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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_ConicalSurface_HeaderFile |
18 | #define _Geom_ConicalSurface_HeaderFile |
19 | |
20 | #include <Standard.hxx> |
21 | #include <Standard_Type.hxx> |
22 | |
23 | #include <Standard_Real.hxx> |
24 | #include <Geom_ElementarySurface.hxx> |
25 | #include <Standard_Boolean.hxx> |
26 | #include <Standard_Integer.hxx> |
27 | class Standard_ConstructionError; |
28 | class Standard_RangeError; |
29 | class gp_Ax3; |
30 | class gp_Cone; |
31 | class gp_Trsf; |
32 | class gp_GTrsf2d; |
33 | class gp_Pnt; |
34 | class Geom_Curve; |
35 | class gp_Vec; |
36 | class Geom_Geometry; |
37 | |
38 | |
39 | class Geom_ConicalSurface; |
40 | DEFINE_STANDARD_HANDLE(Geom_ConicalSurface, Geom_ElementarySurface) |
41 | |
42 | //! Describes a cone. |
43 | //! A cone is defined by the half-angle at its apex, and |
44 | //! is positioned in space by a coordinate system (a |
45 | //! gp_Ax3 object) and a reference radius as follows: |
46 | //! - The "main Axis" of the coordinate system is the |
47 | //! axis of revolution of the cone. |
48 | //! - The plane defined by the origin, the "X Direction" |
49 | //! and the "Y Direction" of the coordinate system is |
50 | //! the reference plane of the cone. The intersection |
51 | //! of the cone with this reference plane is a circle of |
52 | //! radius equal to the reference radius. |
53 | //! - The apex of the cone is on the negative side of |
54 | //! the "main Axis" of the coordinate system if the |
55 | //! half-angle is positive, and on the positive side if |
56 | //! the half-angle is negative. |
57 | //! This coordinate system is the "local coordinate |
58 | //! system" of the cone. The following apply: |
59 | //! - Rotation around its "main Axis", in the |
60 | //! trigonometric sense given by the "X Direction" |
61 | //! and the "Y Direction", defines the u parametric direction. |
62 | //! - Its "X Axis" gives the origin for the u parameter. |
63 | //! - Its "main Direction" is the v parametric direction of the cone. |
64 | //! - Its origin is the origin of the v parameter. |
65 | //! The parametric range of the two parameters is: |
66 | //! - [ 0, 2.*Pi ] for u, and - ] -infinity, +infinity [ for v |
67 | //! The parametric equation of the cone is: P(u, v) = |
68 | //! O + (R + v*sin(Ang)) * (cos(u)*XDir + sin(u)*YDir) + v*cos(Ang)*ZDir where: |
69 | //! - O, XDir, YDir and ZDir are respectively |
70 | //! the origin, the "X Direction", the "Y Direction" and |
71 | //! the "Z Direction" of the cone's local coordinate system, |
72 | //! - Ang is the half-angle at the apex of the cone, and |
73 | //! - R is the reference radius. |
74 | class Geom_ConicalSurface : public Geom_ElementarySurface |
75 | { |
76 | |
77 | public: |
78 | |
79 | |
80 | |
81 | //! A3 defines the local coordinate system of the conical surface. |
82 | //! Ang is the conical surface semi-angle ]0, PI/2[. |
83 | //! Radius is the radius of the circle Viso in the placement plane |
84 | //! of the conical surface defined with "XAxis" and "YAxis". |
85 | //! The "ZDirection" of A3 defines the direction of the surface's |
86 | //! axis of symmetry. |
87 | //! If the location point of A3 is the apex of the surface |
88 | //! Radius = 0 . |
89 | //! At the creation the parametrization of the surface is defined |
90 | //! such that the normal Vector (N = D1U ^ D1V) is oriented towards |
91 | //! the "outside region" of the surface. |
92 | //! |
93 | //! Raised if Radius < 0.0 or Ang < Resolution from gp or |
94 | //! Ang >= PI/2 - Resolution |
95 | Standard_EXPORT Geom_ConicalSurface(const gp_Ax3& A3, const Standard_Real Ang, const Standard_Real Radius); |
96 | |
97 | |
98 | //! Creates a ConicalSurface from a non transient Cone from |
99 | //! package gp. |
100 | Standard_EXPORT Geom_ConicalSurface(const gp_Cone& C); |
101 | |
102 | |
103 | //! Set <me> so that <me> has the same geometric properties as C. |
104 | Standard_EXPORT void SetCone (const gp_Cone& C); |
105 | |
106 | |
107 | //! Changes the radius of the conical surface in the placement |
108 | //! plane (Z = 0, V = 0). The local coordinate system is not |
109 | //! modified. |
110 | //! Raised if R < 0.0 |
111 | Standard_EXPORT void SetRadius (const Standard_Real R); |
112 | |
113 | |
114 | //! Changes the semi angle of the conical surface. |
115 | //! |
116 | //! Raised if Ang < Resolution or Ang >= PI/2 - Resolution |
117 | Standard_EXPORT void SetSemiAngle (const Standard_Real Ang); |
118 | |
119 | |
120 | //! returns a non transient cone with the same geometric properties |
121 | //! as <me>. |
122 | Standard_EXPORT gp_Cone Cone() const; |
123 | |
124 | //! return 2.PI - U. |
125 | Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const; |
126 | |
127 | //! Computes the u (or v) parameter on the modified |
128 | //! surface, when reversing its u (or v) parametric |
129 | //! direction, for any point of u parameter U (or of v |
130 | //! parameter V) on this cone. |
131 | //! In the case of a cone, these functions return respectively: |
132 | //! - 2.*Pi - U, -V. |
133 | Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const; |
134 | |
135 | //! Changes the orientation of this cone in the v |
136 | //! parametric direction. The bounds of the surface are |
137 | //! not changed but the v parametric direction is reversed. |
138 | //! As a consequence, for a cone: |
139 | //! - the "main Direction" of the local coordinate system |
140 | //! is reversed, and |
141 | //! - the half-angle at the apex is inverted. |
142 | Standard_EXPORT virtual void VReverse() Standard_OVERRIDE; |
143 | |
144 | //! Computes the parameters on the transformed surface for |
145 | //! the transform of the point of parameters U,V on <me>. |
146 | //! |
147 | //! me->Transformed(T)->Value(U',V') |
148 | //! |
149 | //! is the same point as |
150 | //! |
151 | //! me->Value(U,V).Transformed(T) |
152 | //! |
153 | //! Where U',V' are the new values of U,V after calling |
154 | //! |
155 | //! me->TranformParameters(U,V,T) |
156 | //! |
157 | //! This methods multiplies V by T.ScaleFactor() |
158 | Standard_EXPORT virtual void TransformParameters (Standard_Real& U, Standard_Real& V, const gp_Trsf& T) const Standard_OVERRIDE; |
159 | |
160 | //! Returns a 2d transformation used to find the new |
161 | //! parameters of a point on the transformed surface. |
162 | //! |
163 | //! me->Transformed(T)->Value(U',V') |
164 | //! |
165 | //! is the same point as |
166 | //! |
167 | //! me->Value(U,V).Transformed(T) |
168 | //! |
169 | //! Where U',V' are obtained by transforming U,V with |
170 | //! th 2d transformation returned by |
171 | //! |
172 | //! me->ParametricTransformation(T) |
173 | //! |
174 | //! This methods returns a scale centered on the |
175 | //! U axis with T.ScaleFactor |
176 | Standard_EXPORT virtual gp_GTrsf2d ParametricTransformation (const gp_Trsf& T) const Standard_OVERRIDE; |
177 | |
178 | //! Computes the apex of this cone. It is on the negative |
179 | //! side of the axis of revolution of this cone if the |
180 | //! half-angle at the apex is positive, and on the positive |
181 | //! side of the "main Axis" if the half-angle is negative. |
182 | Standard_EXPORT gp_Pnt Apex() const; |
183 | |
184 | |
185 | //! The conical surface is infinite in the V direction so |
186 | //! V1 = Realfirst from Standard and V2 = RealLast. |
187 | //! U1 = 0 and U2 = 2*PI. |
188 | Standard_EXPORT void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const; |
189 | |
190 | |
191 | //! Returns the coefficients of the implicit equation of the |
192 | //! quadric in the absolute cartesian coordinate system : |
193 | //! These coefficients are normalized. |
194 | //! A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + |
195 | //! 2.(C1.X + C2.Y + C3.Z) + D = 0.0 |
196 | Standard_EXPORT void Coefficients (Standard_Real& A1, Standard_Real& A2, Standard_Real& A3, Standard_Real& B1, Standard_Real& B2, Standard_Real& B3, Standard_Real& C1, Standard_Real& C2, Standard_Real& C3, Standard_Real& D) const; |
197 | |
198 | //! Returns the reference radius of this cone. |
199 | //! The reference radius is the radius of the circle formed |
200 | //! by the intersection of this cone and its reference |
201 | //! plane (i.e. the plane defined by the origin, "X |
202 | //! Direction" and "Y Direction" of the local coordinate |
203 | //! system of this cone). |
204 | //! If the apex of this cone is on the origin of the local |
205 | //! coordinate system of this cone, the returned value is 0. |
206 | Standard_EXPORT Standard_Real RefRadius() const; |
207 | |
208 | |
209 | //! returns the semi-angle of the conical surface ]0.0, PI/2[. |
210 | Standard_EXPORT Standard_Real SemiAngle() const; |
211 | |
212 | //! returns True. |
213 | Standard_EXPORT Standard_Boolean IsUClosed() const; |
214 | |
215 | //! returns False. |
216 | Standard_EXPORT Standard_Boolean IsVClosed() const; |
217 | |
218 | //! Returns True. |
219 | Standard_EXPORT Standard_Boolean IsUPeriodic() const; |
220 | |
221 | //! Returns False. |
222 | Standard_EXPORT Standard_Boolean IsVPeriodic() const; |
223 | |
224 | //! Builds the U isoparametric line of this cone. The |
225 | //! origin of this line is on the reference plane of this |
226 | //! cone (i.e. the plane defined by the origin, "X Direction" |
227 | //! and "Y Direction" of the local coordinate system of this cone). |
228 | Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const; |
229 | |
230 | //! Builds the V isoparametric circle of this cone. It is the |
231 | //! circle on this cone, located in the plane of Z |
232 | //! coordinate V*cos(Semi-Angle) in the local coordinate system of this |
233 | //! cone. The "Axis" of this circle is the axis of revolution |
234 | //! of this cone. Its starting point is defined by the "X |
235 | //! Direction" of this cone. |
236 | //! Warning |
237 | //! If the V isoparametric circle is close to the apex of |
238 | //! this cone, the radius of the circle becomes very small. |
239 | //! It is possible to have a circle with radius equal to 0.0. |
240 | Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const; |
241 | |
242 | |
243 | //! Computes the point P (U, V) on the surface. |
244 | //! P (U, V) = Loc + |
245 | //! (RefRadius + V * sin (Semi-Angle)) * (cos (U) * XDir + sin (U) * YDir) + |
246 | //! V * cos (Semi-Angle) * ZDir |
247 | //! where Loc is the origin of the placement plane (XAxis, YAxis) |
248 | //! XDir is the direction of the XAxis and YDir the direction of |
249 | //! the YAxis. |
250 | Standard_EXPORT void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const; |
251 | |
252 | |
253 | //! Computes the current point and the first derivatives in the |
254 | //! directions U and V. |
255 | Standard_EXPORT void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const; |
256 | |
257 | |
258 | //! Computes the current point, the first and the second derivatives |
259 | //! in the directions U and V. |
260 | Standard_EXPORT void D2 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V, gp_Vec& D2U, gp_Vec& D2V, gp_Vec& D2UV) const; |
261 | |
262 | |
263 | //! Computes the current point, the first,the second and the third |
264 | //! derivatives in the directions U and V. |
265 | Standard_EXPORT void D3 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V, gp_Vec& D2U, gp_Vec& D2V, gp_Vec& D2UV, gp_Vec& D3U, gp_Vec& D3V, gp_Vec& D3UUV, gp_Vec& D3UVV) const; |
266 | |
267 | //! Computes the derivative of order Nu in the u |
268 | //! parametric direction, and Nv in the v parametric |
269 | //! direction at the point of parameters (U, V) of this cone. |
270 | //! Exceptions |
271 | //! Standard_RangeError if: |
272 | //! - Nu + Nv is less than 1, |
273 | //! - Nu or Nv is negative. |
274 | Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const; |
275 | |
276 | //! Applies the transformation T to this cone. |
277 | Standard_EXPORT void Transform (const gp_Trsf& T); |
278 | |
279 | //! Creates a new object which is a copy of this cone. |
280 | Standard_EXPORT Handle(Geom_Geometry) Copy() const; |
281 | |
282 | |
283 | |
284 | |
285 | DEFINE_STANDARD_RTTI(Geom_ConicalSurface,Geom_ElementarySurface) |
286 | |
287 | protected: |
288 | |
289 | |
290 | |
291 | |
292 | private: |
293 | |
294 | |
295 | Standard_Real radius; |
296 | Standard_Real semiAngle; |
297 | |
298 | |
299 | }; |
300 | |
301 | |
302 | |
303 | |
304 | |
305 | |
306 | |
307 | #endif // _Geom_ConicalSurface_HeaderFile |