1 -- Created on: 1993-03-09
3 -- Copyright (c) 1993-1999 Matra Datavision
4 -- Copyright (c) 1999-2012 OPEN CASCADE SAS
6 -- The content of this file is subject to the Open CASCADE Technology Public
7 -- License Version 6.5 (the "License"). You may not use the content of this file
8 -- except in compliance with the License. Please obtain a copy of the License
9 -- at http://www.opencascade.org and read it completely before using this file.
11 -- The Initial Developer of the Original Code is Open CASCADE S.A.S., having its
12 -- main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France.
14 -- The Original Code and all software distributed under the License is
15 -- distributed on an "AS IS" basis, without warranty of any kind, and the
16 -- Initial Developer hereby disclaims all such warranties, including without
17 -- limitation, any warranties of merchantability, fitness for a particular
18 -- purpose or non-infringement. Please see the License for the specific terms
19 -- and conditions governing the rights and limitations under the License.
21 -- xab : modified 15-Mar-95 : added cache mecanism to speed up evaluation
22 -- mei : modified 08-Jun-95 : added method MovePoint
25 class BSplineCurve from Geom inherits BoundedCurve from Geom
27 ---Purpose : Definition of the B_spline curve.
28 -- A B-spline curve can be
29 -- Uniform or non-uniform
30 -- Rational or non-rational
31 -- Periodic or non-periodic
33 -- a b-spline curve is defined by :
34 -- its degree; the degree for a
35 -- Geom_BSplineCurve is limited to a value (25)
36 -- which is defined and controlled by the system.
37 -- This value is returned by the function MaxDegree;
38 -- - its periodic or non-periodic nature;
39 -- - a table of poles (also called control points), with
40 -- their associated weights if the BSpline curve is
41 -- rational. The poles of the curve are "control
42 -- points" used to deform the curve. If the curve is
43 -- non-periodic, the first pole is the start point of
44 -- the curve, and the last pole is the end point of
45 -- the curve. The segment which joins the first pole
46 -- to the second pole is the tangent to the curve at
47 -- its start point, and the segment which joins the
48 -- last pole to the second-from-last pole is the
49 -- tangent to the curve at its end point. If the curve
50 -- is periodic, these geometric properties are not
51 -- verified. It is more difficult to give a geometric
52 -- signification to the weights but are useful for
53 -- providing exact representations of the arcs of a
54 -- circle or ellipse. Moreover, if the weights of all the
55 -- poles are equal, the curve has a polynomial
56 -- equation; it is therefore a non-rational curve.
57 -- - a table of knots with their multiplicities. For a
58 -- Geom_BSplineCurve, the table of knots is an
59 -- increasing sequence of reals without repetition;
60 -- the multiplicities define the repetition of the knots.
61 -- A BSpline curve is a piecewise polynomial or
62 -- rational curve. The knots are the parameters of
63 -- junction points between two pieces. The
64 -- multiplicity Mult(i) of the knot Knot(i) of
65 -- the BSpline curve is related to the degree of
66 -- continuity of the curve at the knot Knot(i),
67 -- which is equal to Degree - Mult(i)
68 -- where Degree is the degree of the BSpline curve.
69 -- If the knots are regularly spaced (i.e. the difference
70 -- between two consecutive knots is a constant), three
71 -- specific and frequently used cases of knot
72 -- distribution can be identified:
73 -- - "uniform" if all multiplicities are equal to 1,
74 -- - "quasi-uniform" if all multiplicities are equal to 1,
75 -- except the first and the last knot which have a
76 -- multiplicity of Degree + 1, where Degree is
77 -- the degree of the BSpline curve,
78 -- - "Piecewise Bezier" if all multiplicities are equal to
79 -- Degree except the first and last knot which
80 -- have a multiplicity of Degree + 1, where
81 -- Degree is the degree of the BSpline curve. A
82 -- curve of this type is a concatenation of arcs of Bezier curves.
83 -- If the BSpline curve is not periodic:
84 -- - the bounds of the Poles and Weights tables are 1
85 -- and NbPoles, where NbPoles is the number
86 -- of poles of the BSpline curve,
87 -- - the bounds of the Knots and Multiplicities tables
88 -- are 1 and NbKnots, where NbKnots is the
89 -- number of knots of the BSpline curve.
90 -- If the BSpline curve is periodic, and if there are k
91 -- periodic knots and p periodic poles, the period is:
92 -- period = Knot(k + 1) - Knot(1)
93 -- and the poles and knots tables can be considered
94 -- as infinite tables, verifying:
95 -- - Knot(i+k) = Knot(i) + period
96 -- - Pole(i+p) = Pole(i)
97 -- Note: data structures of a periodic BSpline curve
98 -- are more complex than those of a non-periodic one.
100 -- In this class, weight value is considered to be zero if
101 -- the weight is less than or equal to gp::Resolution().
104 -- . A survey of curve and surface methods in CADG Wolfgang BOHM
106 -- . On de Boor-like algorithms and blossoming Wolfgang BOEHM
108 -- . Blossoming and knot insertion algorithms for B-spline curves
110 -- . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA
111 -- . Curves and Surfaces for Computer Aided Geometric Design,
112 -- a practical guide Gerald Farin
114 uses Array1OfInteger from TColStd,
115 Array1OfReal from TColStd,
116 HArray1OfInteger from TColStd,
117 HArray1OfReal from TColStd,
118 Array1OfPnt from TColgp,
122 HArray1OfPnt from TColgp,
125 BSplKnotDistribution from GeomAbs,
130 raises ConstructionError from Standard,
131 DimensionError from Standard,
132 DomainError from Standard,
133 OutOfRange from Standard,
134 RangeError from Standard,
135 NoSuchObject from Standard,
136 UndefinedDerivative from Geom
140 Create (Poles : Array1OfPnt from TColgp;
141 Knots : Array1OfReal from TColStd;
142 Multiplicities : Array1OfInteger from TColStd;
144 Periodic : Boolean = Standard_False)
146 returns mutable BSplineCurve from Geom
148 ---Purpose : Creates a non-rational B_spline curve on the
149 -- basis <Knots, Multiplicities> of degree <Degree>.
151 raises ConstructionError;
153 -- The following conditions must be verified.
155 -- 0 < Degree <= MaxDegree.
157 -- Knots.Length() == Mults.Length() >= 2
159 -- Knots(i) < Knots(i+1) (Knots are increasing)
161 -- 1 <= Mults(i) <= Degree
163 -- On a non periodic curve the first and last multiplicities
164 -- may be Degree+1 (this is even recommanded if you want the
165 -- curve to start and finish on the first and last pole).
167 -- On a periodic curve the first and the last multicities
170 -- on non-periodic curves
172 -- Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2
174 -- on periodic curves
176 -- Poles.Length() == Sum(Mults(i)) except the first or last
179 Create (Poles : Array1OfPnt from TColgp;
180 Weights : Array1OfReal from TColStd;
181 Knots : Array1OfReal from TColStd;
182 Multiplicities : Array1OfInteger from TColStd;
184 Periodic : Boolean = Standard_False;
185 CheckRational : Boolean = Standard_True)
187 returns mutable BSplineCurve from Geom
189 ---Purpose : Creates a rational B_spline curve on the basis
190 -- <Knots, Multiplicities> of degree <Degree>.
191 -- Raises ConstructionError subject to the following conditions
192 -- 0 < Degree <= MaxDegree.
194 -- Weights.Length() == Poles.Length()
196 -- Knots.Length() == Mults.Length() >= 2
198 -- Knots(i) < Knots(i+1) (Knots are increasing)
200 -- 1 <= Mults(i) <= Degree
202 -- On a non periodic curve the first and last multiplicities
203 -- may be Degree+1 (this is even recommanded if you want the
204 -- curve to start and finish on the first and last pole).
206 -- On a periodic curve the first and the last multicities
209 -- on non-periodic curves
211 -- Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2
213 -- on periodic curves
215 -- Poles.Length() == Sum(Mults(i)) except the first or last
217 raises ConstructionError;
222 IncreaseDegree (me : mutable; Degree : Integer)
224 ---Purpose: Increases the degree of this BSpline curve to
225 -- Degree. As a result, the poles, weights and
226 -- multiplicities tables are modified; the knots table is
227 -- not changed. Nothing is done if Degree is less than
228 -- or equal to the current degree.
230 -- Standard_ConstructionError if Degree is greater than
231 -- Geom_BSplineCurve::MaxDegree().
232 raises ConstructionError;
234 IncreaseMultiplicity (me : mutable; Index : Integer; M : Integer)
236 ---Purpose :Increases the multiplicity of the knot <Index> to
239 -- If <M> is lower or equal to the current
240 -- multiplicity nothing is done. If <M> is higher than
241 -- the degree the degree is used.
245 ---Purpose: If <Index> is not in [FirstUKnotIndex, LastUKnotIndex]
248 IncreaseMultiplicity (me : mutable; I1, I2 : Integer; M : Integer)
250 ---Purpose :Increases the multiplicities of the knots in
253 -- For each knot if <M> is lower or equal to the
254 -- current multiplicity nothing is done. If <M> is
255 -- higher than the degree the degree is used.
259 ---Purpose: If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]
261 IncrementMultiplicity (me : mutable; I1, I2 : Integer; M : Integer)
263 ---Purpose :Increment the multiplicities of the knots in
266 -- If <M> is not positive nithing is done.
268 -- For each knot the resulting multiplicity is
269 -- limited to the Degree.
273 ---Purpose: If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]
278 InsertKnot (me : mutable;
281 ParametricTolerance : Real = 0.0;
282 Add : Boolean = Standard_True);
284 ---Purpose: Inserts a knot value in the sequence of knots. If
285 -- <U> is an existing knot the multiplicity is
288 -- If U is not on the parameter range nothing is
291 -- If the multiplicity is negative or null nothing is
292 -- done. The new multiplicity is limited to the
295 -- The tolerance criterion for knots equality is
296 -- the max of Epsilon(U) and ParametricTolerance.
299 InsertKnots (me : mutable; Knots : Array1OfReal from TColStd;
300 Mults : Array1OfInteger from TColStd;
301 ParametricTolerance : Real = 0.0;
302 Add : Boolean = Standard_False);
304 ---Purpose: Inserts a set of knots values in the sequence of
307 -- For each U = Knots(i), M = Mults(i)
309 -- If <U> is an existing knot the multiplicity is
310 -- increased by <M> if <Add> is True, increased to
311 -- <M> if <Add> is False.
313 -- If U is not on the parameter range nothing is
316 -- If the multiplicity is negative or null nothing is
317 -- done. The new multiplicity is limited to the
320 -- The tolerance criterion for knots equality is
321 -- the max of Epsilon(U) and ParametricTolerance.
327 RemoveKnot(me : mutable; Index : Integer;
329 Tolerance : Real) returns Boolean
331 ---Purpose : Reduces the multiplicity of the knot of index Index
332 -- to M. If M is equal to 0, the knot is removed.
333 -- With a modification of this type, the array of poles is also modified.
334 -- Two different algorithms are systematically used to
335 -- compute the new poles of the curve. If, for each
336 -- pole, the distance between the pole calculated
337 -- using the first algorithm and the same pole
338 -- calculated using the second algorithm, is less than
339 -- Tolerance, this ensures that the curve is not
340 -- modified by more than Tolerance. Under these
341 -- conditions, true is returned; otherwise, false is returned.
342 -- A low tolerance is used to prevent modification of
343 -- the curve. A high tolerance is used to "smooth" the curve.
345 -- Standard_OutOfRange if Index is outside the
346 -- bounds of the knots table.
350 ---Purpose : pole insertion and pole removing
351 -- this operation is limited to the Uniform or QuasiUniform
352 -- BSplineCurve. The knot values are modified . If the BSpline is
353 -- NonUniform or Piecewise Bezier an exception Construction error
357 Reverse (me : mutable);
359 -- Changes the direction of parametrization of <me>. The Knot
360 -- sequence is modified, the FirstParameter and the
361 -- LastParameter are not modified. The StartPoint of the
362 -- initial curve becomes the EndPoint of the reversed curve
363 -- and the EndPoint of the initial curve becomes the StartPoint
364 -- of the reversed curve.
367 ReversedParameter(me; U : Real) returns Real;
368 ---Purpose: Returns the parameter on the reversed curve for
369 -- the point of parameter U on <me>.
371 -- returns UFirst + ULast - U
373 Segment (me : mutable; U1, U2 : Real)
374 ---Purpose : Modifies this BSpline curve by segmenting it between
375 -- U1 and U2. Either of these values can be outside the
376 -- bounds of the curve, but U2 must be greater than U1.
377 -- All data structure tables of this BSpline curve are
378 -- modified, but the knots located between U1 and U2
379 -- are retained. The degree of the curve is not modified.
381 -- Even if <me> is not closed it can become closed after the
382 -- segmentation for example if U1 or U2 are out of the bounds
383 -- of the curve <me> or if the curve makes loop.
384 -- After the segmentation the length of a curve can be null.
385 raises DomainError from Standard;
386 ---Purpose: raises if U2 < U1.
389 SetKnot (me : mutable; Index : Integer; K : Real)
390 ---Purpose : Modifies this BSpline curve by assigning the value K
391 -- to the knot of index Index in the knots table. This is a
392 -- relatively local modification because K must be such that:
393 -- Knots(Index - 1) < K < Knots(Index + 1)
394 -- The second syntax allows you also to increase the
395 -- multiplicity of the knot to M (but it is not possible to
396 -- decrease the multiplicity of the knot with this function).
397 -- Standard_ConstructionError if:
398 -- - K is not such that:
399 -- Knots(Index - 1) < K < Knots(Index + 1)
400 -- - M is greater than the degree of this BSpline curve
401 -- or lower than the previous multiplicity of knot of
402 -- index Index in the knots table.
403 -- Standard_OutOfRange if Index is outside the bounds of the knots table.
404 raises ConstructionError,
408 SetKnots (me : mutable; K : Array1OfReal from TColStd)
409 ---Purpose : Modifies this BSpline curve by assigning the array
410 -- K to its knots table. The multiplicity of the knots is not modified.
412 -- Standard_ConstructionError if the values in the
413 -- array K are not in ascending order.
414 -- Standard_OutOfRange if the bounds of the array
415 -- K are not respectively 1 and the number of knots of this BSpline curve.
416 raises ConstructionError,
419 SetKnot (me : mutable; Index : Integer; K : Real; M : Integer)
421 -- Changes the knot of range Index with its multiplicity.
422 -- You can increase the multiplicity of a knot but it is
423 -- not allowed to decrease the multiplicity of an existing knot.
424 raises ConstructionError,
426 -- Raised if K >= Knots(Index+1) or K <= Knots(Index-1).
427 -- Raised if M is greater than Degree or lower than the previous
428 -- multiplicity of knot of range Index.
430 ---Purpose : Raised if Index < 1 || Index > NbKnots
432 PeriodicNormalization(me ; U : in out Real) ;
434 ---Purpose : returns the parameter normalized within
435 -- the period if the curve is periodic : otherwise
436 -- does not do anything
438 SetPeriodic (me : mutable)
439 ---Purpose : Changes this BSpline curve into a periodic curve.
440 -- To become periodic, the curve must first be closed.
441 -- Next, the knot sequence must be periodic. For this,
442 -- FirstUKnotIndex and LastUKnotIndex are used
443 -- to compute I1 and I2, the indexes in the knots
444 -- array of the knots corresponding to the first and
445 -- last parameters of this BSpline curve.
446 -- The period is therefore: Knots(I2) - Knots(I1).
447 -- Consequently, the knots and poles tables are modified.
449 -- Standard_ConstructionError if this BSpline curve is not closed.
450 raises ConstructionError;
453 SetOrigin (me : mutable; Index : Integer)
454 ---Purpose: Assigns the knot of index Index in the knots table as
455 -- the origin of this periodic BSpline curve. As a
456 -- consequence, the knots and poles tables are modified.
458 -- Standard_NoSuchObject if this curve is not periodic.
459 -- Standard_DomainError if Index is outside the bounds of the knots table.
463 SetOrigin (me : mutable;
464 U : Real from Standard;
465 Tol : Real from Standard)
466 ---Purpose: Set the origin of a periodic curve at Knot U. If U
467 -- is not a knot of the BSpline a new knot is
468 -- inseted. KnotVector and poles are modified.
470 ---Purpose: Raised if the curve is not periodic
473 SetNotPeriodic (me : mutable);
474 ---Purpose : Changes this BSpline curve into a non-periodic
475 -- curve. If this curve is already non-periodic, it is not modified.
476 -- Note: the poles and knots tables are modified.
478 -- If this curve is periodic, as the multiplicity of the first
479 -- and last knots is not modified, and is not equal to
480 -- Degree + 1, where Degree is the degree of
481 -- this BSpline curve, the start and end points of the
482 -- curve are not its first and last poles.
486 SetPole (me : mutable; Index : Integer; P : Pnt)
487 ---Purpose : Modifies this BSpline curve by assigning P to the pole
488 -- of index Index in the poles table.
490 -- Standard_OutOfRange if Index is outside the
491 -- bounds of the poles table.
492 -- Standard_ConstructionError if Weight is negative or null.
495 SetPole (me : mutable; Index : Integer; P : Pnt; Weight : Real)
496 ---Purpose: Modifies this BSpline curve by assigning P to the pole
497 -- of index Index in the poles table.
498 -- This syntax also allows you to modify the
499 -- weight of the modified pole, which becomes Weight.
500 -- In this case, if this BSpline curve is non-rational, it
501 -- can become rational and vice versa.
503 -- Standard_OutOfRange if Index is outside the
504 -- bounds of the poles table.
505 -- Standard_ConstructionError if Weight is negative or null.
510 SetWeight (me : mutable; Index : Integer; Weight : Real)
512 -- Changes the weight for the pole of range Index.
513 -- If the curve was non rational it can become rational.
514 -- If the curve was rational it can become non rational.
517 -- Raised if Index < 1 || Index > NbPoles
519 ---Purpose : Raised if Weight <= 0.0
521 MovePoint (me : mutable; U: Real; P: Pnt; Index1, Index2: Integer;
522 FirstModifiedPole, LastModifiedPole: out Integer)
523 ---Purpose : Moves the point of parameter U of this BSpline curve
524 -- to P. Index1 and Index2 are the indexes in the table
525 -- of poles of this BSpline curve of the first and last
526 -- poles designated to be moved.
527 -- FirstModifiedPole and LastModifiedPole are the
528 -- indexes of the first and last poles which are effectively modified.
529 -- In the event of incompatibility between Index1, Index2 and the value U:
530 -- - no change is made to this BSpline curve, and
531 -- - the FirstModifiedPole and LastModifiedPole are returned null.
533 -- Standard_OutOfRange if:
534 -- - Index1 is greater than or equal to Index2, or
535 -- - Index1 or Index2 is less than 1 or greater than the
536 -- number of poles of this BSpline curve.
539 MovePointAndTangent (me : mutable;
545 EndingCondition : Integer;
546 ErrorStatus : out Integer)
549 -- Move a point with parameter U to P.
550 -- and makes it tangent at U be Tangent.
551 -- StartingCondition = -1 means first can move
552 -- EndingCondition = -1 means last point can move
553 -- StartingCondition = 0 means the first point cannot move
554 -- EndingCondition = 0 means the last point cannot move
555 -- StartingCondition = 1 means the first point and tangent cannot move
556 -- EndingCondition = 1 means the last point and tangent cannot move
558 -- ErrorStatus != 0 means that there are not enought degree of freedom
559 -- with the constrain to deform the curve accordingly
563 IsCN (me; N : Integer) returns Boolean
565 -- Returns the continuity of the curve, the curve is at least C0.
567 ---Purpose : Raised if N < 0.
570 IsClosed (me) returns Boolean;
572 -- Returns true if the distance between the first point and the
573 -- last point of the curve is lower or equal to Resolution
576 -- The first and the last point can be different from the first
577 -- pole and the last pole of the curve.
580 IsPeriodic (me) returns Boolean;
581 ---Purpose : Returns True if the curve is periodic.
584 IsRational (me) returns Boolean;
586 -- Returns True if the weights are not identical.
587 -- The tolerance criterion is Epsilon of the class Real.
589 IsCacheValid(me; Parameter : Real) returns Boolean
592 -- Tells whether the Cache is valid for the
594 -- Warnings : the parameter must be normalized within
595 -- the period if the curve is periodic. Otherwise
596 -- the answer will be false
600 Continuity (me) returns Shape from GeomAbs;
602 -- Returns the global continuity of the curve :
603 -- C0 : only geometric continuity,
604 -- C1 : continuity of the first derivative all along the Curve,
605 -- C2 : continuity of the second derivative all along the Curve,
606 -- C3 : continuity of the third derivative all along the Curve,
607 -- CN : the order of continuity is infinite.
608 -- For a B-spline curve of degree d if a knot Ui has a
609 -- multiplicity p the B-spline curve is only Cd-p continuous
610 -- at Ui. So the global continuity of the curve can't be greater
611 -- than Cd-p where p is the maximum multiplicity of the interior
612 -- Knots. In the interior of a knot span the curve is infinitely
613 -- continuously differentiable.
616 Degree (me) returns Integer;
617 ---Purpose: Returns the degree of this BSpline curve.
618 -- The degree of a Geom_BSplineCurve curve cannot
619 -- be greater than Geom_BSplineCurve::MaxDegree().
621 ---Purpose : Computation of value and derivatives
623 D0 (me ; U : Real; P : out Pnt);
624 ---Purpose: Returns in P the point of parameter U.
626 D1 (me; U : Real; P : out Pnt; V1 : out Vec)
627 raises UndefinedDerivative;
628 ---Purpose : Raised if the continuity of the curve is not C1.
631 D2 (me; U : Real; P : out Pnt; V1, V2 : out Vec)
632 raises UndefinedDerivative;
633 ---Purpose : Raised if the continuity of the curve is not C2.
636 D3 (me; U : Real; P : out Pnt; V1, V2, V3 : out Vec)
637 raises UndefinedDerivative;
638 ---Purpose : Raised if the continuity of the curve is not C3.
641 DN (me; U : Real; N : Integer) returns Vec
642 ---Purpose : For the point of parameter U of this BSpline curve,
643 -- computes the vector corresponding to the Nth derivative.
645 -- On a point where the continuity of the curve is not the
646 -- one requested, this function impacts the part defined
647 -- by the parameter with a value greater than U, i.e. the
648 -- part of the curve to the "right" of the singularity.
650 -- Standard_RangeError if N is less than 1.
651 raises UndefinedDerivative,
655 -- The following functions compute the point of parameter U
656 -- and the derivatives at this point on the B-spline curve
657 -- arc defined between the knot FromK1 and the knot ToK2.
658 -- U can be out of bounds [Knot (FromK1), Knot (ToK2)] but
659 -- for the computation we only use the definition of the curve
660 -- between these two knots. This method is useful to compute
661 -- local derivative, if the order of continuity of the whole
662 -- curve is not greater enough. Inside the parametric
663 -- domain Knot (FromK1), Knot (ToK2) the evaluations are
664 -- the same as if we consider the whole definition of the
665 -- curve. Of course the evaluations are different outside
666 -- this parametric domain.
669 LocalValue (me; U : Real; FromK1, ToK2 : Integer) returns Pnt
671 ---Purpose : Raised if FromK1 = ToK2.
674 -- Raised if FromK1 and ToK2 are not in the range
675 -- [FirstUKnotIndex, LastUKnotIndex].
677 LocalD0 (me; U : Real; FromK1, ToK2 : Integer; P : out Pnt)
679 ---Purpose : Raised if FromK1 = ToK2.
682 -- Raised if FromK1 and ToK2 are not in the range
683 -- [FirstUKnotIndex, LastUKnotIndex].
685 LocalD1 (me; U : Real; FromK1, ToK2 : Integer; P : out Pnt; V1 : out Vec)
686 raises UndefinedDerivative,
688 -- Raised if the local continuity of the curve is not C1
689 -- between the knot K1 and the knot K2.
691 ---Purpose : Raised if FromK1 = ToK2.
694 -- Raised if FromK1 and ToK2 are not in the range
695 -- [FirstUKnotIndex, LastUKnotIndex].
698 LocalD2 (me; U : Real; FromK1, ToK2 : Integer; P : out Pnt; V1, V2 : out Vec)
699 raises UndefinedDerivative,
701 -- Raised if the local continuity of the curve is not C2
702 -- between the knot K1 and the knot K2.
704 ---Purpose : Raised if FromK1 = ToK2.
707 -- Raised if FromK1 and ToK2 are not in the range
708 -- [FirstUKnotIndex, LastUKnotIndex].
712 LocalD3 (me; U : Real; FromK1, ToK2 : Integer;
713 P : out Pnt; V1, V2, V3 : out Vec)
714 raises UndefinedDerivative,
716 -- Raised if the local continuity of the curve is not C3
717 -- between the knot K1 and the knot K2.
719 ---Purpose : Raised if FromK1 = ToK2.
722 -- Raised if FromK1 and ToK2 are not in the range
723 -- [FirstUKnotIndex, LastUKnotIndex].
726 LocalDN (me; U : Real; FromK1, ToK2 : Integer; N : Integer) returns Vec
727 raises UndefinedDerivative,
729 -- Raised if the local continuity of the curve is not CN
730 -- between the knot K1 and the knot K2.
732 ---Purpose : Raised if FromK1 = ToK2.
734 ---Purpose : Raised if N < 1.
737 -- Raises if FromK1 and ToK2 are not in the range
738 -- [FirstUKnotIndex, LastUKnotIndex].
741 EndPoint (me) returns Pnt;
743 -- Returns the last point of the curve.
745 -- The last point of the curve is different from the last
746 -- pole of the curve if the multiplicity of the last knot
747 -- is lower than Degree.
750 FirstUKnotIndex (me) returns Integer;
751 ---Purpose : Returns the index in the knot array of the knot
752 -- corresponding to the first or last parameter of this BSpline curve.
753 -- For a BSpline curve, the first (or last) parameter
754 -- (which gives the start (or end) point of the curve) is a
755 -- knot value. However, if the multiplicity of the first (or
756 -- last) knot is less than Degree + 1, where
757 -- Degree is the degree of the curve, it is not the first
758 -- (or last) knot of the curve.
761 FirstParameter (me) returns Real;
762 ---Purpose : Returns the value of the first parameter of this
763 -- BSpline curve. This is a knot value.
764 -- The first parameter is the one of the start point of the BSpline curve.
768 Knot (me; Index : Integer) returns Real
770 -- Returns the knot of range Index. When there is a knot
771 -- with a multiplicity greater than 1 the knot is not repeated.
772 -- The method Multiplicity can be used to get the multiplicity
775 ---Purpose : Raised if Index < 1 or Index > NbKnots
778 Knots (me; K : out Array1OfReal from TColStd)
779 ---Purpose : returns the knot values of the B-spline curve;
781 -- A knot with a multiplicity greater than 1 is not
782 -- repeated in the knot table. The Multiplicity function
783 -- can be used to obtain the multiplicity of each knot.
784 raises DimensionError;
786 -- Raised if the length of K is not equal to the number of knots.
789 KnotSequence (me; K : out Array1OfReal from TColStd)
790 ---Purpose : Returns K, the knots sequence of this BSpline curve.
791 -- In this sequence, knots with a multiplicity greater than 1 are repeated.
792 -- In the case of a non-periodic curve the length of the
793 -- sequence must be equal to the sum of the NbKnots
794 -- multiplicities of the knots of the curve (where
795 -- NbKnots is the number of knots of this BSpline
796 -- curve). This sum is also equal to : NbPoles + Degree + 1
797 -- where NbPoles is the number of poles and
798 -- Degree the degree of this BSpline curve.
799 -- In the case of a periodic curve, if there are k periodic
800 -- knots, the period is Knot(k+1) - Knot(1).
801 -- The initial sequence is built by writing knots 1 to k+1,
802 -- which are repeated according to their corresponding multiplicities.
803 -- If Degree is the degree of the curve, the degree of
804 -- continuity of the curve at the knot of index 1 (or k+1)
805 -- is equal to c = Degree + 1 - Mult(1). c
806 -- knots are then inserted at the beginning and end of
807 -- the initial sequence:
808 -- - the c values of knots preceding the first item
809 -- Knot(k+1) in the initial sequence are inserted
810 -- at the beginning; the period is subtracted from these c values;
811 -- - the c values of knots following the last item
812 -- Knot(1) in the initial sequence are inserted at
813 -- the end; the period is added to these c values.
814 -- The length of the sequence must therefore be equal to:
815 -- NbPoles + 2*Degree - Mult(1) + 2.
817 -- For a non-periodic BSpline curve of degree 2 where:
818 -- - the array of knots is: { k1 k2 k3 k4 },
819 -- - with associated multiplicities: { 3 1 2 3 },
820 -- the knot sequence is:
821 -- K = { k1 k1 k1 k2 k3 k3 k4 k4 k4 }
822 -- For a periodic BSpline curve of degree 4 , which is
823 -- "C1" continuous at the first knot, and where :
824 -- - the periodic knots are: { k1 k2 k3 (k4) }
825 -- (3 periodic knots: the points of parameter k1 and k4
826 -- are identical, the period is p = k4 - k1),
827 -- - with associated multiplicities: { 3 1 2 (3) },
828 -- the degree of continuity at knots k1 and k4 is:
829 -- Degree + 1 - Mult(i) = 2.
830 -- 2 supplementary knots are added at the beginning
831 -- and end of the sequence:
832 -- - at the beginning: the 2 knots preceding k4 minus
833 -- the period; in this example, this is k3 - p both times;
834 -- - at the end: the 2 knots following k1 plus the period;
835 -- in this example, this is k2 + p and k3 + p.
836 -- The knot sequence is therefore:
837 -- K = { k3-p k3-p k1 k1 k1 k2 k3 k3
838 -- k4 k4 k4 k2+p k3+p }
840 -- Standard_DimensionError if the array K is not of
841 -- the appropriate length.Returns the knots sequence.
842 raises DimensionError;
846 KnotDistribution (me) returns BSplKnotDistribution from GeomAbs;
848 -- Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier.
849 -- If all the knots differ by a positive constant from the
850 -- preceding knot the BSpline Curve can be :
851 -- - Uniform if all the knots are of multiplicity 1,
852 -- - QuasiUniform if all the knots are of multiplicity 1 except for
853 -- the first and last knot which are of multiplicity Degree + 1,
854 -- - PiecewiseBezier if the first and last knots have multiplicity
855 -- Degree + 1 and if interior knots have multiplicity Degree
856 -- A piecewise Bezier with only two knots is a BezierCurve.
857 -- else the curve is non uniform.
858 -- The tolerance criterion is Epsilon from class Real.
861 LastUKnotIndex (me) returns Integer;
863 -- For a BSpline curve the last parameter (which gives the
864 -- end point of the curve) is a knot value but if the
865 -- multiplicity of the last knot index is lower than
866 -- Degree + 1 it is not the last knot of the curve. This
867 -- method computes the index of the knot corresponding to
868 -- the last parameter.
871 LastParameter (me) returns Real;
873 -- Computes the parametric value of the end point of the curve.
874 -- It is a knot value.
879 ParametricTolerance : Real;
880 I1, I2 : in out Integer;
881 WithKnotRepetition : Boolean = Standard_False);
883 -- Locates the parametric value U in the sequence of knots.
884 -- If "WithKnotRepetition" is True we consider the knot's
885 -- representation with repetition of multiple knot value,
886 -- otherwise we consider the knot's representation with
887 -- no repetition of multiple knot values.
888 -- Knots (I1) <= U <= Knots (I2)
889 -- . if I1 = I2 U is a knot value (the tolerance criterion
890 -- ParametricTolerance is used).
891 -- . if I1 < 1 => U < Knots (1) - Abs(ParametricTolerance)
892 -- . if I2 > NbKnots => U > Knots (NbKnots) + Abs(ParametricTolerance)
895 Multiplicity (me; Index : Integer) returns Integer
897 -- Returns the multiplicity of the knots of range Index.
899 ---Purpose : Raised if Index < 1 or Index > NbKnots
902 Multiplicities (me; M : out Array1OfInteger from TColStd)
904 -- Returns the multiplicity of the knots of the curve.
905 raises DimensionError;
907 -- Raised if the length of M is not equal to NbKnots.
910 NbKnots (me) returns Integer;
912 -- Returns the number of knots. This method returns the number of
913 -- knot without repetition of multiple knots.
916 NbPoles (me) returns Integer;
917 ---Purpose : Returns the number of poles
920 Pole (me; Index : Integer) returns Pnt
921 ---Purpose : Returns the pole of range Index.
923 ---Purpose : Raised if Index < 1 or Index > NbPoles.
926 Poles (me; P : out Array1OfPnt from TColgp)
927 ---Purpose : Returns the poles of the B-spline curve;
928 raises DimensionError;
930 -- Raised if the length of P is not equal to the number of poles.
933 StartPoint (me) returns Pnt;
935 -- Returns the start point of the curve.
937 -- This point is different from the first pole of the curve if the
938 -- multiplicity of the first knot is lower than Degree.
941 Weight (me; Index : Integer) returns Real
942 ---Purpose : Returns the weight of the pole of range Index .
944 ---Purpose : Raised if Index < 1 or Index > NbPoles.
947 Weights (me; W : out Array1OfReal from TColStd)
948 ---Purpose : Returns the weights of the B-spline curve;
949 raises DimensionError;
951 -- Raised if the length of W is not equal to NbPoles.
959 Transform (me : mutable; T : Trsf);
960 ---Purpose: Applies the transformation T to this BSpline curve.
961 MaxDegree (myclass) returns Integer;
963 -- Returns the value of the maximum degree of the normalized
964 -- B-spline basis functions in this package.
966 Resolution(me : mutable;
968 UTolerance : out Real)
969 ---Purpose: Computes for this BSpline curve the parametric
970 -- tolerance UTolerance for a given 3D tolerance Tolerance3D.
971 -- If f(t) is the equation of this BSpline curve,
972 -- UTolerance ensures that:
973 -- | t1 - t0| < Utolerance ===>
974 -- |f(t1) - f(t0)| < Tolerance3D
977 Copy (me) returns mutable like me;
978 ---Purpose: Creates a new object which is a copy of this BSpline curve.
980 InvalidateCache(me : mutable)
981 ---Purpose : Invalidates the cache. This has to be private
982 -- this has to be private
985 UpdateKnots(me : mutable)
986 ---Purpose : Recompute the flatknots, the knotsdistribution, the continuity.
989 ValidateCache(me : mutable ; Parameter : Real)
992 ---Purpose : updates the cache and validates it
1002 knotSet : BSplKnotDistribution from GeomAbs;
1003 smooth : Shape from GeomAbs;
1005 poles : HArray1OfPnt from TColgp;
1006 weights : HArray1OfReal from TColStd;
1007 flatknots : HArray1OfReal from TColStd;
1008 knots : HArray1OfReal from TColStd;
1009 mults : HArray1OfInteger from TColStd;
1010 cachepoles : HArray1OfPnt from TColgp;
1011 -- Taylor expansion of the poles function, in homogeneous
1012 -- form if the curve is rational. The taylor expansion
1013 -- is normalized so that the span corresponds to
1015 cacheweights : HArray1OfReal from TColStd;
1016 -- Taylor expansion of the poles function, in homogeneous
1017 -- form if the curve is rational. The taylor expansion
1018 -- is normalized so that the span corresponds to
1020 validcache : Integer;
1021 -- = 1 the cache is valid
1022 -- = 0 the cache is invalid
1023 parametercache : Real;
1024 -- Parameter at which the Taylor expension is stored in
1026 spanlenghtcache : Real;
1027 -- Since the Taylor expansion is normalized in the
1028 -- cache to evaluate the cache one has to use
1029 -- (Parameter - parametercache) / nspanlenghtcache
1030 spanindexcache : Integer;
1031 -- the span for which the cache is valid if
1034 -- usefull to evaluate the parametric resolution
1035 maxderivinv : Real from Standard;
1036 maxderivinvok : Boolean from Standard;
projects / occt.git / blob