-- 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;