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-- Created on: 1991-10-03
-- Created by: JeanClaude VAUTHIER
-- Copyright (c) 1991-1999 Matra Datavision
-- Copyright (c) 1999-2012 OPEN CASCADE SAS
--
-- The content of this file is subject to the Open CASCADE Technology Public
-- License Version 6.5 (the "License"). You may not use the content of this file
-- except in compliance with the License. Please obtain a copy of the License
-- at http://www.opencascade.org and read it completely before using this file.
--
-- The Initial Developer of the Original Code is Open CASCADE S.A.S., having its
-- main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France.
--
-- The Original Code and all software distributed under the License is
-- distributed on an "AS IS" basis, without warranty of any kind, and the
-- Initial Developer hereby disclaims all such warranties, including without
-- limitation, any warranties of merchantability, fitness for a particular
-- purpose or non-infringement. Please see the License for the specific terms
-- and conditions governing the rights and limitations under the License.
-- Modified : 07/10/97 : JPI/RBV/SMN : traitement des courbes offset
-- et surfaces offset par approximation
package GeomConvert
--- Purpose : The GeomConvert package provides some global functions as follows
-- - converting classical Geom curves into BSpline curves,
-- - segmenting BSpline curves, particularly at knots
-- values: this function may be used in conjunction with the
-- GeomConvert_BSplineCurveKnotSplitting
-- class to segment a BSpline curve into arcs which
-- comply with required continuity levels,
-- - converting classical Geom surfaces into BSpline surfaces, and
-- - segmenting BSpline surfaces, particularly at
-- knots values: this function may be used in conjunction with the
-- GeomConvert_BSplineSurfaceKnotSplitting
-- class to segment a BSpline surface into patches
-- which comply with required continuity levels.
-- All geometric entities used in this package are bounded.
--
-- References :
-- . Generating the Bezier Points of B-spline curves and surfaces
-- (Wolfgang Bohm) CAGD volume 13 number 6 november 1981
-- . On NURBS: A Survey (Leslie Piegl) IEEE Computer Graphics and
-- Application January 1991
-- . Curve and surface construction using rational B-splines
-- (Leslie Piegl and Wayne Tiller) CAD Volume 19 number 9 november
-- 1987
-- . A survey of curve and surface methods in CAGD (Wolfgang BOHM)
-- CAGD 1 1984
uses Standard,
TColStd,
TColGeom,
TColgp,
GeomAbs,
gp,
Geom,
Geom2d,
Convert,
AdvApp2Var
is
class BSplineCurveKnotSplitting;
--- Purpose : This algorithm searches the knot values corresponding to the
-- splitting of a given B-spline curve into several arcs with
-- the same continuity. The continuity order is given at the
-- construction time. It is possible to compute the curve arcs
-- corresponding to this splitting with the method of package
-- SplitBSplineCurve.
class BSplineSurfaceKnotSplitting;
--- Purpose :
-- This algorithm searches the knot values corresponding to the
-- splitting of a given B-spline surface into several patches with
-- the same continuity. The continuity order is given at the
-- construction time. It is possible to compute the surface patches
-- corresponding to the splitting with the method of package
-- SplitBSplineSurface.
class BSplineCurveToBezierCurve;
--- Purpose :
-- This algorithm converts a B-spline curve from the package Geom
-- into several Bezier curves.
class CompCurveToBSplineCurve;
--- Purpose :
-- This algorithm converts and concat sevral curve in a
-- B-spline curve.
class BSplineSurfaceToBezierSurface;
--- Purpose :
-- This algorithm converts a B-spline surface from the package Geom
-- into several Bezier surfaces.
class CompBezierSurfacesToBSplineSurface;
---Purpose: Convert a grid of Bezier Surfaces
-- that are have continuity CM to an
-- Bspline Surface that has continuity CM
class ApproxSurface;
---Purpose: Convert a surface from Geom by an approximation method
--
class ApproxCurve;
---Purpose: Convert a curve from Geom by an approximation method
--
SplitBSplineCurve (C : BSplineCurve from Geom;
FromK1, ToK2 : Integer;
SameOrientation : Boolean = Standard_True)
returns mutable BSplineCurve from Geom
--- Purpose :
-- This method computes the arc of B-spline curve between the two
-- knots FromK1 and ToK2. If C is periodic the arc has the same
-- orientation as C if SameOrientation = Standard_True.
-- If C is not periodic SameOrientation is not used for the
-- computation and C is oriented from the knot fromK1 to the knot toK2.
-- We just keep the local definition of C between the knots
-- FromK1 and ToK2. The returned B-spline curve has its first
-- and last knots with a multiplicity equal to degree + 1, where
-- degree is the polynomial degree of C.
-- The indexes of the knots FromK1 and ToK2 doesn't include the
-- repetition of multiple knots in their definition.
raises DomainError from Standard;
--- Purpose : Raised if FromK1 = ToK2
-- Raised if FromK1 or ToK2 are out of the bounds
-- [FirstUKnotIndex, LastUKnotIndex]
SplitBSplineCurve (C : BSplineCurve from Geom;
FromU1, ToU2 : Real;
ParametricTolerance : Real;
SameOrientation : Boolean = Standard_True)
returns mutable BSplineCurve from Geom
--- Purpose :
-- This function computes the segment of B-spline curve between the
-- parametric values FromU1, ToU2.
-- If C is periodic the arc has the same orientation as C if
-- SameOrientation = True.
-- If C is not periodic SameOrientation is not used for the
-- computation and C is oriented fromU1 toU2.
-- If U1 and U2 and two parametric values we consider that
-- U1 = U2 if Abs (U1 - U2) <= ParametricTolerance and
-- ParametricTolerance must be greater or equal to Resolution
-- from package gp.
raises DomainError from Standard;
--- Purpose :
-- Raised if FromU1 or ToU2 are out of the parametric bounds of the
-- curve (The tolerance criterion is ParametricTolerance).
-- Raised if Abs (FromU1 - ToU2) <= ParametricTolerance
-- Raised if ParametricTolerance < Resolution from gp.
SplitBSplineSurface (S : BSplineSurface from Geom;
FromUK1, ToUK2, FromVK1, ToVK2 : Integer;
SameUOrientation : Boolean = Standard_True;
SameVOrientation : Boolean = Standard_True)
returns mutable BSplineSurface from Geom
--- Purpose :
-- Computes the B-spline surface patche between the knots values
-- FromUK1, ToUK2, FromVK1, ToVK2.
-- If S is periodic in one direction the patche has the same
-- orientation as S in this direction if the flag is true in this
-- direction (SameUOrientation, SameVOrientation).
-- If S is not periodic SameUOrientation and SameVOrientation are not
-- used for the computation and S is oriented FromUK1 ToUK2 and
-- FromVK1 ToVK2.
raises DomainError from Standard;
--- Purpose : Raised if
-- FromUK1 = ToUK2 or FromVK1 = ToVK2
-- FromUK1 or ToUK2 are out of the bounds
-- [FirstUKnotIndex, LastUKnotIndex]
-- FromVK1 or ToVK2 are out of the bounds
-- [FirstVKnotIndex, LastVKnotIndex]
SplitBSplineSurface (S : BSplineSurface from Geom;
FromK1, ToK2 : Integer;
USplit : Boolean;
SameOrientation : Boolean = Standard_True)
returns mutable BSplineSurface from Geom
--- Purpose :
-- This method splits a B-spline surface patche between the
-- knots values FromK1, ToK2 in one direction.
-- If USplit = True then the splitting direction is the U parametric
-- direction else it is the V parametric direction.
-- If S is periodic in the considered direction the patche has the
-- same orientation as S in this direction if SameOrientation is True
-- If S is not periodic in this direction SameOrientation is not used
-- for the computation and S is oriented FromK1 ToK2.
raises DomainError from Standard;
--- Purpose : Raised if FromK1 = ToK2 or if
-- FromK1 or ToK2 are out of the bounds
-- [FirstUKnotIndex, LastUKnotIndex] in the
-- considered parametric direction.
SplitBSplineSurface (S : BSplineSurface from Geom;
FromU1, ToU2, FromV1, ToV2 : Real;
ParametricTolerance : Real;
SameUOrientation : Boolean = Standard_True;
SameVOrientation : Boolean = Standard_True)
returns mutable BSplineSurface from Geom
--- Purpose :
-- This method computes the B-spline surface patche between the
-- parametric values FromU1, ToU2, FromV1, ToV2.
-- If S is periodic in one direction the patche has the same
-- orientation as S in this direction if the flag is True in this
-- direction (SameUOrientation, SameVOrientation).
-- If S is not periodic SameUOrientation and SameVOrientation are not
-- used for the computation and S is oriented FromU1 ToU2 and
-- FromV1 ToV2.
-- If U1 and U2 and two parametric values we consider that U1 = U2 if
-- Abs (U1 - U2) <= ParametricTolerance and ParametricTolerance must
-- be greater or equal to Resolution from package gp.
raises DomainError from Standard;
--- Purpose :
-- Raised if FromU1 or ToU2 or FromV1 or ToU2 are out of the
-- parametric bounds of the surface (the tolerance criterion is
-- ParametricTolerance).
-- Raised if Abs (FromU1 - ToU2) <= ParametricTolerance or
-- Abs (FromV1 - ToV2) <= ParametricTolerance.
-- Raised if ParametricTolerance < Resolution.
SplitBSplineSurface (S : BSplineSurface from Geom;
FromParam1, ToParam2 : Real;
USplit : Boolean;
ParametricTolerance : Real;
SameOrientation : Boolean = Standard_True)
returns mutable BSplineSurface from Geom
--- Purpose :
-- This method splits the B-spline surface S in one direction
-- between the parametric values FromParam1, ToParam2.
-- If USplit = True then the Splitting direction is the U parametric
-- direction else it is the V parametric direction.
-- If S is periodic in the considered direction the patche has
-- the same orientation as S in this direction if SameOrientation
-- is true.
-- If S is not periodic in the considered direction SameOrientation
-- is not used for the computation and S is oriented FromParam1
-- ToParam2.
-- If U1 and U2 and two parametric values we consider that U1 = U2
-- if Abs (U1 - U2) <= ParametricTolerance and ParametricTolerance
-- must be greater or equal to Resolution from package gp.
raises DomainError from Standard;
--- Purpose :
-- Raises if FromParam1 or ToParam2 are out of the parametric bounds
-- of the surface in the considered direction.
-- Raises if Abs (FromParam1 - ToParam2) <= ParametricTolerance.
CurveToBSplineCurve (C : Curve from Geom ;
Parameterisation : ParameterisationType from Convert
= Convert_TgtThetaOver2)
returns mutable BSplineCurve from Geom
--- Purpose : This function converts a non infinite curve from
-- Geom into a B-spline curve. C must be an ellipse or a
-- circle or a trimmed conic or a trimmed line or a Bezier
-- curve or a trimmed Bezier curve or a BSpline curve or a
-- trimmed BSpline curve or an OffsetCurve. The returned B-spline is
-- not periodic except if C is a Circle or an Ellipse. If
-- the Parameterisation is QuasiAngular than the returned
-- curve is NOT periodic in case a periodic Geom_Circle or
-- Geom_Ellipse. For TgtThetaOver2_1 and TgtThetaOver2_2 the
-- method raises an exception in case of a periodic
-- Geom_Circle or a Geom_Ellipse ParameterisationType applies
-- only if the curve is a Circle or an ellipse :
-- TgtThetaOver2, -- TgtThetaOver2_1, -- TgtThetaOver2_2, --
-- TgtThetaOver2_3, -- TgtThetaOver2_4,
--
-- Purpose: this is the classical rational parameterisation
-- 2
-- 1 - t
-- cos(theta) = ------
-- 2
-- 1 + t
--
-- 2t
-- sin(theta) = ------
-- 2
-- 1 + t
--
-- t = tan (theta/2)
--
-- with TgtThetaOver2 the routine will compute the number of spans
-- using the rule num_spans = [ (ULast - UFirst) / 1.2 ] + 1
-- with TgtThetaOver2_N, N spans will be forced: an error will
-- be raized if (ULast - UFirst) >= PI and N = 1,
-- ULast - UFirst >= 2 PI and N = 2
--
-- QuasiAngular,
-- here t is a rational function that approximates
-- theta ----> tan(theta/2).
-- Neverthless the composing with above function yields exact
-- functions whose square sum up to 1
-- RationalC1 ;
-- t is replaced by a polynomial function of u so as to grant
-- C1 contiuity across knots.
-- Exceptions
-- Standard_DomainError:
-- - if the curve C is infinite, or
-- - if C is a (complete) circle or ellipse, and Parameterisation is equal to
-- Convert_TgtThetaOver2_1 or Convert_TgtThetaOver2_2.
-- Standard_ConstructionError:
-- - if C is a (complete) circle or ellipse, and if Parameterisation is not equal to
-- Convert_TgtThetaOver2, Convert_RationalC1,
-- Convert_QuasiAngular (the curve is converted
-- in these three cases) or to Convert_TgtThetaOver2_1 or
-- Convert_TgtThetaOver2_2 (another exception is raised in these two cases).
-- - if C is a trimmed circle or ellipse, if Parameterisation is equal to
-- Convert_TgtThetaOver2_1 and if U2 - U1 > 0.9999 * Pi, where U1 and U2 are
-- respectively the first and the last parameters of the
-- trimmed curve (this method of parameterization
-- cannot be used to convert a half-circle or a half-ellipse, for example), or
-- - if C is a trimmed circle or ellipse, if
-- Parameterisation is equal to Convert_TgtThetaOver2_2 and U2 - U1 >
-- 1.9999 * Pi where U1 and U2 are
-- respectively the first and the last parameters of the
-- trimmed curve (this method of parameterization
-- cannot be used to convert a quasi-complete circle or ellipse).
raises DomainError,
ConstructionError;
SurfaceToBSplineSurface (S : Surface from Geom)
returns mutable BSplineSurface from Geom
--- Purpose :
-- This algorithm converts a non infinite surface from Geom
-- into a B-spline surface.
-- S must be a trimmed plane or a trimmed cylinder or a trimmed cone
-- or a trimmed sphere or a trimmed torus or a sphere or a torus or
-- a Bezier surface of a trimmed Bezier surface or a trimmed swept
-- surface with a corresponding basis curve which can be turned into
-- a B-spline curve (see the method CurveToBSplineCurve).
-- Raises DomainError if the type of the surface is not previously defined.
raises DomainError;
ConcatG1(ArrayOfCurves : in out Array1OfBSplineCurve from TColGeom;
ArrayOfToler : in Array1OfReal from TColStd;
ArrayOfConcatenated : out HArray1OfBSplineCurve from TColGeom;
ClosedG1Flag : in Boolean from Standard ;
ClosedTolerance : in Real from Standard) ;
--- Purpose : This Method concatenates G1 the ArrayOfCurves as far
-- as it is possible.
-- ArrayOfCurves[0..N-1]
-- ArrayOfToler contains the biggest tolerance of the two
-- points shared by two consecutives curves.
-- Its dimension: [0..N-2]
-- ClosedG1 indicates if the ArrayOfCurves is closed.
-- In this case ClosedG1 contains the biggest tolerance
-- of the two points which are at the closure.
-- Otherwise its value is 0.0
ConcatC1(ArrayOfCurves : in out Array1OfBSplineCurve from TColGeom;
ArrayOfToler : in Array1OfReal from TColStd;
ArrayOfIndices : out HArray1OfInteger from TColStd;
ArrayOfConcatenated : out HArray1OfBSplineCurve from TColGeom;
ClosedG1Flag : in Boolean from Standard ;
ClosedTolerance : in Real from Standard) ;
--- Purpose : This Method concatenates C1 the ArrayOfCurves as far
-- as it is possible.
-- ArrayOfCurves[0..N-1]
-- ArrayOfToler contains the biggest tolerance of the two
-- points shared by two consecutives curves.
-- Its dimension: [0..N-2]
-- ClosedG1 indicates if the ArrayOfCurves is closed.
-- In this case ClosedG1 contains the biggest tolerance
-- of the two points which are at the closure.
-- Otherwise its value is 0.0
ConcatC1(ArrayOfCurves : in out Array1OfBSplineCurve from TColGeom;
ArrayOfToler : in Array1OfReal from TColStd;
ArrayOfIndices : out HArray1OfInteger from TColStd;
ArrayOfConcatenated : out HArray1OfBSplineCurve from TColGeom;
ClosedG1Flag : in Boolean from Standard ;
ClosedTolerance : in Real from Standard ;
AngularTolerance : in Real from Standard) ;
--- Purpose : This Method concatenates C1 the ArrayOfCurves as far
-- as it is possible.
-- ArrayOfCurves[0..N-1]
-- ArrayOfToler contains the biggest tolerance of the two
-- points shared by two consecutives curves.
-- Its dimension: [0..N-2]
-- ClosedG1 indicates if the ArrayOfCurves is closed.
-- In this case ClosedG1 contains the biggest tolerance
-- of the two points which are at the closure.
-- Otherwise its value is 0.0
--
C0BSplineToC1BSplineCurve(BS : in out BSplineCurve from Geom;
tolerance : in Real from Standard;
AngularTolerance: in Real = 1.0e-7);
---Purpose : This Method reduces as far as it is possible the
-- multiplicities of the knots of the BSpline BS.(keeping the
-- geometry). It returns a new BSpline which could still be C0.
-- tolerance is a geometrical tolerance.
-- The Angular toleranceis in radians and mesures the angle of
-- the tangents on the left and on the right to decide if the
-- curve is G1 or not at a given point
C0BSplineToArrayOfC1BSplineCurve(BS : in BSplineCurve from Geom;
tabBS : out HArray1OfBSplineCurve from TColGeom;
tolerance : in Real from Standard);
--- Purpose : This Method reduces as far as it is possible the
-- multiplicities of the knots of the BSpline BS.(keeping the geometry).
-- It returns an array of BSpline C1. tolerance is a geometrical tolerance.
C0BSplineToArrayOfC1BSplineCurve(BS : in BSplineCurve from Geom;
tabBS : out HArray1OfBSplineCurve from TColGeom;
AngularTolerance : in Real from Standard ;
tolerance : in Real from Standard);
--- Purpose :This Method reduces as far as it is possible the
-- multiplicities of the knots of the BSpline BS.(keeping the
-- geometry). It returns an array of BSpline C1. tolerance is a
-- geometrical tolerance : it allows for the maximum deformation
-- The Angular tolerance is in radians and mesures the angle of
-- the tangents on the left and on the right to decide if the curve
-- is C1 or not at a given point
end GeomConvert;
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