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-- File: Geom_Parabola.cdl
-- Created: Wed Mar 10 09:57:52 1993
-- Author: JCV
-- <fid@phylox>
-- Copyright: Matra Datavision 1993
class Parabola from Geom inherits Conic from Geom
---Purpose : Describes a parabola in 3D space.
-- A parabola is defined by its focal length (i.e. the
-- distance between its focus and its apex) and is
-- positioned in space with a coordinate system
-- (gp_Ax2 object) where:
-- - the origin is the apex of the parabola,
-- - the "X Axis" defines the axis of symmetry; the
-- parabola is on the positive side of this axis,
-- - the origin, "X Direction" and "Y Direction" define the
-- plane of the parabola.
-- This coordinate system is the local coordinate
-- system of the parabola.
-- The "main Direction" of this coordinate system is a
-- vector normal to the plane of the parabola. The axis,
-- of which the origin and unit vector are respectively the
-- origin and "main Direction" of the local coordinate
-- system, is termed the "Axis" or "main Axis" of the parabola.
-- The "main Direction" 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 Ax1 from gp,
Ax2 from gp,
Parab from gp,
Pnt from gp,
Trsf from gp,
Vec from gp,
Geometry from Geom
raises ConstructionError from Standard,
RangeError from Standard
is
Create (Prb : Parab) returns mutable Parabola;
---Purpose : Creates a parabola from a non transient one.
Create (A2 : Ax2; Focal : Real) returns mutable Parabola
---Purpose :
-- Creates a parabola with its local coordinate system "A2"
-- and it's focal length "Focal".
-- The XDirection of A2 defines the axis of symmetry of the
-- parabola. The YDirection of A2 is parallel to the directrix
-- of the parabola. The Location point of A2 is the vertex of
-- the parabola
raises ConstructionError;
---Purpose : Raised if Focal < 0.0
Create (D : Ax1; F : Pnt) 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. The normal to the plane
-- of the parabola is the cross product between the XAxis and the
-- YAxis.
SetFocal (me : mutable; Focal : Real)
---Purpose : Assigns the value Focal to the focal distance of this parabola.
-- Exceptions Standard_ConstructionError if Focal is negative.
raises ConstructionError
is static;
SetParab (me : mutable; Prb : Parab)
---Purpose: Converts the gp_Parab parabola Prb into this parabola.
is static;
Parab (me) returns Parab
---Purpose :
-- Returns the non transient parabola from gp with the same
-- geometric properties as <me>.
is static;
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 the value of the first or last parameter of this
-- parabola. This is, respectively:
-- - Standard_Real::RealFirst(), or
-- - Standard_Real::RealLast().
LastParameter (me) returns Real is redefined static;
---Purpose : Returns the value of the first or last parameter of this
-- parabola. This is, respectively:
-- - Standard_Real::RealFirst(), or
-- - Standard_Real::RealLast().
IsClosed (me) returns Boolean is redefined static;
---Purpose : Returns False
IsPeriodic (me) returns Boolean is redefined static;
---Purpose : Returns False
Directrix (me) returns Ax1;
---Purpose : Computes the directrix of this parabola.
-- This is a line normal to the axis of symmetry, in the
-- plane of this parabola, located on the negative side
-- of its axis of symmetry, at a distance from the apex
-- equal to the focal length.
-- The directrix is returned as an axis (gp_Ax1 object),
-- where the origin is located on the "X Axis" of this parabola.
Eccentricity (me) returns Real is redefined static;
---Purpose : Returns 1. (which is the eccentricity of any parabola).
Focus (me) returns Pnt;
---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 distance of this parabola
-- The focal distance 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 Pnt) 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 Pnt; V1 : out Vec) is redefined static;
---Purpose :
-- Returns the point P of parameter U and the first derivative V1.
D2 (me; U : Real; P : out Pnt; V1, V2 : out Vec) 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 Pnt; V1, V2, V3 : out Vec) 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 Vec
---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 : Trsf) is redefined static;
---Purpose: Applies the transformation T to this parabola.
TransformedParameter(me; U : Real; T : Trsf from gp) returns Real
---Purpose: Returns the parameter on the transformed curve for
-- the transform of the point of parameter U on <me>.
--
-- me->Transformed(T)->Value(me->TransformedParameter(U,T))
--
-- is the same point as
--
-- me->Value(U).Transformed(T)
--
-- This methods returns <U> * T.ScaleFactor()
is redefined static;
ParametricTransformation(me; T : Trsf 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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