-- 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;