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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_Ellipse_HeaderFile |
18 | #define _Geom_Ellipse_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_Elips; |
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_Ellipse; |
39 | DEFINE_STANDARD_HANDLE(Geom_Ellipse, Geom_Conic) |
40 | |
41 | //! Describes an ellipse in 3D space. |
42 | //! An ellipse is defined by its major and minor radii and, |
43 | //! as with any conic curve, is positioned in space with a |
44 | //! right-handed coordinate system (gp_Ax2 object) where: |
45 | //! - the origin is the center of the ellipse, |
46 | //! - the "X Direction" defines the major axis, and |
47 | //! - the "Y Direction" defines the minor axis. |
48 | //! The origin, "X Direction" and "Y Direction" of this |
49 | //! coordinate system define the plane of the ellipse. The |
50 | //! coordinate system is the local coordinate system of the ellipse. |
51 | //! The "main Direction" of this coordinate system is the |
52 | //! vector normal to the plane of the ellipse. The axis, of |
53 | //! which the origin and unit vector are respectively the |
54 | //! origin and "main Direction" of the local coordinate |
55 | //! system, is termed the "Axis" or "main Axis" of the ellipse. |
56 | //! The "main Direction" of the local coordinate system |
57 | //! gives an explicit orientation to the ellipse (definition of |
58 | //! the trigonometric sense), determining the direction in |
59 | //! which the parameter increases along the ellipse. |
60 | //! The Geom_Ellipse ellipse is parameterized by an angle: |
61 | //! P(U) = O + MajorRad*Cos(U)*XDir + MinorRad*Sin(U)*YDir |
62 | //! where: |
63 | //! - P is the point of parameter U, |
64 | //! - O, XDir and YDir are respectively the origin, "X |
65 | //! Direction" and "Y Direction" of its local coordinate system, |
66 | //! - MajorRad and MinorRad are the major and minor radii of the ellipse. |
67 | //! The "X Axis" of the local coordinate system therefore |
68 | //! defines the origin of the parameter of the ellipse. |
69 | //! An ellipse is a closed and periodic curve. The period |
70 | //! is 2.*Pi and the parameter range is [ 0, 2.*Pi [. |
71 | class Geom_Ellipse : public Geom_Conic |
72 | { |
73 | |
74 | public: |
75 | |
76 | |
77 | //! Constructs an ellipse by conversion of the gp_Elips ellipse E. |
78 | Standard_EXPORT Geom_Ellipse(const gp_Elips& E); |
79 | |
80 | //! Constructs an ellipse |
81 | //! defined by its major and minor radii, MajorRadius |
82 | //! and MinorRadius, where A2 locates the ellipse |
83 | //! and defines its orientation in 3D space such that: |
84 | //! - the center of the ellipse is the origin of A2, |
85 | //! - the "X Direction" of A2 defines the major axis |
86 | //! of the ellipse, i.e. the major radius |
87 | //! MajorRadius is measured along this axis, |
88 | //! - the "Y Direction" of A2 defines the minor axis |
89 | //! of the ellipse, i.e. the minor radius |
90 | //! MinorRadius is measured along this axis, |
91 | //! - A2 is the local coordinate system of the ellipse. |
92 | //! Exceptions |
93 | //! Standard_ConstructionError if: |
94 | //! - MajorRadius is less than MinorRadius, or |
95 | //! - MinorRadius is less than 0. |
96 | //! Warning The Geom package does not prevent the |
97 | //! construction of an ellipse where MajorRadius and |
98 | //! MinorRadius are equal. |
99 | Standard_EXPORT Geom_Ellipse(const gp_Ax2& A2, const Standard_Real MajorRadius, const Standard_Real MinorRadius); |
100 | |
101 | //! Converts the gp_Elips ellipse E into this ellipse. |
102 | Standard_EXPORT void SetElips (const gp_Elips& E); |
103 | |
104 | //! Assigns a value to the major radius of this ellipse. |
105 | //! ConstructionError raised if MajorRadius < MinorRadius. |
106 | Standard_EXPORT void SetMajorRadius (const Standard_Real MajorRadius); |
107 | |
108 | //! Assigns a value to the minor radius of this ellipse. |
109 | //! ConstructionError raised if MajorRadius < MinorRadius or if MinorRadius < 0. |
110 | Standard_EXPORT void SetMinorRadius (const Standard_Real MinorRadius); |
111 | |
112 | |
113 | //! returns the non transient ellipse from gp with the same |
114 | Standard_EXPORT gp_Elips Elips() const; |
115 | |
116 | //! Computes the parameter on the reversed ellipse for |
117 | //! the point of parameter U on this ellipse. |
118 | //! For an ellipse, the returned value is: 2.*Pi - U. |
119 | Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; |
120 | |
121 | |
122 | //! This directrix is the line normal to the XAxis of the ellipse |
123 | //! in the local plane (Z = 0) at a distance d = MajorRadius / e |
124 | //! from the center of the ellipse, where e is the eccentricity of |
125 | //! the ellipse. |
126 | //! This line is parallel to the "YAxis". The intersection point |
127 | //! between directrix1 and the "XAxis" is the "Location" point |
128 | //! of the directrix1. This point is on the positive side of |
129 | //! the "XAxis". |
130 | //! Raised if Eccentricity = 0.0. (The ellipse degenerates |
131 | //! into a circle) |
132 | Standard_EXPORT gp_Ax1 Directrix1() const; |
133 | |
134 | |
135 | //! This line is obtained by the symmetrical transformation |
136 | //! of "Directrix1" with respect to the "YAxis" of the ellipse. |
137 | //! |
138 | //! Raised if Eccentricity = 0.0. (The ellipse degenerates into a |
139 | //! circle). |
140 | Standard_EXPORT gp_Ax1 Directrix2() const; |
141 | |
142 | |
143 | //! Returns the eccentricity of the ellipse between 0.0 and 1.0 |
144 | //! If f is the distance between the center of the ellipse and |
145 | //! the Focus1 then the eccentricity e = f / MajorRadius. |
146 | //! Returns 0 if MajorRadius = 0 |
147 | Standard_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE; |
148 | |
149 | |
150 | //! Computes the focal distance. It is the distance between the |
151 | //! the two focus of the ellipse. |
152 | Standard_EXPORT Standard_Real Focal() const; |
153 | |
154 | |
155 | //! Returns the first focus of the ellipse. This focus is on the |
156 | //! positive side of the "XAxis" of the ellipse. |
157 | Standard_EXPORT gp_Pnt Focus1() const; |
158 | |
159 | |
160 | //! Returns the second focus of the ellipse. This focus is on |
161 | //! the negative side of the "XAxis" of the ellipse. |
162 | Standard_EXPORT gp_Pnt Focus2() const; |
163 | |
164 | //! Returns the major radius of this ellipse. |
165 | Standard_EXPORT Standard_Real MajorRadius() const; |
166 | |
167 | //! Returns the minor radius of this ellipse. |
168 | Standard_EXPORT Standard_Real MinorRadius() const; |
169 | |
170 | |
171 | //! Returns p = (1 - e * e) * MajorRadius where e is the eccentricity |
172 | //! of the ellipse. |
173 | //! Returns 0 if MajorRadius = 0 |
174 | Standard_EXPORT Standard_Real Parameter() const; |
175 | |
176 | //! Returns the value of the first parameter of this |
177 | //! ellipse. This is respectively: |
178 | //! - 0.0, which gives the start point of this ellipse, or |
179 | //! The start point and end point of an ellipse are coincident. |
180 | Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; |
181 | |
182 | //! Returns the value of the last parameter of this |
183 | //! ellipse. This is respectively: |
184 | //! - 2.*Pi, which gives the end point of this ellipse. |
185 | //! The start point and end point of an ellipse are coincident. |
186 | Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; |
187 | |
188 | //! return True. |
189 | Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; |
190 | |
191 | //! return True. |
192 | Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; |
193 | |
194 | //! Returns in P the point of parameter U. |
195 | //! P = C + MajorRadius * Cos (U) * XDir + MinorRadius * Sin (U) * YDir |
196 | //! where C is the center of the ellipse , XDir the direction of |
197 | //! the "XAxis" and "YDir" the "YAxis" of the ellipse. |
198 | Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt& P) const Standard_OVERRIDE; |
199 | |
200 | Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const Standard_OVERRIDE; |
201 | |
202 | |
203 | //! Returns the point P of parameter U. The vectors V1 and V2 |
204 | //! are the first and second derivatives at this point. |
205 | Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) const Standard_OVERRIDE; |
206 | |
207 | |
208 | //! Returns the point P of parameter U, the first second and |
209 | //! third derivatives V1 V2 and V3. |
210 | Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const Standard_OVERRIDE; |
211 | |
212 | //! For the point of parameter U of this ellipse, computes |
213 | //! the vector corresponding to the Nth derivative. |
214 | //! Exceptions Standard_RangeError if N is less than 1. |
215 | Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; |
216 | |
217 | //! Applies the transformation T to this ellipse. |
218 | Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE; |
219 | |
220 | //! Creates a new object which is a copy of this ellipse. |
221 | Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE; |
222 | |
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223 | //! Dumps the content of me into the stream |
224 | Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE; |
225 | |
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226 | |
227 | |
228 | |
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229 | DEFINE_STANDARD_RTTIEXT(Geom_Ellipse,Geom_Conic) |
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230 | |
231 | protected: |
232 | |
233 | |
234 | |
235 | |
236 | private: |
237 | |
238 | |
239 | Standard_Real majorRadius; |
240 | Standard_Real minorRadius; |
241 | |
242 | |
243 | }; |
244 | |
245 | |
246 | |
247 | |
248 | |
249 | |
250 | |
251 | #endif // _Geom_Ellipse_HeaderFile |