| 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. |
| 122 | Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const; |
| 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. |
| 128 | Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const; |
| 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. |
| 135 | Standard_EXPORT void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const; |
| 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. |
| 156 | Standard_EXPORT Standard_Boolean IsUClosed() const; |
| 157 | |
| 158 | //! Returns False. |
| 159 | Standard_EXPORT Standard_Boolean IsVClosed() const; |
| 160 | |
| 161 | //! Returns True. |
| 162 | Standard_EXPORT Standard_Boolean IsUPeriodic() const; |
| 163 | |
| 164 | //! Returns False. |
| 165 | Standard_EXPORT Standard_Boolean IsVPeriodic() const; |
| 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. |
| 174 | Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const; |
| 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. |
| 186 | Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const; |
| 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. |
| 195 | Standard_EXPORT void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const; |
| 196 | |
| 197 | |
| 198 | //! Computes the current point and the first derivatives in the |
| 199 | //! directions U and V. |
| 200 | Standard_EXPORT void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const; |
| 201 | |
| 202 | |
| 203 | //! Computes the current point, the first and the second derivatives |
| 204 | //! in the directions U and V. |
| 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; |
| 206 | |
| 207 | |
| 208 | //! Computes the current point, the first,the second and the third |
| 209 | //! derivatives in the directions U and V. |
| 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; |
| 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. |
| 216 | Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const; |
| 217 | |
| 218 | //! Applies the transformation T to this sphere. |
| 219 | Standard_EXPORT void Transform (const gp_Trsf& T); |
| 220 | |
| 221 | //! Creates a new object which is a copy of this sphere. |
| 222 | Standard_EXPORT Handle(Geom_Geometry) Copy() const; |
| 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 |