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1 | // Copyright (c) 1991-1999 Matra Datavision |
2 | // Copyright (c) 1999-2014 OPEN CASCADE SAS |
3 | // |
4 | // This file is part of Open CASCADE Technology software library. |
5 | // |
6 | // This library is free software; you can redistribute it and/or modify it under |
7 | // the terms of the GNU Lesser General Public License version 2.1 as published |
8 | // by the Free Software Foundation, with special exception defined in the file |
9 | // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT |
10 | // distribution for complete text of the license and disclaimer of any warranty. |
11 | // |
12 | // Alternatively, this file may be used under the terms of Open CASCADE |
13 | // commercial license or contractual agreement. |
14 | |
15 | #ifndef _gp_Ax2_HeaderFile |
16 | #define _gp_Ax2_HeaderFile |
17 | |
18 | #include <Standard.hxx> |
19 | #include <Standard_DefineAlloc.hxx> |
20 | #include <Standard_Handle.hxx> |
21 | |
22 | #include <gp_Ax1.hxx> |
23 | #include <gp_Dir.hxx> |
24 | #include <Standard_Real.hxx> |
25 | #include <Standard_Boolean.hxx> |
26 | class Standard_ConstructionError; |
27 | class gp_Pnt; |
28 | class gp_Dir; |
29 | class gp_Ax1; |
30 | class gp_Trsf; |
31 | class gp_Vec; |
32 | |
33 | |
34 | |
35 | //! Describes a right-handed coordinate system in 3D space. |
36 | //! A coordinate system is defined by: |
37 | //! - its origin (also referred to as its "Location point"), and |
38 | //! - three orthogonal unit vectors, termed respectively the |
39 | //! "X Direction", the "Y Direction" and the "Direction" (also |
40 | //! referred to as the "main Direction"). |
41 | //! The "Direction" of the coordinate system is called its |
42 | //! "main Direction" because whenever this unit vector is |
43 | //! modified, the "X Direction" and the "Y Direction" are |
44 | //! recomputed. However, when we modify either the "X |
45 | //! Direction" or the "Y Direction", "Direction" is not modified. |
46 | //! The "main Direction" is also the "Z Direction". |
47 | //! Since an Ax2 coordinate system is right-handed, its |
48 | //! "main Direction" is always equal to the cross product of |
49 | //! its "X Direction" and "Y Direction". (To define a |
50 | //! left-handed coordinate system, use gp_Ax3.) |
51 | //! A coordinate system is used: |
52 | //! - to describe geometric entities, in particular to position |
53 | //! them. The local coordinate system of a geometric |
54 | //! entity serves the same purpose as the STEP function |
55 | //! "axis placement two axes", or |
56 | //! - to define geometric transformations. |
57 | //! Note: we refer to the "X Axis", "Y Axis" and "Z Axis", |
58 | //! respectively, as to axes having: |
59 | //! - the origin of the coordinate system as their origin, and |
60 | //! - the unit vectors "X Direction", "Y Direction" and "main |
61 | //! Direction", respectively, as their unit vectors. |
62 | //! The "Z Axis" is also the "main Axis". |
63 | class gp_Ax2 |
64 | { |
65 | public: |
66 | |
67 | DEFINE_STANDARD_ALLOC |
68 | |
69 | |
70 | //! Creates an object corresponding to the reference |
71 | //! coordinate system (OXYZ). |
72 | gp_Ax2(); |
73 | |
74 | |
75 | //! Creates an axis placement with an origin P such that: |
76 | //! - N is the Direction, and |
77 | //! - the "X Direction" is normal to N, in the plane |
78 | //! defined by the vectors (N, Vx): "X |
79 | //! Direction" = (N ^ Vx) ^ N, |
80 | //! Exception: raises ConstructionError if N and Vx are parallel (same or opposite orientation). |
81 | gp_Ax2(const gp_Pnt& P, const gp_Dir& N, const gp_Dir& Vx); |
82 | |
83 | |
84 | //! Creates - a coordinate system with an origin P, where V |
85 | //! gives the "main Direction" (here, "X Direction" and "Y |
86 | //! Direction" are defined automatically). |
87 | Standard_EXPORT gp_Ax2(const gp_Pnt& P, const gp_Dir& V); |
88 | |
89 | //! Assigns the origin and "main Direction" of the axis A1 to |
90 | //! this coordinate system, then recomputes its "X Direction" and "Y Direction". |
91 | //! Note: The new "X Direction" is computed as follows: |
92 | //! new "X Direction" = V1 ^(previous "X Direction" ^ V) |
93 | //! where V is the "Direction" of A1. |
94 | //! Exceptions |
95 | //! Standard_ConstructionError if A1 is parallel to the "X |
96 | //! Direction" of this coordinate system. |
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97 | void SetAxis (const gp_Ax1& A1); |
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98 | |
99 | |
100 | //! Changes the "main Direction" of this coordinate system, |
101 | //! then recomputes its "X Direction" and "Y Direction". |
102 | //! Note: the new "X Direction" is computed as follows: |
103 | //! new "X Direction" = V ^ (previous "X Direction" ^ V) |
104 | //! Exceptions |
105 | //! Standard_ConstructionError if V is parallel to the "X |
106 | //! Direction" of this coordinate system. |
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107 | void SetDirection (const gp_Dir& V); |
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108 | |
109 | |
110 | //! Changes the "Location" point (origin) of <me>. |
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111 | void SetLocation (const gp_Pnt& P); |
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112 | |
113 | |
114 | //! Changes the "Xdirection" of <me>. The main direction |
115 | //! "Direction" is not modified, the "Ydirection" is modified. |
116 | //! If <Vx> is not normal to the main direction then <XDirection> |
117 | //! is computed as follows XDirection = Direction ^ (Vx ^ Direction). |
118 | //! Exceptions |
119 | //! Standard_ConstructionError if Vx or Vy is parallel to |
120 | //! the "main Direction" of this coordinate system. |
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121 | void SetXDirection (const gp_Dir& Vx); |
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122 | |
123 | |
124 | //! Changes the "Ydirection" of <me>. The main direction is not |
125 | //! modified but the "Xdirection" is changed. |
126 | //! If <Vy> is not normal to the main direction then "YDirection" |
127 | //! is computed as follows |
128 | //! YDirection = Direction ^ (<Vy> ^ Direction). |
129 | //! Exceptions |
130 | //! Standard_ConstructionError if Vx or Vy is parallel to |
131 | //! the "main Direction" of this coordinate system. |
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132 | void SetYDirection (const gp_Dir& Vy); |
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133 | |
134 | |
135 | //! Computes the angular value, in radians, between the main direction of |
136 | //! <me> and the main direction of <Other>. Returns the angle |
137 | //! between 0 and PI in radians. |
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138 | Standard_Real Angle (const gp_Ax2& Other) const; |
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139 | |
140 | |
141 | //! Returns the main axis of <me>. It is the "Location" point |
142 | //! and the main "Direction". |
143 | const gp_Ax1& Axis() const; |
144 | |
145 | |
146 | //! Returns the main direction of <me>. |
147 | const gp_Dir& Direction() const; |
148 | |
149 | |
150 | //! Returns the "Location" point (origin) of <me>. |
151 | const gp_Pnt& Location() const; |
152 | |
153 | |
154 | //! Returns the "XDirection" of <me>. |
155 | const gp_Dir& XDirection() const; |
156 | |
157 | |
158 | //! Returns the "YDirection" of <me>. |
159 | const gp_Dir& YDirection() const; |
160 | |
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161 | Standard_Boolean IsCoplanar (const gp_Ax2& Other, const Standard_Real LinearTolerance, const Standard_Real AngularTolerance) const; |
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162 | |
163 | |
164 | //! Returns True if |
165 | //! . the distance between <me> and the "Location" point of A1 |
166 | //! is lower of equal to LinearTolerance and |
167 | //! . the main direction of <me> and the direction of A1 are normal. |
168 | //! Note: the tolerance criterion for angular equality is given by AngularTolerance. |
169 | Standard_Boolean IsCoplanar (const gp_Ax1& A1, const Standard_Real LinearTolerance, const Standard_Real AngularTolerance) const; |
170 | |
171 | |
172 | //! Performs a symmetrical transformation of this coordinate |
173 | //! system with respect to: |
174 | //! - the point P, and assigns the result to this coordinate system. |
175 | //! Warning |
176 | //! This transformation is always performed on the origin. |
177 | //! In case of a reflection with respect to a point: |
178 | //! - the main direction of the coordinate system is not changed, and |
179 | //! - the "X Direction" and the "Y Direction" are simply reversed |
180 | //! In case of a reflection with respect to an axis or a plane: |
181 | //! - the transformation is applied to the "X Direction" |
182 | //! and the "Y Direction", then |
183 | //! - the "main Direction" is recomputed as the cross |
184 | //! product "X Direction" ^ "Y Direction". |
185 | //! This maintains the right-handed property of the |
186 | //! coordinate system. |
187 | Standard_EXPORT void Mirror (const gp_Pnt& P); |
188 | |
189 | |
190 | //! Performs a symmetrical transformation of this coordinate |
191 | //! system with respect to: |
192 | //! - the point P, and creates a new one. |
193 | //! Warning |
194 | //! This transformation is always performed on the origin. |
195 | //! In case of a reflection with respect to a point: |
196 | //! - the main direction of the coordinate system is not changed, and |
197 | //! - the "X Direction" and the "Y Direction" are simply reversed |
198 | //! In case of a reflection with respect to an axis or a plane: |
199 | //! - the transformation is applied to the "X Direction" |
200 | //! and the "Y Direction", then |
201 | //! - the "main Direction" is recomputed as the cross |
202 | //! product "X Direction" ^ "Y Direction". |
203 | //! This maintains the right-handed property of the |
204 | //! coordinate system. |
205 | Standard_EXPORT gp_Ax2 Mirrored (const gp_Pnt& P) const; |
206 | |
207 | |
208 | //! Performs a symmetrical transformation of this coordinate |
209 | //! system with respect to: |
210 | //! - the axis A1, and assigns the result to this coordinate systeme. |
211 | //! Warning |
212 | //! This transformation is always performed on the origin. |
213 | //! In case of a reflection with respect to a point: |
214 | //! - the main direction of the coordinate system is not changed, and |
215 | //! - the "X Direction" and the "Y Direction" are simply reversed |
216 | //! In case of a reflection with respect to an axis or a plane: |
217 | //! - the transformation is applied to the "X Direction" |
218 | //! and the "Y Direction", then |
219 | //! - the "main Direction" is recomputed as the cross |
220 | //! product "X Direction" ^ "Y Direction". |
221 | //! This maintains the right-handed property of the |
222 | //! coordinate system. |
223 | Standard_EXPORT void Mirror (const gp_Ax1& A1); |
224 | |
225 | |
226 | //! Performs a symmetrical transformation of this coordinate |
227 | //! system with respect to: |
228 | //! - the axis A1, and creates a new one. |
229 | //! Warning |
230 | //! This transformation is always performed on the origin. |
231 | //! In case of a reflection with respect to a point: |
232 | //! - the main direction of the coordinate system is not changed, and |
233 | //! - the "X Direction" and the "Y Direction" are simply reversed |
234 | //! In case of a reflection with respect to an axis or a plane: |
235 | //! - the transformation is applied to the "X Direction" |
236 | //! and the "Y Direction", then |
237 | //! - the "main Direction" is recomputed as the cross |
238 | //! product "X Direction" ^ "Y Direction". |
239 | //! This maintains the right-handed property of the |
240 | //! coordinate system. |
241 | Standard_EXPORT gp_Ax2 Mirrored (const gp_Ax1& A1) const; |
242 | |
243 | |
244 | //! Performs a symmetrical transformation of this coordinate |
245 | //! system with respect to: |
246 | //! - the plane defined by the origin, "X Direction" and "Y |
247 | //! Direction" of coordinate system A2 and assigns the result to this coordinate systeme. |
248 | //! Warning |
249 | //! This transformation is always performed on the origin. |
250 | //! In case of a reflection with respect to a point: |
251 | //! - the main direction of the coordinate system is not changed, and |
252 | //! - the "X Direction" and the "Y Direction" are simply reversed |
253 | //! In case of a reflection with respect to an axis or a plane: |
254 | //! - the transformation is applied to the "X Direction" |
255 | //! and the "Y Direction", then |
256 | //! - the "main Direction" is recomputed as the cross |
257 | //! product "X Direction" ^ "Y Direction". |
258 | //! This maintains the right-handed property of the |
259 | //! coordinate system. |
260 | Standard_EXPORT void Mirror (const gp_Ax2& A2); |
261 | |
262 | |
263 | //! Performs a symmetrical transformation of this coordinate |
264 | //! system with respect to: |
265 | //! - the plane defined by the origin, "X Direction" and "Y |
266 | //! Direction" of coordinate system A2 and creates a new one. |
267 | //! Warning |
268 | //! This transformation is always performed on the origin. |
269 | //! In case of a reflection with respect to a point: |
270 | //! - the main direction of the coordinate system is not changed, and |
271 | //! - the "X Direction" and the "Y Direction" are simply reversed |
272 | //! In case of a reflection with respect to an axis or a plane: |
273 | //! - the transformation is applied to the "X Direction" |
274 | //! and the "Y Direction", then |
275 | //! - the "main Direction" is recomputed as the cross |
276 | //! product "X Direction" ^ "Y Direction". |
277 | //! This maintains the right-handed property of the |
278 | //! coordinate system. |
279 | Standard_EXPORT gp_Ax2 Mirrored (const gp_Ax2& A2) const; |
280 | |
281 | void Rotate (const gp_Ax1& A1, const Standard_Real Ang); |
282 | |
283 | |
284 | //! Rotates an axis placement. <A1> is the axis of the |
285 | //! rotation . Ang is the angular value of the rotation |
286 | //! in radians. |
287 | gp_Ax2 Rotated (const gp_Ax1& A1, const Standard_Real Ang) const; |
288 | |
289 | void Scale (const gp_Pnt& P, const Standard_Real S); |
290 | |
291 | |
292 | //! Applies a scaling transformation on the axis placement. |
293 | //! The "Location" point of the axisplacement is modified. |
294 | //! Warnings : |
295 | //! If the scale <S> is negative : |
296 | //! . the main direction of the axis placement is not changed. |
297 | //! . The "XDirection" and the "YDirection" are reversed. |
298 | //! So the axis placement stay right handed. |
299 | gp_Ax2 Scaled (const gp_Pnt& P, const Standard_Real S) const; |
300 | |
301 | void Transform (const gp_Trsf& T); |
302 | |
303 | |
304 | //! Transforms an axis placement with a Trsf. |
305 | //! The "Location" point, the "XDirection" and the |
306 | //! "YDirection" are transformed with T. The resulting |
307 | //! main "Direction" of <me> is the cross product between |
308 | //! the "XDirection" and the "YDirection" after transformation. |
309 | gp_Ax2 Transformed (const gp_Trsf& T) const; |
310 | |
311 | void Translate (const gp_Vec& V); |
312 | |
313 | |
314 | //! Translates an axis plaxement in the direction of the vector |
315 | //! <V>. The magnitude of the translation is the vector's magnitude. |
316 | gp_Ax2 Translated (const gp_Vec& V) const; |
317 | |
318 | void Translate (const gp_Pnt& P1, const gp_Pnt& P2); |
319 | |
320 | |
321 | //! Translates an axis placement from the point <P1> to the |
322 | //! point <P2>. |
323 | gp_Ax2 Translated (const gp_Pnt& P1, const gp_Pnt& P2) const; |
324 | |
325 | |
326 | |
327 | |
328 | protected: |
329 | |
330 | |
331 | |
332 | |
333 | |
334 | private: |
335 | |
336 | |
337 | |
338 | gp_Ax1 axis; |
339 | gp_Dir vydir; |
340 | gp_Dir vxdir; |
341 | |
342 | |
343 | }; |
344 | |
345 | |
346 | #include <gp_Ax2.lxx> |
347 | |
348 | |
349 | |
350 | |
351 | |
352 | #endif // _gp_Ax2_HeaderFile |