1 // Created on: 1993-03-24
3 // Copyright (c) 1993-1999 Matra Datavision
4 // Copyright (c) 1999-2014 OPEN CASCADE SAS
6 // This file is part of Open CASCADE Technology software library.
8 // This library is free software; you can redistribute it and/or modify it under
9 // the terms of the GNU Lesser General Public License version 2.1 as published
10 // by the Free Software Foundation, with special exception defined in the file
11 // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
12 // distribution for complete text of the license and disclaimer of any warranty.
14 // Alternatively, this file may be used under the terms of Open CASCADE
15 // commercial license or contractual agreement.
17 #ifndef _Geom2d_Parabola_HeaderFile
18 #define _Geom2d_Parabola_HeaderFile
20 #include <Standard.hxx>
21 #include <Standard_Type.hxx>
23 #include <Standard_Real.hxx>
24 #include <Geom2d_Conic.hxx>
25 #include <Standard_Boolean.hxx>
26 #include <Standard_Integer.hxx>
27 class Standard_ConstructionError;
28 class Standard_RangeError;
35 class Geom2d_Geometry;
38 class Geom2d_Parabola;
39 DEFINE_STANDARD_HANDLE(Geom2d_Parabola, Geom2d_Conic)
41 //! Describes a parabola in the plane (2D space).
42 //! A parabola is defined by its focal length (i.e. the
43 //! distance between its focus and its apex) and is
44 //! positioned in the plane with a coordinate system
45 //! (gp_Ax22d object) where:
46 //! - the origin is the apex of the parabola, and
47 //! - the "X Axis" defines the axis of symmetry; the
48 //! parabola is on the positive side of this axis.
49 //! This coordinate system is the local coordinate
50 //! system of the parabola.
51 //! The orientation (direct or indirect) of the local
52 //! coordinate system gives an explicit orientation to the
53 //! parabola, determining the direction in which the
54 //! parameter increases along the parabola.
55 //! The Geom_Parabola parabola is parameterized as follows:
56 //! P(U) = O + U*U/(4.*F)*XDir + U*YDir, where:
57 //! - P is the point of parameter U,
58 //! - O, XDir and YDir are respectively the origin, "X
59 //! Direction" and "Y Direction" of its local coordinate system,
60 //! - F is the focal length of the parabola.
61 //! The parameter of the parabola is therefore its Y
62 //! coordinate in the local coordinate system, with the "X
63 //! Axis" of the local coordinate system defining the
64 //! origin of the parameter.
65 //! The parameter range is ] -infinite,+infinite [.
66 class Geom2d_Parabola : public Geom2d_Conic
72 //! Creates a parabola from a non persistent one.
73 Standard_EXPORT Geom2d_Parabola(const gp_Parab2d& Prb);
76 //! Creates a parabola with its "MirrorAxis" and it's focal
78 //! MirrorAxis is the axis of symmetry of the curve, it is the
79 //! "XAxis". The "YAxis" is parallel to the directrix of the
80 //! parabola and is in the direct sense if Sense is True.
81 //! The "Location" point of "MirrorAxis" is the vertex of the parabola
82 //! Raised if Focal < 0.0
83 Standard_EXPORT Geom2d_Parabola(const gp_Ax2d& MirrorAxis, const Standard_Real Focal, const Standard_Boolean Sense = Standard_True);
86 //! Creates a parabola with its Axis and it's focal
88 //! The XDirection of Axis is the axis of symmetry of the curve,
89 //! it is the "XAxis". The "YAxis" is parallel to the directrix of the
90 //! parabola. The "Location" point of "Axis" is the vertex
92 //! Raised if Focal < 0.0
93 Standard_EXPORT Geom2d_Parabola(const gp_Ax22d& Axis, const Standard_Real Focal);
96 //! D is the directrix of the parabola and F the focus point.
97 //! The symmetry axis "XAxis" of the parabola is normal to the
98 //! directrix and pass through the focus point F, but its
99 //! "Location" point is the vertex of the parabola.
100 //! The "YAxis" of the parabola is parallel to D and its "Location"
101 //! point is the vertex of the parabola.
102 Standard_EXPORT Geom2d_Parabola(const gp_Ax2d& D, const gp_Pnt2d& F);
104 //! Assigns the value Focal to the focal length of this parabola.
105 //! Exceptions Standard_ConstructionError if Focal is negative.
106 Standard_EXPORT void SetFocal (const Standard_Real Focal);
108 //! Converts the gp_Parab2d parabola Prb into this parabola.
109 Standard_EXPORT void SetParab2d (const gp_Parab2d& Prb);
112 //! Returns the non persistent parabola from gp with the same
113 //! geometric properties as <me>.
114 Standard_EXPORT gp_Parab2d Parab2d() const;
116 //! Computes the parameter on the reversed parabola
117 //! for the point of parameter U on this parabola.
118 //! For a parabola, the returned value is -U.
119 Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
121 //! Returns RealFirst from Standard.
122 Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE;
124 //! Returns RealLast from Standard.
125 Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE;
128 Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE;
131 Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE;
133 //! The directrix is parallel to the "YAxis" of the parabola.
134 //! The "Location" point of the directrix is the intersection
135 //! point between the directrix and the symmetry axis ("XAxis") of the parabola.
136 Standard_EXPORT gp_Ax2d Directrix() const;
138 //! Returns the eccentricity e = 1.0
139 Standard_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE;
141 //! Computes the focus of this parabola The focus is on the
142 //! positive side of the "X Axis" of the local coordinate system of the parabola.
143 Standard_EXPORT gp_Pnt2d Focus() const;
145 //! Computes the focal length of this parabola.
146 //! The focal length is the distance between the apex and the focus of the parabola.
147 Standard_EXPORT Standard_Real Focal() const;
149 //! Computes the parameter of this parabola, which is
150 //! the distance between its focus and its directrix. This
151 //! distance is twice the focal length.
152 //! If P is the parameter of the parabola, the equation of
153 //! the parabola in its local coordinate system is: Y**2 = 2.*P*X.
154 Standard_EXPORT Standard_Real Parameter() const;
156 //! Returns in P the point of parameter U.
157 //! If U = 0 the returned point is the origin of the XAxis and
158 //! the YAxis of the parabola and it is the vertex of the parabola.
159 //! P = S + F * (U * U * XDir + * U * YDir)
160 //! where S is the vertex of the parabola, XDir the XDirection and
161 //! YDir the YDirection of the parabola's local coordinate system.
162 Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE;
165 //! Returns the point P of parameter U and the first derivative V1.
166 Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE;
169 //! Returns the point P of parameter U, the first and second
170 //! derivatives V1 and V2.
171 Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE;
174 //! Returns the point P of parameter U, the first second and third
175 //! derivatives V1 V2 and V3.
176 Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE;
178 //! For the point of parameter U of this parabola,
179 //! computes the vector corresponding to the Nth derivative.
180 //! Exceptions Standard_RangeError if N is less than 1.
181 Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
183 //! Applies the transformation T to this parabola.
184 Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE;
186 //! Computes the parameter on the transformed
187 //! parabola, for the point of parameter U on this parabola.
188 //! For a parabola, the returned value is equal to U
189 //! multiplied by the scale factor of transformation T.
190 Standard_EXPORT Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf2d& T) const Standard_OVERRIDE;
192 //! Returns a coefficient to compute the parameter on
193 //! the transformed curve for the transform of the
196 //! Transformed(T)->Value(U * ParametricTransformation(T))
198 //! is the same point as
200 //! Value(U).Transformed(T)
202 //! This methods returns T.ScaleFactor()
203 Standard_EXPORT Standard_Real ParametricTransformation (const gp_Trsf2d& T) const Standard_OVERRIDE;
205 //! Creates a new object, which is a copy of this parabola.
206 Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE;
211 DEFINE_STANDARD_RTTIEXT(Geom2d_Parabola,Geom2d_Conic)
221 Standard_Real focalLength;
232 #endif // _Geom2d_Parabola_HeaderFile