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42cf5bc1 | 1 | // Created on: 1993-03-24 |

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 _Geom2d_BezierCurve_HeaderFile | |

18 | #define _Geom2d_BezierCurve_HeaderFile | |

19 | ||

20 | #include <Standard.hxx> | |

21 | #include <Standard_Type.hxx> | |

22 | ||

23 | #include <Standard_Boolean.hxx> | |

24 | #include <TColgp_HArray1OfPnt2d.hxx> | |

25 | #include <TColStd_HArray1OfReal.hxx> | |

26 | #include <Standard_Integer.hxx> | |

27 | #include <Standard_Real.hxx> | |

28 | #include <Geom2d_BoundedCurve.hxx> | |

29 | #include <TColgp_Array1OfPnt2d.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_Pnt2d; | |

39 | class gp_Vec2d; | |

40 | class gp_Trsf2d; | |

41 | class Geom2d_Geometry; | |

42 | ||

43 | ||

44 | class Geom2d_BezierCurve; | |

45 | DEFINE_STANDARD_HANDLE(Geom2d_BezierCurve, Geom2d_BoundedCurve) | |

46 | ||

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

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

49 | //! of 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_Pnt2d 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 | //! which joins the first pole to the second pole is the | |

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

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

62 | //! second-from-last pole is the tangent to the curve | |

63 | //! at its end point. | |

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

65 | //! to the weights but they are useful for providing | |

66 | //! exact representations of the arcs of a circle or | |

67 | //! ellipse. Moreover, if the weights of all the poles are | |

68 | //! equal, the curve is polynomial; it is therefore a | |

69 | //! non-rational curve. The non-rational curve is a | |

70 | //! special and frequently used case. The weights are | |

71 | //! defined and used only in case of a rational curve. | |

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

73 | //! number of poles, minus 1. It must be greater than or | |

74 | //! equal to 1. However, the degree of a | |

75 | //! Geom2d_BezierCurve curve is limited to a value | |

76 | //! (25) which is defined and controlled by the system. | |

77 | //! This value is returned by the function MaxDegree. | |

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

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

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

81 | //! For example, to create a closed Bezier curve with | |

82 | //! four control points, you have to give a set of control | |

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

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

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

86 | //! negative weights. We consider that a weight value | |

87 | //! is zero if it is less than or equal to | |

88 | //! gp::Resolution(). We also consider that | |

89 | //! two weight values W1 and W2 are equal if: | |

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

91 | //! Warning | |

92 | //! - When considering the continuity of a closed | |

93 | //! Bezier curve at the junction point, remember that | |

94 | //! a curve of this type is never periodic. This means | |

95 | //! that the derivatives for the parameter u = 0 | |

96 | //! have no reason to be the same as the | |

97 | //! derivatives for the parameter u = 1 even if the curve is closed. | |

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

99 | class Geom2d_BezierCurve : public Geom2d_BoundedCurve | |

100 | { | |

101 | ||

102 | public: | |

103 | ||

104 | ||

105 | ||

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

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

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

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

110 | Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles); | |

111 | ||

112 | ||

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

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

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

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

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

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

119 | //! or one weight value is lower or equal to Resolution from | |

120 | //! package gp. | |

121 | Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles, const TColStd_Array1OfReal& PoleWeights); | |

122 | ||

123 | ||

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

125 | //! degree of <me>. | |

126 | //! raises ConstructionError if Degree is greater than MaxDegree or lower than 2 | |

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

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

129 | ||

130 | ||

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

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

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

134 | //! Raised if Index is not in the range [0, NbPoles] | |

135 | //! | |

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

137 | //! MaxDegree + 1. | |

138 | Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0); | |

139 | ||

140 | ||

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

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

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

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

145 | //! | |

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

147 | //! MaxDegree + 1. | |

148 | Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0); | |

149 | ||

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

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

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

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

154 | ||

155 | ||

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

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

79104795 | 158 | Standard_EXPORT void Reverse() Standard_OVERRIDE; |

42cf5bc1 | 159 | |

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

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

162 | //! | |

163 | //! returns 1-U | |

79104795 | 164 | Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; |

42cf5bc1 | 165 | |

166 | ||

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

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

169 | //! to U2. | |

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

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

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

173 | //! Warnings : | |

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

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

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

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

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

179 | ||

180 | ||

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

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

183 | //! is not modified. | |

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

185 | Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P); | |

186 | ||

187 | ||

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

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

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

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

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

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

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

195 | Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight); | |

196 | ||

197 | ||

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

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

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

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

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

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

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

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

206 | ||

207 | ||

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

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

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

79104795 | 211 | Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; |

42cf5bc1 | 212 | |

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

79104795 | 214 | Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE; |

42cf5bc1 | 215 | |

216 | ||

217 | //! Returns False. A BezierCurve cannot be periodic in this | |

218 | //! package | |

79104795 | 219 | Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; |

42cf5bc1 | 220 | |

221 | ||

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

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

224 | Standard_EXPORT Standard_Boolean IsRational() const; | |

225 | ||

226 | //! Returns GeomAbs_CN, which is the continuity of any Bezier curve. | |

79104795 | 227 | Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE; |

42cf5bc1 | 228 | |

229 | ||

230 | //! Returns the polynomial degree of the curve. It is the number | |

231 | //! of poles less one. In this package the Degree of a Bezier | |

232 | //! curve cannot be greater than "MaxDegree". | |

233 | Standard_EXPORT Standard_Integer Degree() const; | |

234 | ||

79104795 | 235 | Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE; |

42cf5bc1 | 236 | |

79104795 | 237 | Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE; |

42cf5bc1 | 238 | |

79104795 | 239 | Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE; |

42cf5bc1 | 240 | |

79104795 | 241 | Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE; |

42cf5bc1 | 242 | |

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

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

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

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

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

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

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

250 | //! Raises RangeError if N < 1. | |

79104795 | 251 | Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; |

42cf5bc1 | 252 | |

253 | //! Returns the end point or start point of this Bezier curve. | |

79104795 | 254 | Standard_EXPORT gp_Pnt2d EndPoint() const Standard_OVERRIDE; |

42cf5bc1 | 255 | |

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

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

79104795 | 258 | Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; |

42cf5bc1 | 259 | |

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

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

79104795 | 262 | Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; |

42cf5bc1 | 263 | |

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

265 | Standard_EXPORT Standard_Integer NbPoles() const; | |

266 | ||

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

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

269 | Standard_EXPORT gp_Pnt2d Pole (const Standard_Integer Index) const; | |

270 | ||

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

272 | //! | |

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

274 | Standard_EXPORT void Poles (TColgp_Array1OfPnt2d& P) const; | |

275 | ||

c8b5b3d8 | 276 | //! Returns all the poles of the curve. |

277 | const TColgp_Array1OfPnt2d& Poles() const | |

278 | { | |

279 | return poles->Array1(); | |

280 | } | |

42cf5bc1 | 281 | |

282 | //! Returns Value (U=1), it is the first control point | |

283 | //! of the curve. | |

79104795 | 284 | Standard_EXPORT gp_Pnt2d StartPoint() const Standard_OVERRIDE; |

42cf5bc1 | 285 | |

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

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

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

289 | ||

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

291 | //! | |

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

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

c8b5b3d8 | 294 | |

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

296 | const TColStd_Array1OfReal* Weights() const | |

297 | { | |

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

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

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

301 | } | |

302 | ||

42cf5bc1 | 303 | //! Applies the transformation T to this Bezier curve. |

79104795 | 304 | Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE; |

42cf5bc1 | 305 | |

306 | ||

307 | //! Returns the value of the maximum polynomial degree of a | |

308 | //! BezierCurve. This value is 25. | |

309 | Standard_EXPORT static Standard_Integer MaxDegree(); | |

310 | ||

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

312 | //! tolerance UTolerance for a given tolerance | |

313 | //! Tolerance3D (relative to dimensions in the plane). | |

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

315 | //! UTolerance ensures that | |

316 | //! | t1 - t0| < Utolerance ===> | |

317 | //! |f(t1) - f(t0)| < ToleranceUV | |

318 | Standard_EXPORT void Resolution (const Standard_Real ToleranceUV, Standard_Real& UTolerance); | |

319 | ||

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

79104795 | 321 | Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE; |

42cf5bc1 | 322 | |

323 | ||

324 | ||

325 | ||

326 | DEFINE_STANDARD_RTTI(Geom2d_BezierCurve,Geom2d_BoundedCurve) | |

327 | ||

328 | protected: | |

329 | ||

330 | ||

331 | ||

332 | ||

333 | private: | |

334 | ||

335 | ||

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

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

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

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

340 | //! coefficient 1. | |

341 | //! | |

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

343 | //! | |

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

c8b5b3d8 | 345 | void Init (const Handle(TColgp_HArray1OfPnt2d)& Poles, const Handle(TColStd_HArray1OfReal)& Weights); |

346 | ||

42cf5bc1 | 347 | |

348 | Standard_Boolean rational; | |

349 | Standard_Boolean closed; | |

350 | Handle(TColgp_HArray1OfPnt2d) poles; | |

351 | Handle(TColStd_HArray1OfReal) weights; | |

42cf5bc1 | 352 | Standard_Real maxderivinv; |

353 | Standard_Boolean maxderivinvok; | |

354 | ||

355 | ||

356 | }; | |

357 | ||

358 | ||

359 | ||

360 | ||

361 | ||

362 | ||

363 | ||

364 | #endif // _Geom2d_BezierCurve_HeaderFile |