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-- File: Geom2d_Parabola.cdl
-- Created: Wed Mar 24 18:22:05 1993
-- Author: JCV
-- <fid@sdsun2>
-- Copyright: Matra Datavision 1993
---Copyright: Matra Datavision 1991, 1992
class Parabola from Geom2d inherits Conic from Geom2d
--- Purpose : Describes a parabola in the plane (2D space).
-- A parabola is defined by its focal length (i.e. the
-- distance between its focus and its apex) and is
-- positioned in the plane with a coordinate system
-- (gp_Ax22d object) where:
-- - the origin is the apex of the parabola, and
-- - the "X Axis" defines the axis of symmetry; the
-- parabola is on the positive side of this axis.
-- This coordinate system is the local coordinate
-- system of the parabola.
-- The orientation (direct or indirect) of the local
-- coordinate system gives an explicit orientation to the
-- parabola, determining the direction in which the
-- parameter increases along the parabola.
-- The Geom_Parabola parabola is parameterized as follows:
-- P(U) = O + U*U/(4.*F)*XDir + U*YDir, where:
-- - P is the point of parameter U,
-- - O, XDir and YDir are respectively the origin, "X
-- Direction" and "Y Direction" of its local coordinate system,
-- - F is the focal length of the parabola.
-- The parameter of the parabola is therefore its Y
-- coordinate in the local coordinate system, with the "X
-- Axis" of the local coordinate system defining the
-- origin of the parameter.
-- The parameter range is ] -infinite,+infinite [.
uses Ax2d from gp,
Ax22d from gp,
Parab2d from gp,
Pnt2d from gp,
Trsf2d from gp,
Vec2d from gp,
Geometry from Geom2d
raises ConstructionError from Standard,
RangeError from Standard
is
Create (Prb : Parab2d) returns mutable Parabola;
--- Purpose : Creates a parabola from a non persistent one.
Create (MirrorAxis : Ax2d; Focal : Real;
Sense: Boolean from Standard = Standard_True)
returns mutable Parabola
--- Purpose :
-- Creates a parabola with its "MirrorAxis" and it's focal
-- length "Focal".
-- MirrorAxis is the axis of symmetry of the curve, it is the
-- "XAxis". The "YAxis" is parallel to the directrix of the
-- parabola and is in the direct sense if Sense is True.
-- The "Location" point of "MirrorAxis" is the vertex of the parabola
raises ConstructionError;
--- Purpose : Raised if Focal < 0.0
Create (Axis : Ax22d; Focal : Real) returns mutable Parabola
--- Purpose :
-- Creates a parabola with its Axis and it's focal
-- length "Focal".
-- The XDirection of Axis is the axis of symmetry of the curve,
-- it is the "XAxis". The "YAxis" is parallel to the directrix of the
-- parabola. The "Location" point of "Axis" is the vertex
-- of the parabola.
raises ConstructionError;
--- Purpose : Raised if Focal < 0.0
Create (D : Ax2d; F : Pnt2d) returns mutable Parabola;
--- Purpose :
-- D is the directrix of the parabola and F the focus point.
-- The symmetry axis "XAxis" of the parabola is normal to the
-- directrix and pass through the focus point F, but its
-- "Location" point is the vertex of the parabola.
-- The "YAxis" of the parabola is parallel to D and its "Location"
-- point is the vertex of the parabola.
SetFocal (me : mutable; Focal : Real)
--- Purpose : Assigns the value Focal to the focal length of this parabola.
-- Exceptions Standard_ConstructionError if Focal is negative.
raises ConstructionError;
SetParab2d (me : mutable; Prb : Parab2d);
--- Purpose: Converts the gp_Parab2d parabola Prb into this parabola.
Parab2d (me) returns Parab2d;
--- Purpose :
-- Returns the non persistent parabola from gp with the same
-- geometric properties as <me>.
ReversedParameter(me; U : Real) returns Real is redefined static;
---Purpose: Computes the parameter on the reversed parabola
-- for the point of parameter U on this parabola.
-- For a parabola, the returned value is -U.
FirstParameter (me) returns Real is redefined static;
--- Purpose : Returns RealFirst from Standard.
LastParameter (me) returns Real is redefined static;
--- Purpose : Returns RealLast from Standard.
IsClosed (me) returns Boolean is redefined static;
--- Purpose : Returns False
IsPeriodic (me) returns Boolean is redefined static;
--- Purpose : Returns False
Directrix (me) returns Ax2d;
--- Purpose : The directrix is parallel to the "YAxis" of the parabola.
-- The "Location" point of the directrix is the intersection
-- point between the directrix and the symmetry axis ("XAxis") of the parabola.
Eccentricity (me) returns Real is redefined static;
--- Purpose : Returns the eccentricity e = 1.0
Focus (me) returns Pnt2d;
---Purpose: Computes the focus of this parabola The focus is on the
-- positive side of the "X Axis" of the local coordinate system of the parabola.
Focal (me) returns Real;
--- Purpose : Computes the focal length of this parabola.
-- The focal length is the distance between the apex and the focus of the parabola.
Parameter (me) returns Real;
--- Purpose : Computes the parameter of this parabola, which is
-- the distance between its focus and its directrix. This
-- distance is twice the focal length.
-- If P is the parameter of the parabola, the equation of
-- the parabola in its local coordinate system is: Y**2 = 2.*P*X.
D0(me; U : Real; P : out Pnt2d) is redefined static;
---Purpose: Returns in P the point of parameter U.
-- If U = 0 the returned point is the origin of the XAxis and
-- the YAxis of the parabola and it is the vertex of the parabola.
-- P = S + F * (U * U * XDir + * U * YDir)
-- where S is the vertex of the parabola, XDir the XDirection and
-- YDir the YDirection of the parabola's local coordinate system.
D1 (me; U : Real; P : out Pnt2d; V1 : out Vec2d) is redefined static;
--- Purpose :
-- Returns the point P of parameter U and the first derivative V1.
D2 (me; U : Real; P : out Pnt2d; V1, V2 : out Vec2d) is redefined static;
--- Purpose :
-- Returns the point P of parameter U, the first and second
-- derivatives V1 and V2.
D3 (me; U : Real; P : out Pnt2d; V1, V2, V3 : out Vec2d) is redefined static;
--- Purpose :
-- Returns the point P of parameter U, the first second and third
-- derivatives V1 V2 and V3.
DN (me; U : Real; N : Integer) returns Vec2d
--- Purpose : For the point of parameter U of this parabola,
-- computes the vector corresponding to the Nth derivative.
-- Exceptions Standard_RangeError if N is less than 1.
raises RangeError
is redefined static;
Transform (me : mutable; T : Trsf2d) is redefined static;
---Purpose: Applies the transformation T to this parabola.
TransformedParameter(me; U : Real; T : Trsf2d from gp) returns Real
---Purpose: Computes the parameter on the transformed
-- parabola, for the point of parameter U on this parabola.
-- For a parabola, the returned value is equal to U
-- multiplied by the scale factor of transformation T.
is redefined static;
ParametricTransformation(me; T : Trsf2d from gp) returns Real
---Purpose: Returns a coefficient to compute the parameter on
-- the transformed curve for the transform of the
-- point on <me>.
--
-- Transformed(T)->Value(U * ParametricTransformation(T))
--
-- is the same point as
--
-- Value(U).Transformed(T)
--
-- This methods returns T.ScaleFactor()
is redefined static;
Copy (me) returns mutable like me
is redefined static;
---Purpose: Creates a new object, which is a copy of this parabola.
fields
focalLength : Real;
end;
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