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-- File: Geom2dConvert.cdl
-- Created: Thu Oct 3 14:34:29 1991
-- Author: Jean Claude VAUTHIER
---Copyright: Matra Datavision 1991, 1992
package Geom2dConvert
--- Purpose :
-- This package provides an implementation of algorithmes to do
-- the conversion between equivalent geometric entities from
-- package Geom2d.
-- It gives the possibility :
-- . to obtain the B-spline representation of bounded curves.
-- . to split a B-spline curve into several B-spline curves
-- with some constraints of continuity,
-- . to convert a B-spline curve into several Bezier curves
-- or surfaces.
-- All the 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, TColGeom2d,gp, Geom2d, Convert,GeomAbs
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 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 ApproxCurve;
---Purpose : -- Convert a curve to BSpline by Approximation
--
SplitBSplineCurve (C : BSplineCurve from Geom2d;
FromK1, ToK2 : Integer;
SameOrientation : Boolean = Standard_True)
returns mutable BSplineCurve from Geom2d
--- 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 OutOfRange from Standard,
--- Purpose :
-- Raised if FromK1 or ToK2 are out of the bounds
-- [FirstUKnotIndex, LastUKnotIndex]
DomainError from Standard;
--- Purpose : Raised if FromK1 = ToK2
SplitBSplineCurve (C : BSplineCurve from Geom2d;
FromU1, ToU2 : Real;
ParametricTolerance : Real;
SameOrientation : Boolean = Standard_True)
returns mutable BSplineCurve from Geom2d
--- 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.
CurveToBSplineCurve (C : Curve from Geom2d ;
Parameterisation : ParameterisationType from Convert
= Convert_TgtThetaOver2)
returns mutable BSplineCurve from Geom2d
--- 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 Offset curve or a trimmed
-- Offset curve.
-- The returned B-spline is not periodic except if C is a
-- Circle or an 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.
-- Standard_ConstructionError:
-- - if C is a complete circle or ellipse, and if
-- Parameterisation is not equal to
-- Convert_TgtThetaOver2 or to Convert_RationalC1, or
-- - if C is a trimmed circle or ellipse and 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 and
-- 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;
ConcatG1(ArrayOfCurves : in out Array1OfBSplineCurve from TColGeom2d;
ArrayOfToler : in Array1OfReal from TColStd;
ArrayOfConcatenated : out HArray1OfBSplineCurve from TColGeom2d;
ClosedFlag : 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]
-- ClosedTolerance indicates if the ArrayOfCurves is closed.
-- In this case ClosedTolerance 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 TColGeom2d;
ArrayOfToler : in Array1OfReal from TColStd;
ArrayOfIndices : out HArray1OfInteger from TColStd;
ArrayOfConcatenated : out HArray1OfBSplineCurve from TColGeom2d;
ClosedFlag : 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]
-- ClosedTolerance indicates if the ArrayOfCurves is closed.
-- In this case ClosedTolerance 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 TColGeom2d;
ArrayOfToler : in Array1OfReal from TColStd;
ArrayOfIndices : out HArray1OfInteger from TColStd;
ArrayOfConcatenated : out HArray1OfBSplineCurve from TColGeom2d;
ClosedFlag : 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]
-- ClosedTolerance indicates if the ArrayOfCurves is closed.
-- In this case ClosedTolerance 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 Geom2d;
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 a new BSpline which could still be C0.
-- tolerance is a geometrical tolerance
C0BSplineToArrayOfC1BSplineCurve(BS : in BSplineCurve from Geom2d;
tabBS : out HArray1OfBSplineCurve from TColGeom2d;
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 Geom2d;
tabBS : out HArray1OfBSplineCurve from TColGeom2d;
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
end Geom2dConvert;
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