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-- File: Convert.cdl
-- Created: Thu Oct 10 11:23:08 1991
-- Author: Jean Claude VAUTHIER
---Copyright: Matra Datavision 1991, 1992
package Convert
--- Purpose:
--The Convert package provides algorithms to convert the following into a BSpline curve or surface:
-- - a bounded curve based on an elementary 2D curve (line, circle or conic) from the gp package,
-- - a bounded surface based on an elementary surface (cylinder, cone, sphere or torus) from the gp package,
-- - a series of adjacent 2D or 3D Bezier curves defined by their poles.
-- These algorithms compute the data needed to define the resulting BSpline curve or surface.
-- This elementary data (degrees, periodic characteristics, poles and weights, knots and
-- multiplicities) may then be used directly in an algorithm, or can be used to construct the curve
-- or the surface by calling the appropriate constructor provided by the classes
-- Geom2d_BSplineCurve, Geom_BSplineCurve or Geom_BSplineSurface.
uses TColStd,
TColgp,
StdFail,
gp,
GeomAbs,
TCollection
is
enumeration ParameterisationType is
TgtThetaOver2,
TgtThetaOver2_1,
TgtThetaOver2_2,
TgtThetaOver2_3,
TgtThetaOver2_4,
---Purpose:
-- Identifies a type of parameterization of a circle or ellipse represented as a BSpline curve.
-- For a circle with a center C and a radius R (for example a Geom2d_Circle or a Geom_Circle),
-- the natural parameterization is angular. It uses the angle Theta made by the vector CM with
-- the 'X Axis' of the circle's local coordinate system as parameter for the current point M. The
-- coordinates of the point M are as follows:
-- X = R *cos ( Theta )
-- y = R * sin ( Theta )
-- Similarly, for an ellipse with a center C, a major radius R and a minor radius r, the circle Circ
-- with center C and radius R (and located in the same plane as the ellipse) lends its natural
-- angular parameterization to the ellipse. This is achieved by an affine transformation in the plane
-- of the ellipse, in the ratio r / R, about the 'X Axis' of its local coordinate system. The
-- coordinates of the current point M are as follows:
-- X = R * cos ( Theta )
-- y = r * sin ( Theta )
-- The process of converting a circle or an ellipse into a rational or non-rational BSpline curve
-- transforms the Theta angular parameter into a parameter t. This ensures the rational or
-- polynomial parameterization of the resulting BSpline curve. Several types of parametric
-- transformations are available.
-- TgtThetaOver2
-- The most usual method is Convert_TgtThetaOver2 where the parameter t on the BSpline
-- curve is obtained by means of transformation of the following type:
-- t = tan ( Theta / 2 )
-- The result of this definition is:
-- cos ( Theta ) = ( 1. - t**2 ) / ( 1. + t**2 )
-- sin ( Theta ) = 2. * t / ( 1. + t**2 )
-- which ensures the rational parameterization of the circle or the ellipse. However, this is not the
-- most suitable parameterization method where the arc of the circle or ellipse has a large opening
-- angle. In such cases, the curve will be represented by a BSpline with intermediate knots. Each
-- span, i.e. each portion of curve between two different knot values, will use parameterization of
-- this type.
-- The number of spans is calculated using the following rule:
-- ( 1.2 * Delta / Pi ) + 1
-- where Delta is equal to the opening angle (in radians) of the arc of the circle (Delta is
-- equal to 2.* Pi in the case of a complete circle).
-- The resulting BSpline curve is "exact", i.e. computing any point of parameter t on the BSpline
-- curve gives an exact point on the circle or the ellipse.
-- TgtThetaOver2_N
-- Where N is equal to 1, 2, 3 or 4, this ensures the same type of parameterization as
-- Convert_TgtThetaOver2 but sets the number of spans in the resulting BSpline curve to N
-- rather than allowing the algorithm to make this calculation.
-- However, the opening angle Delta (parametric angle, given in radians) of the arc of the circle
-- (or of the ellipse) must comply with the following:
-- - Delta <= 0.9999 * Pi for the Convert_TgtThetaOver2_1 method, or
-- - Delta <= 1.9999 * Pi for the Convert_TgtThetaOver2_2 method.
-- QuasiAngular
-- The Convert_QuasiAngular method of parameterization uses a different type of rational
-- parameterization. This method ensures that the parameter t along the resulting BSpline curve is
-- very close to the natural parameterization angle Theta of the circle or ellipse (i.e. which uses
-- the functions sin ( Theta ) and cos ( Theta ).
-- The resulting BSpline curve is "exact", i.e. computing any point of parameter t on the BSpline
-- curve gives an exact point on the circle or the ellipse.
-- RationalC1
-- The Convert_RationalC1 method of parameterization uses a further type of rational
-- parameterization. This method ensures that the equation relating to the resulting BSpline curve
-- has a "C1" continuous denominator, which is not the case with the above methods. RationalC1
-- enhances the degree of continuity at the junction point of the different spans of the curve.
-- The resulting BSpline curve is "exact", i.e. computing any point of parameter t on the BSpline
-- curve gives an exact point on the circle or the ellipse.
-- Polynomial
-- The Convert_Polynomial method is used to produce polynomial (i.e. non-rational)
-- parameterization of the resulting BSpline curve with 8 poles (i.e. a polynomial degree equal to 7).
-- However, the result is an approximation of the circle or ellipse (i.e. computing the point of
-- parameter t on the BSpline curve does not give an exact point on the circle or the ellipse).
QuasiAngular,
RationalC1,
Polynomial;
imported CosAndSinEvalFunction ;
-- typedef void *CosAndSinEvalFunction(Standard_Real,
-- const Standard_Integer,
-- const TColgp_Array1OfPnt2d&
-- const TColStd_Array1OfReal&
-- const TColStd_Array1OfInteger&
-- Standard_Real Result[2]
--
deferred class ConicToBSplineCurve;
--- Purpose :
-- Super class of the following classes :
class CircleToBSplineCurve;
--- Purpose : Converts a circle into a B-spline curve.
class EllipseToBSplineCurve;
--- Purpose : Converts an ellipse into a B-spline curve.
class HyperbolaToBSplineCurve;
--- Purpose : Converts an hyperbola into a B-spline curve.
class ParabolaToBSplineCurve;
--- Purpose : Converts a parabola into a B-spline curve.
deferred class ElementarySurfaceToBSplineSurface;
-- Super class of the following classes :
class CylinderToBSplineSurface;
--- Purpose : Converts a bounded cylinder into a B-spline surface.
class ConeToBSplineSurface;
--- Purpose : Converts a bounded cone into a B-spline surface.
class TorusToBSplineSurface;
--- Purpose : Converts a torus into a B-spline surface.
class SphereToBSplineSurface;
--- Purpose : Converts a sphere into a B-spline surface.
class SequenceOfArray1OfPoles
instantiates Sequence from TCollection( HArray1OfPnt from TColgp);
class CompBezierCurvesToBSplineCurve;
---Purpose: Converts a list of connecting BezierCurves
-- into a B-spline curve.
alias SequenceOfArray1OfPoles2d is SequenceOfArray1OfPnt2d from TColgp;
class CompBezierCurves2dToBSplineCurve2d;
---Purpose: Converts a list of connecting BezierCurves
-- into a B-spline curve.
class CompPolynomialToPoles;
---Purpose: Convert a serie of Polynomial N-Dimensional
-- Curves that are have continuity CM to an
-- N-Dimensional Bspline Curve that has continuity
-- CM
class GridPolynomialToPoles;
---Purpose: Convert a grid of Polynomial Surfaces
-- that are have continuity CM to an
-- Bspline Surface that has continuity
-- CM
end Convert;
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