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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_SphericalSurface_HeaderFile |
18 | #define _Geom_SphericalSurface_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_Sphere; |
31 | class Geom_Curve; |
32 | class gp_Pnt; |
33 | class gp_Vec; |
34 | class gp_Trsf; |
35 | class Geom_Geometry; |
36 | |
37 | |
38 | class Geom_SphericalSurface; |
39 | DEFINE_STANDARD_HANDLE(Geom_SphericalSurface, Geom_ElementarySurface) |
40 | |
41 | //! Describes a sphere. |
42 | //! A sphere is defined by its radius, and is positioned in |
43 | //! space by a coordinate system (a gp_Ax3 object), the |
44 | //! origin of which is the center of the sphere. |
45 | //! This coordinate system is the "local coordinate |
46 | //! system" of the sphere. The following apply: |
47 | //! - Rotation around its "main Axis", in the trigonometric |
48 | //! sense given by the "X Direction" and the "Y |
49 | //! Direction", defines the u parametric direction. |
50 | //! - Its "X Axis" gives the origin for the u parameter. |
51 | //! - The "reference meridian" of the sphere is a |
52 | //! half-circle, of radius equal to the radius of the |
53 | //! sphere. It is located in the plane defined by the |
54 | //! origin, "X Direction" and "main Direction", centered |
55 | //! on the origin, and positioned on the positive side of the "X Axis". |
56 | //! - Rotation around the "Y Axis" gives the v parameter |
57 | //! on the reference meridian. |
58 | //! - The "X Axis" gives the origin of the v parameter on |
59 | //! the reference meridian. |
60 | //! - The v parametric direction is oriented by the "main |
61 | //! Direction", i.e. when v increases, the Z coordinate |
62 | //! increases. (This implies that the "Y Direction" |
63 | //! orients the reference meridian only when the local |
64 | //! coordinate system is indirect.) |
65 | //! - The u isoparametric curve is a half-circle obtained |
66 | //! by rotating the reference meridian of the sphere |
67 | //! through an angle u around the "main Axis", in the |
68 | //! trigonometric sense defined by the "X Direction" |
69 | //! and the "Y Direction". |
70 | //! The parametric equation of the sphere is: |
71 | //! P(u,v) = O + R*cos(v)*(cos(u)*XDir + sin(u)*YDir)+R*sin(v)*ZDir |
72 | //! where: |
73 | //! - O, XDir, YDir and ZDir are respectively the |
74 | //! origin, the "X Direction", the "Y Direction" and the "Z |
75 | //! Direction" of its local coordinate system, and |
76 | //! - R is the radius of the sphere. |
77 | //! The parametric range of the two parameters is: |
78 | //! - [ 0, 2.*Pi ] for u, and |
79 | //! - [ - Pi/2., + Pi/2. ] for v. |
80 | class Geom_SphericalSurface : public Geom_ElementarySurface |
81 | { |
82 | |
83 | public: |
84 | |
85 | |
86 | |
87 | //! A3 is the local coordinate system of the surface. |
88 | //! At the creation the parametrization of the surface is defined |
89 | //! such as the normal Vector (N = D1U ^ D1V) is directed away from |
90 | //! the center of the sphere. |
91 | //! The direction of increasing parametric value V is defined by the |
92 | //! rotation around the "YDirection" of A2 in the trigonometric sense |
93 | //! and the orientation of increasing parametric value U is defined |
94 | //! by the rotation around the main direction of A2 in the |
95 | //! trigonometric sense. |
96 | //! Warnings : |
97 | //! It is not forbidden to create a spherical surface with |
98 | //! Radius = 0.0 |
99 | //! Raised if Radius < 0.0. |
100 | Standard_EXPORT Geom_SphericalSurface(const gp_Ax3& A3, const Standard_Real Radius); |
101 | |
102 | |
103 | //! Creates a SphericalSurface from a non persistent Sphere from |
104 | //! package gp. |
105 | Standard_EXPORT Geom_SphericalSurface(const gp_Sphere& S); |
106 | |
107 | //! Assigns the value R to the radius of this sphere. |
108 | //! Exceptions Standard_ConstructionError if R is less than 0.0. |
109 | Standard_EXPORT void SetRadius (const Standard_Real R); |
110 | |
111 | //! Converts the gp_Sphere S into this sphere. |
112 | Standard_EXPORT void SetSphere (const gp_Sphere& S); |
113 | |
114 | //! Returns a non persistent sphere with the same geometric |
115 | //! properties as <me>. |
116 | Standard_EXPORT gp_Sphere Sphere() const; |
117 | |
118 | //! Computes the u parameter on the modified |
119 | //! surface, when reversing its u parametric |
120 | //! direction, for any point of u parameter U on this sphere. |
121 | //! In the case of a sphere, these functions returns 2.PI - U. |
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122 | Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const Standard_OVERRIDE; |
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123 | |
124 | //! Computes the v parameter on the modified |
125 | //! surface, when reversing its v parametric |
126 | //! direction, for any point of v parameter V on this sphere. |
127 | //! In the case of a sphere, these functions returns -U. |
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128 | Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const Standard_OVERRIDE; |
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129 | |
130 | //! Computes the aera of the spherical surface. |
131 | Standard_EXPORT Standard_Real Area() const; |
132 | |
133 | //! Returns the parametric bounds U1, U2, V1 and V2 of this sphere. |
134 | //! For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2. |
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135 | Standard_EXPORT void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const Standard_OVERRIDE; |
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136 | |
137 | //! Returns the coefficients of the implicit equation of the |
138 | //! quadric in the absolute cartesian coordinates system : |
139 | //! These coefficients are normalized. |
140 | //! A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + |
141 | //! 2.(C1.X + C2.Y + C3.Z) + D = 0.0 |
142 | 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; |
143 | |
144 | //! Computes the coefficients of the implicit equation of |
145 | //! this quadric in the absolute Cartesian coordinate system: |
146 | //! A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + |
147 | //! 2.(C1.X + C2.Y + C3.Z) + D = 0.0 |
148 | //! An implicit normalization is applied (i.e. A1 = A2 = 1. |
149 | //! in the local coordinate system of this sphere). |
150 | Standard_EXPORT Standard_Real Radius() const; |
151 | |
152 | //! Computes the volume of the spherical surface. |
153 | Standard_EXPORT Standard_Real Volume() const; |
154 | |
155 | //! Returns True. |
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156 | Standard_EXPORT Standard_Boolean IsUClosed() const Standard_OVERRIDE; |
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157 | |
158 | //! Returns False. |
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159 | Standard_EXPORT Standard_Boolean IsVClosed() const Standard_OVERRIDE; |
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160 | |
161 | //! Returns True. |
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162 | Standard_EXPORT Standard_Boolean IsUPeriodic() const Standard_OVERRIDE; |
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163 | |
164 | //! Returns False. |
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165 | Standard_EXPORT Standard_Boolean IsVPeriodic() const Standard_OVERRIDE; |
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166 | |
167 | //! Computes the U isoparametric curve. |
168 | //! The U isoparametric curves of the surface are defined by the |
169 | //! section of the spherical surface with plane obtained by rotation |
170 | //! of the plane (Location, XAxis, ZAxis) around ZAxis. This plane |
171 | //! defines the origin of parametrization u. |
172 | //! For a SphericalSurface the UIso curve is a Circle. |
173 | //! Warnings : The radius of this circle can be zero. |
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174 | Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const Standard_OVERRIDE; |
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175 | |
176 | //! Computes the V isoparametric curve. |
177 | //! The V isoparametric curves of the surface are defined by |
178 | //! the section of the spherical surface with plane parallel to the |
179 | //! plane (Location, XAxis, YAxis). This plane defines the origin of |
180 | //! parametrization V. |
181 | //! Be careful if V is close to PI/2 or 3*PI/2 the radius of the |
182 | //! circle becomes tiny. It is not forbidden in this toolkit to |
183 | //! create circle with radius = 0.0 |
184 | //! For a SphericalSurface the VIso curve is a Circle. |
185 | //! Warnings : The radius of this circle can be zero. |
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186 | Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const Standard_OVERRIDE; |
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187 | |
188 | |
189 | //! Computes the point P (U, V) on the surface. |
190 | //! P (U, V) = Loc + Radius * Sin (V) * Zdir + |
191 | //! Radius * Cos (V) * (cos (U) * XDir + sin (U) * YDir) |
192 | //! where Loc is the origin of the placement plane (XAxis, YAxis) |
193 | //! XDir is the direction of the XAxis and YDir the direction of |
194 | //! the YAxis and ZDir the direction of the ZAxis. |
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195 | Standard_EXPORT void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const Standard_OVERRIDE; |
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196 | |
197 | |
198 | //! Computes the current point and the first derivatives in the |
199 | //! directions U and V. |
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200 | Standard_EXPORT void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const Standard_OVERRIDE; |
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201 | |
202 | |
203 | //! Computes the current point, the first and the second derivatives |
204 | //! in the directions U and V. |
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205 | 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 Standard_OVERRIDE; |
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206 | |
207 | |
208 | //! Computes the current point, the first,the second and the third |
209 | //! derivatives in the directions U and V. |
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210 | 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 Standard_OVERRIDE; |
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211 | |
212 | |
213 | //! Computes the derivative of order Nu in the direction u |
214 | //! and Nv in the direction v. |
215 | //! Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0. |
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216 | Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const Standard_OVERRIDE; |
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217 | |
218 | //! Applies the transformation T to this sphere. |
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219 | Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE; |
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220 | |
221 | //! Creates a new object which is a copy of this sphere. |
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222 | Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE; |
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223 | |
224 | |
225 | |
226 | |
227 | DEFINE_STANDARD_RTTI(Geom_SphericalSurface,Geom_ElementarySurface) |
228 | |
229 | protected: |
230 | |
231 | |
232 | |
233 | |
234 | private: |
235 | |
236 | |
237 | Standard_Real radius; |
238 | |
239 | |
240 | }; |
241 | |
242 | |
243 | |
244 | |
245 | |
246 | |
247 | |
248 | #endif // _Geom_SphericalSurface_HeaderFile |