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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> |
32 | class Standard_ConstructionError; |
33 | class Standard_DimensionError; |
34 | class Standard_RangeError; |
35 | class Standard_OutOfRange; |
36 | class gp_Pnt2d; |
37 | class gp_Vec2d; |
38 | class gp_Trsf2d; |
39 | class Geom2d_Geometry; |
40 | |
41 | |
42 | class Geom2d_BezierCurve; |
43 | DEFINE_STANDARD_HANDLE(Geom2d_BezierCurve, Geom2d_BoundedCurve) |
44 | |
45 | //! Describes a rational or non-rational Bezier curve |
46 | //! - a non-rational Bezier curve is defined by a table |
47 | //! of poles (also called control points), |
48 | //! - a rational Bezier curve is defined by a table of |
49 | //! poles with varying weights. |
50 | //! These data are manipulated by two parallel arrays: |
51 | //! - the poles table, which is an array of gp_Pnt2d points, and |
52 | //! - the weights table, which is an array of reals. |
53 | //! The bounds of these arrays are 1 and "the number of poles" of the curve. |
54 | //! The poles of the curve are "control points" used to deform the curve. |
55 | //! The first pole is the start point of the curve, and the |
56 | //! last pole is the end point of the curve. The segment |
57 | //! which joins the first pole to the second pole is the |
58 | //! tangent to the curve at its start point, and the |
59 | //! segment which joins the last pole to the |
60 | //! second-from-last pole is the tangent to the curve |
61 | //! at its end point. |
62 | //! It is more difficult to give a geometric signification |
63 | //! to the weights but they are useful for providing |
64 | //! exact representations of the arcs of a circle or |
65 | //! ellipse. Moreover, if the weights of all the poles are |
66 | //! equal, the curve is polynomial; it is therefore a |
67 | //! non-rational curve. The non-rational curve is a |
68 | //! special and frequently used case. The weights are |
69 | //! defined and used only in case of a rational curve. |
70 | //! The degree of a Bezier curve is equal to the |
71 | //! number of poles, minus 1. It must be greater than or |
72 | //! equal to 1. However, the degree of a |
73 | //! Geom2d_BezierCurve curve is limited to a value |
74 | //! (25) which is defined and controlled by the system. |
75 | //! 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 |
78 | //! curve are the same point then the curve is closed. |
79 | //! For example, to create a closed Bezier curve with |
80 | //! four control points, you have to give a 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 |
84 | //! negative weights. We consider that a weight value |
85 | //! is zero if it is less than or equal to |
86 | //! gp::Resolution(). We also consider that |
87 | //! two weight values W1 and W2 are equal if: |
88 | //! |W2 - W1| <= gp::Resolution(). |
89 | //! Warning |
90 | //! - When considering the continuity of a closed |
91 | //! Bezier curve at the junction point, remember that |
92 | //! a curve of this type is never periodic. This means |
93 | //! that the derivatives for the parameter u = 0 |
94 | //! have no reason to be the same as the |
95 | //! derivatives for the parameter u = 1 even if the curve is closed. |
96 | //! - The length of a Bezier curve can be null. |
97 | class Geom2d_BezierCurve : public Geom2d_BoundedCurve |
98 | { |
99 | |
100 | public: |
101 | |
102 | |
103 | |
104 | //! Creates a non rational Bezier curve with a set of poles : |
105 | //! CurvePoles. The weights are defaulted to all being 1. |
106 | //! Raises ConstructionError if the number of poles is greater than MaxDegree + 1 |
107 | //! or lower than 2. |
108 | Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles); |
109 | |
110 | |
111 | //! Creates a rational Bezier curve with the set of poles |
112 | //! CurvePoles and the set of weights PoleWeights . |
113 | //! If all the weights are identical the curve is considered |
114 | //! as non rational. Raises ConstructionError if |
115 | //! the number of poles is greater than MaxDegree + 1 or lower |
116 | //! than 2 or CurvePoles and CurveWeights have not the same length |
117 | //! or one weight value is lower or equal to Resolution from |
118 | //! package gp. |
119 | Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles, const TColStd_Array1OfReal& PoleWeights); |
120 | |
121 | |
122 | //! Increases the degree of a bezier curve. Degree is the new |
123 | //! degree of <me>. |
124 | //! raises ConstructionError if Degree is greater than MaxDegree or lower than 2 |
125 | //! or lower than the initial degree of <me>. |
126 | Standard_EXPORT void Increase (const Standard_Integer Degree); |
127 | |
128 | |
129 | //! Inserts a pole with its weight in the set of poles after the |
130 | //! pole of range Index. If the curve was non rational it can |
131 | //! become rational if all the weights are not identical. |
132 | //! Raised if Index is not in the range [0, NbPoles] |
133 | //! |
134 | //! Raised if the resulting number of poles is greater than |
135 | //! MaxDegree + 1. |
136 | Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0); |
137 | |
138 | |
139 | //! Inserts a pole with its weight in the set of poles after |
140 | //! the pole of range Index. If the curve was non rational it |
141 | //! can become rational if all the weights are not identical. |
142 | //! Raised if Index is not in the range [1, NbPoles+1] |
143 | //! |
144 | //! Raised if the resulting number of poles is greater than |
145 | //! MaxDegree + 1. |
146 | Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0); |
147 | |
148 | //! Removes the pole of range Index. |
149 | //! If the curve was rational it can become non rational. |
150 | //! Raised if Index is not in the range [1, NbPoles] |
151 | Standard_EXPORT void RemovePole (const Standard_Integer Index); |
152 | |
153 | |
154 | //! Reverses the direction of parametrization of <me> |
155 | //! Value (NewU) = Value (1 - OldU) |
156 | Standard_EXPORT void Reverse(); |
157 | |
158 | //! Returns the parameter on the reversed curve for |
159 | //! the point of parameter U on <me>. |
160 | //! |
161 | //! returns 1-U |
162 | Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const; |
163 | |
164 | |
165 | //! Segments the curve between U1 and U2 which can be out |
166 | //! of the bounds of the curve. The curve is oriented from U1 |
167 | //! to U2. |
168 | //! The control points are modified, the first and the last point |
169 | //! are not the same but the parametrization range is [0, 1] |
170 | //! else it could not be a Bezier curve. |
171 | //! Warnings : |
172 | //! Even if <me> is not closed it can become closed after the |
173 | //! segmentation for example if U1 or U2 are out of the bounds |
174 | //! of the curve <me> or if the curve makes loop. |
175 | //! After the segmentation the length of a curve can be null. |
176 | Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2); |
177 | |
178 | |
179 | //! Substitutes the pole of range index with P. |
180 | //! If the curve <me> is rational the weight of range Index |
181 | //! is not modified. |
182 | //! raiseD if Index is not in the range [1, NbPoles] |
183 | Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P); |
184 | |
185 | |
186 | //! Substitutes the pole and the weights of range Index. |
187 | //! If the curve <me> is not rational it can become rational |
188 | //! if all the weights are not identical. |
189 | //! If the curve was rational it can become non rational if |
190 | //! all the weights are identical. |
191 | //! Raised if Index is not in the range [1, NbPoles] |
192 | //! Raised if Weight <= Resolution from package gp |
193 | Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight); |
194 | |
195 | |
196 | //! Changes the weight of the pole of range Index. |
197 | //! If the curve <me> is not rational it can become rational |
198 | //! if all the weights are not identical. |
199 | //! If the curve was rational it can become non rational if |
200 | //! all the weights are identical. |
201 | //! Raised if Index is not in the range [1, NbPoles] |
202 | //! Raised if Weight <= Resolution from package gp |
203 | Standard_EXPORT void SetWeight (const Standard_Integer Index, const Standard_Real Weight); |
204 | |
205 | |
206 | //! Returns True if the distance between the first point |
207 | //! and the last point of the curve is lower or equal to |
208 | //! the Resolution from package gp. |
209 | Standard_EXPORT Standard_Boolean IsClosed() const; |
210 | |
211 | //! Continuity of the curve, returns True. |
212 | Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const; |
213 | |
214 | |
215 | //! Returns False. A BezierCurve cannot be periodic in this |
216 | //! package |
217 | Standard_EXPORT Standard_Boolean IsPeriodic() const; |
218 | |
219 | |
220 | //! Returns false if all the weights are identical. The tolerance |
221 | //! criterion is Resolution from package gp. |
222 | Standard_EXPORT Standard_Boolean IsRational() const; |
223 | |
224 | //! Returns GeomAbs_CN, which is the continuity of any Bezier curve. |
225 | Standard_EXPORT GeomAbs_Shape Continuity() const; |
226 | |
227 | |
228 | //! Returns the polynomial degree of the curve. It is the number |
229 | //! of poles less one. In this package the Degree of a Bezier |
230 | //! curve cannot be greater than "MaxDegree". |
231 | Standard_EXPORT Standard_Integer Degree() const; |
232 | |
233 | Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const; |
234 | |
235 | Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const; |
236 | |
237 | Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const; |
238 | |
239 | Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const; |
240 | |
241 | //! For this Bezier curve, computes |
242 | //! - the point P of parameter U, or |
243 | //! - the point P and one or more of the following values: |
244 | //! - V1, the first derivative vector, |
245 | //! - V2, the second derivative vector, |
246 | //! - V3, the third derivative vector. |
247 | //! Note: the parameter U can be outside the bounds of the curve. |
248 | //! Raises RangeError if N < 1. |
249 | Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const; |
250 | |
251 | //! Returns the end point or start point of this Bezier curve. |
252 | Standard_EXPORT gp_Pnt2d EndPoint() const; |
253 | |
254 | //! Returns the value of the first parameter of this |
255 | //! Bezier curve. This is 0.0, which gives the start point of this Bezier curve. |
256 | Standard_EXPORT Standard_Real FirstParameter() const; |
257 | |
258 | //! Returns the value of the last parameter of this |
259 | //! Bezier curve. This is 1.0, which gives the end point of this Bezier curve. |
260 | Standard_EXPORT Standard_Real LastParameter() const; |
261 | |
262 | //! Returns the number of poles for this Bezier curve. |
263 | Standard_EXPORT Standard_Integer NbPoles() const; |
264 | |
265 | //! Returns the pole of range Index. |
266 | //! Raised if Index is not in the range [1, NbPoles] |
267 | Standard_EXPORT gp_Pnt2d Pole (const Standard_Integer Index) const; |
268 | |
269 | //! Returns all the poles of the curve. |
270 | //! |
271 | //! Raised if the length of P is not equal to the number of poles. |
272 | Standard_EXPORT void Poles (TColgp_Array1OfPnt2d& P) const; |
273 | |
274 | |
275 | //! Returns Value (U=1), it is the first control point |
276 | //! of the curve. |
277 | Standard_EXPORT gp_Pnt2d StartPoint() const; |
278 | |
279 | //! Returns the weight of range Index. |
280 | //! Raised if Index is not in the range [1, NbPoles] |
281 | Standard_EXPORT Standard_Real Weight (const Standard_Integer Index) const; |
282 | |
283 | //! Returns all the weights of the curve. |
284 | //! |
285 | //! Raised if the length of W is not equal to the number of poles. |
286 | Standard_EXPORT void Weights (TColStd_Array1OfReal& W) const; |
287 | |
288 | //! Applies the transformation T to this Bezier curve. |
289 | Standard_EXPORT void Transform (const gp_Trsf2d& T); |
290 | |
291 | |
292 | //! Returns the value of the maximum polynomial degree of a |
293 | //! BezierCurve. This value is 25. |
294 | Standard_EXPORT static Standard_Integer MaxDegree(); |
295 | |
296 | //! Computes for this Bezier curve the parametric |
297 | //! tolerance UTolerance for a given tolerance |
298 | //! Tolerance3D (relative to dimensions in the plane). |
299 | //! If f(t) is the equation of this Bezier curve, |
300 | //! UTolerance ensures that |
301 | //! | t1 - t0| < Utolerance ===> |
302 | //! |f(t1) - f(t0)| < ToleranceUV |
303 | Standard_EXPORT void Resolution (const Standard_Real ToleranceUV, Standard_Real& UTolerance); |
304 | |
305 | //! Creates a new object which is a copy of this Bezier curve. |
306 | Standard_EXPORT Handle(Geom2d_Geometry) Copy() const; |
307 | |
308 | |
309 | |
310 | |
311 | DEFINE_STANDARD_RTTI(Geom2d_BezierCurve,Geom2d_BoundedCurve) |
312 | |
313 | protected: |
314 | |
315 | |
316 | |
317 | |
318 | private: |
319 | |
320 | |
321 | //! Set poles to Poles, weights to Weights (not |
322 | //! copied). If Weights is null the curve is non |
323 | //! rational. Create the arrays of coefficients. Poles |
324 | //! and Weights are assumed to have the first |
325 | //! coefficient 1. |
326 | //! |
327 | //! Update rational and closed. |
328 | //! |
329 | //! if nbpoles < 2 or nbboles > MaDegree + 1 |
330 | Standard_EXPORT void Init (const Handle(TColgp_HArray1OfPnt2d)& Poles, const Handle(TColStd_HArray1OfReal)& Weights); |
331 | |
332 | //! returns true if the coefficients have been |
333 | //! computed with the right value of cacheparameter |
334 | //! for the given U value. |
335 | Standard_EXPORT Standard_Boolean CoefficientsOK (const Standard_Real U) const; |
336 | |
337 | //! Recompute the coeficients. |
338 | Standard_EXPORT void UpdateCoefficients (const Standard_Real U = 0.0); |
339 | |
340 | Standard_Boolean rational; |
341 | Standard_Boolean closed; |
342 | Handle(TColgp_HArray1OfPnt2d) poles; |
343 | Handle(TColStd_HArray1OfReal) weights; |
344 | Handle(TColgp_HArray1OfPnt2d) coeffs; |
345 | Handle(TColStd_HArray1OfReal) wcoeffs; |
346 | Standard_Integer validcache; |
347 | Standard_Real parametercache; |
348 | Standard_Real spanlenghtcache; |
349 | Standard_Real maxderivinv; |
350 | Standard_Boolean maxderivinvok; |
351 | |
352 | |
353 | }; |
354 | |
355 | |
356 | |
357 | |
358 | |
359 | |
360 | |
361 | #endif // _Geom2d_BezierCurve_HeaderFile |