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
6 // This file is part of Open CASCADE Technology software library.
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.
14 // Alternatively, this file may be used under the terms of Open CASCADE
15 // commercial license or contractual agreement.
17 #ifndef _Geom_BezierCurve_HeaderFile
18 #define _Geom_BezierCurve_HeaderFile
20 #include <Standard.hxx>
21 #include <Standard_Type.hxx>
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>
32 #include <BSplCLib.hxx>
34 class Standard_ConstructionError;
35 class Standard_DimensionError;
36 class Standard_RangeError;
37 class Standard_OutOfRange;
44 class Geom_BezierCurve;
45 DEFINE_STANDARD_HANDLE(Geom_BezierCurve, Geom_BoundedCurve)
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().
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
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
106 Standard_EXPORT Geom_BezierCurve(const TColgp_Array1OfPnt& CurvePoles);
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);
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);
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]
128 //! raised if the resulting number of poles is greater than
130 Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt& P);
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]
138 //! Raised if the resulting number of poles is greater than
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);
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]
148 //! Raised if the resulting number of poles is greater than
150 Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt& P);
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]
158 //! Raised if the resulting number of poles is greater than
160 //! Raised if Weight is lower or equal to Resolution from
162 Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight);
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);
171 //! Reverses the direction of parametrization of <me>
172 //! Value (NewU) = Value (1 - OldU)
173 Standard_EXPORT void Reverse() Standard_OVERRIDE;
175 //! Returns the parameter on the reversed curve for
176 //! the point of parameter U on <me>.
179 Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
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
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.
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);
196 //! Substitutes the pole of range index with P.
197 //! If the curve <me> is rational the weight of range Index
199 //! raiseD if Index is not in the range [1, NbPoles]
200 Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt& P);
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);
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);
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.
226 Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE;
228 //! Continuity of the curve, returns True.
229 Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE;
232 //! Returns True if the parametrization of a curve is periodic.
233 //! (P(u) = P(u + T) T = constante)
234 Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE;
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;
241 //! a Bezier curve is CN
242 Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
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;
251 Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt& P) const Standard_OVERRIDE;
253 Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const Standard_OVERRIDE;
255 Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) const Standard_OVERRIDE;
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.
264 Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const Standard_OVERRIDE;
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.
270 Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
272 //! Returns Value (U=0.), it is the first control point of the curve.
273 Standard_EXPORT gp_Pnt StartPoint() const Standard_OVERRIDE;
275 //! Returns Value (U=1.), it is the last control point of the Bezier curve.
276 Standard_EXPORT gp_Pnt EndPoint() const Standard_OVERRIDE;
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
280 Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE;
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.
284 Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE;
286 //! Returns the number of poles of this Bezier curve.
287 Standard_EXPORT Standard_Integer NbPoles() const;
289 //! Returns the pole of range Index.
290 //! Raised if Index is not in the range [1, NbPoles]
291 Standard_EXPORT const gp_Pnt& Pole (const Standard_Integer Index) const;
293 //! Returns all the poles of the curve.
295 //! Raised if the length of P is not equal to the number of poles.
296 Standard_EXPORT void Poles (TColgp_Array1OfPnt& P) const;
298 //! Returns all the poles of the curve.
299 Standard_EXPORT const TColgp_Array1OfPnt& Poles () const;
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;
305 //! Returns all the weights of the curve.
307 //! Raised if the length of W is not equal to the number of poles.
308 Standard_EXPORT void Weights (TColStd_Array1OfReal& W) const;
310 //! Returns all the weights of the curve.
311 const TColStd_Array1OfReal* Weights() const
313 if (!weights.IsNull())
314 return &weights->Array1();
315 return BSplCLib::NoWeights();
318 //! Applies the transformation T to this Bezier curve.
319 Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE;
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();
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);
333 //! Creates a new object which is a copy of this Bezier curve.
334 Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE;
336 //! Dumps the content of me into the stream
337 Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE;
342 DEFINE_STANDARD_RTTIEXT(Geom_BezierCurve,Geom_BoundedCurve)
352 //! Set poles to Poles, weights to Weights (not
353 //! copied). If Weights is null the curve is non
354 //! rational. Create the arrays of coefficients. Poles
355 //! and Weights are assumed to have the first
357 //! Update rational and closed.
359 //! if nbpoles < 2 or nbboles > MaDegree + 1
360 void Init (const Handle(TColgp_HArray1OfPnt)& Poles, const Handle(TColStd_HArray1OfReal)& Weights);
362 Standard_Boolean rational;
363 Standard_Boolean closed;
364 Handle(TColgp_HArray1OfPnt) poles;
365 Handle(TColStd_HArray1OfReal) weights;
366 Standard_Real maxderivinv;
367 Standard_Boolean maxderivinvok;
378 #endif // _Geom_BezierCurve_HeaderFile