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---Copyright: Matra Datavision 1991
class Parab from gp inherits Storable
---Purpose:
-- Describes a parabola in 3D space.
-- A parabola is defined by its focal length (that is, the
-- distance between its focus and apex) and positioned in
-- space with a coordinate system (a gp_Ax2 object)
-- where:
-- - the origin of the coordinate system is on the apex of
-- the parabola,
-- - the "X Axis" of the coordinate system is the axis of
-- symmetry; the parabola is on the positive side of this axis, and
-- - the origin, "X Direction" and "Y Direction" of the
-- coordinate system define the plane of the parabola.
-- The equation of the parabola in this coordinate system,
-- which is the "local coordinate system" of the parabola, is:
-- Y**2 = (2*P) * X.
-- where P, referred to as the parameter of the parabola, is
-- the distance between the focus and the directrix (P is
-- twice the focal length).
-- The "main Direction" of the local coordinate system gives
-- the normal vector to the plane of the parabola.
-- See Also
-- gce_MakeParab which provides functions for more
-- complex parabola constructions
-- Geom_Parabola which provides additional functions for
-- constructing parabolas and works, in particular, with the
-- parametric equations of parabolas
uses Ax1, Ax2, Pnt, Trsf, Vec
raises ConstructionError from Standard
is
Create returns Parab;
---C++: inline
--- Purpose : Creates an indefinite Parabola.
Create (A2 : Ax2; Focal : Real) returns Parab
---C++: inline
--- 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 if Focal < 0.0
raises ConstructionError;
--- Purpose : Raised if Focal < 0.0
Create (D : Ax1; F : Pnt) returns Parab;
---C++: inline
--- 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.
SetAxis (me : in out; A1 : Ax1)
---C++: inline
--- Purpose : Modifies this parabola by redefining its local coordinate system so that
-- - its origin and "main Direction" become those of the
-- axis A1 (the "X Direction" and "Y Direction" are then
-- recomputed in the same way as for any gp_Ax2)
-- Raises ConstructionError if the direction of A1 is parallel to the previous
-- XAxis of the parabola.
raises ConstructionError
is static;
SetFocal (me : in out; Focal : Real)
---C++: inline
--- Purpose : Changes the focal distance of the parabola.
-- Raises ConstructionError if Focal < 0.0
raises ConstructionError
is static;
SetLocation (me : in out; P : Pnt) is static;
---C++: inline
--- Purpose :
-- Changes the location of the parabola. It is the vertex of
-- the parabola.
SetPosition (me : in out; A2 : Ax2) is static;
--- Purpose : Changes the local coordinate system of the parabola.
Axis (me) returns Ax1 is static;
---C++: inline
--- Purpose :
-- Returns the main axis of the parabola.
-- It is the axis normal to the plane of the parabola passing
-- through the vertex of the parabola.
---C++: return const&
Directrix (me) returns Ax1 is static;
---C++: inline
--- Purpose : Computes the directrix of this parabola.
-- The directrix is:
-- - a line parallel to the "Y Direction" of the local
-- coordinate system of this parabola, and
-- - located on the negative side of the axis of symmetry,
-- at a distance from the apex which is equal to the focal
-- length of this parabola.
-- The directrix is returned as an axis (a gp_Ax1 object),
-- the origin of which is situated on the "X Axis" of this parabola.
Focal (me) returns Real is static;
---C++: inline
--- Purpose :
-- Returns the distance between the vertex and the focus
-- of the parabola.
Focus (me) returns Pnt is static;
---C++: inline
---Purpose: - Computes the focus of the parabola.
Location (me) returns Pnt is static;
---C++: inline
--- Purpose :
-- Returns the vertex of the parabola. It is the "Location"
-- point of the coordinate system of the parabola.
---C++: return const&
Parameter (me) returns Real is static;
---C++: inline
--- Purpose :
-- Computes the parameter of the parabola.
-- It is the distance between the focus and the directrix of
-- the parabola. This distance is twice the focal length.
Position (me) returns Ax2 is static;
--- Purpose :
-- Returns the local coordinate system of the parabola.
---C++: inline
---C++: return const&
XAxis (me) returns Ax1 is static;
---C++: inline
--- Purpose :
-- Returns the symmetry axis of the parabola. The location point
-- of the axis is the vertex of the parabola.
YAxis (me) returns Ax1 is static;
---C++: inline
--- Purpose :
-- It is an axis parallel to the directrix of the parabola.
-- The location point of this axis is the vertex of the parabola.
Mirror (me : in out; P : Pnt) is static;
Mirrored (me; P : Pnt) returns Parab is static;
--- Purpose :
-- Performs the symmetrical transformation of a parabola
-- with respect to the point P which is the center of the
-- symmetry.
Mirror (me : in out; A1 : Ax1) is static;
Mirrored (me; A1 : Ax1) returns Parab is static;
--- Purpose :
-- Performs the symmetrical transformation of a parabola
-- with respect to an axis placement which is the axis of
-- the symmetry.
Mirror (me : in out; A2 : Ax2) is static;
Mirrored (me; A2 : Ax2) returns Parab is static;
--- Purpose :
-- Performs the symmetrical transformation of a parabola
-- with respect to a plane. The axis placement A2 locates
-- the plane of the symmetry (Location, XDirection, YDirection).
Rotate (me : in out; A1 : Ax1; Ang : Real) is static;
---C++: inline
Rotated (me; A1 : Ax1; Ang : Real) returns Parab is static;
---C++: inline
--- Purpose :
-- Rotates a parabola. A1 is the axis of the rotation.
-- Ang is the angular value of the rotation in radians.
Scale (me : in out; P : Pnt; S : Real) is static;
---C++: inline
Scaled (me; P : Pnt; S : Real) returns Parab is static;
---C++: inline
--- Purpose :
-- Scales a parabola. S is the scaling value.
-- If S is negative the direction of the symmetry axis
-- XAxis is reversed and the direction of the YAxis too.
Transform (me : in out; T : Trsf) is static;
---C++: inline
Transformed (me; T : Trsf) returns Parab is static;
---C++: inline
--- Purpose :
-- Transforms a parabola with the transformation T from class Trsf.
Translate (me : in out; V : Vec) is static;
---C++: inline
Translated (me; V : Vec) returns Parab is static;
---C++: inline
--- Purpose :
-- Translates a parabola in the direction of the vector V.
-- The magnitude of the translation is the vector's magnitude.
Translate (me : in out; P1, P2 : Pnt) is static;
---C++: inline
Translated (me; P1, P2 : Pnt) returns Parab is static;
---C++: inline
--- Purpose :
-- Translates a parabola from the point P1 to the point P2.
fields
pos : Ax2;
focalLength : Real;
end;
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