWeight (const Standard_Integer UIndex, const Standard_Integer VIndex, const Standard_Real Weight)
 Changes the weight of the pole of range UIndex, VIndex.
If the surface was non rational it can become rational.
If the surface was rational it can become non rational.
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
VIndex > NbVPoles
Raised if weight is lower or equal to Resolution from
package gp

void SetWeightCol (const Standard_Integer VIndex, const TColStd_Array1OfReal &CPoleWeights)
 Changes a column of weights of a part of this column.
Raised if VIndex < 1 or VIndex > NbVPoles
Raised if CPoleWeights.Lower() < 1 or
CPoleWeights.Upper() > NbUPoles.
Raised if a weight value is lower or equal to Resolution
from package gp.

void SetWeightRow (const Standard_Integer UIndex, const TColStd_Array1OfReal &CPoleWeights)
 Changes a row of weights or a part of this row.
Raised if UIndex < 1 or UIndex > NbUPoles
Raised if CPoleWeights.Lower() < 1 or
CPoleWeights.Upper() > NbVPoles.
Raised if a weight value is lower or equal to Resolution
from package gp.

void MovePoint (const Standard_Real U, const Standard_Real V, const gp_Pnt &P, const Standard_Integer UIndex1, const Standard_Integer UIndex2, const Standard_Integer VIndex1, const Standard_Integer VIndex2, Standard_Integer &UFirstIndex, Standard_Integer &ULastIndex, Standard_Integer &VFirstIndex, Standard_Integer &VLastIndex)
 Move a point with parameter U and V to P.
given u,v as parameters) to reach a new position
UIndex1, UIndex2, VIndex1, VIndex2:
indicates the poles which can be moved
if Problem in BSplineBasis calculation, no change
for the curve and
UFirstIndex, VLastIndex = 0
VFirstIndex, VLastIndex = 0
Raised if UIndex1 < UIndex2 or VIndex1 < VIndex2 or
UIndex1 < 1 || UIndex1 > NbUPoles or
UIndex2 < 1 || UIndex2 > NbUPoles
VIndex1 < 1 || VIndex1 > NbVPoles or
VIndex2 < 1 || VIndex2 > NbVPoles
//! characteristics of the surface

Standard_Boolean IsUClosed () const
 Returns true if the first control points row and the last
control points row are identical. The tolerance criterion
is Resolution from package gp.

Standard_Boolean IsVClosed () const
 Returns true if the first control points column and the
last last control points column are identical.
The tolerance criterion is Resolution from package gp.

Standard_Boolean IsCNu (const Standard_Integer N) const
 Returns True if the order of continuity of the surface in the
U direction is N.
//! Raised if N < 0.

Standard_Boolean IsCNv (const Standard_Integer N) const
 Returns True if the order of continuity of the surface
in the V direction is N.
//! Raised if N < 0.

Standard_Boolean IsUPeriodic () const
 Returns True if the surface is closed in the U direction
and if the B-spline has been turned into a periodic surface
using the function SetUPeriodic.

Standard_Boolean IsURational () const
 Returns False if for each row of weights all the weights
are identical.
The tolerance criterion is resolution from package gp.
Example :
|1.0, 1.0, 1.0|
if Weights = |0.5, 0.5, 0.5| returns False
|2.0, 2.0, 2.0|

Standard_Boolean IsVPeriodic () const
 Returns True if the surface is closed in the V direction
and if the B-spline has been turned into a periodic
surface using the function SetVPeriodic.

Standard_Boolean IsVRational () const
 Returns False if for each column of weights all the weights
are identical.
The tolerance criterion is resolution from package gp.
Examples :
|1.0, 2.0, 0.5|
if Weights = |1.0, 2.0, 0.5| returns False
|1.0, 2.0, 0.5|

Standard_Boolean IsCacheValid (const Standard_Real UParameter, const Standard_Real VParameter) const
 
      Tells whether the Cache is valid for the <br>
      given parameter <br>

Warnings : the parameter must be normalized within
the period if the curve is periodic. Otherwise
the answer will be false


void Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const
 Returns the parametric bounds of the surface.
Warnings :
These parametric values are the bounds of the array of
knots UKnots and VKnots only if the first knots and the
last knots have a multiplicity equal to UDegree + 1 or
VDegree + 1

GeomAbs_Shape Continuity () const
 Returns the continuity of the surface :
C0 : only geometric continuity,
C1 : continuity of the first derivative all along the Surface,
C2 : continuity of the second derivative all along the Surface,
C3 : continuity of the third derivative all along the Surface,
CN : the order of continuity is infinite.
A B-spline surface is infinitely continuously differentiable
for the couple of parameters U, V such thats U != UKnots(i)
and V != VKnots(i). The continuity of the surface at a knot
value depends on the multiplicity of this knot.
Example :
If the surface is C1 in the V direction and C2 in the U
direction this function returns Shape = C1.

Standard_Integer FirstUKnotIndex () const
 Computes the Index of the UKnots which gives the first
parametric value of the surface in the U direction.
The UIso curve corresponding to this value is a
boundary curve of the surface.

Standard_Integer FirstVKnotIndex () const
 Computes the Index of the VKnots which gives the
first parametric value of the surface in the V direction.
The VIso curve corresponding to this knot is a boundary
curve of the surface.

Standard_Integer LastUKnotIndex () const
 Computes the Index of the UKnots which gives the
last parametric value of the surface in the U direction.
The UIso curve corresponding to this knot is a boundary
curve of the surface.

Standard_Integer LastVKnotIndex () const
 Computes the Index of the VKnots which gives the
last parametric value of the surface in the V direction.
The VIso curve corresponding to this knot is a
boundary curve of the surface.

Standard_Integer NbUKnots () const
 Returns the number of knots in the U direction.

Standard_Integer NbUPoles () const
 Returns number of poles in the U direction.

Standard_Integer NbVKnots () const
 Returns the number of knots in the V direction.

Standard_Integer NbVPoles () const
 Returns the number of poles in the V direction.

gp_Pnt Pole (const Standard_Integer UIndex, const Standard_Integer VIndex) const
 Returns the pole of range (UIndex, VIndex).
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
VIndex > NbVPoles.

void Poles (TColgp_Array2OfPnt &P) const
 Returns the poles of the B-spline surface.
Raised if the length of P in the U and V direction
is not equal to NbUpoles and NbVPoles.

Standard_Integer UDegree () const
 Returns the degree of the normalized B-splines Ni,n in the U
direction.

Standard_Real UKnot (const Standard_Integer UIndex) const
 Returns the Knot value of range UIndex.
//! Raised if UIndex < 1 or UIndex > NbUKnots

GeomAbs_BSplKnotDistribution UKnotDistribution () const
 Returns NonUniform or Uniform or QuasiUniform or
PiecewiseBezier. If all the knots differ by a
positive constant from the preceding knot in the U
direction the B-spline surface can be :

void UKnots (TColStd_Array1OfReal &Ku) const
 Returns the knots in the U direction.
Raised if the length of Ku is not equal to the number of knots
in the U direction.

void UKnotSequence (TColStd_Array1OfReal &Ku) const
 Returns the uknots sequence.
In this sequence the knots with a multiplicity greater than 1
are repeated.
Example :
Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}
Raised if the length of Ku is not equal to NbUPoles + UDegree + 1

Standard_Integer UMultiplicity (const Standard_Integer UIndex) const
 Returns the multiplicity value of knot of range UIndex in
the u direction.
//! Raised if UIndex < 1 or UIndex > NbUKnots.

void UMultiplicities (TColStd_Array1OfInteger &Mu) const
 Returns the multiplicities of the knots in the U direction.
Raised if the length of Mu is not equal to the number of
knots in the U direction.

Standard_Integer VDegree () const
 Returns the degree of the normalized B-splines Ni,d in the
V direction.

Standard_Real VKnot (const Standard_Integer VIndex) const
 Returns the Knot value of range VIndex.

GeomAbs_BSplKnotDistribution VKnotDistribution () const
 Returns NonUniform or Uniform or QuasiUniform or
PiecewiseBezier. If all the knots differ by a positive
constant from the preceding knot in the V direction the
B-spline surface can be :

void VKnots (TColStd_Array1OfReal &Kv) const
 Returns the knots in the V direction.
Raised if the length of Kv is not equal to the number of
knots in the V direction.

void VKnotSequence (TColStd_Array1OfReal &Kv) const
 Returns the vknots sequence.
In this sequence the knots with a multiplicity greater than 1
are repeated.
Example :
Kv = {k1, k1, k1, k2, k3, k3, k4, k4, k4}
Raised if the length of Kv is not equal to NbVPoles + VDegree + 1

Standard_Integer VMultiplicity (const Standard_Integer VIndex) const
 Returns the multiplicity value of knot of range VIndex in
the v direction.
//! Raised if VIndex < 1 or VIndex > NbVKnots

void VMultiplicities (TColStd_Array1OfInteger &Mv) const
 Returns the multiplicities of the knots in the V direction.
Raised if the length of Mv is not equal to the number of
knots in the V direction.

Standard_Real Weight (const Standard_Integer UIndex, const Standard_Integer VIndex) const
 Returns the weight value of range UIndex, VIndex.
Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1
or VIndex > NbVPoles.

void Weights (TColStd_Array2OfReal &W) const
 Returns the weights of the B-spline surface.
Raised if the length of W in the U and V direction is
not equal to NbUPoles and NbVPoles.
//! value and derivatives computation

void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const
 Computes the point of parameter U,V on the surface.
Raised only for an "OffsetSurface" if it is not possible to
compute the current point.

void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const
 Raised if the continuity of the surface is not C1.

void D2 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV) const
 Raised if the continuity of the surface is not C2.

void D3 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV, gp_Vec &D3U, gp_Vec &D3V, gp_Vec &D3UUV, gp_Vec &D3UVV) const
 Raised if the continuity of the surface is not C3.

gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const
 Nu is the order of derivation in the U parametric direction and
Nv is the order of derivation in the V parametric direction.
Raised if the continuity of the surface is not CNu in the U
direction and CNv in the V direction.
Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
The following functions computes the point for the
parametric values (U, V) and the derivatives at
this point on the B-spline surface patch delimited
with the knots FromUK1, FromVK1 and the knots ToUK2,
ToVK2. (U, V) can be out of these parametric bounds
but for the computation we only use the definition
of the surface between these knots. This method is
useful to compute local derivative, if the order of
continuity of the whole surface is not greater enough.
Inside the parametric knot's domain previously defined
the evaluations are the same as if we consider the whole
definition of the surface. Of course the evaluations are
different outside this parametric domain.

void LocalD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, gp_Pnt &P) const
 Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

void LocalD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const
 Raised if the local continuity of the surface is not C1
between the knots FromUK1, ToUK2 and FromVK1, ToVK2.
//! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

void LocalD2 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV) const
 Raised if the local continuity of the surface is not C2
between the knots FromUK1, ToUK2 and FromVK1, ToVK2.
//! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

void LocalD3 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV, gp_Vec &D3U, gp_Vec &D3V, gp_Vec &D3UUV, gp_Vec &D3UVV) const
 Raised if the local continuity of the surface is not C3
between the knots FromUK1, ToUK2 and FromVK1, ToVK2.
//! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

gp_Vec LocalDN (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, const Standard_Integer Nu, const Standard_Integer Nv) const
 Raised if the local continuity of the surface is not CNu
between the knots FromUK1, ToUK2 and CNv between the knots
FromVK1, ToVK2.
//! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

gp_Pnt LocalValue (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2) const
 Computes the point of parameter U, V on the BSpline surface patch
defines between the knots UK1 UK2, VK1, VK2. U can be out of the
bounds [Knot UK1, Knot UK2] and V can be outof the bounds
[Knot VK1, Knot VK2] but for the computation we only use the
definition of the surface between these knot values.
//! Raises if FromUK1 = ToUK2 or FromVK1 = ToVK2.
Raises if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

Handle_Geom_Curve UIso (const Standard_Real U) const
 Computes the U isoparametric curve.
A B-spline curve is returned.

Handle_Geom_Curve VIso (const Standard_Real V) const
 Computes the V isoparametric curve.
A B-spline curve is returned.

Handle_Geom_Curve UIso (const Standard_Real U, const Standard_Boolean CheckRational) const
 Computes the U isoparametric curve.
If CheckRational=False, no try to make it non-rational.
A B-spline curve is returned.

Handle_Geom_Curve VIso (const Standard_Real V, const Standard_Boolean CheckRational) const
 Computes the V isoparametric curve.
If CheckRational=False, no try to make it non-rational.
A B-spline curve is returned.
//! transformations

void Transform (const gp_Trsf &T)
 Applies the transformation T to this BSpline surface.

void Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance, Standard_Real &VTolerance)
 Computes two tolerance values for this BSpline
surface, based on the given tolerance in 3D space
Tolerance3D. The tolerances computed are:

Handle_Geom_Geometry Copy () const
 Creates a new object which is a copy of this BSpline surface.

Static Public Member Functions

static Standard_Integer MaxDegree ()
 Returns the value of the maximum degree of the normalized
B-spline basis functions in the u and v directions.


Detailed Description


Constructor & Destructor Documentation


Member Function Documentation

void Geom_BSplineSurface::Bounds ( Standard_Real U1,
Standard_Real U2,
Standard_Real V1,
Standard_Real V2 
) const [virtual]

Implements Geom_Surface.

Implements Geom_Surface.

Handle_Geom_Geometry Geom_BSplineSurface::Copy ( ) const [virtual]

Implements Geom_Geometry.

void Geom_BSplineSurface::D0 ( const Standard_Real  U,
const Standard_Real  V,
gp_Pnt P 
) const [virtual]

Implements Geom_Surface.

void Geom_BSplineSurface::D1 ( const Standard_Real  U,
const Standard_Real  V,
gp_Pnt P,
gp_Vec D1U,
gp_Vec D1V 
) const [virtual]

Implements Geom_Surface.

void Geom_BSplineSurface::D2 ( const Standard_Real  U,
const Standard_Real  V,
gp_Pnt P,
gp_Vec D1U,
gp_Vec D1V,
gp_Vec D2U,
gp_Vec D2V,
gp_Vec D2UV 
) const [virtual]

Implements Geom_Surface.

void Geom_BSplineSurface::D3 ( const Standard_Real  U,
const Standard_Real  V,
gp_Pnt P,
gp_Vec D1U,
gp_Vec D1V,
gp_Vec D2U,
gp_Vec D2V,
gp_Vec D2UV,
gp_Vec D3U,
gp_Vec D3V,
gp_Vec D3UUV,
gp_Vec D3UVV 
) const [virtual]

Implements Geom_Surface.

Implements Geom_Surface.

  • the poles and weights tables are transposed,
  • the knots and multiplicities tables are exchanged,
  • degrees of continuity, and rational, periodic and
    uniform characteristics are exchanged, and
  • the orientation of the surface is inverted.
  • the value U, or V, with the multiplicity M (defaulted to 1), or
  • the values of the array Knots, with their respective
    multiplicities, Mults.
    If the knot value to insert already exists in the table, its multiplicity is:
  • increased by M, if Add is true (the default), or
  • increased to M, if Add is false.
    The tolerance criterion used to check the equality of
    the knots is the larger of the values ParametricTolerance and
    Standard_Real::Epsilon(val), where val is the knot value to be inserted.
    Warning
  • If a given multiplicity coefficient is null, or negative, nothing is done.
  • The new multiplicity of a knot is limited to the degree of this BSpline surface in the
    corresponding parametric direction.
    Exceptions
    Standard_ConstructionError if a knot value to
    insert is outside the bounds of this BSpline surface in
    the specified parametric direction. The comparison
    uses the precision criterion ParametricTolerance.

Implements Geom_Surface.

Implements Geom_Surface.

Implements Geom_Surface.

Implements Geom_Surface.

Implements Geom_Surface.

Implements Geom_Surface.

void Geom_BSplineSurface::LocalD2 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  FromUK1,
const Standard_Integer  ToUK2,
const Standard_Integer  FromVK1,
const Standard_Integer  ToVK2,
gp_Pnt P,
gp_Vec D1U,
gp_Vec D1V,
gp_Vec D2U,
gp_Vec D2V,
gp_Vec D2UV 
) const
void Geom_BSplineSurface::LocalD3 ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  FromUK1,
const Standard_Integer  ToUK2,
const Standard_Integer  FromVK1,
const Standard_Integer  ToVK2,
gp_Pnt P,
gp_Vec D1U,
gp_Vec D1V,
gp_Vec D2U,
gp_Vec D2V,
gp_Vec D2UV,
gp_Vec D3U,
gp_Vec D3V,
gp_Vec D3UUV,
gp_Vec D3UVV 
) const
void Geom_BSplineSurface::LocateU ( const Standard_Real  U,
const Standard_Real  ParametricTolerance,
Standard_Integer I1,
Standard_Integer I2,
const Standard_Boolean  WithKnotRepetition = Standard_False 
) const
void Geom_BSplineSurface::LocateV ( const Standard_Real  V,
const Standard_Real  ParametricTolerance,
Standard_Integer I1,
Standard_Integer I2,
const Standard_Boolean  WithKnotRepetition = Standard_False 
) const
void Geom_BSplineSurface::MovePoint ( const Standard_Real  U,
const Standard_Real  V,
const gp_Pnt P,
const Standard_Integer  UIndex1,
const Standard_Integer  UIndex2,
const Standard_Integer  VIndex1,
const Standard_Integer  VIndex2,
Standard_Integer UFirstIndex,
Standard_Integer ULastIndex,
Standard_Integer VFirstIndex,
Standard_Integer VLastIndex 
)
void Geom_BSplineSurface::Resolution ( const Standard_Real  Tolerance3D,
Standard_Real UTolerance,
Standard_Real VTolerance 
)
  • UTolerance in the u parametric direction, and
  • VTolerance in the v parametric direction.
    If f(u,v) is the equation of this BSpline surface,
    UTolerance and VTolerance guarantee that :
    | u1 - u0 | < UTolerance and
    | v1 - v0 | < VTolerance
    ====> |f (u1,v1) - f (u0,v0)| < Tolerance3D

Implements Geom_Geometry.

Handle_Geom_Curve Geom_BSplineSurface::UIso ( const Standard_Real  U) const [virtual]

Implements Geom_Surface.

Handle_Geom_Curve Geom_BSplineSurface::UIso ( const Standard_Real  U,
const Standard_Boolean  CheckRational 
) const
  • Uniform if all the knots are of multiplicity 1,
  • QuasiUniform if all the knots are of multiplicity 1
    except for the first and last knot which are of
    multiplicity Degree + 1,
  • PiecewiseBezier if the first and last knots have
    multiplicity Degree + 1 and if interior knots have
    multiplicity Degree
    otherwise the surface is non uniform in the U direction
    The tolerance criterion is Resolution from package gp.

Implements Geom_Surface.

Implements Geom_Surface.

Handle_Geom_Curve Geom_BSplineSurface::VIso ( const Standard_Real  V) const [virtual]

Implements Geom_Surface.

Handle_Geom_Curve Geom_BSplineSurface::VIso ( const Standard_Real  V,
const Standard_Boolean  CheckRational 
) const
  • Uniform if all the knots are of multiplicity 1,
  • QuasiUniform if all the knots are of multiplicity 1
    except for the first and last knot which are of
    multiplicity Degree + 1,
  • PiecewiseBezier if the first and last knots have
    multiplicity Degree + 1 and if interior knots have
    multiplicity Degree
    otherwise the surface is non uniform in the V direction.
    The tolerance criterion is Resolution from package gp.

Implements Geom_Surface.

  • UFirst + ULast - U, or
  • VFirst + VLast - V,
    where UFirst, ULast, VFirst and VLast are
    the values of the first and last parameters of this
    BSpline surface, in the u and v parametric directions.

Implements Geom_Surface.


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