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42cf5bc1 | 1 | // Created on: 1993-03-09 |

2 | // Created by: Philippe DAUTRY | |

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_BezierCurve_HeaderFile | |

18 | #define _Geom_BezierCurve_HeaderFile | |

19 | ||

20 | #include <Standard.hxx> | |

21 | #include <Standard_Type.hxx> | |

22 | ||

23 | #include <Standard_Boolean.hxx> | |

24 | #include <TColgp_HArray1OfPnt.hxx> | |

25 | #include <TColStd_HArray1OfReal.hxx> | |

26 | #include <Standard_Integer.hxx> | |

27 | #include <Standard_Real.hxx> | |

28 | #include <Geom_BoundedCurve.hxx> | |

29 | #include <TColgp_Array1OfPnt.hxx> | |

30 | #include <TColStd_Array1OfReal.hxx> | |

31 | #include <GeomAbs_Shape.hxx> | |

c8b5b3d8 | 32 | #include <BSplCLib.hxx> |

33 | ||

42cf5bc1 | 34 | class Standard_ConstructionError; |

35 | class Standard_DimensionError; | |

36 | class Standard_RangeError; | |

37 | class Standard_OutOfRange; | |

38 | class gp_Pnt; | |

39 | class gp_Vec; | |

40 | class gp_Trsf; | |

41 | class Geom_Geometry; | |

42 | ||

43 | ||

44 | class Geom_BezierCurve; | |

45 | DEFINE_STANDARD_HANDLE(Geom_BezierCurve, Geom_BoundedCurve) | |

46 | ||

47 | //! Describes a rational or non-rational Bezier curve | |

48 | //! - a non-rational Bezier curve is defined by a table of | |

49 | //! poles (also called control points), | |

50 | //! - a rational Bezier curve is defined by a table of | |

51 | //! poles with varying weights. | |

52 | //! These data are manipulated by two parallel arrays: | |

53 | //! - the poles table, which is an array of gp_Pnt points, and | |

54 | //! - the weights table, which is an array of reals. | |

55 | //! The bounds of these arrays are 1 and "the number of "poles" of the curve. | |

56 | //! The poles of the curve are "control points" used to deform the curve. | |

57 | //! The first pole is the start point of the curve, and the | |

58 | //! last pole is the end point of the curve. The segment | |

59 | //! that joins the first pole to the second pole is the | |

60 | //! tangent to the curve at its start point, and the | |

61 | //! segment that joins the last pole to the | |

62 | //! second-from-last pole is the tangent to the curve at its end point. | |

63 | //! It is more difficult to give a geometric signification to | |

64 | //! the weights but they are useful for providing the exact | |

65 | //! representations of arcs of a circle or ellipse. | |

66 | //! Moreover, if the weights of all poles are equal, the | |

67 | //! curve is polynomial; it is therefore a non-rational | |

68 | //! curve. The non-rational curve is a special and | |

69 | //! frequently used case. The weights are defined and | |

70 | //! used only in the case of a rational curve. | |

71 | //! The degree of a Bezier curve is equal to the number | |

72 | //! of poles, minus 1. It must be greater than or equal to | |

73 | //! 1. However, the degree of a Geom_BezierCurve | |

74 | //! curve is limited to a value (25) which is defined and | |

75 | //! controlled by the system. This value is returned by the function MaxDegree. | |

76 | //! The parameter range for a Bezier curve is [ 0, 1 ]. | |

77 | //! If the first and last control points of the Bezier curve | |

78 | //! are the same point then the curve is closed. For | |

79 | //! example, to create a closed Bezier curve with four | |

80 | //! control points, you have to give the set of control | |

81 | //! points P1, P2, P3 and P1. | |

82 | //! The continuity of a Bezier curve is infinite. | |

83 | //! It is not possible to build a Bezier curve with negative | |

84 | //! weights. We consider that a weight value is zero if it | |

85 | //! is less than or equal to gp::Resolution(). We | |

86 | //! also consider that two weight values W1 and W2 are equal if: | |

87 | //! |W2 - W1| <= gp::Resolution(). | |

88 | //! Warning | |

89 | //! - When considering the continuity of a closed Bezier | |

90 | //! curve at the junction point, remember that a curve | |

91 | //! of this type is never periodic. This means that the | |

92 | //! derivatives for the parameter u = 0 have no | |

93 | //! reason to be the same as the derivatives for the | |

94 | //! parameter u = 1 even if the curve is closed. | |

95 | //! - The length of a Bezier curve can be null. | |

96 | class Geom_BezierCurve : public Geom_BoundedCurve | |

97 | { | |

98 | ||

99 | public: | |

100 | ||

101 | ||

102 | //! Creates a non rational Bezier curve with a set of poles | |

103 | //! CurvePoles. The weights are defaulted to all being 1. | |

104 | //! Raises ConstructionError if the number of poles is greater than MaxDegree + 1 | |

105 | //! or lower than 2. | |

106 | Standard_EXPORT Geom_BezierCurve(const TColgp_Array1OfPnt& CurvePoles); | |

107 | ||

108 | //! Creates a rational Bezier curve with the set of poles | |

109 | //! CurvePoles and the set of weights PoleWeights . | |

110 | //! If all the weights are identical the curve is considered | |

111 | //! as non rational. Raises ConstructionError if | |

112 | //! the number of poles is greater than MaxDegree + 1 or lower | |

113 | //! than 2 or CurvePoles and CurveWeights have not the same length | |

114 | //! or one weight value is lower or equal to Resolution from package gp. | |

115 | Standard_EXPORT Geom_BezierCurve(const TColgp_Array1OfPnt& CurvePoles, const TColStd_Array1OfReal& PoleWeights); | |

116 | ||

117 | //! Increases the degree of a bezier curve. Degree is the new | |

118 | //! degree of <me>. Raises ConstructionError | |

119 | //! if Degree is greater than MaxDegree or lower than 2 | |

120 | //! or lower than the initial degree of <me>. | |

121 | Standard_EXPORT void Increase (const Standard_Integer Degree); | |

122 | ||

123 | //! Inserts a pole P after the pole of range Index. | |

124 | //! If the curve <me> is rational the weight value for the new | |

125 | //! pole of range Index is 1.0. | |

126 | //! raised if Index is not in the range [1, NbPoles] | |

127 | //! | |

128 | //! raised if the resulting number of poles is greater than | |

129 | //! MaxDegree + 1. | |

130 | Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt& P); | |

131 | ||

132 | ||

133 | //! Inserts a pole with its weight in the set of poles after the | |

134 | //! pole of range Index. If the curve was non rational it can | |

135 | //! become rational if all the weights are not identical. | |

136 | //! Raised if Index is not in the range [1, NbPoles] | |

137 | //! | |

138 | //! Raised if the resulting number of poles is greater than | |

139 | //! MaxDegree + 1. | |

140 | //! Raised if Weight is lower or equal to Resolution from package gp. | |

141 | Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight); | |

142 | ||

143 | //! Inserts a pole P before the pole of range Index. | |

144 | //! If the curve <me> is rational the weight value for the new | |

145 | //! pole of range Index is 1.0. | |

146 | //! Raised if Index is not in the range [1, NbPoles] | |

147 | //! | |

148 | //! Raised if the resulting number of poles is greater than | |

149 | //! MaxDegree + 1. | |

150 | Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt& P); | |

151 | ||

152 | ||

153 | //! Inserts a pole with its weight in the set of poles after | |

154 | //! the pole of range Index. If the curve was non rational it | |

155 | //! can become rational if all the weights are not identical. | |

156 | //! Raised if Index is not in the range [1, NbPoles] | |

157 | //! | |

158 | //! Raised if the resulting number of poles is greater than | |

159 | //! MaxDegree + 1. | |

160 | //! Raised if Weight is lower or equal to Resolution from | |

161 | //! package gp. | |

162 | Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight); | |

163 | ||

164 | //! Removes the pole of range Index. | |

165 | //! If the curve was rational it can become non rational. | |

166 | //! Raised if Index is not in the range [1, NbPoles] | |

167 | //! Raised if Degree is lower than 2. | |

168 | Standard_EXPORT void RemovePole (const Standard_Integer Index); | |

169 | ||

170 | ||

171 | //! Reverses the direction of parametrization of <me> | |

172 | //! Value (NewU) = Value (1 - OldU) | |

79104795 | 173 | Standard_EXPORT void Reverse() Standard_OVERRIDE; |

42cf5bc1 | 174 | |

175 | //! Returns the parameter on the reversed curve for | |

176 | //! the point of parameter U on <me>. | |

177 | //! | |

178 | //! returns 1-U | |

79104795 | 179 | Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; |

42cf5bc1 | 180 | |

181 | ||

182 | //! Segments the curve between U1 and U2 which can be out | |

183 | //! of the bounds of the curve. The curve is oriented from U1 | |

184 | //! to U2. | |

185 | //! The control points are modified, the first and the last point | |

186 | //! are not the same but the parametrization range is [0, 1] | |

187 | //! else it could not be a Bezier curve. | |

188 | //! Warnings : | |

189 | //! Even if <me> is not closed it can become closed after the | |

190 | //! segmentation for example if U1 or U2 are out of the bounds | |

191 | //! of the curve <me> or if the curve makes loop. | |

192 | //! After the segmentation the length of a curve can be null. | |

193 | Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2); | |

194 | ||

195 | ||

196 | //! Substitutes the pole of range index with P. | |

197 | //! If the curve <me> is rational the weight of range Index | |

198 | //! is not modified. | |

199 | //! raiseD if Index is not in the range [1, NbPoles] | |

200 | Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt& P); | |

201 | ||

202 | ||

203 | //! Substitutes the pole and the weights of range Index. | |

204 | //! If the curve <me> is not rational it can become rational | |

205 | //! if all the weights are not identical. | |

206 | //! If the curve was rational it can become non rational if | |

207 | //! all the weights are identical. | |

208 | //! Raised if Index is not in the range [1, NbPoles] | |

209 | //! Raised if Weight <= Resolution from package gp | |

210 | Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight); | |

211 | ||

212 | ||

213 | //! Changes the weight of the pole of range Index. | |

214 | //! If the curve <me> is not rational it can become rational | |

215 | //! if all the weights are not identical. | |

216 | //! If the curve was rational it can become non rational if | |

217 | //! all the weights are identical. | |

218 | //! Raised if Index is not in the range [1, NbPoles] | |

219 | //! Raised if Weight <= Resolution from package gp | |

220 | Standard_EXPORT void SetWeight (const Standard_Integer Index, const Standard_Real Weight); | |

221 | ||

222 | ||

223 | //! Returns True if the distance between the first point | |

224 | //! and the last point of the curve is lower or equal to | |

225 | //! the Resolution from package gp. | |

79104795 | 226 | Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; |

42cf5bc1 | 227 | |

228 | //! Continuity of the curve, returns True. | |

79104795 | 229 | Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE; |

42cf5bc1 | 230 | |

231 | ||

232 | //! Returns True if the parametrization of a curve is periodic. | |

233 | //! (P(u) = P(u + T) T = constante) | |

79104795 | 234 | Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; |

42cf5bc1 | 235 | |

236 | ||

237 | //! Returns false if all the weights are identical. The tolerance | |

238 | //! criterion is Resolution from package gp. | |

239 | Standard_EXPORT Standard_Boolean IsRational() const; | |

240 | ||

241 | //! a Bezier curve is CN | |

79104795 | 242 | Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE; |

42cf5bc1 | 243 | |

244 | //! Returns the polynomial degree of the curve. | |

245 | //! it is the number of poles - 1 | |

246 | //! point P and derivatives (V1, V2, V3) computation | |

247 | //! The Bezier Curve has a Polynomial representation so the | |

248 | //! parameter U can be out of the bounds of the curve. | |

249 | Standard_EXPORT Standard_Integer Degree() const; | |

250 | ||

79104795 | 251 | Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt& P) const Standard_OVERRIDE; |

42cf5bc1 | 252 | |

79104795 | 253 | Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const Standard_OVERRIDE; |

42cf5bc1 | 254 | |

79104795 | 255 | Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) const Standard_OVERRIDE; |

42cf5bc1 | 256 | |

257 | //! For this Bezier curve, computes | |

258 | //! - the point P of parameter U, or | |

259 | //! - the point P and one or more of the following values: | |

260 | //! - V1, the first derivative vector, | |

261 | //! - V2, the second derivative vector, | |

262 | //! - V3, the third derivative vector. | |

263 | //! Note: the parameter U can be outside the bounds of the curve. | |

79104795 | 264 | Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const Standard_OVERRIDE; |

42cf5bc1 | 265 | |

266 | //! For the point of parameter U of this Bezier curve, | |

267 | //! computes the vector corresponding to the Nth derivative. | |

268 | //! Note: the parameter U can be outside the bounds of the curve. | |

269 | //! Exceptions Standard_RangeError if N is less than 1. | |

79104795 | 270 | Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; |

42cf5bc1 | 271 | |

272 | //! Returns Value (U=0.), it is the first control point of the curve. | |

79104795 | 273 | Standard_EXPORT gp_Pnt StartPoint() const Standard_OVERRIDE; |

42cf5bc1 | 274 | |

275 | //! Returns Value (U=1.), it is the last control point of the Bezier curve. | |

79104795 | 276 | Standard_EXPORT gp_Pnt EndPoint() const Standard_OVERRIDE; |

42cf5bc1 | 277 | |

278 | //! Returns the value of the first parameter of this | |

279 | //! Bezier curve. This is 0.0, which gives the start point of this Bezier curve | |

79104795 | 280 | Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; |

42cf5bc1 | 281 | |

282 | //! Returns the value of the last parameter of this | |

283 | //! Bezier curve. This is 1.0, which gives the end point of this Bezier curve. | |

79104795 | 284 | Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; |

42cf5bc1 | 285 | |

286 | //! Returns the number of poles of this Bezier curve. | |

287 | Standard_EXPORT Standard_Integer NbPoles() const; | |

288 | ||

289 | //! Returns the pole of range Index. | |

290 | //! Raised if Index is not in the range [1, NbPoles] | |

291 | Standard_EXPORT gp_Pnt Pole (const Standard_Integer Index) const; | |

292 | ||

293 | //! Returns all the poles of the curve. | |

294 | //! | |

295 | //! Raised if the length of P is not equal to the number of poles. | |

296 | Standard_EXPORT void Poles (TColgp_Array1OfPnt& P) const; | |

bcd19756 | 297 | |

298 | //! Returns all the poles of the curve. | |

299 | Standard_EXPORT const TColgp_Array1OfPnt& Poles () const; | |

42cf5bc1 | 300 | |

301 | //! Returns the weight of range Index. | |

302 | //! Raised if Index is not in the range [1, NbPoles] | |

303 | Standard_EXPORT Standard_Real Weight (const Standard_Integer Index) const; | |

304 | ||

305 | //! Returns all the weights of the curve. | |

306 | //! | |

307 | //! Raised if the length of W is not equal to the number of poles. | |

308 | Standard_EXPORT void Weights (TColStd_Array1OfReal& W) const; | |

c8b5b3d8 | 309 | |

310 | //! Returns all the weights of the curve. | |

311 | const TColStd_Array1OfReal* Weights() const | |

312 | { | |

313 | if (!weights.IsNull()) | |

314 | return &weights->Array1(); | |

315 | return BSplCLib::NoWeights(); | |

316 | } | |

317 | ||

42cf5bc1 | 318 | //! Applies the transformation T to this Bezier curve. |

79104795 | 319 | Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE; |

42cf5bc1 | 320 | |

321 | ||

322 | //! Returns the value of the maximum polynomial degree | |

323 | //! of any Geom_BezierCurve curve. This value is 25. | |

324 | Standard_EXPORT static Standard_Integer MaxDegree(); | |

325 | ||

326 | //! Computes for this Bezier curve the parametric | |

327 | //! tolerance UTolerance for a given 3D tolerance Tolerance3D. | |

328 | //! If f(t) is the equation of this Bezier curve, | |

329 | //! UTolerance ensures that: | |

330 | //! |t1-t0| < UTolerance ===> |f(t1)-f(t0)| < Tolerance3D | |

331 | Standard_EXPORT void Resolution (const Standard_Real Tolerance3D, Standard_Real& UTolerance); | |

332 | ||

333 | //! Creates a new object which is a copy of this Bezier curve. | |

79104795 | 334 | Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE; |

42cf5bc1 | 335 | |

336 | ||

337 | ||

338 | ||

92efcf78 | 339 | DEFINE_STANDARD_RTTIEXT(Geom_BezierCurve,Geom_BoundedCurve) |

42cf5bc1 | 340 | |

341 | protected: | |

342 | ||

343 | ||

344 | ||

345 | ||

346 | private: | |

347 | ||

348 | ||

349 | //! Set poles to Poles, weights to Weights (not | |

350 | //! copied). If Weights is null the curve is non | |

351 | //! rational. Create the arrays of coefficients. Poles | |

352 | //! and Weights are assumed to have the first | |

353 | //! coefficient 1. | |

354 | //! Update rational and closed. | |

355 | //! | |

356 | //! if nbpoles < 2 or nbboles > MaDegree + 1 | |

c8b5b3d8 | 357 | void Init (const Handle(TColgp_HArray1OfPnt)& Poles, const Handle(TColStd_HArray1OfReal)& Weights); |

42cf5bc1 | 358 | |

359 | Standard_Boolean rational; | |

360 | Standard_Boolean closed; | |

361 | Handle(TColgp_HArray1OfPnt) poles; | |

362 | Handle(TColStd_HArray1OfReal) weights; | |

42cf5bc1 | 363 | Standard_Real maxderivinv; |

364 | Standard_Boolean maxderivinvok; | |

365 | ||

366 | ||

367 | }; | |

368 | ||

369 | ||

370 | ||

371 | ||

372 | ||

373 | ||

374 | ||

375 | #endif // _Geom_BezierCurve_HeaderFile |