-- Created on: 1993-03-24 -- Created by: JCV -- Copyright (c) 1993-1999 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. class BezierCurve from Geom2d inherits BoundedCurve from Geom2d --- Purpose : Describes a rational or non-rational Bezier curve -- - a non-rational Bezier curve is defined by a table -- of poles (also called control points), -- - a rational Bezier curve is defined by a table of -- poles with varying weights. -- These data are manipulated by two parallel arrays: -- - the poles table, which is an array of gp_Pnt2d points, and -- - the weights table, which is an array of reals. -- The bounds of these arrays are 1 and "the number of poles" of the curve. -- The poles of the curve are "control points" used to deform the curve. -- The first pole is the start point of the curve, and the -- last pole is the end point of the curve. The segment -- which joins the first pole to the second pole is the -- tangent to the curve at its start point, and the -- segment which joins the last pole to the -- second-from-last pole is the tangent to the curve -- at its end point. -- It is more difficult to give a geometric signification -- to the weights but they are useful for providing -- exact representations of the arcs of a circle or -- ellipse. Moreover, if the weights of all the poles are -- equal, the curve is polynomial; it is therefore a -- non-rational curve. The non-rational curve is a -- special and frequently used case. The weights are -- defined and used only in case of a rational curve. -- The degree of a Bezier curve is equal to the -- number of poles, minus 1. It must be greater than or -- equal to 1. However, the degree of a -- Geom2d_BezierCurve curve is limited to a value -- (25) which is defined and controlled by the system. -- This value is returned by the function MaxDegree. -- The parameter range for a Bezier curve is [ 0, 1 ]. -- If the first and last control points of the Bezier -- curve are the same point then the curve is closed. -- For example, to create a closed Bezier curve with -- four control points, you have to give a set of control -- points P1, P2, P3 and P1. -- The continuity of a Bezier curve is infinite. -- It is not possible to build a Bezier curve with -- negative weights. We consider that a weight value -- is zero if it is less than or equal to -- gp::Resolution(). We also consider that -- two weight values W1 and W2 are equal if: -- |W2 - W1| <= gp::Resolution(). -- Warning -- - When considering the continuity of a closed -- Bezier curve at the junction point, remember that -- a curve of this type is never periodic. This means -- that the derivatives for the parameter u = 0 -- have no reason to be the same as the -- derivatives for the parameter u = 1 even if the curve is closed. -- - The length of a Bezier curve can be null. uses Array1OfReal from TColStd, HArray1OfReal from TColStd, Array1OfPnt2d from TColgp, Ax2d from gp, Pnt2d from gp, HArray1OfPnt2d from TColgp, Vec2d from gp, Trsf2d from gp, Geometry from Geom2d, Shape from GeomAbs raises ConstructionError from Standard, DimensionError from Standard, RangeError from Standard, OutOfRange from Standard is Create (CurvePoles : Array1OfPnt2d from TColgp) returns mutable BezierCurve --- Purpose : -- Creates a non rational Bezier curve with a set of poles : -- CurvePoles. The weights are defaulted to all being 1. -- Raises ConstructionError if the number of poles is greater than MaxDegree + 1 -- or lower than 2. raises ConstructionError; Create (CurvePoles : Array1OfPnt2d from TColgp; PoleWeights : Array1OfReal from TColStd) returns mutable BezierCurve --- Purpose : -- Creates a rational Bezier curve with the set of poles -- CurvePoles and the set of weights PoleWeights . -- If all the weights are identical the curve is considered -- as non rational. Raises ConstructionError if -- the number of poles is greater than MaxDegree + 1 or lower -- than 2 or CurvePoles and CurveWeights have not the same length -- or one weight value is lower or equal to Resolution from -- package gp. raises ConstructionError; Increase (me : mutable; Degree : Integer) --- Purpose : -- Increases the degree of a bezier curve. Degree is the new -- degree of . -- raises ConstructionError if Degree is greater than MaxDegree or lower than 2 -- or lower than the initial degree of . raises ConstructionError; InsertPoleAfter (me : mutable; Index : Integer; P : Pnt2d; Weight : Real = 1.0) --- Purpose : -- Inserts a pole with its weight in the set of poles after the -- pole of range Index. If the curve was non rational it can -- become rational if all the weights are not identical. raises OutOfRange, --- Purpose : Raised if Index is not in the range [0, NbPoles] ConstructionError; --- Purpose : -- Raised if the resulting number of poles is greater than -- MaxDegree + 1. InsertPoleBefore (me : mutable; Index : Integer; P : Pnt2d; Weight : Real = 1.0) --- Purpose : -- Inserts a pole with its weight in the set of poles after -- the pole of range Index. If the curve was non rational it -- can become rational if all the weights are not identical. raises OutOfRange, --- Purpose : Raised if Index is not in the range [1, NbPoles+1] ConstructionError; --- Purpose : -- Raised if the resulting number of poles is greater than -- MaxDegree + 1. RemovePole (me : mutable; Index : Integer) --- Purpose : Removes the pole of range Index. -- If the curve was rational it can become non rational. raises OutOfRange, --- Purpose : Raised if Index is not in the range [1, NbPoles] ConstructionError; -- Purpose : Raised if Degree is lower than 2. Reverse (me : mutable); --- Purpose : -- Reverses the direction of parametrization of -- Value (NewU) = Value (1 - OldU) ReversedParameter(me; U : Real) returns Real; ---Purpose: Returns the parameter on the reversed curve for -- the point of parameter U on . -- -- returns 1-U Segment (me : mutable; U1, U2 : Real); --- Purpose : -- Segments the curve between U1 and U2 which can be out -- of the bounds of the curve. The curve is oriented from U1 -- to U2. -- The control points are modified, the first and the last point -- are not the same but the parametrization range is [0, 1] -- else it could not be a Bezier curve. -- Warnings : -- Even if is not closed it can become closed after the -- segmentation for example if U1 or U2 are out of the bounds -- of the curve or if the curve makes loop. -- After the segmentation the length of a curve can be null. SetPole (me : mutable; Index : Integer; P : Pnt2d) --- Purpose : -- Substitutes the pole of range index with P. -- If the curve is rational the weight of range Index -- is not modified. raises OutOfRange; --- Purpose : raiseD if Index is not in the range [1, NbPoles] SetPole (me : mutable; Index : Integer; P : Pnt2d; Weight : Real) --- Purpose : -- Substitutes the pole and the weights of range Index. -- If the curve is not rational it can become rational -- if all the weights are not identical. -- If the curve was rational it can become non rational if -- all the weights are identical. raises OutOfRange, --- Purpose : Raised if Index is not in the range [1, NbPoles] ConstructionError; --- Purpose : Raised if Weight <= Resolution from package gp SetWeight (me : mutable; Index : Integer; Weight : Real) --- Purpose : -- Changes the weight of the pole of range Index. -- If the curve is not rational it can become rational -- if all the weights are not identical. -- If the curve was rational it can become non rational if -- all the weights are identical. raises OutOfRange, --- Purpose : Raised if Index is not in the range [1, NbPoles] ConstructionError; --- Purpose : Raised if Weight <= Resolution from package gp IsClosed (me) returns Boolean; --- Purpose : -- Returns True if the distance between the first point -- and the last point of the curve is lower or equal to -- the Resolution from package gp. IsCN (me; N : Integer) returns Boolean; --- Purpose : Continuity of the curve, returns True. IsPeriodic (me) returns Boolean; --- Purpose : -- Returns False. A BezierCurve cannot be periodic in this -- package IsRational (me) returns Boolean; --- Purpose : -- Returns false if all the weights are identical. The tolerance -- criterion is Resolution from package gp. Continuity (me) returns Shape from GeomAbs; --- Purpose : Returns GeomAbs_CN, which is the continuity of any Bezier curve. Degree (me) returns Integer; --- Purpose : -- Returns the polynomial degree of the curve. It is the number -- of poles less one. In this package the Degree of a Bezier -- curve cannot be greater than "MaxDegree". D0 (me; U : Real; P : out Pnt2d); D1 (me; U : Real; P : out Pnt2d; V1 : out Vec2d); D2 (me; U : Real; P : out Pnt2d; V1, V2 : out Vec2d); D3 (me; U : Real; P : out Pnt2d; V1, V2, V3 : out Vec2d); DN (me; U : Real; N : Integer) returns Vec2d --- Purpose : For this Bezier curve, computes -- - the point P of parameter U, or -- - the point P and one or more of the following values: -- - V1, the first derivative vector, -- - V2, the second derivative vector, -- - V3, the third derivative vector. -- Note: the parameter U can be outside the bounds of the curve. -- Raises RangeError if N < 1. raises RangeError; EndPoint (me) returns Pnt2d; --- Purpose : Returns the end point or start point of this Bezier curve. FirstParameter (me) returns Real; --- Purpose : Returns the value of the first parameter of this -- Bezier curve. This is 0.0, which gives the start point of this Bezier curve. LastParameter (me) returns Real; --- Purpose : Returns the value of the last parameter of this -- Bezier curve. This is 1.0, which gives the end point of this Bezier curve. NbPoles (me) returns Integer; ---Purpose: Returns the number of poles for this Bezier curve. Pole (me; Index : Integer) returns Pnt2d --- Purpose : Returns the pole of range Index. raises OutOfRange; --- Purpose : Raised if Index is not in the range [1, NbPoles] Poles (me; P : out Array1OfPnt2d from TColgp) --- Purpose : Returns all the poles of the curve. raises DimensionError; --- Purpose : -- Raised if the length of P is not equal to the number of poles. StartPoint (me) returns Pnt2d; --- Purpose : -- Returns Value (U=1), it is the first control point -- of the curve. Weight (me; Index : Integer) returns Real --- Purpose : Returns the weight of range Index. raises OutOfRange; --- Purpose : Raised if Index is not in the range [1, NbPoles] Weights (me; W : out Array1OfReal from TColStd) --- Purpose : Returns all the weights of the curve. raises DimensionError; --- Purpose : -- Raised if the length of W is not equal to the number of poles. Transform (me : mutable; T : Trsf2d); ---Purpose: Applies the transformation T to this Bezier curve. MaxDegree (myclass) returns Integer; --- Purpose: -- Returns the value of the maximum polynomial degree of a -- BezierCurve. This value is 25. Resolution(me : mutable; ToleranceUV : Real; UTolerance : out Real); ---Purpose: Computes for this Bezier curve the parametric -- tolerance UTolerance for a given tolerance -- Tolerance3D (relative to dimensions in the plane). -- If f(t) is the equation of this Bezier curve, -- UTolerance ensures that -- | t1 - t0| < Utolerance ===> -- |f(t1) - f(t0)| < ToleranceUV Copy (me) returns mutable like me; ---Purpose: Creates a new object which is a copy of this Bezier curve. Init (me : mutable; Poles : HArray1OfPnt2d from TColgp; Weights : HArray1OfReal from TColStd) ---Purpose : Set poles to Poles, weights to Weights (not -- copied). If Weights is null the curve is non -- rational. Create the arrays of coefficients. Poles -- and Weights are assumed to have the first -- coefficient 1. -- -- Update rational and closed. -- raises ConstructionError -- if nbpoles < 2 or nbboles > MaDegree + 1 is static private; CoefficientsOK(me; U : Real) returns Boolean ---Purpose : returns true if the coefficients have been -- computed with the right value of cacheparameter -- for the given U value. -- is static private; UpdateCoefficients(me : mutable; U : Real from Standard = 0.0) ---Purpose: Recompute the coeficients. is static private; fields rational : Boolean; closed : Boolean; poles : HArray1OfPnt2d from TColgp; weights : HArray1OfReal from TColStd; coeffs : HArray1OfPnt2d from TColgp; wcoeffs : HArray1OfReal from TColStd; validcache : Integer; -- = 1 the cache is valid -- = 0 the cache is invalid parametercache : Real; -- Parameter at which the Taylor expension is stored in -- the cache, often 0., sometimes 1.. spanlenghtcache : Real; -- always 1. for the moment. -- usefull to evaluate the parametric resolution maxderivinv : Real from Standard; maxderivinvok : Boolean from Standard; end;