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1 | // Created on: 1993-03-10 |
2 | // Created by: JCV |
3 | // Copyright (c) 1993-1999 Matra Datavision |
4 | // Copyright (c) 1999-2014 OPEN CASCADE SAS |
5 | // |
6 | // This file is part of Open CASCADE Technology software library. |
7 | // |
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. |
13 | // |
14 | // Alternatively, this file may be used under the terms of Open CASCADE |
15 | // commercial license or contractual agreement. |
16 | |
17 | #ifndef _Geom_Parabola_HeaderFile |
18 | #define _Geom_Parabola_HeaderFile |
19 | |
20 | #include <Standard.hxx> |
21 | #include <Standard_Type.hxx> |
22 | |
23 | #include <Standard_Real.hxx> |
24 | #include <Geom_Conic.hxx> |
25 | #include <Standard_Boolean.hxx> |
26 | #include <Standard_Integer.hxx> |
27 | class Standard_ConstructionError; |
28 | class Standard_RangeError; |
29 | class gp_Parab; |
30 | class gp_Ax2; |
31 | class gp_Ax1; |
32 | class gp_Pnt; |
33 | class gp_Vec; |
34 | class gp_Trsf; |
35 | class Geom_Geometry; |
36 | |
37 | |
38 | class Geom_Parabola; |
39 | DEFINE_STANDARD_HANDLE(Geom_Parabola, Geom_Conic) |
40 | |
41 | //! Describes a parabola in 3D 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 space with a coordinate system |
45 | //! (gp_Ax2 object) where: |
46 | //! - the origin is the apex of the parabola, |
47 | //! - the "X Axis" defines the axis of symmetry; the |
48 | //! parabola is on the positive side of this axis, |
49 | //! - the origin, "X Direction" and "Y Direction" define the |
50 | //! plane of the parabola. |
51 | //! This coordinate system is the local coordinate |
52 | //! system of the parabola. |
53 | //! The "main Direction" of this coordinate system is a |
54 | //! vector normal to the plane of the parabola. The axis, |
55 | //! of which the origin and unit vector are respectively the |
56 | //! origin and "main Direction" of the local coordinate |
57 | //! system, is termed the "Axis" or "main Axis" of the parabola. |
58 | //! The "main Direction" of the local coordinate system |
59 | //! gives an explicit orientation to the parabola, |
60 | //! determining the direction in which the parameter |
61 | //! increases along the parabola. |
62 | //! The Geom_Parabola parabola is parameterized as follows: |
63 | //! P(U) = O + U*U/(4.*F)*XDir + U*YDir |
64 | //! where: |
65 | //! - P is the point of parameter U, |
66 | //! - O, XDir and YDir are respectively the origin, "X |
67 | //! Direction" and "Y Direction" of its local coordinate system, |
68 | //! - F is the focal length of the parabola. |
69 | //! The parameter of the parabola is therefore its Y |
70 | //! coordinate in the local coordinate system, with the "X |
71 | //! Axis" of the local coordinate system defining the origin |
72 | //! of the parameter. |
73 | //! The parameter range is ] -infinite, +infinite [. |
74 | class Geom_Parabola : public Geom_Conic |
75 | { |
76 | |
77 | public: |
78 | |
79 | |
80 | //! Creates a parabola from a non transient one. |
81 | Standard_EXPORT Geom_Parabola(const gp_Parab& Prb); |
82 | |
83 | |
84 | //! Creates a parabola with its local coordinate system "A2" |
85 | //! and it's focal length "Focal". |
86 | //! The XDirection of A2 defines the axis of symmetry of the |
87 | //! parabola. The YDirection of A2 is parallel to the directrix |
88 | //! of the parabola. The Location point of A2 is the vertex of |
89 | //! the parabola |
90 | //! Raised if Focal < 0.0 |
91 | Standard_EXPORT Geom_Parabola(const gp_Ax2& A2, const Standard_Real Focal); |
92 | |
93 | |
94 | //! D is the directrix of the parabola and F the focus point. |
95 | //! The symmetry axis (XAxis) of the parabola is normal to the |
96 | //! directrix and pass through the focus point F, but its |
97 | //! location point is the vertex of the parabola. |
98 | //! The YAxis of the parabola is parallel to D and its location |
99 | //! point is the vertex of the parabola. The normal to the plane |
100 | //! of the parabola is the cross product between the XAxis and the |
101 | //! YAxis. |
102 | Standard_EXPORT Geom_Parabola(const gp_Ax1& D, const gp_Pnt& F); |
103 | |
104 | //! Assigns the value Focal to the focal distance of this parabola. |
105 | //! Exceptions Standard_ConstructionError if Focal is negative. |
106 | Standard_EXPORT void SetFocal (const Standard_Real Focal); |
107 | |
108 | //! Converts the gp_Parab parabola Prb into this parabola. |
109 | Standard_EXPORT void SetParab (const gp_Parab& Prb); |
110 | |
111 | |
112 | //! Returns the non transient parabola from gp with the same |
113 | //! geometric properties as <me>. |
114 | Standard_EXPORT gp_Parab Parab() const; |
115 | |
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; |
120 | |
121 | //! Returns the value of the first or last parameter of this |
122 | //! parabola. This is, respectively: |
123 | //! - Standard_Real::RealFirst(), or |
124 | //! - Standard_Real::RealLast(). |
125 | Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; |
126 | |
127 | //! Returns the value of the first or last parameter of this |
128 | //! parabola. This is, respectively: |
129 | //! - Standard_Real::RealFirst(), or |
130 | //! - Standard_Real::RealLast(). |
131 | Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; |
132 | |
133 | //! Returns False |
134 | Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; |
135 | |
136 | //! Returns False |
137 | Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; |
138 | |
139 | //! Computes the directrix of this parabola. |
140 | //! This is a line normal to the axis of symmetry, in the |
141 | //! plane of this parabola, located on the negative side |
142 | //! of its axis of symmetry, at a distance from the apex |
143 | //! equal to the focal length. |
144 | //! The directrix is returned as an axis (gp_Ax1 object), |
145 | //! where the origin is located on the "X Axis" of this parabola. |
146 | Standard_EXPORT gp_Ax1 Directrix() const; |
147 | |
148 | //! Returns 1. (which is the eccentricity of any parabola). |
149 | Standard_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE; |
150 | |
151 | //! Computes the focus of this parabola. The focus is on the |
152 | //! positive side of the "X Axis" of the local coordinate |
153 | //! system of the parabola. |
154 | Standard_EXPORT gp_Pnt Focus() const; |
155 | |
156 | //! Computes the focal distance of this parabola |
157 | //! The focal distance is the distance between the apex |
158 | //! and the focus of the parabola. |
159 | Standard_EXPORT Standard_Real Focal() const; |
160 | |
161 | //! Computes the parameter of this parabola which is the |
162 | //! distance between its focus and its directrix. This |
163 | //! distance is twice the focal length. |
164 | //! If P is the parameter of the parabola, the equation of |
165 | //! the parabola in its local coordinate system is: Y**2 = 2.*P*X. |
166 | Standard_EXPORT Standard_Real Parameter() const; |
167 | |
168 | //! Returns in P the point of parameter U. |
169 | //! If U = 0 the returned point is the origin of the XAxis and |
170 | //! the YAxis of the parabola and it is the vertex of the parabola. |
171 | //! P = S + F * (U * U * XDir + * U * YDir) |
172 | //! where S is the vertex of the parabola, XDir the XDirection and |
173 | //! YDir the YDirection of the parabola's local coordinate system. |
174 | Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt& P) const Standard_OVERRIDE; |
175 | |
176 | |
177 | //! Returns the point P of parameter U and the first derivative V1. |
178 | Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const Standard_OVERRIDE; |
179 | |
180 | |
181 | //! Returns the point P of parameter U, the first and second |
182 | //! derivatives V1 and V2. |
183 | Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) const Standard_OVERRIDE; |
184 | |
185 | |
186 | //! Returns the point P of parameter U, the first second and third |
187 | //! derivatives V1 V2 and V3. |
188 | Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const Standard_OVERRIDE; |
189 | |
190 | //! For the point of parameter U of this parabola, |
191 | //! computes the vector corresponding to the Nth derivative. |
192 | //! Exceptions Standard_RangeError if N is less than 1. |
193 | Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; |
194 | |
195 | //! Applies the transformation T to this parabola. |
196 | Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE; |
197 | |
198 | //! Returns the parameter on the transformed curve for |
199 | //! the transform of the point of parameter U on <me>. |
200 | //! |
201 | //! me->Transformed(T)->Value(me->TransformedParameter(U,T)) |
202 | //! |
203 | //! is the same point as |
204 | //! |
205 | //! me->Value(U).Transformed(T) |
206 | //! |
207 | //! This methods returns <U> * T.ScaleFactor() |
208 | Standard_EXPORT Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf& T) const Standard_OVERRIDE; |
209 | |
210 | //! Returns a coefficient to compute the parameter on |
211 | //! the transformed curve for the transform of the |
212 | //! point on <me>. |
213 | //! |
214 | //! Transformed(T)->Value(U * ParametricTransformation(T)) |
215 | //! |
216 | //! is the same point as |
217 | //! |
218 | //! Value(U).Transformed(T) |
219 | //! |
220 | //! This methods returns T.ScaleFactor() |
221 | Standard_EXPORT Standard_Real ParametricTransformation (const gp_Trsf& T) const Standard_OVERRIDE; |
222 | |
223 | //! Creates a new object which is a copy of this parabola. |
224 | Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE; |
225 | |
226 | |
227 | |
228 | |
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229 | DEFINE_STANDARD_RTTIEXT(Geom_Parabola,Geom_Conic) |
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230 | |
231 | protected: |
232 | |
233 | |
234 | |
235 | |
236 | private: |
237 | |
238 | |
239 | Standard_Real focalLength; |
240 | |
241 | |
242 | }; |
243 | |
244 | |
245 | |
246 | |
247 | |
248 | |
249 | |
250 | #endif // _Geom_Parabola_HeaderFile |