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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_Hyperbola_HeaderFile |
18 | #define _Geom_Hyperbola_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_DomainError; |
29 | class Standard_RangeError; |
30 | class gp_Hypr; |
31 | class gp_Ax2; |
32 | class gp_Ax1; |
33 | class gp_Pnt; |
34 | class gp_Vec; |
35 | class gp_Trsf; |
36 | class Geom_Geometry; |
37 | |
38 | |
39 | class Geom_Hyperbola; |
40 | DEFINE_STANDARD_HANDLE(Geom_Hyperbola, Geom_Conic) |
41 | |
42 | //! Describes a branch of a hyperbola in 3D space. |
43 | //! A hyperbola is defined by its major and minor radii |
44 | //! and, as with any conic curve, is positioned in space |
45 | //! with a right-handed coordinate system (gp_Ax2 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 | //! The origin, "X Direction" and "Y Direction" of this |
50 | //! coordinate system define the plane of the hyperbola. |
51 | //! The coordinate system is the local coordinate |
52 | //! system of the hyperbola. |
53 | //! The branch of the hyperbola described is the one |
54 | //! located on the positive side of the major axis. |
55 | //! The "main Direction" of the local coordinate system is |
56 | //! a vector normal to the plane of the hyperbola. The |
57 | //! axis, of which the origin and unit vector are |
58 | //! respectively the origin and "main Direction" of the |
59 | //! local coordinate system, is termed the "Axis" or "main |
60 | //! Axis" of the hyperbola. |
61 | //! The "main Direction" of the local coordinate system |
62 | //! gives an explicit orientation to the hyperbola, |
63 | //! determining the direction in which the parameter |
64 | //! increases along the hyperbola. |
65 | //! The Geom_Hyperbola hyperbola is parameterized as follows: |
66 | //! P(U) = O + MajRad*Cosh(U)*XDir + MinRad*Sinh(U)*YDir, where: |
67 | //! - P is the point of parameter U, |
68 | //! - O, XDir and YDir are respectively the origin, "X |
69 | //! Direction" and "Y Direction" of its local coordinate system, |
70 | //! - MajRad and MinRad are the major and minor radii of the hyperbola. |
71 | //! The "X Axis" of the local coordinate system therefore |
72 | //! defines the origin of the parameter of the hyperbola. |
73 | //! The parameter range is ] -infinite, +infinite [. |
74 | //! The following diagram illustrates the respective |
75 | //! positions, in the plane of the hyperbola, of the three |
76 | //! branches of hyperbolas constructed using the |
77 | //! functions OtherBranch, ConjugateBranch1 and |
78 | //! ConjugateBranch2: Defines the main branch of an hyperbola. |
79 | //! ^YAxis |
80 | //! | |
81 | //! FirstConjugateBranch |
82 | //! | |
83 | //! Other | Main |
84 | //! --------------------- C ------------------------------>XAxis |
85 | //! Branch | Branch |
86 | //! | |
87 | //! SecondConjugateBranch |
88 | //! | |
89 | //! Warning |
90 | //! The value of the major radius (on the major axis) can |
91 | //! be less than the value of the minor radius (on the minor axis). |
92 | class Geom_Hyperbola : public Geom_Conic |
93 | { |
94 | |
95 | public: |
96 | |
97 | |
98 | //! Constructs a hyperbola by conversion of the gp_Hypr hyperbola H. |
99 | Standard_EXPORT Geom_Hyperbola(const gp_Hypr& H); |
100 | |
101 | //! Constructs a hyperbola defined by its major and |
102 | //! minor radii, MajorRadius and MinorRadius, where A2 locates the |
103 | //! hyperbola and defines its orientation in 3D space such that: |
104 | //! - the center of the hyperbola is the origin of A2, |
105 | //! - the "X Direction" of A2 defines the major axis |
106 | //! of the hyperbola, i.e. the major radius |
107 | //! MajorRadius is measured along this axis, |
108 | //! - the "Y Direction" of A2 defines the minor axis |
109 | //! of the hyperbola, i.e. the minor radius |
110 | //! MinorRadius is measured along this axis, |
111 | //! - A2 is the local coordinate system of the hyperbola. |
112 | //! Exceptions |
113 | //! Standard_ConstructionError if: |
114 | //! - MajorRadius is less than 0.0, |
115 | //! - MinorRadius is less than 0.0. |
116 | Standard_EXPORT Geom_Hyperbola(const gp_Ax2& A2, const Standard_Real MajorRadius, const Standard_Real MinorRadius); |
117 | |
118 | //! Converts the gp_Hypr hyperbola H into this hyperbola. |
119 | Standard_EXPORT void SetHypr (const gp_Hypr& H); |
120 | |
121 | //! Assigns a value to the major radius of this hyperbola. |
122 | //! Exceptions |
123 | //! Standard_ConstructionError if: |
124 | //! - MajorRadius is less than 0.0, or |
125 | //! - MinorRadius is less than 0.0.Raised if MajorRadius < 0.0 |
126 | Standard_EXPORT void SetMajorRadius (const Standard_Real MajorRadius); |
127 | |
128 | //! Assigns a value to the minor radius of this hyperbola. |
129 | //! Exceptions |
130 | //! Standard_ConstructionError if: |
131 | //! - MajorRadius is less than 0.0, or |
132 | //! - MinorRadius is less than 0.0.Raised if MajorRadius < 0.0 |
133 | Standard_EXPORT void SetMinorRadius (const Standard_Real MinorRadius); |
134 | |
135 | |
136 | //! returns the non transient parabola from gp with the same |
137 | //! geometric properties as <me>. |
138 | Standard_EXPORT gp_Hypr Hypr() const; |
139 | |
140 | //! Computes the parameter on the reversed hyperbola, |
141 | //! for the point of parameter U on this hyperbola. |
142 | //! For a hyperbola, the returned value is: -U. |
143 | Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; |
144 | |
145 | //! Returns RealFirst from Standard. |
146 | Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; |
147 | |
148 | //! returns RealLast from Standard. |
149 | Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; |
150 | |
151 | //! Returns False. |
152 | Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; |
153 | |
154 | //! return False for an hyperbola. |
155 | Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; |
156 | |
157 | |
158 | //! In the local coordinate system of the hyperbola the equation of |
159 | //! the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the |
160 | //! equation of the first asymptote is Y = (B/A)*X. |
161 | //! Raises ConstructionError if MajorRadius = 0.0 |
162 | Standard_EXPORT gp_Ax1 Asymptote1() const; |
163 | |
164 | |
165 | //! In the local coordinate system of the hyperbola the equation of |
166 | //! the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the |
167 | //! equation of the first asymptote is Y = -(B/A)*X. |
168 | //! Raises ConstructionError if MajorRadius = 0.0 |
169 | Standard_EXPORT gp_Ax1 Asymptote2() const; |
170 | |
171 | |
172 | //! This branch of hyperbola is on the positive side of the |
173 | //! YAxis of <me>. |
174 | Standard_EXPORT gp_Hypr ConjugateBranch1() const; |
175 | |
176 | |
177 | //! This branch of hyperbola is on the negative side of the |
178 | //! YAxis of <me>. |
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_Hypr 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 between |
190 | //! directrix1 and the XAxis is the location point of the directrix1. |
191 | //! This point is on the positive side of the XAxis. |
192 | Standard_EXPORT gp_Ax1 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_Ax1 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_Pnt 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_Pnt 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 | //! Computes the "other" branch of this hyperbola. This |
234 | //! is the symmetrical branch with respect to the center of this hyperbola. |
235 | //! Note: The diagram given under the class purpose |
236 | //! indicates where the "other" branch is positioned in |
237 | //! relation to this branch of the hyperbola. |
238 | Standard_EXPORT gp_Hypr OtherBranch() const; |
239 | |
240 | |
241 | //! Returns p = (e * e - 1) * MajorRadius where e is the |
242 | //! eccentricity of the hyperbola. |
243 | //! raised if MajorRadius = 0.0 |
244 | Standard_EXPORT Standard_Real Parameter() const; |
245 | |
246 | //! Returns in P the point of parameter U. |
247 | //! P = C + MajorRadius * Cosh (U) * XDir + |
248 | //! MinorRadius * Sinh (U) * YDir |
249 | //! where C is the center of the hyperbola , XDir the XDirection and |
250 | //! YDir the YDirection of the hyperbola's local coordinate system. |
251 | Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt& P) const Standard_OVERRIDE; |
252 | |
253 | |
254 | //! Returns the point P of parameter U and the first derivative V1. |
255 | Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const Standard_OVERRIDE; |
256 | |
257 | |
258 | //! Returns the point P of parameter U, the first and second |
259 | //! derivatives V1 and V2. |
260 | Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) const Standard_OVERRIDE; |
261 | |
262 | |
263 | //! Returns the point P of parameter U, the first second and |
264 | //! third derivatives V1 V2 and V3. |
265 | Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const Standard_OVERRIDE; |
266 | |
267 | |
268 | //! The returned vector gives the value of the derivative for the |
269 | //! order of derivation N. |
270 | //! Raised if N < 1. |
271 | Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; |
272 | |
273 | //! Applies the transformation T to this hyperbola. |
274 | Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE; |
275 | |
276 | //! Creates a new object which is a copy of this hyperbola. |
277 | Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE; |
278 | |
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279 | //! Dumps the content of me into the stream |
280 | Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE; |
281 | |
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282 | |
283 | |
284 | |
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285 | DEFINE_STANDARD_RTTIEXT(Geom_Hyperbola,Geom_Conic) |
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286 | |
287 | protected: |
288 | |
289 | |
290 | |
291 | |
292 | private: |
293 | |
294 | |
295 | Standard_Real majorRadius; |
296 | Standard_Real minorRadius; |
297 | |
298 | |
299 | }; |
300 | |
301 | |
302 | |
303 | |
304 | |
305 | |
306 | |
307 | #endif // _Geom_Hyperbola_HeaderFile |