#include <Geom_BezierSurface.hxx>
Inheritance diagram for Geom_BezierSurface:
Public Member Functions | |
Standard_EXPORT | Geom_BezierSurface (const TColgp_Array2OfPnt &SurfacePoles) |
Creates a non-rational Bezier surface with a set of poles. Control points representation : SPoles(Uorigin,Vorigin) ...................SPoles(Uorigin,Vend) . . . . SPoles(Uend, Vorigin) .....................SPoles(Uend, Vend) For the double array the row indice corresponds to the parametric U direction and the columns indice corresponds to the parametric V direction. The weights are defaulted to all being 1. Raised if the number of poles of the surface is lower than 2 or greater than MaxDegree + 1 in one of the two directions U or V. . | |
Standard_EXPORT | Geom_BezierSurface (const TColgp_Array2OfPnt &SurfacePoles, const TColStd_Array2OfReal &PoleWeights) |
---Purpose Creates a rational Bezier surface with a set of poles and a set of weights. For the double array the row indice corresponds to the parametric U direction and the columns indice corresponds to the parametric V direction. If all the weights are identical the surface is considered as non-rational (the tolerance criterion is Resolution from package gp). Raised if SurfacePoles and PoleWeights have not the same Rowlength or have not the same ColLength. Raised if PoleWeights (i, j) <= Resolution from gp; Raised if the number of poles of the surface is lower than 2 or greater than MaxDegree + 1 in one of the two directions U or V. | |
Standard_EXPORT void | ExchangeUV () |
Exchanges the direction U and V on a Bezier surface As a consequence: - the poles and weights tables are transposed, - degrees, rational characteristics and so on are exchanged between the two parametric directions, and - the orientation of the surface is reversed. . | |
Standard_EXPORT void | Increase (const Standard_Integer UDeg, const Standard_Integer VDeg) |
Increases the degree of this Bezier surface in the two parametric directions. Raised if UDegree < UDegree <me> or VDegree < VDegree <me> Raised if the degree of the surface is greater than MaxDegree in one of the two directions U or V. . | |
Standard_EXPORT void | InsertPoleColAfter (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles) |
Inserts a column of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1. Raised if Vindex < 1 or VIndex > NbVPoles. raises if VDegree is greater than MaxDegree. raises if the Length of CPoles is not equal to NbUPoles . | |
Standard_EXPORT void | InsertPoleColAfter (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights) |
Inserts a column of poles and weights. If the surface was non-rational it can become rational. Raised if Vindex < 1 or VIndex > NbVPoles. //! Raised if . VDegree is greater than MaxDegree. . the Length of CPoles is not equal to NbUPoles . a weight value is lower or equal to Resolution from package gp . | |
Standard_EXPORT void | InsertPoleColBefore (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles) |
Inserts a column of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1. Raised if Vindex < 1 or VIndex > NbVPoles. Raised if VDegree is greater than MaxDegree. Raised if the Length of CPoles is not equal to NbUPoles . | |
Standard_EXPORT void | InsertPoleColBefore (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights) |
Inserts a column of poles and weights. If the surface was non-rational it can become rational. Raised if Vindex < 1 or VIndex > NbVPoles. //! Raised if : . VDegree is greater than MaxDegree. . the Length of CPoles is not equal to NbUPoles . a weight value is lower or equal to Resolution from package gp . | |
Standard_EXPORT void | InsertPoleRowAfter (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles) |
Inserts a row of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1. Raised if Uindex < 1 or UIndex > NbUPoles. Raised if UDegree is greater than MaxDegree. Raised if the Length of CPoles is not equal to NbVPoles . | |
Standard_EXPORT void | InsertPoleRowAfter (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights) |
Inserts a row of poles and weights. If the surface was non-rational it can become rational. Raised if Uindex < 1 or UIndex > NbUPoles. //! Raised if : . UDegree is greater than MaxDegree. . the Length of CPoles is not equal to NbVPoles . a weight value is lower or equal to Resolution from package gp . | |
Standard_EXPORT void | InsertPoleRowBefore (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles) |
Inserts a row of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1. Raised if Uindex < 1 or UIndex > NbUPoles. Raised if UDegree is greater than MaxDegree. Raised if the Length of CPoles is not equal to NbVPoles . | |
Standard_EXPORT void | InsertPoleRowBefore (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights) |
Inserts a row of poles and weights. If the surface was non-rational it can become rational. Raised if Uindex < 1 or UIndex > NbUPoles. //! Raised if : . UDegree is greater than MaxDegree. . the Length of CPoles is not equal to NbVPoles . a weight value is lower or equal to Resolution from pacakage gp . | |
Standard_EXPORT void | RemovePoleCol (const Standard_Integer VIndex) |
Removes a column of poles. If the surface was rational it can become non-rational. Raised if NbVPoles <= 2 after removing, a Bezier surface must have at least two columns of poles. //! Raised if Vindex < 1 or VIndex > NbVPoles . | |
Standard_EXPORT void | RemovePoleRow (const Standard_Integer UIndex) |
Removes a row of poles. If the surface was rational it can become non-rational. Raised if NbUPoles <= 2 after removing, a Bezier surface must have at least two rows of poles. //! Raised if Uindex < 1 or UIndex > NbUPoles . | |
Standard_EXPORT void | Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2) |
Modifies this Bezier surface by segmenting it between U1 and U2 in the u parametric direction, and between V1 and V2 in the v parametric direction. U1, U2, V1, and V2 can be outside the bounds of this surface. - U1 and U2 isoparametric Bezier curves, segmented between V1 and V2, become the two bounds of the surface in the v parametric direction (0. and 1. u isoparametric curves). - V1 and V2 isoparametric Bezier curves, segmented between U1 and U2, become the two bounds of the surface in the u parametric direction (0. and 1. v isoparametric curves). The poles and weights tables are modified, but the degree of this surface in the u and v parametric directions does not change. U1 can be greater than U2, and V1 can be greater than V2. In these cases, the corresponding parametric direction is inverted. The orientation of the surface is inverted if one (and only one) parametric direction is inverted. . | |
Standard_EXPORT void | SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt &P) |
Modifies a pole value. 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. If the surface <me> is not rational it can become rational. if the surface was rational it can become non-rational. raises 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) |
Modifies a column of poles. The length of CPoles can be lower but not greater than NbUPoles so you can modify just a part of the 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) |
Modifies a column of poles. If the surface was rational it can become non-rational If the surface was non-rational it can become rational. The length of CPoles can be lower but not greater than NbUPoles so you can modify just a part of the column. //! Raised if VIndex < 1 or VIndex > NbVPoles Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles Raised if CPoleWeights and CPoles have not the same bounds. Raised if one of the weight value CPoleWeights (i) is lower or equal to Resolution from package gp. . | |
Standard_EXPORT void | SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles) |
Modifies a row of poles. The length of CPoles can be lower but not greater than NbVPoles so you can modify just a part of the row. //! Raised if UIndex < 1 or UIndex > NbUPoles Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles . | |
Standard_EXPORT void | SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights) |
Modifies a row of poles and weights. If the surface was rational it can become non-rational. If the surface was non-rational it can become rational. The length of CPoles can be lower but not greater than NbVPoles so you can modify just a part of the row. //! Raised if UIndex < 1 or UIndex > NbUPoles Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles Raised if CPoleWeights and CPoles have not the same bounds. Raised if one of the weight value CPoleWeights (i) is lower or equal to Resolution from gp. . | |
Standard_EXPORT void | SetWeight (const Standard_Integer UIndex, const Standard_Integer VIndex, const Standard_Real Weight) |
Modifies 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 <= Resolution from package gp. . | |
Standard_EXPORT void | SetWeightCol (const Standard_Integer VIndex, const TColStd_Array1OfReal &CPoleWeights) |
Modifies a column of weights. If the surface was rational it can become non-rational. If the surface was non-rational it can become rational. The length of CPoleWeights can be lower but not greater than NbUPoles. //! Raised if VIndex < 1 or VIndex > NbVPoles Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() > NbUPoles Raised if one of the weight value CPoleWeights (i) is lower or equal to Resolution from package gp. . | |
Standard_EXPORT void | SetWeightRow (const Standard_Integer UIndex, const TColStd_Array1OfReal &CPoleWeights) |
Modifies a row of weights. If the surface was rational it can become non-rational. If the surface was non-rational it can become rational. The length of CPoleWeights can be lower but not greater than NbVPoles. //! Raised if UIndex < 1 or UIndex > NbUPoles Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() > NbVPoles Raised if one of the weight value CPoleWeights (i) is lower or equal to Resolution from package gp. . | |
Standard_EXPORT void | UReverse () |
Changes the orientation of this Bezier surface in the u 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. . | |
Standard_EXPORT Standard_Real | UReversedParameter (const Standard_Real U) const |
Computes the u (or v) parameter on the modified surface, produced by reversing its u (or v) parametric direction, for any point of u parameter U (or of v parameter V) on this Bezier surface. In the case of a Bezier surface, these functions return respectively: - 1.-U, or 1.-V. . | |
Standard_EXPORT void | VReverse () |
Changes the orientation of this Bezier surface in the 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. . | |
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 any point of u parameter U (or of v parameter V) on this Bezier surface. In the case of a Bezier surface, these functions return respectively: - 1.-U, or 1.-V. . | |
Standard_EXPORT void | Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const |
Returns the parametric bounds U1, U2, V1 and V2 of this Bezier surface. In the case of a Bezier surface, this function returns U1 = 0, V1 = 0, U2 = 1, V2 = 1. . | |
Standard_EXPORT GeomAbs_Shape | Continuity () const |
Returns the continuity of the surface CN : the order of continuity is infinite. . | |
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 |
Computes the point P and the first derivatives in the directions U and V at this point. //! 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 |
Computes the point P, the first and the second derivatives in the directions U and V at this point. //! 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 |
Computes P, the point of parameters (U, V) of this Bezier surface, and - one or more of the following sets of vectors: - D1U and D1V, the first derivative vectors at this point, - D2U, D2V and D2UV, the second derivative vectors at this point, - D3U, D3V, D3UUV and D3UVV, the third derivative vectors at this point. Note: The parameters U and V can be outside the bounds of the surface. . | |
Standard_EXPORT gp_Vec | DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const |
Computes the derivative of order Nu in the u parametric direction, and Nv in the v parametric direction, at the point of parameters (U, V) of this Bezier surface. Note: The parameters U and V can be outside the bounds of the surface. Exceptions Standard_RangeError if: - Nu + Nv is less than 1, or Nu or Nv is negative. . | |
Standard_EXPORT Standard_Integer | NbUPoles () const |
Returns the number of poles in the U 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 Bezier surface. Raised if the length of P in the U an V direction is not equal to NbUPoles and NbVPoles. . | |
Standard_EXPORT Standard_Integer | UDegree () const |
Returns the degree of the surface in the U direction it is NbUPoles - 1 . | |
Standard_EXPORT Handle_Geom_Curve | UIso (const Standard_Real U) const |
Computes the U isoparametric curve. For a Bezier surface the UIso curve is a Bezier curve. . | |
Standard_EXPORT Standard_Integer | VDegree () const |
Returns the degree of the surface in the V direction it is NbVPoles - 1 . | |
Standard_EXPORT Handle_Geom_Curve | VIso (const Standard_Real V) const |
Computes the V isoparametric curve. For a Bezier surface the VIso curve is a Bezier curve. . | |
Standard_EXPORT Standard_Real | Weight (const Standard_Integer UIndex, const Standard_Integer VIndex) const |
Returns the weight 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 Bezier surface. Raised if the length of W in the U an V direction is not equal to NbUPoles and NbVPoles. . | |
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 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, a Bezier surface is always CN . | |
Standard_EXPORT Standard_Boolean | IsCNv (const Standard_Integer N) const |
Returns True, a BezierSurface is always CN . | |
Standard_EXPORT Standard_Boolean | IsUPeriodic () const |
Returns False. . | |
Standard_EXPORT Standard_Boolean | IsVPeriodic () const |
Returns False. . | |
Standard_EXPORT Standard_Boolean | IsURational () const |
Returns False if the weights are identical in the U direction, 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 | IsVRational () const |
Returns False if the weights are identical in the V direction, The tolerance criterion is Resolution from package gp. Example : |1.0, 2.0, 0.5| if Weights = |1.0, 2.0, 0.5| returns False |1.0, 2.0, 0.5| . | |
Standard_EXPORT void | Transform (const gp_Trsf &T) |
Applies the transformation T to this Bezier surface. . | |
Standard_EXPORT void | Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance, Standard_Real &VTolerance) |
Computes two tolerance values for this Bezier 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 Bezier 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 Bezier 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 polynomial degree of a Bezier surface. This value is 25. . | |
Private Member Functions | |
Standard_EXPORT | Geom_BezierSurface (const Handle(TColgp_HArray2OfPnt)&SurfacePoles, const Handle(TColgp_HArray2OfPnt)&SurfaceCoefficients, const Handle(TColStd_HArray2OfReal)&PoleWeights, const Handle(TColStd_HArray2OfReal)&CoefficientWeights, const Standard_Boolean IsURational, const Standard_Boolean IsVRational) |
Standard_EXPORT void | Init (const Handle(TColgp_HArray2OfPnt)&Poles, const Handle(TColStd_HArray2OfReal)&Weights) |
Set poles to Poles, weights to Weights (not copied). Create the arrays of coefficients. Poles and Weights are assumed to have the first coefficient 1. if nbpoles < 2 or nbpoles > MaDegree . | |
Standard_EXPORT void | UpdateCoefficients (const Standard_Real U=0.0, const Standard_Real V=0.0) |
Recompute the coeficients. . | |
Private Attributes | |
Standard_Boolean | urational |
Standard_Boolean | vrational |
Handle_TColgp_HArray2OfPnt | poles |
Handle_TColStd_HArray2OfReal | weights |
Handle_TColgp_HArray2OfPnt | coeffs |
Handle_TColStd_HArray2OfReal | wcoeffs |
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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