#include <Geom_BSplineSurface.hxx>
Inheritance diagram for Geom_BSplineSurface:
Public Member Functions | |
Standard_EXPORT | 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. . | |
Standard_EXPORT | 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. . | |
Standard_EXPORT void | ExchangeUV () |
Exchanges the u and v parametric directions on this BSpline surface. As a consequence: - 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. . | |
Standard_EXPORT void | SetUPeriodic () |
Sets the surface U periodic. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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 | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT void | SetUNotPeriodic () |
Standard_EXPORT 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. . | |
Standard_EXPORT void | UReverse () |
Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. . | |
Standard_EXPORT 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_EXPORT 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_EXPORT 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: - 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. . | |
Standard_EXPORT 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(). . | |
Standard_EXPORT void | InsertUKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_True) |
Standard_EXPORT 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: - 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. . | |
Standard_EXPORT Standard_Boolean | RemoveUKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance) |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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]. . | |
Standard_EXPORT 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]. . | |
Standard_EXPORT 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 . | |
Standard_EXPORT 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 . | |
Standard_EXPORT 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) . | |
Standard_EXPORT 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 . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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) . | |
Standard_EXPORT 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 . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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) . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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 . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT Standard_Boolean | IsCacheValid (const Standard_Real UParameter, const Standard_Real VParameter) const |
Tells whether the Cache is valid for the given parameter Warnings : the parameter must be normalized within the period if the curve is periodic. Otherwise the answer will be false . | |
Standard_EXPORT 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 . | |
Standard_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT 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_EXPORT Standard_Integer | NbUKnots () const |
Returns the number of knots in the U direction. . | |
Standard_EXPORT Standard_Integer | NbUPoles () const |
Returns number of poles in the U direction. . | |
Standard_EXPORT Standard_Integer | NbVKnots () const |
Returns the number of knots in the V direction. . | |
Standard_EXPORT Standard_Integer | NbVPoles () const |
Returns the number of poles in the V direction. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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_EXPORT Standard_Integer | UDegree () const |
Returns the degree of the normalized B-splines Ni,n in the U direction. . | |
Standard_EXPORT Standard_Real | UKnot (const Standard_Integer UIndex) const |
Returns the Knot value of range UIndex. //! Raised if UIndex < 1 or UIndex > NbUKnots . | |
Standard_EXPORT 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 : - 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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_EXPORT 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. . | |
Standard_EXPORT 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_EXPORT Standard_Integer | VDegree () const |
Returns the degree of the normalized B-splines Ni,d in the V direction. . | |
Standard_EXPORT Standard_Real | VKnot (const Standard_Integer VIndex) const |
Returns the Knot value of range VIndex. . | |
Standard_EXPORT 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 : - 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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_EXPORT 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 . | |
Standard_EXPORT 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_EXPORT 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. . | |
Standard_EXPORT 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 . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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] . | |
Standard_EXPORT 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] . | |
Standard_EXPORT 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] . | |
Standard_EXPORT 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] . | |
Standard_EXPORT 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] . | |
Standard_EXPORT 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] . | |
Standard_EXPORT Handle_Geom_Curve | UIso (const Standard_Real U) const |
Computes the U isoparametric curve. A B-spline curve is returned. . | |
Standard_EXPORT Handle_Geom_Curve | VIso (const Standard_Real V) const |
Computes the V isoparametric curve. A B-spline curve is returned. . | |
Standard_EXPORT 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. . | |
Standard_EXPORT 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 . | |
Standard_EXPORT void | Transform (const gp_Trsf &T) |
Applies the transformation T to this BSpline surface. . | |
Standard_EXPORT 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: - 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 . | |
Standard_EXPORT Handle_Geom_Geometry | Copy () const |
Creates a new object which is a copy of this BSpline surface. . | |
Standard_EXPORT const | Handle (Standard_Type)&DynamicType() const |
Static Public Member Functions | |
static Standard_EXPORT Standard_Integer | MaxDegree () |
Returns the value of the maximum degree of the normalized B-spline basis functions in the u and v directions. . | |
Private Member Functions | |
Standard_EXPORT void | UpdateUKnots () |
Recompute the flatknots, the knotsdistribution, the continuity for U. . | |
Standard_EXPORT void | UpdateVKnots () |
Recompute the flatknots, the knotsdistribution, the continuity for V. . | |
Standard_EXPORT void | InvalidateCache () |
Invalidates the cache. This has to be private this has to be private . | |
Standard_EXPORT void | ValidateCache (const Standard_Real UParameter, const Standard_Real VParameter) |
updates the cache and validates it | |
Private Attributes | |
Standard_Boolean | urational |
Standard_Boolean | vrational |
Standard_Boolean | uperiodic |
Standard_Boolean | vperiodic |
GeomAbs_BSplKnotDistribution | uknotSet |
GeomAbs_BSplKnotDistribution | vknotSet |
GeomAbs_Shape | Usmooth |
GeomAbs_Shape | Vsmooth |
Standard_Integer | udeg |
Standard_Integer | vdeg |
Handle_TColgp_HArray2OfPnt | poles |
Handle_TColStd_HArray2OfReal | weights |
Handle_TColStd_HArray1OfReal | ufknots |
Handle_TColStd_HArray1OfReal | vfknots |
Handle_TColStd_HArray1OfReal | uknots |
Handle_TColStd_HArray1OfReal | vknots |
Handle_TColStd_HArray1OfInteger | umults |
Handle_TColStd_HArray1OfInteger | vmults |
Handle_TColgp_HArray2OfPnt | cachepoles |
Handle_TColStd_HArray2OfReal | cacheweights |
Standard_Real | ucacheparameter |
Standard_Real | vcacheparameter |
Standard_Real | ucachespanlenght |
Standard_Real | vcachespanlenght |
Standard_Integer | ucachespanindex |
Standard_Integer | vcachespanindex |
Standard_Integer | validcache |
Standard_Real | umaxderivinv |
Standard_Real | vmaxderivinv |
Standard_Boolean | maxderivinvok |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Geometry. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Reimplemented from Geom_BoundedSurface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Geometry. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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Implements Geom_Surface. |
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