1 // Created on: 1993-03-10
3 // Copyright (c) 1993-1999 Matra Datavision
4 // Copyright (c) 1999-2014 OPEN CASCADE SAS
6 // This file is part of Open CASCADE Technology software library.
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.
14 // Alternatively, this file may be used under the terms of Open CASCADE
15 // commercial license or contractual agreement.
17 #ifndef _Geom_SphericalSurface_HeaderFile
18 #define _Geom_SphericalSurface_HeaderFile
20 #include <Standard.hxx>
21 #include <Standard_Type.hxx>
23 #include <Geom_ElementarySurface.hxx>
24 #include <Standard_Integer.hxx>
34 class Geom_SphericalSurface;
35 DEFINE_STANDARD_HANDLE(Geom_SphericalSurface, Geom_ElementarySurface)
37 //! Describes a sphere.
38 //! A sphere is defined by its radius, and is positioned in
39 //! space by a coordinate system (a gp_Ax3 object), the
40 //! origin of which is the center of the sphere.
41 //! This coordinate system is the "local coordinate
42 //! system" of the sphere. The following apply:
43 //! - Rotation around its "main Axis", in the trigonometric
44 //! sense given by the "X Direction" and the "Y
45 //! Direction", defines the u parametric direction.
46 //! - Its "X Axis" gives the origin for the u parameter.
47 //! - The "reference meridian" of the sphere is a
48 //! half-circle, of radius equal to the radius of the
49 //! sphere. It is located in the plane defined by the
50 //! origin, "X Direction" and "main Direction", centered
51 //! on the origin, and positioned on the positive side of the "X Axis".
52 //! - Rotation around the "Y Axis" gives the v parameter
53 //! on the reference meridian.
54 //! - The "X Axis" gives the origin of the v parameter on
55 //! the reference meridian.
56 //! - The v parametric direction is oriented by the "main
57 //! Direction", i.e. when v increases, the Z coordinate
58 //! increases. (This implies that the "Y Direction"
59 //! orients the reference meridian only when the local
60 //! coordinate system is indirect.)
61 //! - The u isoparametric curve is a half-circle obtained
62 //! by rotating the reference meridian of the sphere
63 //! through an angle u around the "main Axis", in the
64 //! trigonometric sense defined by the "X Direction"
65 //! and the "Y Direction".
66 //! The parametric equation of the sphere is:
67 //! P(u,v) = O + R*cos(v)*(cos(u)*XDir + sin(u)*YDir)+R*sin(v)*ZDir
69 //! - O, XDir, YDir and ZDir are respectively the
70 //! origin, the "X Direction", the "Y Direction" and the "Z
71 //! Direction" of its local coordinate system, and
72 //! - R is the radius of the sphere.
73 //! The parametric range of the two parameters is:
74 //! - [ 0, 2.*Pi ] for u, and
75 //! - [ - Pi/2., + Pi/2. ] for v.
76 class Geom_SphericalSurface : public Geom_ElementarySurface
83 //! A3 is the local coordinate system of the surface.
84 //! At the creation the parametrization of the surface is defined
85 //! such as the normal Vector (N = D1U ^ D1V) is directed away from
86 //! the center of the sphere.
87 //! The direction of increasing parametric value V is defined by the
88 //! rotation around the "YDirection" of A2 in the trigonometric sense
89 //! and the orientation of increasing parametric value U is defined
90 //! by the rotation around the main direction of A2 in the
91 //! trigonometric sense.
93 //! It is not forbidden to create a spherical surface with
95 //! Raised if Radius < 0.0.
96 Standard_EXPORT Geom_SphericalSurface(const gp_Ax3& A3, const Standard_Real Radius);
99 //! Creates a SphericalSurface from a non persistent Sphere from
101 Standard_EXPORT Geom_SphericalSurface(const gp_Sphere& S);
103 //! Assigns the value R to the radius of this sphere.
104 //! Exceptions Standard_ConstructionError if R is less than 0.0.
105 Standard_EXPORT void SetRadius (const Standard_Real R);
107 //! Converts the gp_Sphere S into this sphere.
108 Standard_EXPORT void SetSphere (const gp_Sphere& S);
110 //! Returns a non persistent sphere with the same geometric
111 //! properties as <me>.
112 Standard_EXPORT gp_Sphere Sphere() const;
114 //! Computes the u parameter on the modified
115 //! surface, when reversing its u parametric
116 //! direction, for any point of u parameter U on this sphere.
117 //! In the case of a sphere, these functions returns 2.PI - U.
118 Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
120 //! Computes the v parameter on the modified
121 //! surface, when reversing its v parametric
122 //! direction, for any point of v parameter V on this sphere.
123 //! In the case of a sphere, these functions returns -U.
124 Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const Standard_OVERRIDE;
126 //! Computes the aera of the spherical surface.
127 Standard_EXPORT Standard_Real Area() const;
129 //! Returns the parametric bounds U1, U2, V1 and V2 of this sphere.
130 //! For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2.
131 Standard_EXPORT void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const Standard_OVERRIDE;
133 //! Returns the coefficients of the implicit equation of the
134 //! quadric in the absolute cartesian coordinates system :
135 //! These coefficients are normalized.
136 //! A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) +
137 //! 2.(C1.X + C2.Y + C3.Z) + D = 0.0
138 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;
140 //! Computes the coefficients of the implicit equation of
141 //! this quadric in the absolute Cartesian coordinate system:
142 //! A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) +
143 //! 2.(C1.X + C2.Y + C3.Z) + D = 0.0
144 //! An implicit normalization is applied (i.e. A1 = A2 = 1.
145 //! in the local coordinate system of this sphere).
146 Standard_EXPORT Standard_Real Radius() const;
148 //! Computes the volume of the spherical surface.
149 Standard_EXPORT Standard_Real Volume() const;
152 Standard_EXPORT Standard_Boolean IsUClosed() const Standard_OVERRIDE;
155 Standard_EXPORT Standard_Boolean IsVClosed() const Standard_OVERRIDE;
158 Standard_EXPORT Standard_Boolean IsUPeriodic() const Standard_OVERRIDE;
161 Standard_EXPORT Standard_Boolean IsVPeriodic() const Standard_OVERRIDE;
163 //! Computes the U isoparametric curve.
164 //! The U isoparametric curves of the surface are defined by the
165 //! section of the spherical surface with plane obtained by rotation
166 //! of the plane (Location, XAxis, ZAxis) around ZAxis. This plane
167 //! defines the origin of parametrization u.
168 //! For a SphericalSurface the UIso curve is a Circle.
169 //! Warnings : The radius of this circle can be zero.
170 Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const Standard_OVERRIDE;
172 //! Computes the V isoparametric curve.
173 //! The V isoparametric curves of the surface are defined by
174 //! the section of the spherical surface with plane parallel to the
175 //! plane (Location, XAxis, YAxis). This plane defines the origin of
176 //! parametrization V.
177 //! Be careful if V is close to PI/2 or 3*PI/2 the radius of the
178 //! circle becomes tiny. It is not forbidden in this toolkit to
179 //! create circle with radius = 0.0
180 //! For a SphericalSurface the VIso curve is a Circle.
181 //! Warnings : The radius of this circle can be zero.
182 Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const Standard_OVERRIDE;
185 //! Computes the point P (U, V) on the surface.
186 //! P (U, V) = Loc + Radius * Sin (V) * Zdir +
187 //! Radius * Cos (V) * (cos (U) * XDir + sin (U) * YDir)
188 //! where Loc is the origin of the placement plane (XAxis, YAxis)
189 //! XDir is the direction of the XAxis and YDir the direction of
190 //! the YAxis and ZDir the direction of the ZAxis.
191 Standard_EXPORT void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const Standard_OVERRIDE;
194 //! Computes the current point and the first derivatives in the
195 //! directions U and V.
196 Standard_EXPORT void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const Standard_OVERRIDE;
199 //! Computes the current point, the first and the second derivatives
200 //! in the directions U and V.
201 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;
204 //! Computes the current point, the first,the second and the third
205 //! derivatives in the directions U and V.
206 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;
209 //! Computes the derivative of order Nu in the direction u
210 //! and Nv in the direction v.
211 //! Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
212 Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const Standard_OVERRIDE;
214 //! Applies the transformation T to this sphere.
215 Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE;
217 //! Creates a new object which is a copy of this sphere.
218 Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE;
220 //! Dumps the content of me into the stream
221 Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE;
226 DEFINE_STANDARD_RTTIEXT(Geom_SphericalSurface,Geom_ElementarySurface)
236 Standard_Real radius;
247 #endif // _Geom_SphericalSurface_HeaderFile