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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_Ellipse_HeaderFile |
18 | #define _Geom2d_Ellipse_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_RangeError; |
29 | class gp_Elips2d; |
30 | class gp_Ax2d; |
31 | class gp_Ax22d; |
32 | class gp_Pnt2d; |
33 | class gp_Vec2d; |
34 | class gp_Trsf2d; |
35 | class Geom2d_Geometry; |
36 | |
37 | |
38 | class Geom2d_Ellipse; |
39 | DEFINE_STANDARD_HANDLE(Geom2d_Ellipse, Geom2d_Conic) |
40 | |
41 | //! Describes an ellipse in the plane (2D space). |
42 | //! An ellipse is defined by its major and minor radii and, |
43 | //! as with any conic curve, is positioned in the plane |
44 | //! with a coordinate system (gp_Ax22d 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 | //! This coordinate system is the local coordinate system of the ellipse. |
49 | //! The orientation (direct or indirect) of the local |
50 | //! coordinate system gives an explicit orientation to the |
51 | //! ellipse, determining the direction in which the |
52 | //! parameter increases along the ellipse. |
53 | //! The Geom2d_Ellipse ellipse is parameterized by an angle: |
54 | //! P(U) = O + MajorRad*Cos(U)*XDir + MinorRad*Sin(U)*YDir |
55 | //! where: |
56 | //! - P is the point of parameter U, |
57 | //! - O, XDir and YDir are respectively the origin, "X |
58 | //! Direction" and "Y Direction" of its local coordinate system, |
59 | //! - MajorRad and MinorRad are the major and |
60 | //! minor radii of the ellipse. |
61 | //! The "X Axis" of the local coordinate system therefore |
62 | //! defines the origin of the parameter of the ellipse. |
63 | //! An ellipse is a closed and periodic curve. The period |
64 | //! is 2.*Pi and the parameter range is [ 0,2.*Pi [. |
65 | //! See Also |
66 | //! GCE2d_MakeEllipse which provides functions for |
67 | //! more complex ellipse constructions |
68 | //! gp_Ax22d |
69 | //! gp_Elips2d for an equivalent, non-parameterized data structure |
70 | class Geom2d_Ellipse : public Geom2d_Conic |
71 | { |
72 | |
73 | public: |
74 | |
75 | |
76 | |
77 | //! Creates an ellipse by conversion of the gp_Elips2d ellipse E. |
78 | Standard_EXPORT Geom2d_Ellipse(const gp_Elips2d& E); |
79 | |
80 | //! Creates an ellipse defined by its major and minor radii, |
81 | //! MajorRadius and MinorRadius, and positioned |
82 | //! in the plane by its major axis MajorAxis; the |
83 | //! center of the ellipse is the origin of MajorAxis |
84 | //! and the unit vector of MajorAxis is the "X |
85 | //! Direction" of the local coordinate system of the |
86 | //! ellipse; this coordinate system is direct if Sense |
87 | //! is true (default value) or indirect if Sense is false. |
88 | //! Warnings : |
89 | //! It is not forbidden to create an ellipse with MajorRadius = |
90 | //! MinorRadius. |
91 | //! Exceptions |
92 | //! Standard_ConstructionError if: |
93 | //! - MajorRadius is less than MinorRadius, or |
94 | //! - MinorRadius is less than 0. |
95 | Standard_EXPORT Geom2d_Ellipse(const gp_Ax2d& MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense = Standard_True); |
96 | |
97 | //! Creates an ellipse defined by its major and minor radii, |
98 | //! MajorRadius and MinorRadius, where the |
99 | //! coordinate system Axis locates the ellipse and |
100 | //! defines its orientation in the plane such that: |
101 | //! - the center of the ellipse is the origin of Axis, |
102 | //! - the "X Direction" of Axis defines the major |
103 | //! axis of the ellipse, |
104 | //! - the "Y Direction" of Axis defines the minor |
105 | //! axis of the ellipse, |
106 | //! - the orientation of Axis (direct or indirect) |
107 | //! gives the orientation of the ellipse. |
108 | //! Warnings : |
109 | //! It is not forbidden to create an ellipse with MajorRadius = |
110 | //! MinorRadius. |
111 | //! Exceptions |
112 | //! Standard_ConstructionError if: |
113 | //! - MajorRadius is less than MinorRadius, or |
114 | //! - MinorRadius is less than 0. |
115 | Standard_EXPORT Geom2d_Ellipse(const gp_Ax22d& Axis, const Standard_Real MajorRadius, const Standard_Real MinorRadius); |
116 | |
117 | //! Converts the gp_Elips2d ellipse E into this ellipse. |
118 | Standard_EXPORT void SetElips2d (const gp_Elips2d& E); |
119 | |
120 | //! Assigns a value to the major radius of this ellipse. |
121 | //! Exceptions |
122 | //! Standard_ConstructionError if: |
123 | //! - the major radius of this ellipse becomes less than |
124 | //! the minor radius, or |
125 | //! - MinorRadius is less than 0. |
126 | Standard_EXPORT void SetMajorRadius (const Standard_Real MajorRadius); |
127 | |
128 | //! Assigns a value to the minor radius of this ellipse. |
129 | //! Exceptions |
130 | //! Standard_ConstructionError if: |
131 | //! - the major radius of this ellipse becomes less than |
132 | //! the minor radius, or |
133 | //! - MinorRadius is less than 0. |
134 | Standard_EXPORT void SetMinorRadius (const Standard_Real MinorRadius); |
135 | |
136 | //! Converts this ellipse into a gp_Elips2d ellipse. |
137 | Standard_EXPORT gp_Elips2d Elips2d() const; |
138 | |
139 | //! Computes the parameter on the reversed ellipse for |
140 | //! the point of parameter U on this ellipse. |
141 | //! For an ellipse, the returned value is: 2.*Pi - U. |
142 | Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; |
143 | |
144 | //! Computes the directrices of this ellipse. |
145 | //! This directrix is the line normal to the XAxis of the ellipse |
146 | //! in the local plane (Z = 0) at a distance d = MajorRadius / e |
147 | //! from the center of the ellipse, where e is the eccentricity of |
148 | //! the ellipse. |
149 | //! This line is parallel to the "YAxis". The intersection point |
150 | //! between directrix1 and the "XAxis" is the "Location" point |
151 | //! of the directrix1. This point is on the positive side of |
152 | //! the "XAxis". |
153 | //! Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates |
154 | //! into a circle) |
155 | Standard_EXPORT gp_Ax2d Directrix1() const; |
156 | |
157 | |
158 | //! This line is obtained by the symmetrical transformation |
159 | //! of "Directrix1" with respect to the "YAxis" of the ellipse. |
160 | //! Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates into a |
161 | //! circle). |
162 | Standard_EXPORT gp_Ax2d Directrix2() const; |
163 | |
164 | |
165 | //! Returns the eccentricity of the ellipse between 0.0 and 1.0 |
166 | //! If f is the distance between the center of the ellipse and |
167 | //! the Focus1 then the eccentricity e = f / MajorRadius. |
168 | //! Returns 0 if MajorRadius = 0 |
169 | Standard_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE; |
170 | |
171 | |
172 | //! Computes the focal distance. The focal distance is the distance between the center |
173 | //! and a focus of the ellipse. |
174 | Standard_EXPORT Standard_Real Focal() const; |
175 | |
176 | |
177 | //! Returns the first focus of the ellipse. This focus is on the |
178 | //! positive side of the "XAxis" of the ellipse. |
179 | Standard_EXPORT gp_Pnt2d Focus1() const; |
180 | |
181 | |
182 | //! Returns the second focus of the ellipse. This focus is on |
183 | //! the negative side of the "XAxis" of the ellipse. |
184 | Standard_EXPORT gp_Pnt2d Focus2() const; |
185 | |
186 | //! Returns the major radius of this ellipse. |
187 | Standard_EXPORT Standard_Real MajorRadius() const; |
188 | |
189 | //! Returns the minor radius of this ellipse. |
190 | Standard_EXPORT Standard_Real MinorRadius() const; |
191 | |
192 | |
193 | //! Computes the parameter of this ellipse. This value is |
194 | //! given by the formula p = (1 - e * e) * MajorRadius where e is the eccentricity |
195 | //! of the ellipse. |
196 | //! Returns 0 if MajorRadius = 0 |
197 | Standard_EXPORT Standard_Real Parameter() const; |
198 | |
199 | //! Returns the value of the first parameter of this |
200 | //! ellipse. This is 0.0, which gives the start point of this ellipse. |
201 | //! The start point and end point of an ellipse are coincident. |
202 | Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; |
203 | |
204 | //! Returns the value of the last parameter of this |
205 | //! ellipse. This is 2.*Pi, which gives the end point of this ellipse. |
206 | //! The start point and end point of an ellipse are coincident. |
207 | Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; |
208 | |
209 | //! return True. |
210 | Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; |
211 | |
212 | //! return True. |
213 | Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; |
214 | |
215 | //! Returns in P the point of parameter U. |
216 | //! P = C + MajorRadius * Cos (U) * XDir + MinorRadius * Sin (U) * YDir |
217 | //! where C is the center of the ellipse , XDir the direction of |
218 | //! the "XAxis" and "YDir" the "YAxis" of the ellipse. |
219 | Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE; |
220 | |
221 | Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE; |
222 | |
223 | |
224 | //! Returns the point P of parameter U. The vectors V1 and V2 |
225 | //! are the first and second derivatives at this point. |
226 | Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE; |
227 | |
228 | |
229 | //! Returns the point P of parameter U, the first second and |
230 | //! third derivatives V1 V2 and V3. |
231 | Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE; |
232 | |
233 | //! For the point of parameter U of this ellipse, |
234 | //! computes the vector corresponding to the Nth derivative. |
235 | //! Exceptions Standard_RangeError if N is less than 1. |
236 | Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; |
237 | |
238 | //! Applies the transformation T to this ellipse. |
239 | Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE; |
240 | |
241 | //! Creates a new object which is a copy of this ellipse. |
242 | Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE; |
243 | |
244 | |
245 | |
246 | |
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247 | DEFINE_STANDARD_RTTIEXT(Geom2d_Ellipse,Geom2d_Conic) |
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248 | |
249 | protected: |
250 | |
251 | |
252 | |
253 | |
254 | private: |
255 | |
256 | |
257 | Standard_Real majorRadius; |
258 | Standard_Real minorRadius; |
259 | |
260 | |
261 | }; |
262 | |
263 | |
264 | |
265 | |
266 | |
267 | |
268 | |
269 | #endif // _Geom2d_Ellipse_HeaderFile |