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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> |
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32 | #include <BSplCLib.hxx> |
33 | |
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34 | class gp_Pnt2d; |
35 | class gp_Vec2d; |
36 | class gp_Trsf2d; |
37 | class Geom2d_Geometry; |
38 | |
39 | |
40 | class Geom2d_BezierCurve; |
41 | DEFINE_STANDARD_HANDLE(Geom2d_BezierCurve, Geom2d_BoundedCurve) |
42 | |
43 | //! Describes a rational or non-rational Bezier curve |
44 | //! - a non-rational Bezier curve is defined by a table |
45 | //! of poles (also called control points), |
46 | //! - a rational Bezier curve is defined by a table of |
47 | //! poles with varying weights. |
48 | //! These data are manipulated by two parallel arrays: |
49 | //! - the poles table, which is an array of gp_Pnt2d points, and |
50 | //! - the weights table, which is an array of reals. |
51 | //! The bounds of these arrays are 1 and "the number of poles" of the curve. |
52 | //! The poles of the curve are "control points" used to deform the curve. |
53 | //! The first pole is the start point of the curve, and the |
54 | //! last pole is the end point of the curve. The segment |
55 | //! which joins the first pole to the second pole is the |
56 | //! tangent to the curve at its start point, and the |
57 | //! segment which joins the last pole to the |
58 | //! second-from-last pole is the tangent to the curve |
59 | //! at its end point. |
60 | //! It is more difficult to give a geometric signification |
61 | //! to the weights but they are useful for providing |
62 | //! exact representations of the arcs of a circle or |
63 | //! ellipse. Moreover, if the weights of all the poles are |
64 | //! equal, the curve is polynomial; it is therefore a |
65 | //! non-rational curve. The non-rational curve is a |
66 | //! special and frequently used case. The weights are |
67 | //! defined and used only in case of a rational curve. |
68 | //! The degree of a Bezier curve is equal to the |
69 | //! number of poles, minus 1. It must be greater than or |
70 | //! equal to 1. However, the degree of a |
71 | //! Geom2d_BezierCurve curve is limited to a value |
72 | //! (25) which is defined and controlled by the system. |
73 | //! This value is returned by the function MaxDegree. |
74 | //! The parameter range for a Bezier curve is [ 0, 1 ]. |
75 | //! If the first and last control points of the Bezier |
76 | //! curve are the same point then the curve is closed. |
77 | //! For example, to create a closed Bezier curve with |
78 | //! four control points, you have to give a set of control |
79 | //! points P1, P2, P3 and P1. |
80 | //! The continuity of a Bezier curve is infinite. |
81 | //! It is not possible to build a Bezier curve with |
82 | //! negative weights. We consider that a weight value |
83 | //! is zero if it is less than or equal to |
84 | //! gp::Resolution(). We also consider that |
85 | //! two weight values W1 and W2 are equal if: |
86 | //! |W2 - W1| <= gp::Resolution(). |
87 | //! Warning |
88 | //! - When considering the continuity of a closed |
89 | //! Bezier curve at the junction point, remember that |
90 | //! a curve of this type is never periodic. This means |
91 | //! that the derivatives for the parameter u = 0 |
92 | //! have no reason to be the same as the |
93 | //! derivatives for the parameter u = 1 even if the curve is closed. |
94 | //! - The length of a Bezier curve can be null. |
95 | class Geom2d_BezierCurve : public Geom2d_BoundedCurve |
96 | { |
97 | |
98 | public: |
99 | |
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 Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles); |
107 | |
108 | |
109 | //! Creates a rational Bezier curve with the set of poles |
110 | //! CurvePoles and the set of weights PoleWeights . |
111 | //! If all the weights are identical the curve is considered |
112 | //! as non rational. Raises ConstructionError if |
113 | //! the number of poles is greater than MaxDegree + 1 or lower |
114 | //! than 2 or CurvePoles and CurveWeights have not the same length |
115 | //! or one weight value is lower or equal to Resolution from |
116 | //! package gp. |
117 | Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles, const TColStd_Array1OfReal& PoleWeights); |
118 | |
119 | |
120 | //! Increases the degree of a bezier curve. Degree is the new |
121 | //! degree of <me>. |
122 | //! raises ConstructionError if Degree is greater than MaxDegree or lower than 2 |
123 | //! or lower than the initial degree of <me>. |
124 | Standard_EXPORT void Increase (const Standard_Integer Degree); |
125 | |
126 | |
127 | //! Inserts a pole with its weight in the set of poles after the |
128 | //! pole of range Index. If the curve was non rational it can |
129 | //! become rational if all the weights are not identical. |
130 | //! Raised if Index is not in the range [0, NbPoles] |
131 | //! |
132 | //! Raised if the resulting number of poles is greater than |
133 | //! MaxDegree + 1. |
134 | Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0); |
135 | |
136 | |
137 | //! Inserts a pole with its weight in the set of poles after |
138 | //! the pole of range Index. If the curve was non rational it |
139 | //! can become rational if all the weights are not identical. |
140 | //! Raised if Index is not in the range [1, NbPoles+1] |
141 | //! |
142 | //! Raised if the resulting number of poles is greater than |
143 | //! MaxDegree + 1. |
144 | Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0); |
145 | |
146 | //! Removes the pole of range Index. |
147 | //! If the curve was rational it can become non rational. |
148 | //! Raised if Index is not in the range [1, NbPoles] |
149 | Standard_EXPORT void RemovePole (const Standard_Integer Index); |
150 | |
151 | |
152 | //! Reverses the direction of parametrization of <me> |
153 | //! Value (NewU) = Value (1 - OldU) |
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154 | Standard_EXPORT void Reverse() Standard_OVERRIDE; |
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155 | |
156 | //! Returns the parameter on the reversed curve for |
157 | //! the point of parameter U on <me>. |
158 | //! |
159 | //! returns 1-U |
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160 | Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; |
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161 | |
162 | |
163 | //! Segments the curve between U1 and U2 which can be out |
164 | //! of the bounds of the curve. The curve is oriented from U1 |
165 | //! to U2. |
166 | //! The control points are modified, the first and the last point |
167 | //! are not the same but the parametrization range is [0, 1] |
168 | //! else it could not be a Bezier curve. |
169 | //! Warnings : |
170 | //! Even if <me> is not closed it can become closed after the |
171 | //! segmentation for example if U1 or U2 are out of the bounds |
172 | //! of the curve <me> or if the curve makes loop. |
173 | //! After the segmentation the length of a curve can be null. |
174 | Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2); |
175 | |
176 | |
177 | //! Substitutes the pole of range index with P. |
178 | //! If the curve <me> is rational the weight of range Index |
179 | //! is not modified. |
180 | //! raiseD if Index is not in the range [1, NbPoles] |
181 | Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P); |
182 | |
183 | |
184 | //! Substitutes the pole and the weights of range Index. |
185 | //! If the curve <me> is not rational it can become rational |
186 | //! if all the weights are not identical. |
187 | //! If the curve was rational it can become non rational if |
188 | //! all the weights are identical. |
189 | //! Raised if Index is not in the range [1, NbPoles] |
190 | //! Raised if Weight <= Resolution from package gp |
191 | Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight); |
192 | |
193 | |
194 | //! Changes the weight of the pole of range Index. |
195 | //! If the curve <me> is not rational it can become rational |
196 | //! if all the weights are not identical. |
197 | //! If the curve was rational it can become non rational if |
198 | //! all the weights are identical. |
199 | //! Raised if Index is not in the range [1, NbPoles] |
200 | //! Raised if Weight <= Resolution from package gp |
201 | Standard_EXPORT void SetWeight (const Standard_Integer Index, const Standard_Real Weight); |
202 | |
203 | |
204 | //! Returns True if the distance between the first point |
205 | //! and the last point of the curve is lower or equal to |
206 | //! the Resolution from package gp. |
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207 | Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; |
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208 | |
209 | //! Continuity of the curve, returns True. |
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210 | Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE; |
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211 | |
212 | |
213 | //! Returns False. A BezierCurve cannot be periodic in this |
214 | //! package |
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215 | Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; |
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216 | |
217 | |
218 | //! Returns false if all the weights are identical. The tolerance |
219 | //! criterion is Resolution from package gp. |
220 | Standard_EXPORT Standard_Boolean IsRational() const; |
221 | |
222 | //! Returns GeomAbs_CN, which is the continuity of any Bezier curve. |
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223 | Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE; |
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224 | |
225 | |
226 | //! Returns the polynomial degree of the curve. It is the number |
227 | //! of poles less one. In this package the Degree of a Bezier |
228 | //! curve cannot be greater than "MaxDegree". |
229 | Standard_EXPORT Standard_Integer Degree() const; |
230 | |
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231 | Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE; |
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232 | |
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233 | Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE; |
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234 | |
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235 | Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE; |
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236 | |
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237 | Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE; |
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238 | |
239 | //! For this Bezier curve, computes |
240 | //! - the point P of parameter U, or |
241 | //! - the point P and one or more of the following values: |
242 | //! - V1, the first derivative vector, |
243 | //! - V2, the second derivative vector, |
244 | //! - V3, the third derivative vector. |
245 | //! Note: the parameter U can be outside the bounds of the curve. |
246 | //! Raises RangeError if N < 1. |
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247 | Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; |
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248 | |
249 | //! Returns the end point or start point of this Bezier curve. |
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250 | Standard_EXPORT gp_Pnt2d EndPoint() const Standard_OVERRIDE; |
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251 | |
252 | //! Returns the value of the first parameter of this |
253 | //! Bezier curve. This is 0.0, which gives the start point of this Bezier curve. |
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254 | Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; |
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255 | |
256 | //! Returns the value of the last parameter of this |
257 | //! Bezier curve. This is 1.0, which gives the end point of this Bezier curve. |
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258 | Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; |
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259 | |
260 | //! Returns the number of poles for this Bezier curve. |
261 | Standard_EXPORT Standard_Integer NbPoles() const; |
262 | |
263 | //! Returns the pole of range Index. |
264 | //! Raised if Index is not in the range [1, NbPoles] |
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265 | Standard_EXPORT const gp_Pnt2d& Pole (const Standard_Integer Index) const; |
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266 | |
267 | //! Returns all the poles of the curve. |
268 | //! |
269 | //! Raised if the length of P is not equal to the number of poles. |
270 | Standard_EXPORT void Poles (TColgp_Array1OfPnt2d& P) const; |
271 | |
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272 | //! Returns all the poles of the curve. |
273 | const TColgp_Array1OfPnt2d& Poles() const |
274 | { |
275 | return poles->Array1(); |
276 | } |
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277 | |
278 | //! Returns Value (U=1), it is the first control point |
279 | //! of the curve. |
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280 | Standard_EXPORT gp_Pnt2d StartPoint() const Standard_OVERRIDE; |
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281 | |
282 | //! Returns the weight of range Index. |
283 | //! Raised if Index is not in the range [1, NbPoles] |
284 | Standard_EXPORT Standard_Real Weight (const Standard_Integer Index) const; |
285 | |
286 | //! Returns all the weights of the curve. |
287 | //! |
288 | //! Raised if the length of W is not equal to the number of poles. |
289 | Standard_EXPORT void Weights (TColStd_Array1OfReal& W) const; |
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290 | |
291 | //! Returns all the weights of the curve. |
292 | const TColStd_Array1OfReal* Weights() const |
293 | { |
294 | if (!weights.IsNull()) |
295 | return &weights->Array1(); |
296 | return BSplCLib::NoWeights(); |
297 | } |
298 | |
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299 | //! Applies the transformation T to this Bezier curve. |
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300 | Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE; |
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301 | |
302 | |
303 | //! Returns the value of the maximum polynomial degree of a |
304 | //! BezierCurve. This value is 25. |
305 | Standard_EXPORT static Standard_Integer MaxDegree(); |
306 | |
307 | //! Computes for this Bezier curve the parametric |
308 | //! tolerance UTolerance for a given tolerance |
309 | //! Tolerance3D (relative to dimensions in the plane). |
310 | //! If f(t) is the equation of this Bezier curve, |
311 | //! UTolerance ensures that |
312 | //! | t1 - t0| < Utolerance ===> |
313 | //! |f(t1) - f(t0)| < ToleranceUV |
314 | Standard_EXPORT void Resolution (const Standard_Real ToleranceUV, Standard_Real& UTolerance); |
315 | |
316 | //! Creates a new object which is a copy of this Bezier curve. |
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317 | Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE; |
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318 | |
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319 | //! Dumps the content of me into the stream |
320 | Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE; |
321 | |
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322 | |
323 | |
324 | |
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325 | DEFINE_STANDARD_RTTIEXT(Geom2d_BezierCurve,Geom2d_BoundedCurve) |
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326 | |
327 | protected: |
328 | |
329 | |
330 | |
331 | |
332 | private: |
333 | |
334 | |
335 | //! Set poles to Poles, weights to Weights (not |
336 | //! copied). If Weights is null the curve is non |
337 | //! rational. Create the arrays of coefficients. Poles |
338 | //! and Weights are assumed to have the first |
339 | //! coefficient 1. |
340 | //! |
341 | //! Update rational and closed. |
342 | //! |
343 | //! if nbpoles < 2 or nbboles > MaDegree + 1 |
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344 | void Init (const Handle(TColgp_HArray1OfPnt2d)& Poles, const Handle(TColStd_HArray1OfReal)& Weights); |
345 | |
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346 | |
347 | Standard_Boolean rational; |
348 | Standard_Boolean closed; |
349 | Handle(TColgp_HArray1OfPnt2d) poles; |
350 | Handle(TColStd_HArray1OfReal) weights; |
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351 | Standard_Real maxderivinv; |
352 | Standard_Boolean maxderivinvok; |
353 | |
354 | |
355 | }; |
356 | |
357 | |
358 | |
359 | |
360 | |
361 | |
362 | |
363 | #endif // _Geom2d_BezierCurve_HeaderFile |