1 // Created on: 1993-03-24
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 _Geom2d_BSplineCurve_HeaderFile
18 #define _Geom2d_BSplineCurve_HeaderFile
20 #include <Standard.hxx>
21 #include <Standard_Type.hxx>
23 #include <Precision.hxx>
24 #include <Standard_Boolean.hxx>
25 #include <GeomAbs_BSplKnotDistribution.hxx>
26 #include <GeomAbs_Shape.hxx>
27 #include <Standard_Integer.hxx>
28 #include <TColgp_HArray1OfPnt2d.hxx>
29 #include <TColStd_HArray1OfReal.hxx>
30 #include <TColStd_HArray1OfInteger.hxx>
31 #include <Standard_Real.hxx>
32 #include <Geom2d_BoundedCurve.hxx>
33 #include <TColgp_Array1OfPnt2d.hxx>
34 #include <TColStd_Array1OfReal.hxx>
35 #include <TColStd_Array1OfInteger.hxx>
36 class Standard_ConstructionError;
37 class Standard_DimensionError;
38 class Standard_DomainError;
39 class Standard_OutOfRange;
40 class Standard_RangeError;
41 class Standard_NoSuchObject;
42 class Geom2d_UndefinedDerivative;
46 class Geom2d_Geometry;
49 class Geom2d_BSplineCurve;
50 DEFINE_STANDARD_HANDLE(Geom2d_BSplineCurve, Geom2d_BoundedCurve)
52 //! Describes a BSpline curve.
53 //! A BSpline curve can be:
54 //! - uniform or non-uniform,
55 //! - rational or non-rational,
56 //! - periodic or non-periodic.
57 //! A BSpline curve is defined by:
58 //! - its degree; the degree for a
59 //! Geom2d_BSplineCurve is limited to a value (25)
60 //! which is defined and controlled by the system. This
61 //! value is returned by the function MaxDegree;
62 //! - its periodic or non-periodic nature;
63 //! - a table of poles (also called control points), with
64 //! their associated weights if the BSpline curve is
65 //! rational. The poles of the curve are "control points"
66 //! used to deform the curve. If the curve is
67 //! non-periodic, the first pole is the start point of the
68 //! curve, and the last pole is the end point of the
69 //! curve. The segment, which joins the first pole to the
70 //! second pole, is the tangent to the curve at its start
71 //! point, and the segment, which joins the last pole to
72 //! the second-from-last pole, is the tangent to the
73 //! curve at its end point. If the curve is periodic, these
74 //! geometric properties are not verified. It is more
75 //! difficult to give a geometric signification to the
76 //! weights but they are useful for providing exact
77 //! representations of the arcs of a circle or ellipse.
78 //! Moreover, if the weights of all the poles are equal,
79 //! the curve has a polynomial equation; it is
80 //! therefore a non-rational curve.
81 //! - a table of knots with their multiplicities. For a
82 //! Geom2d_BSplineCurve, the table of knots is an
83 //! increasing sequence of reals without repetition; the
84 //! multiplicities define the repetition of the knots. A
85 //! BSpline curve is a piecewise polynomial or rational
86 //! curve. The knots are the parameters of junction
87 //! points between two pieces. The multiplicity
88 //! Mult(i) of the knot Knot(i) of the BSpline
89 //! curve is related to the degree of continuity of the
90 //! curve at the knot Knot(i), which is equal to
91 //! Degree - Mult(i) where Degree is the
92 //! degree of the BSpline curve.
93 //! If the knots are regularly spaced (i.e. the difference
94 //! between two consecutive knots is a constant), three
95 //! specific and frequently used cases of knot distribution
96 //! can be identified:
97 //! - "uniform" if all multiplicities are equal to 1,
98 //! - "quasi-uniform" if all multiplicities are equal to 1,
99 //! except the first and the last knot which have a
100 //! multiplicity of Degree + 1, where Degree is
101 //! the degree of the BSpline curve,
102 //! - "Piecewise Bezier" if all multiplicities are equal to
103 //! Degree except the first and last knot which have
104 //! a multiplicity of Degree + 1, where Degree is
105 //! the degree of the BSpline curve. A curve of this
106 //! type is a concatenation of arcs of Bezier curves.
107 //! If the BSpline curve is not periodic:
108 //! - the bounds of the Poles and Weights tables are 1
109 //! and NbPoles, where NbPoles is the number of
110 //! poles of the BSpline curve,
111 //! - the bounds of the Knots and Multiplicities tables are
112 //! 1 and NbKnots, where NbKnots is the number
113 //! of knots of the BSpline curve.
114 //! If the BSpline curve is periodic, and if there are k
115 //! periodic knots and p periodic poles, the period is:
116 //! period = Knot(k + 1) - Knot(1)
117 //! and the poles and knots tables can be considered as
118 //! infinite tables, such that:
119 //! - Knot(i+k) = Knot(i) + period
120 //! - Pole(i+p) = Pole(i)
121 //! Note: data structures of a periodic BSpline curve are
122 //! more complex than those of a non-periodic one.
124 //! In this class we consider that a weight value is zero if
125 //! Weight <= Resolution from package gp.
126 //! For two parametric values (or two knot values) U1, U2 we
127 //! consider that U1 = U2 if Abs (U2 - U1) <= Epsilon (U1).
128 //! For two weights values W1, W2 we consider that W1 = W2 if
129 //! Abs (W2 - W1) <= Epsilon (W1). The method Epsilon is
130 //! defined in the class Real from package Standard.
133 //! . A survey of curve and surface methods in CADG Wolfgang BOHM
135 //! . On de Boor-like algorithms and blossoming Wolfgang BOEHM
137 //! . Blossoming and knot insertion algorithms for B-spline curves
138 //! Ronald N. GOLDMAN
139 //! . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA
140 //! . Curves and Surfaces for Computer Aided Geometric Design,
141 //! a practical guide Gerald Farin
142 class Geom2d_BSplineCurve : public Geom2d_BoundedCurve
148 //! Creates a non-rational B_spline curve on the
149 //! basis <Knots, Multiplicities> of degree <Degree>.
150 //! The following conditions must be verified.
151 //! 0 < Degree <= MaxDegree.
153 //! Knots.Length() == Mults.Length() >= 2
155 //! Knots(i) < Knots(i+1) (Knots are increasing)
157 //! 1 <= Mults(i) <= Degree
159 //! On a non periodic curve the first and last multiplicities
160 //! may be Degree+1 (this is even recommanded if you want the
161 //! curve to start and finish on the first and last pole).
163 //! On a periodic curve the first and the last multicities
164 //! must be the same.
166 //! on non-periodic curves
168 //! Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2
170 //! on periodic curves
172 //! Poles.Length() == Sum(Mults(i)) except the first or last
173 Standard_EXPORT Geom2d_BSplineCurve(const TColgp_Array1OfPnt2d& Poles, const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger& Multiplicities, const Standard_Integer Degree, const Standard_Boolean Periodic = Standard_False);
175 //! Creates a rational B_spline curve on the basis
176 //! <Knots, Multiplicities> of degree <Degree>.
177 //! The following conditions must be verified.
178 //! 0 < Degree <= MaxDegree.
180 //! Knots.Length() == Mults.Length() >= 2
182 //! Knots(i) < Knots(i+1) (Knots are increasing)
184 //! 1 <= Mults(i) <= Degree
186 //! On a non periodic curve the first and last multiplicities
187 //! may be Degree+1 (this is even recommanded if you want the
188 //! curve to start and finish on the first and last pole).
190 //! On a periodic curve the first and the last multicities
191 //! must be the same.
193 //! on non-periodic curves
195 //! Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2
197 //! on periodic curves
199 //! Poles.Length() == Sum(Mults(i)) except the first or last
200 Standard_EXPORT Geom2d_BSplineCurve(const TColgp_Array1OfPnt2d& Poles, const TColStd_Array1OfReal& Weights, const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger& Multiplicities, const Standard_Integer Degree, const Standard_Boolean Periodic = Standard_False);
202 //! Increases the degree of this BSpline curve to
203 //! Degree. As a result, the poles, weights and
204 //! multiplicities tables are modified; the knots table is
205 //! not changed. Nothing is done if Degree is less than
206 //! or equal to the current degree.
208 //! Standard_ConstructionError if Degree is greater than
209 //! Geom2d_BSplineCurve::MaxDegree().
210 Standard_EXPORT void IncreaseDegree (const Standard_Integer Degree);
212 //! Increases the multiplicity of the knot <Index> to
215 //! If <M> is lower or equal to the current
216 //! multiplicity nothing is done. If <M> is higher than
217 //! the degree the degree is used.
218 //! If <Index> is not in [FirstUKnotIndex, LastUKnotIndex]
219 Standard_EXPORT void IncreaseMultiplicity (const Standard_Integer Index, const Standard_Integer M);
221 //! Increases the multiplicities of the knots in
224 //! For each knot if <M> is lower or equal to the
225 //! current multiplicity nothing is done. If <M> is
226 //! higher than the degree the degree is used.
227 //! As a result, the poles and weights tables of this curve are modified.
229 //! It is forbidden to modify the multiplicity of the first or
230 //! last knot of a non-periodic curve. Be careful as
231 //! Geom2d does not protect against this.
233 //! Standard_OutOfRange if either Index, I1 or I2 is
234 //! outside the bounds of the knots table.
235 Standard_EXPORT void IncreaseMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M);
237 //! Increases by M the multiplicity of the knots of indexes
238 //! I1 to I2 in the knots table of this BSpline curve. For
239 //! each knot, the resulting multiplicity is limited to the
240 //! degree of this curve. If M is negative, nothing is done.
241 //! As a result, the poles and weights tables of this
242 //! BSpline curve are modified.
244 //! It is forbidden to modify the multiplicity of the first or
245 //! last knot of a non-periodic curve. Be careful as
246 //! Geom2d does not protect against this.
248 //! Standard_OutOfRange if I1 or I2 is outside the
249 //! bounds of the knots table.
250 Standard_EXPORT void IncrementMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M);
252 //! Inserts a knot value in the sequence of knots. If
253 //! <U> is an existing knot the multiplicity is
254 //! increased by <M>.
256 //! If U is not on the parameter range nothing is
259 //! If the multiplicity is negative or null nothing is
260 //! done. The new multiplicity is limited to the
263 //! The tolerance criterion for knots equality is
264 //! the max of Epsilon(U) and ParametricTolerance.
266 //! - If U is less than the first parameter or greater than
267 //! the last parameter of this BSpline curve, nothing is done.
268 //! - If M is negative or null, nothing is done.
269 //! - The multiplicity of a knot is limited to the degree of
270 //! this BSpline curve.
271 Standard_EXPORT void InsertKnot (const Standard_Real U, const Standard_Integer M = 1, const Standard_Real ParametricTolerance = 0.0);
273 //! Inserts the values of the array Knots, with the
274 //! respective multiplicities given by the array Mults, into
275 //! the knots table of this BSpline curve.
276 //! If a value of the array Knots is an existing knot, its multiplicity is:
277 //! - increased by M, if Add is true, or
278 //! - increased to M, if Add is false (default value).
279 //! The tolerance criterion used for knot equality is the
280 //! larger of the values ParametricTolerance (defaulted
281 //! to 0.) and Standard_Real::Epsilon(U),
282 //! where U is the current knot value.
284 //! - For a value of the array Knots which is less than
285 //! the first parameter or greater than the last
286 //! parameter of this BSpline curve, nothing is done.
287 //! - For a value of the array Mults which is negative or
288 //! null, nothing is done.
289 //! - The multiplicity of a knot is limited to the degree of
290 //! this BSpline curve.
291 Standard_EXPORT void InsertKnots (const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger& Mults, const Standard_Real ParametricTolerance = 0.0, const Standard_Boolean Add = Standard_False);
293 //! Reduces the multiplicity of the knot of index Index
294 //! to M. If M is equal to 0, the knot is removed.
295 //! With a modification of this type, the array of poles is also modified.
296 //! Two different algorithms are systematically used to
297 //! compute the new poles of the curve. If, for each
298 //! pole, the distance between the pole calculated
299 //! using the first algorithm and the same pole
300 //! calculated using the second algorithm, is less than
301 //! Tolerance, this ensures that the curve is not
302 //! modified by more than Tolerance. Under these
303 //! conditions, true is returned; otherwise, false is returned.
304 //! A low tolerance is used to prevent modification of
305 //! the curve. A high tolerance is used to "smooth" the curve.
307 //! Standard_OutOfRange if Index is outside the
308 //! bounds of the knots table.
309 Standard_EXPORT Standard_Boolean RemoveKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance);
312 //! The new pole is inserted after the pole of range Index.
313 //! If the curve was non rational it can become rational.
315 //! Raised if the B-spline is NonUniform or PiecewiseBezier or if
317 //! Raised if Index is not in the range [1, Number of Poles]
318 Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0);
321 //! The new pole is inserted before the pole of range Index.
322 //! If the curve was non rational it can become rational.
324 //! Raised if the B-spline is NonUniform or PiecewiseBezier or if
326 //! Raised if Index is not in the range [1, Number of Poles]
327 Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight = 1.0);
330 //! Removes the pole of range Index
331 //! If the curve was rational it can become non rational.
333 //! Raised if the B-spline is NonUniform or PiecewiseBezier.
334 //! Raised if the number of poles of the B-spline curve is lower or
335 //! equal to 2 before removing.
336 //! Raised if Index is not in the range [1, Number of Poles]
337 Standard_EXPORT void RemovePole (const Standard_Integer Index);
339 //! Reverses the orientation of this BSpline curve. As a result
340 //! - the knots and poles tables are modified;
341 //! - the start point of the initial curve becomes the end
342 //! point of the reversed curve;
343 //! - the end point of the initial curve becomes the start
344 //! point of the reversed curve.
345 Standard_EXPORT void Reverse() Standard_OVERRIDE;
347 //! Computes the parameter on the reversed curve for
348 //! the point of parameter U on this BSpline curve.
349 //! The returned value is: UFirst + ULast - U,
350 //! where UFirst and ULast are the values of the
351 //! first and last parameters of this BSpline curve.
352 Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
354 //! Modifies this BSpline curve by segmenting it
355 //! between U1 and U2. Either of these values can be
356 //! outside the bounds of the curve, but U2 must be greater than U1.
357 //! All data structure tables of this BSpline curve are
358 //! modified, but the knots located between U1 and U2
359 //! are retained. The degree of the curve is not modified.
361 //! Parameter theTolerance defines the possible proximity of the segment
362 //! boundaries and B-spline knots to treat them as equal.
365 //! Even if <me> is not closed it can become closed after the
366 //! segmentation for example if U1 or U2 are out of the bounds
367 //! of the curve <me> or if the curve makes loop.
368 //! After the segmentation the length of a curve can be null.
369 //! - The segmentation of a periodic curve over an
370 //! interval corresponding to its period generates a
371 //! non-periodic curve with equivalent geometry.
373 //! Standard_DomainError if U2 is less than U1.
374 //! raises if U2 < U1.
375 //! Standard_DomainError if U2 - U1 exceeds the period for periodic curves.
376 //! i.e. ((U2 - U1) - Period) > Precision::PConfusion().
377 Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2,
378 const Standard_Real theTolerance = Precision::PConfusion());
380 //! Modifies this BSpline curve by assigning the value K
381 //! to the knot of index Index in the knots table. This is a
382 //! relatively local modification because K must be such that:
383 //! Knots(Index - 1) < K < Knots(Index + 1)
385 //! Standard_ConstructionError if:
386 //! - K is not such that:
387 //! Knots(Index - 1) < K < Knots(Index + 1)
388 //! - M is greater than the degree of this BSpline curve
389 //! or lower than the previous multiplicity of knot of
390 //! index Index in the knots table.
391 //! Standard_OutOfRange if Index is outside the bounds of the knots table.
392 Standard_EXPORT void SetKnot (const Standard_Integer Index, const Standard_Real K);
394 //! Modifies this BSpline curve by assigning the array
395 //! K to its knots table. The multiplicity of the knots is not modified.
397 //! Standard_ConstructionError if the values in the
398 //! array K are not in ascending order.
399 //! Standard_OutOfRange if the bounds of the array
400 //! K are not respectively 1 and the number of knots of this BSpline curve.
401 Standard_EXPORT void SetKnots (const TColStd_Array1OfReal& K);
403 //! Modifies this BSpline curve by assigning the value K
404 //! to the knot of index Index in the knots table. This is a
405 //! relatively local modification because K must be such that:
406 //! Knots(Index - 1) < K < Knots(Index + 1)
407 //! The second syntax allows you also to increase the
408 //! multiplicity of the knot to M (but it is not possible to
409 //! decrease the multiplicity of the knot with this function).
411 //! Standard_ConstructionError if:
412 //! - K is not such that:
413 //! Knots(Index - 1) < K < Knots(Index + 1)
414 //! - M is greater than the degree of this BSpline curve
415 //! or lower than the previous multiplicity of knot of
416 //! index Index in the knots table.
417 //! Standard_OutOfRange if Index is outside the bounds of the knots table.
418 Standard_EXPORT void SetKnot (const Standard_Integer Index, const Standard_Real K, const Standard_Integer M);
420 //! Computes the parameter normalized within the
421 //! "first" period of this BSpline curve, if it is periodic:
422 //! the returned value is in the range Param1 and
423 //! Param1 + Period, where:
424 //! - Param1 is the "first parameter", and
425 //! - Period the period of this BSpline curve.
426 //! Note: If this curve is not periodic, U is not modified.
427 Standard_EXPORT void PeriodicNormalization (Standard_Real& U) const;
429 //! Changes this BSpline curve into a periodic curve.
430 //! To become periodic, the curve must first be closed.
431 //! Next, the knot sequence must be periodic. For this,
432 //! FirstUKnotIndex and LastUKnotIndex are used to
433 //! compute I1 and I2, the indexes in the knots array
434 //! of the knots corresponding to the first and last
435 //! parameters of this BSpline curve.
436 //! The period is therefore Knot(I2) - Knot(I1).
437 //! Consequently, the knots and poles tables are modified.
439 //! Standard_ConstructionError if this BSpline curve is not closed.
440 Standard_EXPORT void SetPeriodic();
442 //! Assigns the knot of index Index in the knots table as
443 //! the origin of this periodic BSpline curve. As a
444 //! consequence, the knots and poles tables are modified.
446 //! Standard_NoSuchObject if this curve is not periodic.
447 //! Standard_DomainError if Index is outside the
448 //! bounds of the knots table.
449 Standard_EXPORT void SetOrigin (const Standard_Integer Index);
451 //! Changes this BSpline curve into a non-periodic
452 //! curve. If this curve is already non-periodic, it is not modified.
453 //! Note that the poles and knots tables are modified.
455 //! If this curve is periodic, as the multiplicity of the first
456 //! and last knots is not modified, and is not equal to
457 //! Degree + 1, where Degree is the degree of
458 //! this BSpline curve, the start and end points of the
459 //! curve are not its first and last poles.
460 Standard_EXPORT void SetNotPeriodic();
462 //! Modifies this BSpline curve by assigning P to the
463 //! pole of index Index in the poles table.
465 //! Standard_OutOfRange if Index is outside the
466 //! bounds of the poles table.
467 //! Standard_ConstructionError if Weight is negative or null.
468 Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P);
470 //! Modifies this BSpline curve by assigning P to the
471 //! pole of index Index in the poles table.
472 //! The second syntax also allows you to modify the
473 //! weight of the modified pole, which becomes Weight.
474 //! In this case, if this BSpline curve is non-rational, it
475 //! can become rational and vice versa.
477 //! Standard_OutOfRange if Index is outside the
478 //! bounds of the poles table.
479 //! Standard_ConstructionError if Weight is negative or null.
480 Standard_EXPORT void SetPole (const Standard_Integer Index, const gp_Pnt2d& P, const Standard_Real Weight);
482 //! Assigns the weight Weight to the pole of index Index of the poles table.
483 //! If the curve was non rational it can become rational.
484 //! If the curve was rational it can become non rational.
486 //! Standard_OutOfRange if Index is outside the
487 //! bounds of the poles table.
488 //! Standard_ConstructionError if Weight is negative or null.
489 Standard_EXPORT void SetWeight (const Standard_Integer Index, const Standard_Real Weight);
491 //! Moves the point of parameter U of this BSpline
492 //! curve to P. Index1 and Index2 are the indexes in the
493 //! table of poles of this BSpline curve of the first and
494 //! last poles designated to be moved.
495 //! FirstModifiedPole and LastModifiedPole are the
496 //! indexes of the first and last poles, which are
497 //! effectively modified.
498 //! In the event of incompatibility between Index1,
499 //! Index2 and the value U:
500 //! - no change is made to this BSpline curve, and
501 //! - the FirstModifiedPole and LastModifiedPole are returned null.
503 //! Standard_OutOfRange if:
504 //! - Index1 is greater than or equal to Index2, or
505 //! - Index1 or Index2 is less than 1 or greater than the
506 //! number of poles of this BSpline curve.
507 Standard_EXPORT void MovePoint (const Standard_Real U, const gp_Pnt2d& P, const Standard_Integer Index1, const Standard_Integer Index2, Standard_Integer& FirstModifiedPole, Standard_Integer& LastModifiedPole);
509 //! Move a point with parameter U to P.
510 //! and makes it tangent at U be Tangent.
511 //! StartingCondition = -1 means first can move
512 //! EndingCondition = -1 means last point can move
513 //! StartingCondition = 0 means the first point cannot move
514 //! EndingCondition = 0 means the last point cannot move
515 //! StartingCondition = 1 means the first point and tangent cannot move
516 //! EndingCondition = 1 means the last point and tangent cannot move
518 //! ErrorStatus != 0 means that there are not enought degree of freedom
519 //! with the constrain to deform the curve accordingly
520 Standard_EXPORT void MovePointAndTangent (const Standard_Real U, const gp_Pnt2d& P, const gp_Vec2d& Tangent, const Standard_Real Tolerance, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, Standard_Integer& ErrorStatus);
522 //! Returns true if the degree of continuity of this
523 //! BSpline curve is at least N. A BSpline curve is at least GeomAbs_C0.
524 //! Exceptions Standard_RangeError if N is negative.
525 Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE;
528 //! Check if curve has at least G1 continuity in interval [theTf, theTl]
529 //! Returns true if IsCN(1)
531 //! angle betweem "left" and "right" first derivatives at
532 //! knots with C0 continuity is less then theAngTol
533 //! only knots in interval [theTf, theTl] is checked
534 Standard_EXPORT Standard_Boolean IsG1 (const Standard_Real theTf, const Standard_Real theTl, const Standard_Real theAngTol) const;
537 //! Returns true if the distance between the first point and the
538 //! last point of the curve is lower or equal to Resolution
541 //! The first and the last point can be different from the first
542 //! pole and the last pole of the curve.
543 Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE;
545 //! Returns True if the curve is periodic.
546 Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE;
549 //! Returns True if the weights are not identical.
550 //! The tolerance criterion is Epsilon of the class Real.
551 Standard_EXPORT Standard_Boolean IsRational() const;
554 //! Returns the global continuity of the curve :
555 //! C0 : only geometric continuity,
556 //! C1 : continuity of the first derivative all along the Curve,
557 //! C2 : continuity of the second derivative all along the Curve,
558 //! C3 : continuity of the third derivative all along the Curve,
559 //! CN : the order of continuity is infinite.
560 //! For a B-spline curve of degree d if a knot Ui has a
561 //! multiplicity p the B-spline curve is only Cd-p continuous
562 //! at Ui. So the global continuity of the curve can't be greater
563 //! than Cd-p where p is the maximum multiplicity of the interior
564 //! Knots. In the interior of a knot span the curve is infinitely
565 //! continuously differentiable.
566 Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
568 //! Returns the degree of this BSpline curve.
569 //! In this class the degree of the basis normalized B-spline
570 //! functions cannot be greater than "MaxDegree"
571 //! Computation of value and derivatives
572 Standard_EXPORT Standard_Integer Degree() const;
574 Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE;
576 //! Raised if the continuity of the curve is not C1.
577 Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE;
579 //! Raised if the continuity of the curve is not C2.
580 Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE;
582 //! For this BSpline curve, computes
583 //! - the point P of parameter U, or
584 //! - the point P and one or more of the following values:
585 //! - V1, the first derivative vector,
586 //! - V2, the second derivative vector,
587 //! - V3, the third derivative vector.
589 //! On a point where the continuity of the curve is not the
590 //! one requested, these functions impact the part
591 //! defined by the parameter with a value greater than U,
592 //! i.e. the part of the curve to the "right" of the singularity.
593 //! Raises UndefinedDerivative if the continuity of the curve is not C3.
594 Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE;
596 //! For the point of parameter U of this BSpline curve,
597 //! computes the vector corresponding to the Nth derivative.
599 //! On a point where the continuity of the curve is not the
600 //! one requested, this function impacts the part defined
601 //! by the parameter with a value greater than U, i.e. the
602 //! part of the curve to the "right" of the singularity.
603 //! Raises UndefinedDerivative if the continuity of the curve is not CN.
604 //! RangeError if N < 1.
605 //! The following functions computes the point of parameter U
606 //! and the derivatives at this point on the B-spline curve
607 //! arc defined between the knot FromK1 and the knot ToK2.
608 //! U can be out of bounds [Knot (FromK1), Knot (ToK2)] but
609 //! for the computation we only use the definition of the curve
610 //! between these two knots. This method is useful to compute
611 //! local derivative, if the order of continuity of the whole
612 //! curve is not greater enough. Inside the parametric
613 //! domain Knot (FromK1), Knot (ToK2) the evaluations are
614 //! the same as if we consider the whole definition of the
615 //! curve. Of course the evaluations are different outside
616 //! this parametric domain.
617 Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
619 //! Raised if FromK1 = ToK2.
620 Standard_EXPORT gp_Pnt2d LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const;
622 //! Raised if FromK1 = ToK2.
623 Standard_EXPORT void LocalD0 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt2d& P) const;
626 //! Raised if the local continuity of the curve is not C1
627 //! between the knot K1 and the knot K2.
628 //! Raised if FromK1 = ToK2.
629 Standard_EXPORT void LocalD1 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt2d& P, gp_Vec2d& V1) const;
632 //! Raised if the local continuity of the curve is not C2
633 //! between the knot K1 and the knot K2.
634 //! Raised if FromK1 = ToK2.
635 Standard_EXPORT void LocalD2 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const;
638 //! Raised if the local continuity of the curve is not C3
639 //! between the knot K1 and the knot K2.
640 //! Raised if FromK1 = ToK2.
641 Standard_EXPORT void LocalD3 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const;
644 //! Raised if the local continuity of the curve is not CN
645 //! between the knot K1 and the knot K2.
646 //! Raised if FromK1 = ToK2.
648 Standard_EXPORT gp_Vec2d LocalDN (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Integer N) const;
651 //! Returns the last point of the curve.
653 //! The last point of the curve is different from the last
654 //! pole of the curve if the multiplicity of the last knot
655 //! is lower than Degree.
656 Standard_EXPORT gp_Pnt2d EndPoint() const Standard_OVERRIDE;
659 //! For a B-spline curve the first parameter (which gives the start
660 //! point of the curve) is a knot value but if the multiplicity of
661 //! the first knot index is lower than Degree + 1 it is not the
662 //! first knot of the curve. This method computes the index of the
663 //! knot corresponding to the first parameter.
664 Standard_EXPORT Standard_Integer FirstUKnotIndex() const;
667 //! Computes the parametric value of the start point of the curve.
668 //! It is a knot value.
669 Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE;
672 //! Returns the knot of range Index. When there is a knot
673 //! with a multiplicity greater than 1 the knot is not repeated.
674 //! The method Multiplicity can be used to get the multiplicity
676 //! Raised if Index < 1 or Index > NbKnots
677 Standard_EXPORT Standard_Real Knot (const Standard_Integer Index) const;
679 //! returns the knot values of the B-spline curve;
681 //! Raised K.Lower() is less than number of first knot or
682 //! K.Upper() is more than number of last knot.
683 Standard_EXPORT void Knots (TColStd_Array1OfReal& K) const;
685 //! returns the knot values of the B-spline curve;
686 Standard_EXPORT const TColStd_Array1OfReal& Knots() const;
688 //! Returns the knots sequence.
689 //! In this sequence the knots with a multiplicity greater than 1
692 //! K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}
694 //! Raised if K.Lower() is less than number of first knot
695 //! in knot sequence with repetitions or K.Upper() is more
696 //! than number of last knot in knot sequence with repetitions.
697 Standard_EXPORT void KnotSequence (TColStd_Array1OfReal& K) const;
699 //! Returns the knots sequence.
700 //! In this sequence the knots with a multiplicity greater than 1
703 //! K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}
704 Standard_EXPORT const TColStd_Array1OfReal& KnotSequence() const;
707 //! Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier.
708 //! If all the knots differ by a positive constant from the
709 //! preceding knot the BSpline Curve can be :
710 //! - Uniform if all the knots are of multiplicity 1,
711 //! - QuasiUniform if all the knots are of multiplicity 1 except for
712 //! the first and last knot which are of multiplicity Degree + 1,
713 //! - PiecewiseBezier if the first and last knots have multiplicity
714 //! Degree + 1 and if interior knots have multiplicity Degree
715 //! A piecewise Bezier with only two knots is a BezierCurve.
716 //! else the curve is non uniform.
717 //! The tolerance criterion is Epsilon from class Real.
718 Standard_EXPORT GeomAbs_BSplKnotDistribution KnotDistribution() const;
721 //! For a BSpline curve the last parameter (which gives the
722 //! end point of the curve) is a knot value but if the
723 //! multiplicity of the last knot index is lower than
724 //! Degree + 1 it is not the last knot of the curve. This
725 //! method computes the index of the knot corresponding to
726 //! the last parameter.
727 Standard_EXPORT Standard_Integer LastUKnotIndex() const;
730 //! Computes the parametric value of the end point of the curve.
731 //! It is a knot value.
732 Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE;
735 //! Locates the parametric value U in the sequence of knots.
736 //! If "WithKnotRepetition" is True we consider the knot's
737 //! representation with repetition of multiple knot value,
738 //! otherwise we consider the knot's representation with
739 //! no repetition of multiple knot values.
740 //! Knots (I1) <= U <= Knots (I2)
741 //! . if I1 = I2 U is a knot value (the tolerance criterion
742 //! ParametricTolerance is used).
743 //! . if I1 < 1 => U < Knots (1) - Abs(ParametricTolerance)
744 //! . if I2 > NbKnots => U > Knots (NbKnots) + Abs(ParametricTolerance)
745 Standard_EXPORT void LocateU (const Standard_Real U, const Standard_Real ParametricTolerance, Standard_Integer& I1, Standard_Integer& I2, const Standard_Boolean WithKnotRepetition = Standard_False) const;
748 //! Returns the multiplicity of the knots of range Index.
749 //! Raised if Index < 1 or Index > NbKnots
750 Standard_EXPORT Standard_Integer Multiplicity (const Standard_Integer Index) const;
753 //! Returns the multiplicity of the knots of the curve.
755 //! Raised if the length of M is not equal to NbKnots.
756 Standard_EXPORT void Multiplicities (TColStd_Array1OfInteger& M) const;
758 //! returns the multiplicity of the knots of the curve.
759 Standard_EXPORT const TColStd_Array1OfInteger& Multiplicities() const;
762 //! Returns the number of knots. This method returns the number of
763 //! knot without repetition of multiple knots.
764 Standard_EXPORT Standard_Integer NbKnots() const;
766 //! Returns the number of poles
767 Standard_EXPORT Standard_Integer NbPoles() const;
769 //! Returns the pole of range Index.
770 //! Raised if Index < 1 or Index > NbPoles.
771 Standard_EXPORT const gp_Pnt2d& Pole (const Standard_Integer Index) const;
773 //! Returns the poles of the B-spline curve;
775 //! Raised if the length of P is not equal to the number of poles.
776 Standard_EXPORT void Poles (TColgp_Array1OfPnt2d& P) const;
778 //! Returns the poles of the B-spline curve;
779 Standard_EXPORT const TColgp_Array1OfPnt2d& Poles() const;
782 //! Returns the start point of the curve.
784 //! This point is different from the first pole of the curve if the
785 //! multiplicity of the first knot is lower than Degree.
786 Standard_EXPORT gp_Pnt2d StartPoint() const Standard_OVERRIDE;
788 //! Returns the weight of the pole of range Index .
789 //! Raised if Index < 1 or Index > NbPoles.
790 Standard_EXPORT Standard_Real Weight (const Standard_Integer Index) const;
792 //! Returns the weights of the B-spline curve;
794 //! Raised if the length of W is not equal to NbPoles.
795 Standard_EXPORT void Weights (TColStd_Array1OfReal& W) const;
797 //! Returns the weights of the B-spline curve;
798 Standard_EXPORT const TColStd_Array1OfReal* Weights() const;
800 //! Applies the transformation T to this BSpline curve.
801 Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE;
804 //! Returns the value of the maximum degree of the normalized
805 //! B-spline basis functions in this package.
806 Standard_EXPORT static Standard_Integer MaxDegree();
808 //! Computes for this BSpline curve the parametric
809 //! tolerance UTolerance for a given tolerance
810 //! Tolerance3D (relative to dimensions in the plane).
811 //! If f(t) is the equation of this BSpline curve,
812 //! UTolerance ensures that:
813 //! | t1 - t0| < Utolerance ===>
814 //! |f(t1) - f(t0)| < ToleranceUV
815 Standard_EXPORT void Resolution (const Standard_Real ToleranceUV, Standard_Real& UTolerance);
817 //! Creates a new object which is a copy of this BSpline curve.
818 Standard_EXPORT Handle(Geom2d_Geometry) Copy() const Standard_OVERRIDE;
820 //! Dumps the content of me into the stream
821 Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE;
826 DEFINE_STANDARD_RTTIEXT(Geom2d_BSplineCurve,Geom2d_BoundedCurve)
836 //! Recompute the flatknots, the knotsdistribution, the continuity.
837 Standard_EXPORT void UpdateKnots();
839 Standard_Boolean rational;
840 Standard_Boolean periodic;
841 GeomAbs_BSplKnotDistribution knotSet;
842 GeomAbs_Shape smooth;
843 Standard_Integer deg;
844 Handle(TColgp_HArray1OfPnt2d) poles;
845 Handle(TColStd_HArray1OfReal) weights;
846 Handle(TColStd_HArray1OfReal) flatknots;
847 Handle(TColStd_HArray1OfReal) knots;
848 Handle(TColStd_HArray1OfInteger) mults;
849 Standard_Real maxderivinv;
850 Standard_Boolean maxderivinvok;
861 #endif // _Geom2d_BSplineCurve_HeaderFile