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occt/src/Geom/Geom_BSplineSurface.hxx

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// Created on: 1993-03-09
// Created by: JCV
// Copyright (c) 1993-1999 Matra Datavision
// Copyright (c) 1999-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.
#ifndef _Geom_BSplineSurface_HeaderFile
#define _Geom_BSplineSurface_HeaderFile
#include <Standard.hxx>
#include <Standard_Type.hxx>
#include <Precision.hxx>
#include <GeomAbs_BSplKnotDistribution.hxx>
#include <GeomAbs_Shape.hxx>
#include <Standard_Integer.hxx>
#include <TColgp_HArray2OfPnt.hxx>
#include <TColStd_HArray2OfReal.hxx>
#include <TColStd_HArray1OfReal.hxx>
#include <TColStd_HArray1OfInteger.hxx>
#include <Geom_BoundedSurface.hxx>
#include <TColgp_Array2OfPnt.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColStd_Array1OfInteger.hxx>
#include <TColStd_Array2OfReal.hxx>
#include <TColgp_Array1OfPnt.hxx>
class gp_Pnt;
class gp_Vec;
class Geom_Curve;
class gp_Trsf;
class Geom_Geometry;
class Geom_BSplineSurface;
DEFINE_STANDARD_HANDLE(Geom_BSplineSurface, Geom_BoundedSurface)
//! Describes a BSpline surface.
//! In each parametric direction, a BSpline surface can be:
//! - uniform or non-uniform,
//! - rational or non-rational,
//! - periodic or non-periodic.
//! A BSpline surface is defined by:
//! - its degrees, in the u and v parametric directions,
//! - its periodic characteristic, in the u and v parametric directions,
//! - a table of poles, also called control points (together
//! with the associated weights if the surface is rational), and
//! - a table of knots, together with the associated multiplicities.
//! The degree of a Geom_BSplineSurface is limited to
//! a value (25) which is defined and controlled by the
//! system. This value is returned by the function MaxDegree.
//! Poles and Weights
//! Poles and Weights are manipulated using two associative double arrays:
//! - the poles table, which is a double array of gp_Pnt points, and
//! - the weights table, which is a double array of reals.
//! The bounds of the poles and weights arrays are:
//! - 1 and NbUPoles for the row bounds (provided
//! that the BSpline surface is not periodic in the u
//! parametric direction), where NbUPoles is the
//! number of poles of the surface in the u parametric direction, and
//! - 1 and NbVPoles for the column bounds (provided
//! that the BSpline surface is not periodic in the v
//! parametric direction), where NbVPoles is the
//! number of poles of the surface in the v parametric direction.
//! The poles of the surface are the points used to shape
//! and reshape the surface. They comprise a rectangular network.
//! If the surface is not periodic:
//! - The points (1, 1), (NbUPoles, 1), (1,
//! NbVPoles), and (NbUPoles, NbVPoles)
//! are the four parametric "corners" of the surface.
//! - The first column of poles and the last column of
//! poles define two BSpline curves which delimit the
//! surface in the v parametric direction. These are the
//! v isoparametric curves corresponding to the two
//! bounds of the v parameter.
//! - The first row of poles and the last row of poles
//! define two BSpline curves which delimit the surface
//! in the u parametric direction. These are the u
//! isoparametric curves corresponding to the two bounds of the u parameter.
//! If the surface is periodic, these geometric properties are not verified.
//! It is more difficult to define a geometrical significance
//! for the weights. However they are useful for
//! representing a quadric surface precisely. Moreover, if
//! the weights of all the poles are equal, the surface has
//! a polynomial equation, and hence is a "non-rational surface".
//! The non-rational surface is a special, but frequently
//! used, case, where all poles have identical weights.
//! The weights are defined and used only in the case of
//! a rational surface. The rational characteristic is
//! defined in each parametric direction. A surface can be
//! rational in the u parametric direction, and
//! non-rational in the v parametric direction.
//! Knots and Multiplicities
//! For a Geom_BSplineSurface the table of knots is
//! made up of two increasing sequences of reals, without
//! repetition, one for each parametric direction. The
//! multiplicities define the repetition of the knots.
//! A BSpline surface comprises multiple contiguous
//! patches, which are themselves polynomial or rational
//! surfaces. The knots are the parameters of the
//! isoparametric curves which limit these contiguous
//! patches. The multiplicity of a knot on a BSpline
//! surface (in a given parametric direction) is related to
//! the degree of continuity of the surface at that knot in
//! that parametric direction:
//! Degree of continuity at knot(i) = Degree - Multi(i) where:
//! - Degree is the degree of the BSpline surface in
//! the given parametric direction, and
//! - Multi(i) is the multiplicity of knot number i in
//! the given parametric direction.
//! There are some special cases, where the knots are
//! regularly spaced in one parametric direction (i.e. the
//! difference between two consecutive knots is a constant).
//! - "Uniform": all the multiplicities are equal to 1.
//! - "Quasi-uniform": all the multiplicities are equal to 1,
//! except for the first and last knots in this parametric
//! direction, and these are equal to Degree + 1.
//! - "Piecewise Bezier": all the multiplicities are equal to
//! Degree except for the first and last knots, which
//! are equal to Degree + 1. This surface is a
//! concatenation of Bezier patches in the given
//! parametric direction.
//! If the BSpline surface is not periodic in a given
//! parametric direction, the bounds of the knots and
//! multiplicities tables are 1 and NbKnots, where
//! NbKnots is the number of knots of the BSpline
//! surface in that parametric direction.
//! If the BSpline surface is periodic in a given parametric
//! direction, and there are k periodic knots and p
//! periodic poles in that parametric direction:
//! - the period is such that:
//! period = Knot(k+1) - Knot(1), and
//! - the poles and knots tables in that parametric
//! direction can be considered as infinite tables, such that:
//! Knot(i+k) = Knot(i) + period, and
//! Pole(i+p) = Pole(i)
//! Note: The data structure tables for a periodic BSpline
//! surface are more complex than those of a non-periodic one.
//! References :
//! . A survey of curve and surface methods in CADG Wolfgang BOHM
//! CAGD 1 (1984)
//! . On de Boor-like algorithms and blossoming Wolfgang BOEHM
//! cagd 5 (1988)
//! . Blossoming and knot insertion algorithms for B-spline curves
//! Ronald N. GOLDMAN
//! . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA
//! . Curves and Surfaces for Computer Aided Geometric Design,
//! a practical guide Gerald Farin
class Geom_BSplineSurface : public Geom_BoundedSurface
{
public:
//! 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
//! recommended 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_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
//! recommended 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);
//! 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 ExchangeUV();
//! Sets the surface U periodic.
//! Modifies this surface to be periodic in the U
//! 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 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 SetUPeriodic();
//! Sets the surface V periodic.
//! Modifies this surface to be periodic in the 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 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 SetVPeriodic();
//! returns the parameter normalized within
//! the period if the surface is periodic : otherwise
//! does not do anything
Standard_EXPORT void PeriodicNormalization (Standard_Real& U, Standard_Real& V) const;
//! 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 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);
//! Sets the surface U not periodic.
//! Changes this BSpline surface into a non-periodic
//! surface along U direction.
//! If this surface is already non-periodic, it is not modified.
//! Note: the poles and knots tables are modified.
Standard_EXPORT void SetUNotPeriodic();
//! Sets the surface V not periodic.
//! Changes this BSpline surface into a non-periodic
//! surface along V direction.
//! If this surface is already non-periodic, it is not modified.
//! Note: the poles and knots tables are modified.
Standard_EXPORT void SetVNotPeriodic();
//! Changes the orientation of this BSpline 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.
//! The knots and poles tables are modified.
Standard_EXPORT void UReverse() Standard_OVERRIDE;
//! Changes the orientation of this BSpline 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.
//! The knots and poles tables are modified.
Standard_EXPORT void VReverse() Standard_OVERRIDE;
//! Computes the u parameter on the modified
//! surface, produced by reversing its U parametric
//! direction, for the point of u parameter U, on this BSpline surface.
//! For a BSpline surface, these functions return respectively:
//! - UFirst + ULast - U,
//! where UFirst, ULast are
//! the values of the first and last parameters of this
//! BSpline surface, in the u parametric directions.
Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
//! Computes the v parameter on the modified
//! surface, produced by reversing its V parametric
//! direction, for the point of v parameter V on this BSpline surface.
//! For a BSpline surface, these functions return respectively:
//! - VFirst + VLast - V,
//! VFirst and VLast are
//! the values of the first and last parameters of this
//! BSpline surface, in the v pametric directions.
Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const Standard_OVERRIDE;
//! 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 IncreaseDegree (const Standard_Integer UDegree, const Standard_Integer VDegree);
//! Inserts into the knots table for the U
//! parametric direction of this BSpline surface:
//! - 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 void InsertUKnots (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 V
//! parametric direction of this BSpline surface:
//! - 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 void InsertVKnots (const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger& Mults, const Standard_Real ParametricTolerance = 0.0, const Standard_Boolean Add = Standard_True);
//! Reduces to M the multiplicity of the knot of index
//! Index in the U 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 Standard_Boolean RemoveUKnot (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 V 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 Standard_Boolean RemoveVKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance);
//! 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 UIndex, 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 IncreaseUMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer M);
//! 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 IncrementUMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer Step);
//! 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 VIndex, 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 IncreaseVMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer M);
//! 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 IncrementVMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer Step);
//! 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 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 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 InsertVKnot (const Standard_Real V, const Standard_Integer M, const Standard_Real ParametricTolerance, const Standard_Boolean Add = Standard_True);
//! 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.
//!
//! Parameters theUTolerance, theVTolerance define the possible proximity along the corresponding
//! direction of the segment boundaries and B-spline knots to treat them as equal.
//!
//! 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_DomainError if U2 - U1 exceeds the uperiod for uperiodic surfaces.
//! i.e. ((U2 - U1) - UPeriod) > Precision::PConfusion().
//! Standard_DomainError if V2 - V1 exceeds the vperiod for vperiodic surfaces.
//! i.e. ((V2 - V1) - VPeriod) > Precision::PConfusion()).
Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2,
const Standard_Real theUTolerance = Precision::PConfusion(),
const Standard_Real theVTolerance = Precision::PConfusion());
//! 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
//!
//! Parameters theUTolerance, theVTolerance define the possible proximity along the corresponding
//! direction of the segment boundaries and B-spline knots to treat them as equal.
//!
//! 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_DomainError if U2 - U1 exceeds the uperiod for uperiodic surfaces.
//! i.e. ((U2 - U1) - UPeriod) > Precision::PConfusion().
//! Standard_DomainError if V2 - V1 exceeds the vperiod for vperiodic surfaces.
//! i.e. ((V2 - V1) - VPeriod) > Precision::PConfusion()).
Standard_EXPORT void CheckAndSegment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2,
const Standard_Real theUTolerance = Precision::PConfusion(),
const Standard_Real theVTolerance = Precision::PConfusion());
//! 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 SetUKnot (const Standard_Integer UIndex, const Standard_Real K);
//! 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 SetUKnots (const TColStd_Array1OfReal& UK);
//! 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 SetUKnot (const Standard_Integer UIndex, const Standard_Real K, const Standard_Integer M);
//! 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 SetVKnot (const Standard_Integer VIndex, const Standard_Real K);
//! 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 SetVKnots (const TColStd_Array1OfReal& VK);
//! 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 SetVKnot (const Standard_Integer VIndex, const Standard_Real K, const Standard_Integer M);
//! 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 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 V 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 LocateV (const Standard_Real V, const Standard_Real ParametricTolerance, Standard_Integer& I1, Standard_Integer& I2, const Standard_Boolean WithKnotRepetition = Standard_False) const;
//! 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);
//! 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 SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt& P, const Standard_Real Weight);
//! 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);
//! 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 SetPoleCol (const Standard_Integer VIndex, 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, const TColStd_Array1OfReal& CPoleWeights);
//! 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 SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles);
//! 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 SetWeight (const Standard_Integer UIndex, const Standard_Integer VIndex, const Standard_Real Weight);
//! 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 SetWeightCol (const Standard_Integer VIndex, 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 SetWeightRow (const Standard_Integer UIndex, const TColStd_Array1OfReal& CPoleWeights);
//! 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 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);
//! 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 IsUClosed() const Standard_OVERRIDE;
//! 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 IsVClosed() const Standard_OVERRIDE;
//! Returns True if the order of continuity of the surface in the
//! U direction is N.
//! Raised if N < 0.
Standard_EXPORT Standard_Boolean IsCNu (const Standard_Integer N) const Standard_OVERRIDE;
//! Returns True if the order of continuity of the surface
//! in the V direction is N.
//! Raised if N < 0.
Standard_EXPORT Standard_Boolean IsCNv (const Standard_Integer N) const Standard_OVERRIDE;
//! 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 IsUPeriodic() const Standard_OVERRIDE;
//! 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 IsURational() 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 IsVPeriodic() const Standard_OVERRIDE;
//! 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 IsVRational() 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 void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const Standard_OVERRIDE;
//! 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 that 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 GeomAbs_Shape Continuity() const Standard_OVERRIDE;
//! 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 FirstUKnotIndex() 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 FirstVKnotIndex() 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 LastUKnotIndex() 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 LastVKnotIndex() const;
//! Returns the number of knots in the U direction.
Standard_EXPORT Standard_Integer NbUKnots() const;
//! Returns number of poles in the U direction.
Standard_EXPORT Standard_Integer NbUPoles() const;
//! Returns the number of knots in the V direction.
Standard_EXPORT Standard_Integer NbVKnots() const;
//! Returns the number of poles in the V direction.
Standard_EXPORT Standard_Integer NbVPoles() const;
//! Returns the pole of range (UIndex, VIndex).
//!
//! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
//! VIndex > NbVPoles.
Standard_EXPORT const gp_Pnt& Pole(const Standard_Integer UIndex, const Standard_Integer VIndex) 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 void Poles (TColgp_Array2OfPnt& P) const;
//! Returns the poles of the B-spline surface.
Standard_EXPORT const TColgp_Array2OfPnt& Poles() const;
//! Returns the degree of the normalized B-splines Ni,n in the U
//! direction.
Standard_EXPORT Standard_Integer UDegree() const;
//! Returns the Knot value of range UIndex.
//! Raised if UIndex < 1 or UIndex > NbUKnots
Standard_EXPORT Standard_Real UKnot (const Standard_Integer UIndex) 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 GeomAbs_BSplKnotDistribution UKnotDistribution() 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 UKnots (TColStd_Array1OfReal& Ku) const;
//! Returns the knots in the U direction.
Standard_EXPORT const TColStd_Array1OfReal& UKnots() 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 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}
Standard_EXPORT const TColStd_Array1OfReal& UKnotSequence() const;
//! Returns the multiplicity value of knot of range UIndex in
//! the u direction.
//! Raised if UIndex < 1 or UIndex > NbUKnots.
Standard_EXPORT Standard_Integer UMultiplicity (const Standard_Integer UIndex) 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 void UMultiplicities (TColStd_Array1OfInteger& Mu) const;
//! Returns the multiplicities of the knots in the U direction.
Standard_EXPORT const TColStd_Array1OfInteger& UMultiplicities() const;
//! Returns the degree of the normalized B-splines Ni,d in the
//! V direction.
Standard_EXPORT Standard_Integer VDegree() const;
//! Returns the Knot value of range VIndex.
//! Raised if VIndex < 1 or VIndex > NbVKnots
Standard_EXPORT Standard_Real VKnot (const Standard_Integer VIndex) 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 GeomAbs_BSplKnotDistribution VKnotDistribution() 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 VKnots (TColStd_Array1OfReal& Kv) const;
//! Returns the knots in the V direction.
Standard_EXPORT const TColStd_Array1OfReal& VKnots() 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 void VKnotSequence (TColStd_Array1OfReal& Kv) const;
//! Returns the vknots 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}
Standard_EXPORT const TColStd_Array1OfReal& VKnotSequence() const;
//! Returns the multiplicity value of knot of range VIndex in
//! the v direction.
//! Raised if VIndex < 1 or VIndex > NbVKnots
Standard_EXPORT Standard_Integer VMultiplicity (const Standard_Integer VIndex) 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 void VMultiplicities (TColStd_Array1OfInteger& Mv) const;
//! Returns the multiplicities of the knots in the V direction.
Standard_EXPORT const TColStd_Array1OfInteger& VMultiplicities() const;
//! Returns the weight value of range UIndex, VIndex.
//!
//! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1
//! or VIndex > NbVPoles.
Standard_EXPORT Standard_Real Weight (const Standard_Integer UIndex, const Standard_Integer VIndex) 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.
Standard_EXPORT void Weights (TColStd_Array2OfReal& W) const;
//! Returns the weights of the B-spline surface.
//! value and derivatives computation
Standard_EXPORT const TColStd_Array2OfReal* Weights() const;
Standard_EXPORT void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const Standard_OVERRIDE;
//! Raised if the continuity of the surface is not C1.
Standard_EXPORT void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const Standard_OVERRIDE;
//! Raised if the continuity of the surface is not C2.
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 Standard_OVERRIDE;
//! Raised if the continuity of the surface is not C3.
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 Standard_OVERRIDE;
//! 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 gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const Standard_OVERRIDE;
//! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
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 the local continuity of the surface is not C1
//! between the knots FromUK1, ToUK2 and FromVK1, ToVK2.
//! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
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 C2
//! between the knots FromUK1, ToUK2 and FromVK1, ToVK2.
//! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
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 C3
//! between the knots FromUK1, ToUK2 and FromVK1, ToVK2.
//! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
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 CNu
//! between the knots FromUK1, ToUK2 and CNv between the knots
//! FromVK1, ToVK2.
//! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
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;
//! 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.
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 U isoparametric curve.
//! A B-spline curve is returned.
Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const Standard_OVERRIDE;
//! Computes the V isoparametric curve.
//! A B-spline curve is returned.
Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const Standard_OVERRIDE;
//! 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) UIso (const Standard_Real U, 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 Handle(Geom_Curve) VIso (const Standard_Real V, const Standard_Boolean CheckRational) const;
//! Applies the transformation T to this BSpline surface.
Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE;
//! Returns the value of the maximum degree of the normalized
//! B-spline basis functions in the u and v directions.
Standard_EXPORT static Standard_Integer MaxDegree();
//! 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 void Resolution (const Standard_Real Tolerance3D, Standard_Real& UTolerance, Standard_Real& VTolerance);
//! Creates a new object which is a copy of this BSpline surface.
Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE;
//! Dumps the content of me into the stream
Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE;
DEFINE_STANDARD_RTTIEXT(Geom_BSplineSurface,Geom_BoundedSurface)
protected:
//! 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.
//!
//! Parameters EpsU, EpsV define the proximity along U-Direction and V-Direction respectively.
void segment(const Standard_Real U1, const Standard_Real U2,
const Standard_Real V1, const Standard_Real V2,
const Standard_Real EpsU, const Standard_Real EpsV,
const Standard_Boolean SegmentInU, const Standard_Boolean SegmentInV);
private:
//! Recompute the flatknots, the knotsdistribution, the
//! continuity for U.
Standard_EXPORT void UpdateUKnots();
//! Recompute the flatknots, the knotsdistribution, the
//! continuity for V.
Standard_EXPORT void UpdateVKnots();
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;
Standard_Real umaxderivinv;
Standard_Real vmaxderivinv;
Standard_Boolean maxderivinvok;
};
#endif // _Geom_BSplineSurface_HeaderFile
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