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1 | // Created on: 1993-03-24 |
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 _Geom2d_Hyperbola_HeaderFile |
18 | #define _Geom2d_Hyperbola_HeaderFile |
19 | |
20 | #include <Standard.hxx> |
21 | #include <Standard_Type.hxx> |
22 | |
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_DomainError; |
29 | class Standard_RangeError; |
30 | class gp_Hypr2d; |
31 | class gp_Ax2d; |
32 | class gp_Ax22d; |
33 | class gp_Pnt2d; |
34 | class gp_Vec2d; |
35 | class gp_Trsf2d; |
36 | class Geom2d_Geometry; |
37 | |
38 | |
39 | class Geom2d_Hyperbola; |
40 | DEFINE_STANDARD_HANDLE(Geom2d_Hyperbola, Geom2d_Conic) |
41 | |
42 | //! Describes a branch of a hyperbola in the plane (2D space). |
43 | //! A hyperbola is defined by its major and minor radii |
44 | //! and, as with any conic curve, is positioned in the |
45 | //! plane with a coordinate system (gp_Ax22d object) where: |
46 | //! - the origin is the center of the hyperbola, |
47 | //! - the "X Direction" defines the major axis, and |
48 | //! - the "Y Direction" defines the minor axis. |
49 | //! This coordinate system is the local coordinate |
50 | //! system of the hyperbola. |
51 | //! The branch of the hyperbola described is the one |
52 | //! located on the positive side of the major axis. |
53 | //! The orientation (direct or indirect) of the local |
54 | //! coordinate system gives an explicit orientation to the |
55 | //! hyperbola, determining the direction in which the |
56 | //! parameter increases along the hyperbola. |
57 | //! The Geom2d_Hyperbola hyperbola is parameterized as follows: |
58 | //! P(U) = O + MajRad*Cosh(U)*XDir + MinRad*Sinh(U)*YDir |
59 | //! where: |
60 | //! - P is the point of parameter U, |
61 | //! - O, XDir and YDir are respectively the origin, "X |
62 | //! Direction" and "Y Direction" of its local coordinate system, |
63 | //! - MajRad and MinRad are the major and minor radii of the hyperbola. |
64 | //! The "X Axis" of the local coordinate system therefore |
65 | //! defines the origin of the parameter of the hyperbola. |
66 | //! The parameter range is ] -infinite,+infinite [. |
67 | //! The following diagram illustrates the respective |
68 | //! positions, in the plane of the hyperbola, of the three |
69 | //! branches of hyperbolas constructed using the |
70 | //! functions OtherBranch, ConjugateBranch1 and |
71 | //! ConjugateBranch2: |
72 | //! ^YAxis |
73 | //! | |
74 | //! FirstConjugateBranch |
75 | //! | |
76 | //! Other | Main |
77 | //! --------------------- C |
78 | //! --------------------->XAxis |
79 | //! Branch | |
80 | //! Branch |
81 | //! | |
82 | //! SecondConjugateBranch |
83 | //! | |
84 | //! Warning |
85 | //! The value of the major radius (on the major axis) can |
86 | //! be less than the value of the minor radius (on the minor axis). |
87 | //! See Also |
88 | //! GCE2d_MakeHyperbola which provides functions for |
89 | //! more complex hyperbola constructions |
90 | //! gp_Ax22d |
91 | //! gp_Hypr2d for an equivalent, non-parameterized data structure |
92 | class Geom2d_Hyperbola : public Geom2d_Conic |
93 | { |
94 | |
95 | public: |
96 | |
97 | |
98 | //! Creates an Hyperbola from a non persistent one from package gp |
99 | Standard_EXPORT Geom2d_Hyperbola(const gp_Hypr2d& H); |
100 | |
101 | |
102 | //! MajorAxis is the "XAxis" of the hyperbola. |
103 | //! The YAxis is in the direct sense if "Sense" is True; |
104 | //! The major radius of the hyperbola is on this "XAxis" and |
105 | //! the minor radius is on the "YAxis" of the hyperbola. |
106 | //! Raised if MajorRadius < 0.0 or if MinorRadius < 0.0 |
107 | Standard_EXPORT Geom2d_Hyperbola(const gp_Ax2d& MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense = Standard_True); |
108 | |
109 | |
110 | //! The XDirection of "Axis" is the "XAxis" of the hyperbola and |
111 | //! the YDirection of "Axis" is the "YAxis". |
112 | //! The major radius of the hyperbola is on this "XAxis" and |
113 | //! the minor radius is on the "YAxis" of the hyperbola. |
114 | //! Raised if MajorRadius < 0.0 or if MinorRadius < 0.0 |
115 | Standard_EXPORT Geom2d_Hyperbola(const gp_Ax22d& Axis, const Standard_Real MajorRadius, const Standard_Real MinorRadius); |
116 | |
117 | //! Converts the gp_Hypr2d hyperbola H into this hyperbola. |
118 | Standard_EXPORT void SetHypr2d (const gp_Hypr2d& H); |
119 | |
120 | //! Assigns a value to the major or minor radius of this hyperbola. |
121 | //! Exceptions |
122 | //! Standard_ConstructionError if: |
123 | //! - MajorRadius is less than 0.0, |
124 | //! - MinorRadius is less than 0.0. |
125 | Standard_EXPORT void SetMajorRadius (const Standard_Real MajorRadius); |
126 | |
127 | //! Assigns a value to the major or minor radius of this hyperbola. |
128 | //! Exceptions |
129 | //! Standard_ConstructionError if: |
130 | //! - MajorRadius is less than 0.0, |
131 | //! - MinorRadius is less than 0.0. |
132 | Standard_EXPORT void SetMinorRadius (const Standard_Real MinorRadius); |
133 | |
134 | //! Converts this hyperbola into a gp_Hypr2d one. |
135 | Standard_EXPORT gp_Hypr2d Hypr2d() const; |
136 | |
137 | //! Computes the parameter on the reversed hyperbola, |
138 | //! for the point of parameter U on this hyperbola. |
139 | //! For a hyperbola, the returned value is -U. |
140 | Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; |
141 | |
142 | //! Returns RealFirst from Standard. |
143 | Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; |
144 | |
145 | //! returns RealLast from Standard. |
146 | Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; |
147 | |
148 | //! Returns False. |
149 | Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; |
150 | |
151 | //! return False for an hyperbola. |
152 | Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; |
153 | |
154 | |
155 | //! In the local coordinate system of the hyperbola the |
156 | //! equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 |
157 | //! and the equation of the first asymptote is Y = (B/A)*X |
158 | //! where A is the major radius of the hyperbola and B is the |
159 | //! minor radius of the hyperbola. |
160 | //! Raised if MajorRadius = 0.0 |
161 | Standard_EXPORT gp_Ax2d Asymptote1() const; |
162 | |
163 | |
164 | //! In the local coordinate system of the hyperbola the |
165 | //! equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 |
166 | //! and the equation of the first asymptote is Y = -(B/A)*X. |
167 | //! where A is the major radius of the hyperbola and B is the |
168 | //! minor radius of the hyperbola. |
169 | //! raised if MajorRadius = 0.0 |
170 | Standard_EXPORT gp_Ax2d Asymptote2() const; |
171 | |
172 | //! Computes the first conjugate branch relative to this hyperbola. |
173 | //! Note: The diagram given under the class purpose |
174 | //! indicates where these two branches of hyperbola are |
175 | //! positioned in relation to this branch of hyperbola. |
176 | Standard_EXPORT gp_Hypr2d ConjugateBranch1() const; |
177 | |
178 | //! Computes the second conjugate branch relative to this hyperbola. |
179 | //! Note: The diagram given under the class purpose |
180 | //! indicates where these two branches of hyperbola are |
181 | //! positioned in relation to this branch of hyperbola. |
182 | Standard_EXPORT gp_Hypr2d ConjugateBranch2() const; |
183 | |
184 | |
185 | //! This directrix is the line normal to the XAxis of the hyperbola |
186 | //! in the local plane (Z = 0) at a distance d = MajorRadius / e |
187 | //! from the center of the hyperbola, where e is the eccentricity of |
188 | //! the hyperbola. |
189 | //! This line is parallel to the "YAxis". The intersection point |
190 | //! between directrix1 and the "XAxis" is the location point of the |
191 | //! directrix1. This point is on the positive side of the "XAxis". |
192 | Standard_EXPORT gp_Ax2d Directrix1() const; |
193 | |
194 | |
195 | //! This line is obtained by the symmetrical transformation |
196 | //! of "Directrix1" with respect to the "YAxis" of the hyperbola. |
197 | Standard_EXPORT gp_Ax2d Directrix2() const; |
198 | |
199 | |
200 | //! Returns the excentricity of the hyperbola (e > 1). |
201 | //! If f is the distance between the location of the hyperbola |
202 | //! and the Focus1 then the eccentricity e = f / MajorRadius. |
203 | //! raised if MajorRadius = 0.0 |
204 | Standard_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE; |
205 | |
206 | |
207 | //! Computes the focal distance. It is the distance between the |
208 | //! two focus of the hyperbola. |
209 | Standard_EXPORT Standard_Real Focal() const; |
210 | |
211 | |
212 | //! Returns the first focus of the hyperbola. This focus is on the |
213 | //! positive side of the "XAxis" of the hyperbola. |
214 | Standard_EXPORT gp_Pnt2d Focus1() const; |
215 | |
216 | |
217 | //! Returns the second focus of the hyperbola. This focus is on the |
218 | //! negative side of the "XAxis" of the hyperbola. |
219 | Standard_EXPORT gp_Pnt2d Focus2() const; |
220 | |
221 | //! Returns the major or minor radius of this hyperbola. |
222 | //! The major radius is also the distance between the |
223 | //! center of the hyperbola and the apex of the main |
224 | //! branch (located on the "X Axis" of the hyperbola). |
225 | Standard_EXPORT Standard_Real MajorRadius() const; |
226 | |
227 | //! Returns the major or minor radius of this hyperbola. |
228 | //! The minor radius is also the distance between the |
229 | //! center of the hyperbola and the apex of a conjugate |
230 | //! branch (located on the "Y Axis" of the hyperbola). |
231 | Standard_EXPORT Standard_Real MinorRadius() const; |
232 | |
233 | |
234 | //! Computes the "other" branch of this hyperbola. This |
235 | //! is a symmetrical branch with respect to the center of this hyperbola. |
236 | //! Note: The diagram given under the class purpose |
237 | //! indicates where the "other" branch is positioned in |
238 | //! relation to this branch of the hyperbola. |
239 | //! ^ YAxis |
240 | //! | |
241 | //! FirstConjugateBranch |
242 | //! | |
243 | //! Other | Main |
244 | //! ---------------------------- C |
245 | //! ------------------------------------------>XAxis |
246 | //! Branch | Branch |
247 | //! | |
248 | //! | |
249 | //! SecondConjugateBranch |
250 | //! | |
251 | //! Warning |
252 | //! The major radius can be less than the minor radius. |
253 | Standard_EXPORT gp_Hypr2d OtherBranch() const; |
254 | |
255 | //! Computes the parameter of this hyperbola. |
256 | //! The parameter is: |
257 | //! p = (e*e - 1) * MajorRadius |
258 | //! where e is the eccentricity of this hyperbola and |
259 | //! MajorRadius its major radius. |
260 | //! Exceptions |
261 | //! Standard_DomainError if the major radius of this |
262 | //! hyperbola is null. |
263 | Standard_EXPORT Standard_Real Parameter() const; |
264 | |
265 | //! Returns in P the point of parameter U. |
266 | //! P = C + MajorRadius * Cosh (U) * XDir + |
267 | //! MinorRadius * Sinh (U) * YDir |
268 | //! where C is the center of the hyperbola , XDir the XDirection and |
269 | //! YDir the YDirection of the hyperbola's local coordinate system. |
270 | Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE; |
271 | |
272 | |
273 | //! Returns the point P of parameter U and the first derivative V1. |
274 | Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE; |
275 | |
276 | |
277 | //! Returns the point P of parameter U, the first and second |
278 | //! derivatives V1 and V2. |
279 | Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE; |
280 | |
281 | |
282 | //! Returns the point P of parameter U, the first second and |
283 | //! third derivatives V1 V2 and V3. |
284 | Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE; |
285 | |
286 | //! For the point of parameter U of this hyperbola, |
287 | //! computes the vector corresponding to the Nth derivative. |
288 | //! Exceptions Standard_RangeError if N is less than 1. |
289 | Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; |
290 | |
291 | //! Applies the transformation T to this hyperbola. |
292 | Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE; |
293 | |
294 | //! Creates a new object which is a copy of this hyperbola. |
295 | Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE; |
296 | |
297 | |
298 | |
299 | |
300 | DEFINE_STANDARD_RTTI(Geom2d_Hyperbola,Geom2d_Conic) |
301 | |
302 | protected: |
303 | |
304 | |
305 | |
306 | |
307 | private: |
308 | |
309 | |
310 | Standard_Real majorRadius; |
311 | Standard_Real minorRadius; |
312 | |
313 | |
314 | }; |
315 | |
316 | |
317 | |
318 | |
319 | |
320 | |
321 | |
322 | #endif // _Geom2d_Hyperbola_HeaderFile |