# FoundationClasses
TKMath
BSplCLib

# BSplCLib Class Reference

BSplCLib B-spline curve Library.
The BSplCLib package is a basic library for BSplines. It
provides three categories of functions.
* Management methods to process knots and multiplicities.
* Multi-Dimensions spline methods. BSpline methods where
poles have an arbitrary number of dimensions. They divides
in two groups :
- Global methods modifying the whole set of poles. The
poles are described by an array of Reals and a
Dimension. Example : Inserting knots.
- Local methods computing points and derivatives. The
poles are described by a pointer on a local array of
Reals and a Dimension. The local array is modified.
* 2D and 3D spline curves methods.
Methods for 2d and 3d BSplines curves rational or not
rational.
Those methods have the following structure :
- They extract the pole informations in a working array.
- They process the working array with the
multi-dimension methods. (for example a 3d rational
curve is processed as a 4 dimension curve).
- They get back the result in the original dimension.
Note that the bspline surface methods found in the
package BSplSLib uses the same structure and rely on
BSplCLib.
In the following list of methods the 2d and 3d curve
methods will be described with the corresponding
multi-dimension method.
The 3d or 2d B-spline curve is defined with :
. its control points : TColgp_Array1OfPnt(2d) Poles
. its weights : TColStd_Array1OfReal Weights
. its knots : TColStd_Array1OfReal Knots
. its multiplicities : TColStd_Array1OfInteger Mults
. its degree : Standard_Integer Degree
. its periodicity : Standard_Boolean Periodic
.

`#include <BSplCLib.hxx>`

## Public Member Functions

void * | operator new (size_t, void *anAddress)
void * | operator new (size_t size)
void | operator delete (void *anAddress)

## Static Public Member Functions

static Standard_EXPORT void | Hunt (const TColStd_Array1OfReal &XX, const Standard_Real X, Standard_Integer &Iloc)

This routine searches the position of the real
value X in the ordered set of real values XX.
The elements in the table XX are either
monotonically increasing or monotonically
decreasing.
The input value Iloc is used to initialize the
algorithm : if Iloc is outside of the bounds
[XX.Lower(), -- XX.Upper()] the bisection algorithm
is used else the routine searches from a previous
known position by increasing steps then converges
by bisection.
This routine is used to locate a knot value in a
set of knots.
.

static Standard_EXPORT Standard_Integer | FirstUKnotIndex (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults)
| Computes the index of the knots value which gives the start point of the curve. .
static Standard_EXPORT Standard_Integer | LastUKnotIndex (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults)
| Computes the index of the knots value which gives the end point of the curve. .
static Standard_EXPORT Standard_Integer | FlatIndex (const Standard_Integer Degree, const Standard_Integer Index, const TColStd_Array1OfInteger &Mults, const Standard_Boolean Periodic)
| Computes the index of the flats knots sequence corresponding to <index> in the knots sequence which multiplicities are <mults>. .
static Standard_EXPORT void | LocateParameter (const Standard_Integer Degree, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real U, const Standard_Boolean IsPeriodic, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Integer &KnotIndex, Standard_Real &NewU)

Locates the parametric value U in the knots
sequence between the knot K1 and the knot K2.
The value return in Index verifies.
Knots(Index) <= U < Knots(Index + 1)
if U <= Knots (K1) then Index = K1
if U >= Knots (K2) then Index = K2 - 1
If Periodic is True U may be modified to fit in
the range Knots(K1), Knots(K2). In any case the
correct value is returned in NewU.
Warnings :Index is used as input data to initialize the
searching function.
Warning: Knots have to be "withe repetitions"
.

static Standard_EXPORT void | LocateParameter (const Standard_Integer Degree, const TColStd_Array1OfReal &Knots, const Standard_Real U, const Standard_Boolean IsPeriodic, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Integer &KnotIndex, Standard_Real &NewU)

Locates the parametric value U in the knots
sequence between the knot K1 and the knot K2.
The value return in Index verifies.
Knots(Index) <= U < Knots(Index + 1)
if U <= Knots (K1) then Index = K1
if U >= Knots (K2) then Index = K2 - 1
If Periodic is True U may be modified to fit in
the range Knots(K1), Knots(K2). In any case the
correct value is returned in NewU.
Warnings :Index is used as input data to initialize the
searching function.
Warning: Knots have to be "flat"
.

static Standard_EXPORT void | LocateParameter (const Standard_Integer Degree, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real U, const Standard_Boolean Periodic, Standard_Integer &Index, Standard_Real &NewU)
static Standard_EXPORT Standard_Integer | MaxKnotMult (const TColStd_Array1OfInteger &Mults, const Standard_Integer K1, const Standard_Integer K2)
| Finds the greatest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value. .
static Standard_EXPORT Standard_Integer | MinKnotMult (const TColStd_Array1OfInteger &Mults, const Standard_Integer K1, const Standard_Integer K2)
| Finds the lowest multiplicity in a set of knots between K1 and K2. Mults is the multiplicity associated with each knot value. .
static Standard_EXPORT Standard_Integer | NbPoles (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfInteger &Mults)
| Returns the number of poles of the curve. Returns 0 if one of the multiplicities is incorrect. * Non positive. * Greater than Degree, or Degree+1 at the first and last knot of a non periodic curve. * The last periodicity on a periodic curve is not equal to the first. .
static Standard_EXPORT Standard_Integer | KnotSequenceLength (const TColStd_Array1OfInteger &Mults, const Standard_Integer Degree, const Standard_Boolean Periodic)
| Returns the length of the sequence of knots with repetition. Periodic : Sum(Mults(i), i = Mults.Lower(); i <= Mults.Upper()); Non Periodic : Sum(Mults(i); i = Mults.Lower(); i < Mults.Upper()) + 2 * Degree .
static Standard_EXPORT void | KnotSequence (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColStd_Array1OfReal &KnotSeq)
static Standard_EXPORT void | KnotSequence (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Integer Degree, const Standard_Boolean Periodic, TColStd_Array1OfReal &KnotSeq)
| Computes the sequence of knots KnotSeq with repetition of the knots of multiplicity greater than 1. Length of KnotSeq must be KnotSequenceLength(Mults,Degree,Periodic) .
static Standard_EXPORT Standard_Integer | KnotsLength (const TColStd_Array1OfReal &KnotSeq, const Standard_Boolean Periodic=Standard_False)
| Returns the length of the sequence of knots (and Mults) without repetition. .
static Standard_EXPORT void | Knots (const TColStd_Array1OfReal &KnotSeq, TColStd_Array1OfReal &Knots, TColStd_Array1OfInteger &Mults, const Standard_Boolean Periodic=Standard_False)
| Computes the sequence of knots Knots without repetition of the knots of multiplicity greater than 1. Length of <knots> and <mults> must be KnotsLength(KnotSequence,Periodic) .
static Standard_EXPORT BSplCLib_KnotDistribution | KnotForm (const TColStd_Array1OfReal &Knots, const Standard_Integer FromK1, const Standard_Integer ToK2)
| Analyses if the knots distribution is "Uniform" or "NonUniform" between the knot FromK1 and the knot ToK2. There is no repetition of knot in the knots'sequence <knots>. .
static Standard_EXPORT BSplCLib_MultDistribution | MultForm (const TColStd_Array1OfInteger &Mults, const Standard_Integer FromK1, const Standard_Integer ToK2)
| Analyses the distribution of multiplicities between the knot FromK1 and the Knot ToK2. .
static Standard_EXPORT void | Reparametrize (const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &Knots)
| Reparametrizes a B-spline curve to [U1, U2]. The knot values are recomputed such that Knots (Lower) = U1 and Knots (Upper) = U2 but the knot form is not modified. Warnings : In the array Knots the values must be in ascending order. U1 must not be equal to U2 to avoid division by zero. .
static Standard_EXPORT void | Reverse (TColStd_Array1OfReal &Knots)
| Reverses the array knots to become the knots sequence of the reversed curve. .
static Standard_EXPORT void | Reverse (TColStd_Array1OfInteger &Mults)
| Reverses the array of multiplicities. .
static Standard_EXPORT void | Reverse (TColgp_Array1OfPnt &Poles, const Standard_Integer Last)
| Reverses the array of poles. Last is the index of the new first pole. On a non periodic curve last is Poles.Upper(). On a periodic curve last is (number of flat knots - degree - 1) or (sum of multiplicities(but for the last) + degree - 1) .
static Standard_EXPORT void | Reverse (TColgp_Array1OfPnt2d &Poles, const Standard_Integer Last)
| Reverses the array of poles. .
static Standard_EXPORT void | Reverse (TColStd_Array1OfReal &Weights, const Standard_Integer Last)
| Reverses the array of poles. .
static Standard_EXPORT Standard_Boolean | IsRational (const TColStd_Array1OfReal &Weights, const Standard_Integer I1, const Standard_Integer I2, const Standard_Real Epsilon=0.0)
| Returns False if all the weights of the array <weights> between I1 an I2 are identic. Epsilon is used for comparing weights. If Epsilon is 0. the Epsilon of the first weight is used.
static Standard_EXPORT Standard_Integer | MaxDegree ()
| returns the degree maxima for a BSplineCurve. C++: inline
static Standard_EXPORT void | Eval (const Standard_Real U, const Standard_Integer Degree, Standard_Real &Knots, const Standard_Integer Dimension, Standard_Real &Poles)
| Perform the Boor algorithm to evaluate a point at parameter <u>, with <degree> and <dimension>. Poles is an array of Reals of size <dimension> * <degree>+1 Containing the poles. At the end <poles> contains the current point. .
static Standard_EXPORT void | BoorScheme (const Standard_Real U, const Standard_Integer Degree, Standard_Real &Knots, const Standard_Integer Dimension, Standard_Real &Poles, const Standard_Integer Depth, const Standard_Integer Length)

Performs the Boor Algorithm at parameter <u> with
the given <degree> and the array of <knots> on the
poles <poles> of dimension <dimension>. The schema
is computed until level <depth> on a basis of
<Length+1> poles.
* Knots is an array of reals of length :
<length> + <degree>
* Poles is an array of reals of length :
(2 * <length> + 1) * <dimension>
The poles values must be set in the array at the
positions.
0..Dimension,
2 * Dimension ..
3 * Dimension
4 * Dimension ..
5 * Dimension
...
The results are found in the array poles depending
on the Depth. (See the method GetPole).
.

static Standard_EXPORT Standard_Boolean | AntiBoorScheme (const Standard_Real U, const Standard_Integer Degree, Standard_Real &Knots, const Standard_Integer Dimension, Standard_Real &Poles, const Standard_Integer Depth, const Standard_Integer Length, const Standard_Real Tolerance)
| Compute the content of Pole before the BoorScheme. This method is used to remove poles. U is the poles to remove, Knots should contains the knots of the curve after knot removal. The first and last poles do not change, the other poles are computed by averaging two possible values. The distance between the two possible poles is computed, if it is higher than <tolerance> False is returned. .
static Standard_EXPORT void | Derivative (const Standard_Integer Degree, Standard_Real &Knots, const Standard_Integer Dimension, const Standard_Integer Length, const Standard_Integer Order, Standard_Real &Poles)
| Computes the poles of the BSpline giving the derivatives of order <order>. The formula for the first order is Pole(i) = Degree * (Pole(i+1) - Pole(i)) / (Knots(i+Degree+1) - Knots(i+1)) This formula is repeated (Degree is decremented at each step). .
static Standard_EXPORT void | Bohm (const Standard_Real U, const Standard_Integer Degree, const Standard_Integer N, Standard_Real &Knots, const Standard_Integer Dimension, Standard_Real &Poles)
| Performs the Bohm Algorithm at parameter <u>. This algorithm computes the value and all the derivatives up to order N (N <= Degree). <poles> is the original array of poles. The result in <poles> is the value and the derivatives. Poles[0] is the value, Poles[Degree] is the last derivative. .
static TColStd_Array1OfReal & | NoWeights ()
| Used as argument for a non rational curve. .
static TColStd_Array1OfInteger & | NoMults ()
| Used as argument for a flatknots evaluation. .
static Standard_EXPORT void | BuildKnots (const Standard_Integer Degree, const Standard_Integer Index, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, Standard_Real &LK)
| Stores in LK the usefull knots for the BoorSchem on the span Knots(Index) - Knots(Index+1) .
static Standard_EXPORT Standard_Integer | PoleIndex (const Standard_Integer Degree, const Standard_Integer Index, const Standard_Boolean Periodic, const TColStd_Array1OfInteger &Mults)
| Return the index of the first Pole to use on the span Mults(Index) - Mults(Index+1). This index must be added to Poles.Lower(). .
static Standard_EXPORT void | BuildEval (const Standard_Integer Degree, const Standard_Integer Index, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Weights, Standard_Real &LP)
static Standard_EXPORT void | BuildEval (const Standard_Integer Degree, const Standard_Integer Index, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, Standard_Real &LP)
static Standard_EXPORT void | BuildEval (const Standard_Integer Degree, const Standard_Integer Index, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, Standard_Real &LP)
| Copy in <lp> the poles and weights for the Eval scheme. starting from Poles(Poles.Lower()+Index) .
static Standard_EXPORT void | BuildBoor (const Standard_Integer Index, const Standard_Integer Length, const Standard_Integer Dimension, const TColStd_Array1OfReal &Poles, Standard_Real &LP)
| Copy in <lp> poles for <dimension> Boor scheme. Starting from <index> * <dimension>, copy <Length+1> poles. .
static Standard_EXPORT Standard_Integer | BoorIndex (const Standard_Integer Index, const Standard_Integer Length, const Standard_Integer Depth)
| Returns the index in the Boor result array of the poles <index>. If the Boor algorithm was perform with <length> and <depth>. .
static Standard_EXPORT void | GetPole (const Standard_Integer Index, const Standard_Integer Length, const Standard_Integer Depth, const Standard_Integer Dimension, Standard_Real &LocPoles, Standard_Integer &Position, TColStd_Array1OfReal &Pole)
| Copy the pole at position <index> in the Boor scheme of dimension <dimension> to <position> in the array <pole>. <position> is updated. .

static Standard_EXPORT Standard_Boolean

PrepareInsertKnots (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger &AddMults, Standard_Integer &NbPoles, Standard_Integer &NbKnots, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True)

Returns in <NbPoles, NbKnots> the new number of poles
and knots if the sequence of knots <AddKnots,
AddMults> is inserted in the sequence <Knots, Mults>.
Epsilon is used to compare knots for equality.
If Add is True the multiplicities on equal knots are
added.
If Add is False the max value of the multiplicities is
kept.
Return False if :
The knew knots are knot increasing.
The new knots are not in the range.
.

static Standard_EXPORT void

InsertKnots (const Standard_Integer Degree, const Standard_Boolean Periodic, const Standard_Integer Dimension, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger &AddMults, TColStd_Array1OfReal &NewPoles, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True)

static Standard_EXPORT void

InsertKnots (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger &AddMults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal &NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True)

static Standard_EXPORT void

InsertKnots (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger &AddMults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal &NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True)

Insert a sequence of knots <addknots> with
multiplicities <addmults>. <addknots> must be a non
decreasing sequence and verifies :
Knots(Knots.Lower()) <= AddKnots(AddKnots.Lower())
Knots(Knots.Upper()) >= AddKnots(AddKnots.Upper())
The NewPoles and NewWeights arrays must have a length :
Poles.Length() + Sum(AddMults())
When a knot to insert is identic to an existing knot the
multiplicities are added.
Epsilon is used to test knots for equality.
When AddMult is negative or null the knot is not inserted.
No multiplicity will becomes higher than the degree.
The new Knots and Multiplicities are copied in <newknots>
and <newmults>.
All the New arrays should be correctly dimensioned.
When all the new knots are existing knots, i.e. only the
multiplicities will change it is safe to use the same
arrays as input and output.
.

static Standard_EXPORT void | InsertKnot (const Standard_Integer UIndex, const Standard_Real U, const Standard_Integer UMult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal &NewWeights)
static Standard_EXPORT void | InsertKnot (const Standard_Integer UIndex, const Standard_Real U, const Standard_Integer UMult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal &NewWeights)
| Insert a new knot U of multiplicity UMult in the knot sequence. The location of the new Knot should be given as an input data. UIndex locates the new knot U in the knot sequence and Knots (UIndex) < U < Knots (UIndex + 1). The new control points corresponding to this insertion are returned. Knots and Mults are not updated. .
static Standard_EXPORT void | RaiseMultiplicity (const Standard_Integer KnotIndex, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal &NewWeights)
static Standard_EXPORT void | RaiseMultiplicity (const Standard_Integer KnotIndex, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal &NewWeights)
| Raise the multiplicity of knot to <umult>. The new control points are returned. Knots and Mults are not updated. .

static Standard_EXPORT Standard_Boolean

RemoveKnot (const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const Standard_Integer Dimension, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColStd_Array1OfReal &NewPoles, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Tolerance)

static Standard_EXPORT Standard_Boolean

RemoveKnot (const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal &NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Tolerance)

static Standard_EXPORT Standard_Boolean

RemoveKnot (const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal &NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Tolerance)

Decrement the multiplicity of <Knots(Index)>
to <mult>. If <mult> is null the knot is
removed.
As there are two ways to compute the new poles
the midlle will be used as long as the
distance is lower than Tolerance.
If a distance is bigger than tolerance the
methods returns False and the new arrays are
not modified.
A low tolerance can be used to test if the
knot can be removed without modifying the
curve.
A high tolerance can be used to "smooth" the
curve.
.

static Standard_EXPORT Standard_Integer | IncreaseDegreeCountKnots (const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColStd_Array1OfInteger &Mults)
| Returns the number of knots of a curve with multiplicities <mults> after elevating the degree from <degree> to <newdegree>. See the IncreaseDegree method for more comments. .
static Standard_EXPORT void | IncreaseDegree (const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const Standard_Integer Dimension, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColStd_Array1OfReal &NewPoles, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults)

static Standard_EXPORT void

IncreaseDegree (const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal &NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults)

static Standard_EXPORT void

IncreaseDegree (const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal &NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults)

static Standard_EXPORT void | IncreaseDegree (const Standard_Integer NewDegree, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal &NewWeights)
static Standard_EXPORT void | IncreaseDegree (const Standard_Integer NewDegree, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal &NewWeights)

Increase the degree of a bspline (or bezier) curve
of dimension <dimension> form <degree> to
<newdegree>.
The number of poles in the new curve is :
Poles.Length() + (NewDegree - Degree) * Number of spans
Where the number of spans is :
LastUKnotIndex(Mults) - FirstUKnotIndex(Mults) + 1
for a non-periodic curve
And Knots.Length() - 1 for a periodic curve.
The multiplicities of all knots are increased by
the degree elevation.
The new knots are usually the same knots with the
exception of a non-periodic curve with the first
and last multiplicity not equal to Degree+1 where
knots are removed form the start and the bottom
untils the sum of the multiplicities is equal to
NewDegree+1 at the knots corresponding to the
first and last parameters of the curve.
Example : Suppose a curve of degree 3 starting
with following knots and multiplicities :
knot : 0. 1. 2.
mult : 1 2 1
The FirstUKnot is 2. because the sum of
multiplicities is Degree+1 : 1 + 2 + 1 = 4 = 3 + 1
i.e. the first parameter of the curve is 2. and
will still be 2. after degree elevation. Let
raises this curve to degree 4. The multiplicities
are increased by 2.
They become 2 3 2. But we need a sum of
multiplicities of 5 at knot 2. So the first knot
is removed and the new knots are :
knot : 1. 2.
mult : 3 2
The multipicity of the first knot may also be
reduced if the sum is still to big.
In the most common situations (periodic curve or
curve with first and last multiplicities equals to
Degree+1) the knots are knot changes.
The method IncreaseDegreeCountKnots can be used to
compute the new number of knots.
.

static Standard_EXPORT void | PrepareUnperiodize (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults, Standard_Integer &NbKnots, Standard_Integer &NbPoles)
| Set in <nbknots> and <nbpolestoadd> the number of Knots and Poles of the NotPeriodic Curve identical at the periodic curve with a degree <degree> , a knots-distribution with Multiplicities <mults>. .
static Standard_EXPORT void | Unperiodize (const Standard_Integer Degree, const Standard_Integer Dimension, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfReal &Poles, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfReal &NewPoles)
static Standard_EXPORT void | Unperiodize (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Knots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewKnots, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal &NewWeights)
static Standard_EXPORT void | Unperiodize (const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Knots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewKnots, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal &NewWeights)
static Standard_EXPORT void | PrepareTrimming (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real U1, const Standard_Real U2, Standard_Integer &NbKnots, Standard_Integer &NbPoles)
| Set in <nbknots> and <nbpoles> the number of Knots and Poles of the curve resulting of the trimming of the BSplinecurve definded with <degree>, <knots>, <mults> .
static Standard_EXPORT void | Trimming (const Standard_Integer Degree, const Standard_Boolean Periodic, const Standard_Integer Dimension, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Poles, const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewPoles)

static Standard_EXPORT void

Trimming (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, TColgp_Array1OfPnt &NewPoles, TColStd_Array1OfReal &NewWeights)

static Standard_EXPORT void

Trimming (const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, TColgp_Array1OfPnt2d &NewPoles, TColStd_Array1OfReal &NewWeights)

static Standard_EXPORT void | D0 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, Standard_Real &P)
static Standard_EXPORT void | D0 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Pnt &P)
static Standard_EXPORT void | D0 (const Standard_Real U, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Pnt2d &P)
static Standard_EXPORT void | D0 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &P)
static Standard_EXPORT void | D0 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &P)
static Standard_EXPORT void | D1 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, Standard_Real &P, Standard_Real &V)
static Standard_EXPORT void | D1 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Pnt &P, gp_Vec &V)
static Standard_EXPORT void | D1 (const Standard_Real U, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Pnt2d &P, gp_Vec2d &V)
static Standard_EXPORT void | D1 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &P, gp_Vec &V)
static Standard_EXPORT void | D1 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &P, gp_Vec2d &V)
static Standard_EXPORT void | D2 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, Standard_Real &P, Standard_Real &V1, Standard_Real &V2)
static Standard_EXPORT void | D2 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)
static Standard_EXPORT void | D2 (const Standard_Real U, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)
static Standard_EXPORT void | D2 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)
static Standard_EXPORT void | D2 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)
static Standard_EXPORT void | D3 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, Standard_Real &P, Standard_Real &V1, Standard_Real &V2, Standard_Real &V3)
static Standard_EXPORT void | D3 (const Standard_Real U, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)
static Standard_EXPORT void | D3 (const Standard_Real U, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)
static Standard_EXPORT void | D3 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)
static Standard_EXPORT void | D3 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)
static Standard_EXPORT void | DN (const Standard_Real U, const Standard_Integer N, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, Standard_Real &VN)
static Standard_EXPORT void | DN (const Standard_Real U, const Standard_Integer N, const Standard_Integer Index, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Vec &VN)
static Standard_EXPORT void | DN (const Standard_Real U, const Standard_Integer N, const Standard_Integer UIndex, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, gp_Vec2d &V)
static Standard_EXPORT void | DN (const Standard_Real U, const Standard_Integer N, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &P, gp_Vec &VN)
static Standard_EXPORT void | DN (const Standard_Real U, const Standard_Integer N, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &P, gp_Vec2d &VN)

The above functions compute values and
derivatives in the following situations :
* 3D, 2D and 1D
* Rational or not Rational.
* Knots and multiplicities or "flat knots" without
multiplicities.
* The <index> is the the localization of the
parameter in the knot sequence. If <index> is out
of range the correct value will be searched.
VERY IMPORTANT!!!
USE BSplCLib::NoWeights() as Weights argument for non
rational curves computations.
.

static Standard_EXPORT Standard_Integer | EvalBsplineBasis (const Standard_Integer Side, const Standard_Integer DerivativeOrder, const Standard_Integer Order, const TColStd_Array1OfReal &FlatKnots, const Standard_Real Parameter, Standard_Integer &FirstNonZeroBsplineIndex, math_Matrix &BsplineBasis)

This evaluates the Bspline Basis at a
given parameter Parameter up to the
requested DerivativeOrder and store the
result in the array BsplineBasis in the
following fashion
BSplineBasis(1,1) =
value of first non vanishing
Bspline function which has Index FirstNonZeroBsplineIndex
BsplineBasis(1,2) =
value of second non vanishing
Bspline function which has Index
FirstNonZeroBsplineIndex + 1
BsplineBasis(1,n) =
value of second non vanishing non vanishing
Bspline function which has Index
FirstNonZeroBsplineIndex + n (n <= Order)
BSplineBasis(2,1) =
value of derivative of first non vanishing
Bspline function which has Index FirstNonZeroBsplineIndex
BSplineBasis(N,1) =
value of Nth derivative of first non vanishing
Bspline function which has Index FirstNonZeroBsplineIndex
if N <= DerivativeOrder + 1
.

static Standard_EXPORT Standard_Integer | BuildBSpMatrix (const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &OrderArray, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer Degree, math_Matrix &Matrix, Standard_Integer &UpperBandWidth, Standard_Integer &LowerBandWidth)
| This Builds a fully blown Matrix of (ni) Bi (tj) with i and j within 1..Order + NumPoles The integer ni is the ith slot of the array OrderArray, tj is the jth slot of the array Parameters .
static Standard_EXPORT Standard_Integer | FactorBandedMatrix (math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, Standard_Integer &PivotIndexProblem)
| this factors the Banded Matrix in the LU form with a Banded storage of components of the L matrix WARNING : do not use if the Matrix is totally positive (It is the case for Bspline matrices build as above with parameters being the Schoenberg points
static Standard_EXPORT Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, const Standard_Integer ArrayDimension, Standard_Real &Array)
| This solves the system Matrix.X = B with when Matrix is factored in LU form The Array is an seen as an Array[1..N][1..ArrayDimension] with N = the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension .
static Standard_EXPORT Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, TColgp_Array1OfPnt2d &Array)
| This solves the system Matrix.X = B with when Matrix is factored in LU form The Array has the length of the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension .
static Standard_EXPORT Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, TColgp_Array1OfPnt &Array)
| This solves the system Matrix.X = B with when Matrix is factored in LU form The Array has the length of the rank of the matrix Matrix. The result is stored in Array when each coordinate is solved that is B is the array whose values are B[i] = Array[i][p] for each p in 1..ArrayDimension .
static Standard_EXPORT Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, const Standard_Boolean HomogenousFlag, const Standard_Integer ArrayDimension, Standard_Real &Array, Standard_Real &Weights)
static Standard_EXPORT Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, const Standard_Boolean HomogenousFlag, TColgp_Array1OfPnt2d &Array, TColStd_Array1OfReal &Weights)

This solves the system Matrix.X = B
with when Matrix is factored in LU form
The Array is an seen as an
Array[1..N][1..ArrayDimension] with N =
the rank of the matrix Matrix. The
result is stored in Array when each
coordinate is solved that is B is the
array whose values are B[i] =
Array[i][p] for each p in
1..ArrayDimension. If HomogeneousFlag ==
0 the Poles are multiplied by the
Weights uppon Entry and once
interpolation is carried over the
result of the poles are divided by the
result of the interpolation of the
weights. Otherwise if HomogenousFlag == 1
the Poles and Weigths are treated homogenously
that is that those are interpolated as they
are and result is returned without division
by the interpolated weigths.
.

static Standard_EXPORT Standard_Integer | SolveBandedSystem (const math_Matrix &Matrix, const Standard_Integer UpperBandWidth, const Standard_Integer LowerBandWidth, const Standard_Boolean HomogeneousFlag, TColgp_Array1OfPnt &Array, TColStd_Array1OfReal &Weights)

This solves the system Matrix.X = B
with when Matrix is factored in LU form
The Array is an seen as an
Array[1..N][1..ArrayDimension] with N =
the rank of the matrix Matrix. The
result is stored in Array when each
coordinate is solved that is B is the
array whose values are
B[i] = Array[i][p] for each p in 1..ArrayDimension
If HomogeneousFlag ==
0 the Poles are multiplied by the
Weights uppon Entry and once
interpolation is carried over the
result of the poles are divided by the
result of the interpolation of the
weights. Otherwise if HomogenousFlag == 1
the Poles and Weigths are treated homogenously
that is that those are interpolated as they
are and result is returned without division
by the interpolated weigths.
.

static Standard_EXPORT void

MergeBSplineKnots (const Standard_Real Tolerance, const Standard_Real StartValue, const Standard_Real EndValue, const Standard_Integer Degree1, const TColStd_Array1OfReal &Knots1, const TColStd_Array1OfInteger &Mults1, const Standard_Integer Degree2, const TColStd_Array1OfReal &Knots2, const TColStd_Array1OfInteger &Mults2, Standard_Integer &NumPoles, Handle(TColStd_HArray1OfReal)&NewKnots, Handle(TColStd_HArray1OfInteger)&NewMults)

| Merges two knot vector by setting the starting and ending values to StartValue and EndValue .
static Standard_EXPORT void | FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const Standard_Integer PolesDimension, Standard_Real &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, Standard_Real &NewPoles, Standard_Integer &Status)
| This function will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following: .
static Standard_EXPORT void | FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColStd_Array1OfReal &NewPoles, Standard_Integer &Status)
| This function will compose a given Vectorial BSpline F(t) defined by its BSplineDegree and BSplineFlatKnotsl, its Poles array which are coded as an array of Real of the form [1..NumPoles][1..PolesDimension] with a function a(t) which is assumed to satisfy the following: .
static Standard_EXPORT void | FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColgp_Array1OfPnt &NewPoles, Standard_Integer &Status)

this will compose a given Vectorial BSpline F(t)
defined by its BSplineDegree and BSplineFlatKnotsl,
its Poles array which are coded as an array of Real
of the form [1..NumPoles][1..PolesDimension] with a
function a(t) which is assumed to satisfy the
following : 1. F(a(t)) is a polynomial BSpline
that can be expressed exactly as a BSpline of degree
NewDegree on the knots FlatKnots
2. a(t) defines a differentiable
isomorphism between the range of FlatKnots to the range
of BSplineFlatKnots which is the
same as the range of F(t)
Warning: it is
the caller's responsability to insure that conditions
1. and 2. above are satisfied : no check whatsoever
is made in this method
Status will return 0 if OK else it will return the pivot index
of the matrix that was inverted to compute the multiplied
BSpline : the method used is interpolation at Schoenenberg
points of F(a(t))

static Standard_EXPORT void | FunctionReparameterise (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColgp_Array1OfPnt2d &NewPoles, Standard_Integer &Status)

this will compose a given Vectorial BSpline F(t)
defined by its BSplineDegree and BSplineFlatKnotsl,
its Poles array which are coded as an array of Real
of the form [1..NumPoles][1..PolesDimension] with a
function a(t) which is assumed to satisfy the
following : 1. F(a(t)) is a polynomial BSpline
that can be expressed exactly as a BSpline of degree
NewDegree on the knots FlatKnots
2. a(t) defines a differentiable
isomorphism between the range of FlatKnots to the range
of BSplineFlatKnots which is the
same as the range of F(t)
Warning: it is
the caller's responsability to insure that conditions
1. and 2. above are satisfied : no check whatsoever
is made in this method
Status will return 0 if OK else it will return the pivot index
of the matrix that was inverted to compute the multiplied
BSpline : the method used is interpolation at Schoenenberg
points of F(a(t))

static Standard_EXPORT void | FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const Standard_Integer PolesDimension, Standard_Real &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, Standard_Real &NewPoles, Standard_Integer &Status)

this will multiply a given Vectorial BSpline F(t)
defined by its BSplineDegree and BSplineFlatKnotsl,
its Poles array which are coded as an array of Real
of the form [1..NumPoles][1..PolesDimension] by a
function a(t) which is assumed to satisfy the
following : 1. a(t) * F(t) is a polynomial BSpline
that can be expressed exactly as a BSpline of degree
NewDegree on the knots FlatKnots 2. the range of a(t)
is the same as the range of F(t)
Warning: it is
the caller's responsability to insure that conditions
1. and 2. above are satisfied : no check whatsoever
is made in this method
Status will return 0 if OK else it will return the pivot index
of the matrix that was inverted to compute the multiplied
BSpline : the method used is interpolation at Schoenenberg
points of a(t)*F(t)

static Standard_EXPORT void | FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColStd_Array1OfReal &NewPoles, Standard_Integer &Status)

this will multiply a given Vectorial BSpline F(t)
defined by its BSplineDegree and BSplineFlatKnotsl,
its Poles array which are coded as an array of Real
of the form [1..NumPoles][1..PolesDimension] by a
function a(t) which is assumed to satisfy the
following : 1. a(t) * F(t) is a polynomial BSpline
that can be expressed exactly as a BSpline of degree
NewDegree on the knots FlatKnots 2. the range of a(t)
is the same as the range of F(t)
Warning: it is
the caller's responsability to insure that conditions
1. and 2. above are satisfied : no check whatsoever
is made in this method
Status will return 0 if OK else it will return the pivot index
of the matrix that was inverted to compute the multiplied
BSpline : the method used is interpolation at Schoenenberg
points of a(t)*F(t)

static Standard_EXPORT void | FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColgp_Array1OfPnt2d &NewPoles, Standard_Integer &Status)

this will multiply a given Vectorial BSpline F(t)
defined by its BSplineDegree and BSplineFlatKnotsl,
its Poles array which are coded as an array of Real
of the form [1..NumPoles][1..PolesDimension] by a
function a(t) which is assumed to satisfy the
following : 1. a(t) * F(t) is a polynomial BSpline
that can be expressed exactly as a BSpline of degree
NewDegree on the knots FlatKnots 2. the range of a(t)
is the same as the range of F(t)
Warning: it is
the caller's responsability to insure that conditions
1. and 2. above are satisfied : no check whatsoever
is made in this method
Status will return 0 if OK else it will return the pivot index
of the matrix that was inverted to compute the multiplied
BSpline : the method used is interpolation at Schoenenberg
points of a(t)*F(t)

static Standard_EXPORT void | FunctionMultiply (const BSplCLib_EvaluatorFunction &Function, const Standard_Integer BSplineDegree, const TColStd_Array1OfReal &BSplineFlatKnots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer NewDegree, TColgp_Array1OfPnt &NewPoles, Standard_Integer &Status)

this will multiply a given Vectorial BSpline F(t)
defined by its BSplineDegree and BSplineFlatKnotsl,
its Poles array which are coded as an array of Real
of the form [1..NumPoles][1..PolesDimension] by a
function a(t) which is assumed to satisfy the
following : 1. a(t) * F(t) is a polynomial BSpline
that can be expressed exactly as a BSpline of degree
NewDegree on the knots FlatKnots 2. the range of a(t)
is the same as the range of F(t)
Warning: it is
the caller's responsability to insure that conditions
1. and 2. above are satisfied : no check whatsoever
is made in this method
Status will return 0 if OK else it will return the pivot index
of the matrix that was inverted to compute the multiplied
BSpline : the method used is interpolation at Schoenenberg
points of a(t)*F(t)
--

static Standard_EXPORT void | Eval (const Standard_Real U, const Standard_Boolean PeriodicFlag, const Standard_Integer DerivativeRequest, Standard_Integer &ExtrapMode, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer ArrayDimension, Standard_Real &Poles, Standard_Real &Result)

Perform the De Boor algorithm to evaluate a point at
parameter <u>, with <degree> and <dimension>.
Poles is an array of Reals of size
<dimension> * <degree>+1
Containing the poles. At the end <poles> contains
the current point. Poles Contain all the poles of
the BsplineCurve, Knots also Contains all the knots
of the BsplineCurve. ExtrapMode has two slots [0] =
Degree used to extrapolate before the first knot [1]
= Degre used to extrapolate after the last knot has
to be between 1 and Degree
.

static Standard_EXPORT void | Eval (const Standard_Real U, const Standard_Boolean PeriodicFlag, const Standard_Integer DerivativeRequest, Standard_Integer &ExtrapMode, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer ArrayDimension, Standard_Real &Poles, Standard_Real &Weights, Standard_Real &PolesResult, Standard_Real &WeightsResult)

Perform the De Boor algorithm to evaluate a point at
parameter <u>, with <degree> and <dimension>.
Evaluates by multiplying the Poles by the Weights and
gives the homogeneous result in PolesResult that is
the results of the evaluation of the numerator once it
has been multiplied by the weights and in
WeightsResult one has the result of the evaluation of
the denominator
Warning: <polesresult> and <weightsresult> must be dimensionned
properly.
.

static Standard_EXPORT void | Eval (const Standard_Real U, const Standard_Boolean PeriodicFlag, const Standard_Boolean HomogeneousFlag, Standard_Integer &ExtrapMode, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point, Standard_Real &Weight)
| Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point .
static Standard_EXPORT void | Eval (const Standard_Real U, const Standard_Boolean PeriodicFlag, const Standard_Boolean HomogeneousFlag, Standard_Integer &ExtrapMode, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point, Standard_Real &Weight)
| Perform the evaluation of the Bspline Basis and then multiplies by the weights this just evaluates the current point .

static Standard_EXPORT void

TangExtendToConstraint (const TColStd_Array1OfReal &FlatKnots, const Standard_Real C1Coefficient, const Standard_Integer NumPoles, Standard_Real &Poles, const Standard_Integer Dimension, const Standard_Integer Degree, const TColStd_Array1OfReal &ConstraintPoint, const Standard_Integer Continuity, const Standard_Boolean After, Standard_Integer &NbPolesResult, Standard_Integer &NbKnotsRsult, Standard_Real &KnotsResult, Standard_Real &PolesResult)

| Extend a BSpline nD using the tangency map <c1coefficient> is the coefficient of reparametrisation <continuity> must be equal to 1, 2 or 3. <degree> must be greater or equal than <continuity> + 1. Warning: <knotsresult> and <polesresult> must be dimensionned properly. .
static Standard_EXPORT void | CacheD0 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point)

Perform the evaluation of the of the cache
the parameter must be normalized between
the 0 and 1 for the span.
The Cache must be valid when calling this
routine. Geom Package will insure that.
and then multiplies by the weights
this just evaluates the current point
the CacheParameter is where the Cache was
constructed the SpanLength is to normalize
the polynomial in the cache to avoid bad conditioning
effects
.

static Standard_EXPORT void | CacheD0 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point)

Perform the evaluation of the Bspline Basis
and then multiplies by the weights
this just evaluates the current point
the parameter must be normalized between
the 0 and 1 for the span.
The Cache must be valid when calling this
routine. Geom Package will insure that.
and then multiplies by the weights
ththe CacheParameter is where the Cache was
constructed the SpanLength is to normalize
the polynomial in the cache to avoid bad conditioning
effectsis just evaluates the current point
.

static Standard_EXPORT void | CoefsD0 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point)
| Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! C++: inline .
static Standard_EXPORT void | CoefsD0 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point)
| Calls CacheD0 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! C++: inline .
static Standard_EXPORT void | CacheD1 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point, gp_Vec &Vec)

Perform the evaluation of the of the cache
the parameter must be normalized between
the 0 and 1 for the span.
The Cache must be valid when calling this
routine. Geom Package will insure that.
and then multiplies by the weights
this just evaluates the current point
the CacheParameter is where the Cache was
constructed the SpanLength is to normalize
the polynomial in the cache to avoid bad conditioning
effects
.

static Standard_EXPORT void | CacheD1 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point, gp_Vec2d &Vec)

Perform the evaluation of the Bspline Basis
and then multiplies by the weights
this just evaluates the current point
the parameter must be normalized between
the 0 and 1 for the span.
The Cache must be valid when calling this
routine. Geom Package will insure that.
and then multiplies by the weights
ththe CacheParameter is where the Cache was
constructed the SpanLength is to normalize
the polynomial in the cache to avoid bad conditioning
effectsis just evaluates the current point
.

static Standard_EXPORT void | CoefsD1 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point, gp_Vec &Vec)
| Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! C++: inline .
static Standard_EXPORT void | CoefsD1 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point, gp_Vec2d &Vec)
| Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! C++: inline .
static Standard_EXPORT void | CacheD2 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &Vec2)

Perform the evaluation of the of the cache
the parameter must be normalized between
the 0 and 1 for the span.
The Cache must be valid when calling this
routine. Geom Package will insure that.
and then multiplies by the weights
this just evaluates the current point
the CacheParameter is where the Cache was
constructed the SpanLength is to normalize
the polynomial in the cache to avoid bad conditioning
effects
.

static Standard_EXPORT void | CacheD2 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &Vec2)

Perform the evaluation of the Bspline Basis
and then multiplies by the weights
this just evaluates the current point
the parameter must be normalized between
the 0 and 1 for the span.
The Cache must be valid when calling this
routine. Geom Package will insure that.
and then multiplies by the weights
ththe CacheParameter is where the Cache was
constructed the SpanLength is to normalize
the polynomial in the cache to avoid bad conditioning
effectsis just evaluates the current point
.

static Standard_EXPORT void | CoefsD2 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &Vec2)
| Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! C++: inline .
static Standard_EXPORT void | CoefsD2 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &Vec2)
| Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! C++: inline .
static Standard_EXPORT void | CacheD3 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &Vec2, gp_Vec &Vec3)

Perform the evaluation of the of the cache
the parameter must be normalized between
the 0 and 1 for the span.
The Cache must be valid when calling this
routine. Geom Package will insure that.
and then multiplies by the weights
this just evaluates the current point
the CacheParameter is where the Cache was
constructed the SpanLength is to normalize
the polynomial in the cache to avoid bad conditioning
effects
.

static Standard_EXPORT void | CacheD3 (const Standard_Real U, const Standard_Integer Degree, const Standard_Real CacheParameter, const Standard_Real SpanLenght, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &Vec2, gp_Vec2d &Vec3)

Perform the evaluation of the Bspline Basis
and then multiplies by the weights
this just evaluates the current point
the parameter must be normalized between
the 0 and 1 for the span.
The Cache must be valid when calling this
routine. Geom Package will insure that.
and then multiplies by the weights
ththe CacheParameter is where the Cache was
constructed the SpanLength is to normalize
the polynomial in the cache to avoid bad conditioning
effectsis just evaluates the current point
.

static Standard_EXPORT void | CoefsD3 (const Standard_Real U, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt &Point, gp_Vec &Vec1, gp_Vec &Vec2, gp_Vec &Vec3)
| Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! C++: inline .
static Standard_EXPORT void | CoefsD3 (const Standard_Real U, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, gp_Pnt2d &Point, gp_Vec2d &Vec1, gp_Vec2d &Vec2, gp_Vec2d &Vec3)
| Calls CacheD1 for Bezier Curves Arrays computed with the method PolesCoefficients. Warning: To be used for Beziercurves ONLY!!! C++: inline .
static Standard_EXPORT void | BuildCache (const Standard_Real U, const Standard_Real InverseOfSpanDomain, const Standard_Boolean PeriodicFlag, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, TColgp_Array1OfPnt &CachePoles, TColStd_Array1OfReal &CacheWeights)
| Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expension for the numerator and stores it in CachePoles .
static Standard_EXPORT void | BuildCache (const Standard_Real U, const Standard_Real InverseOfSpanDomain, const Standard_Boolean PeriodicFlag, const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, TColgp_Array1OfPnt2d &CachePoles, TColStd_Array1OfReal &CacheWeights)
| Perform the evaluation of the Taylor expansion of the Bspline normalized between 0 and 1. If rational computes the homogeneous Taylor expension for the numerator and stores it in CachePoles .
static Standard_EXPORT void | PolesCoefficients (const TColgp_Array1OfPnt2d &Poles, TColgp_Array1OfPnt2d &CachePoles)
static Standard_EXPORT void | PolesCoefficients (const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, TColgp_Array1OfPnt2d &CachePoles, TColStd_Array1OfReal &CacheWeights)
static Standard_EXPORT void | PolesCoefficients (const TColgp_Array1OfPnt &Poles, TColgp_Array1OfPnt &CachePoles)
static Standard_EXPORT void | PolesCoefficients (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, TColgp_Array1OfPnt &CachePoles, TColStd_Array1OfReal &CacheWeights)
| Encapsulation of BuildCache to perform the evaluation of the Taylor expansion for beziercurves at parameter 0. Warning: To be used for Beziercurves ONLY!!! .
static Standard_EXPORT void | BuildSchoenbergPoints (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, TColStd_Array1OfReal &Parameters)
| builds the Schoenberg points from the flat knot used to interpolate a BSpline since the BSpline matrix is invertible.
static Standard_EXPORT void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, TColgp_Array1OfPnt &Poles, Standard_Integer &InversionProblem)

Performs the interpolation of the data given in
the Poles array according to the requests in
ContactOrderArray that is : if
ContactOrderArray(i) has value d it means that
Poles(i) containes the dth derivative of the
function to be interpolated. The length L of the
following arrays must be the same :
Parameters, ContactOrderArray, Poles,
The length of FlatKnots is Degree + L + 1
Warning:
the method used to do that interpolation is
gauss elimination WITHOUT pivoting. Thus if the
diagonal is not dominant there is no guarantee
that the algorithm will work. Nevertheless for
Cubic interpolation or interpolation at Scheonberg
points the method will work
The InversionProblem will report 0 if there was no
problem else it will give the index of the faulty
pivot
.

static Standard_EXPORT void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, TColgp_Array1OfPnt2d &Poles, Standard_Integer &InversionProblem)

Performs the interpolation of the data given in
the Poles array according to the requests in
ContactOrderArray that is : if
ContactOrderArray(i) has value d it means that
Poles(i) containes the dth derivative of the
function to be interpolated. The length L of the
following arrays must be the same :
Parameters, ContactOrderArray, Poles,
The length of FlatKnots is Degree + L + 1
Warning:
the method used to do that interpolation is
gauss elimination WITHOUT pivoting. Thus if the
diagonal is not dominant there is no guarantee
that the algorithm will work. Nevertheless for
Cubic interpolation at knots or interpolation at Scheonberg
points the method will work.
The InversionProblem w
ll report 0 if there was no
problem else it will give the index of the faulty
pivot
.

static Standard_EXPORT void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, TColgp_Array1OfPnt &Poles, TColStd_Array1OfReal &Weights, Standard_Integer &InversionProblem)

Performs the interpolation of the data given in
the Poles array according to the requests in
ContactOrderArray that is : if
ContactOrderArray(i) has value d it means that
Poles(i) containes the dth derivative of the
function to be interpolated. The length L of the
following arrays must be the same :
Parameters, ContactOrderArray, Poles,
The length of FlatKnots is Degree + L + 1
Warning:
the method used to do that interpolation is
gauss elimination WITHOUT pivoting. Thus if the
diagonal is not dominant there is no guarantee
that the algorithm will work. Nevertheless for
Cubic interpolation at knots or interpolation at Scheonberg
points the method will work.
The InversionProblem will report 0 if there was no
problem else it will give the index of the faulty
pivot
.

static Standard_EXPORT void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, TColgp_Array1OfPnt2d &Poles, TColStd_Array1OfReal &Weights, Standard_Integer &InversionProblem)

Performs the interpolation of the data given in
the Poles array according to the requests in
ContactOrderArray that is : if
ContactOrderArray(i) has value d it means that
Poles(i) containes the dth derivative of the
function to be interpolated. The length L of the
following arrays must be the same :
Parameters, ContactOrderArray, Poles,
The length of FlatKnots is Degree + L + 1
Warning:
the method used to do that interpolation is
gauss elimination WITHOUT pivoting. Thus if the
diagonal is not dominant there is no guarantee
that the algorithm will work. Nevertheless for
Cubic interpolation at knots or interpolation at Scheonberg
points the method will work.
The InversionProblem w
ll report 0 if there was no
problem else it will give the i
.

static Standard_EXPORT void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, const Standard_Integer ArrayDimension, Standard_Real &Poles, Standard_Integer &InversionProblem)

Performs the interpolation of the data given in
the Poles array according to the requests in
ContactOrderArray that is : if
ContactOrderArray(i) has value d it means that
Poles(i) containes the dth derivative of the
function to be interpolated. The length L of the
following arrays must be the same :
Parameters, ContactOrderArray
The length of FlatKnots is Degree + L + 1
The PolesArray is an seen as an
Array[1..N][1..ArrayDimension] with N = tge length
of the parameters array
Warning:
the method used to do that interpolation is
gauss elimination WITHOUT pivoting. Thus if the
diagonal is not dominant there is no guarantee
that the algorithm will work. Nevertheless for
Cubic interpolation or interpolation at Scheonberg
points the method will work
The InversionProblem will report 0 if there was no
problem else it will give the index of the faulty
pivot
.

static Standard_EXPORT void | Interpolate (const Standard_Integer Degree, const TColStd_Array1OfReal &FlatKnots, const TColStd_Array1OfReal &Parameters, const TColStd_Array1OfInteger &ContactOrderArray, const Standard_Integer ArrayDimension, Standard_Real &Poles, Standard_Real &Weights, Standard_Integer &InversionProblem)

static Standard_EXPORT void

MovePoint (const Standard_Real U, const gp_Vec2d &Displ, const Standard_Integer Index1, const Standard_Integer Index2, const Standard_Integer Degree, const Standard_Boolean Rational, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &FlatKnots, Standard_Integer &FirstIndex, Standard_Integer &LastIndex, TColgp_Array1OfPnt2d &NewPoles)

Find the new poles which allows an old point (with a
given u as parameter) to reach a new position
Index1 and Index2 indicate the range of poles we can move
(1, NbPoles-1) or (2, NbPoles) -> no constraint for one side
don't enter (1,NbPoles) -> error: rigid move
(2, NbPoles-1) -> the ends are enforced
(3, NbPoles-2) -> the ends and the tangency are enforced
if Problem in BSplineBasis calculation, no change for the curve
and FirstIndex, LastIndex = 0
.

static Standard_EXPORT void

MovePoint (const Standard_Real U, const gp_Vec &Displ, const Standard_Integer Index1, const Standard_Integer Index2, const Standard_Integer Degree, const Standard_Boolean Rational, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &FlatKnots, Standard_Integer &FirstIndex, Standard_Integer &LastIndex, TColgp_Array1OfPnt &NewPoles)

Find the new poles which allows an old point (with a
given u as parameter) to reach a new position
Index1 and Index2 indicate the range of poles we can move
(1, NbPoles-1) or (2, NbPoles) -> no constraint for one side
don't enter (1,NbPoles) -> error: rigid move
(2, NbPoles-1) -> the ends are enforced
(3, NbPoles-2) -> the ends and the tangency are enforced
if Problem in BSplineBasis calculation, no change for the curve
and FirstIndex, LastIndex = 0
.

static Standard_EXPORT void

MovePointAndTangent (const Standard_Real U, const Standard_Integer ArrayDimension, Standard_Real &Delta, Standard_Real &DeltaDerivative, const Standard_Real Tolerance, const Standard_Integer Degree, const Standard_Boolean Rational, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, Standard_Real &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &FlatKnots, Standard_Real &NewPoles, Standard_Integer &ErrorStatus)

This is the dimension free version of the utility
U is the parameter must be within the first FlatKnots and the
last FlatKnots Delta is the amount the curve has to be moved
DeltaDerivative is the amount the derivative has to be moved.
Delta and DeltaDerivative must be array of dimension
ArrayDimension Degree is the degree of the BSpline and the
FlatKnots are the knots of the BSpline Starting Condition if =
-1 means the starting point of the curve can move
= 0 means the
starting point of the cuve cannot move but tangen starting
point of the curve cannot move
= 1 means the starting point and tangents cannot move
= 2 means the starting point tangent and curvature cannot move
= ...
Same holds for EndingCondition
Poles are the poles of the curve
Weights are the weights of the curve if Rational = Standard_True
NewPoles are the poles of the deformed curve
ErrorStatus will be 0 if no error happened
1 if there are not enough knots/poles
the imposed conditions
The way to solve this problem is to add knots to the BSpline
If StartCondition = 1 and EndCondition = 1 then you need at least
4 + 2 = 6 poles so for example to have a C1 cubic you will need
have at least 2 internal knots.
.

static Standard_EXPORT void

MovePointAndTangent (const Standard_Real U, const gp_Vec &Delta, const gp_Vec &DeltaDerivative, const Standard_Real Tolerance, const Standard_Integer Degree, const Standard_Boolean Rational, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &FlatKnots, TColgp_Array1OfPnt &NewPoles, Standard_Integer &ErrorStatus)

This is the dimension free version of the utility
U is the parameter must be within the first FlatKnots and the
last FlatKnots Delta is the amount the curve has to be moved
DeltaDerivative is the amount the derivative has to be moved.
Delta and DeltaDerivative must be array of dimension
ArrayDimension Degree is the degree of the BSpline and the
FlatKnots are the knots of the BSpline Starting Condition if =
-1 means the starting point of the curve can move
= 0 means the
starting point of the cuve cannot move but tangen starting
point of the curve cannot move
= 1 means the starting point and tangents cannot move
= 2 means the starting point tangent and curvature cannot move
= ...
Same holds for EndingCondition
Poles are the poles of the curve
Weights are the weights of the curve if Rational = Standard_True
NewPoles are the poles of the deformed curve
ErrorStatus will be 0 if no error happened
1 if there are not enough knots/poles
the imposed conditions
The way to solve this problem is to add knots to the BSpline
If StartCondition = 1 and EndCondition = 1 then you need at least
4 + 2 = 6 poles so for example to have a C1 cubic you will need
have at least 2 internal knots.
.

static Standard_EXPORT void

MovePointAndTangent (const Standard_Real U, const gp_Vec2d &Delta, const gp_Vec2d &DeltaDerivative, const Standard_Real Tolerance, const Standard_Integer Degree, const Standard_Boolean Rational, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &FlatKnots, TColgp_Array1OfPnt2d &NewPoles, Standard_Integer &ErrorStatus)

This is the dimension free version of the utility
U is the parameter must be within the first FlatKnots and the
last FlatKnots Delta is the amount the curve has to be moved
DeltaDerivative is the amount the derivative has to be moved.
Delta and DeltaDerivative must be array of dimension
ArrayDimension Degree is the degree of the BSpline and the
FlatKnots are the knots of the BSpline Starting Condition if =
-1 means the starting point of the curve can move
= 0 means the
starting point of the cuve cannot move but tangen starting
point of the curve cannot move
= 1 means the starting point and tangents cannot move
= 2 means the starting point tangent and curvature cannot move
= ...
Same holds for EndingCondition
Poles are the poles of the curve
Weights are the weights of the curve if Rational = Standard_True
NewPoles are the poles of the deformed curve
ErrorStatus will be 0 if no error happened
1 if there are not enough knots/poles
the imposed conditions
The way to solve this problem is to add knots to the BSpline
If StartCondition = 1 and EndCondition = 1 then you need at least
4 + 2 = 6 poles so for example to have a C1 cubic you will need
have at least 2 internal knots.
.

static Standard_EXPORT void | Resolution (Standard_Real &PolesArray, const Standard_Integer ArrayDimension, const Standard_Integer NumPoles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer Degree, const Standard_Real Tolerance3D, Standard_Real &UTolerance)
| given a tolerance in 3D space returns a tolerance in U parameter space such that all u1 and u0 in the domain of the curve f(u) | u1 - u0 | < UTolerance and we have |f (u1) - f (u0)| < Tolerance3D
static Standard_EXPORT void | Resolution (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const Standard_Integer NumPoles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer Degree, const Standard_Real Tolerance3D, Standard_Real &UTolerance)
| given a tolerance in 3D space returns a tolerance in U parameter space such that all u1 and u0 in the domain of the curve f(u) | u1 - u0 | < UTolerance and we have |f (u1) - f (u0)| < Tolerance3D
static Standard_EXPORT void | Resolution (const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, const Standard_Integer NumPoles, const TColStd_Array1OfReal &FlatKnots, const Standard_Integer Degree, const Standard_Real Tolerance3D, Standard_Real &UTolerance)
| given a tolerance in 3D space returns a tolerance in U parameter space such that all u1 and u0 in the domain of the curve f(u) | u1 - u0 | < UTolerance and we have |f (u1) - f (u0)| < Tolerance3D

## Static Private Member Functions

static Standard_EXPORT void | LocateParameter (const TColStd_Array1OfReal &Knots, const Standard_Real U, const Standard_Boolean Periodic, const Standard_Integer K1, const Standard_Integer K2, Standard_Integer &Index, Standard_Real &NewU, const Standard_Real Uf, const Standard_Real Ue)

## Member Function Documentation

static Standard_EXPORT Standard_Boolean BSplCLib::AntiBoorScheme | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | Standard_Real & | Knots,
|  | const Standard_Integer | Dimension,
|  | Standard_Real & | Poles,
|  | const Standard_Integer | Depth,
|  | const Standard_Integer | Length,
|  | const Standard_Real | Tolerance
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Bohm | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | const Standard_Integer | N,
|  | Standard_Real & | Knots,
|  | const Standard_Integer | Dimension,
|  | Standard_Real & | Poles
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::BoorIndex | ( | const Standard_Integer | Index,
|  | const Standard_Integer | Length,
|  | const Standard_Integer | Depth
| ) | `[static]`

static Standard_EXPORT void BSplCLib::BoorScheme | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | Standard_Real & | Knots,
|  | const Standard_Integer | Dimension,
|  | Standard_Real & | Poles,
|  | const Standard_Integer | Depth,
|  | const Standard_Integer | Length
| ) | `[static]`

static Standard_EXPORT void BSplCLib::BuildBoor | ( | const Standard_Integer | Index,
|  | const Standard_Integer | Length,
|  | const Standard_Integer | Dimension,
|  | const TColStd_Array1OfReal & | Poles,
|  | Standard_Real & | LP
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::BuildBSpMatrix | ( | const TColStd_Array1OfReal & | Parameters,
|  | const TColStd_Array1OfInteger & | OrderArray,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | Degree,
|  | math_Matrix & | Matrix,
|  | Standard_Integer & | UpperBandWidth,
|  | Standard_Integer & | LowerBandWidth
| ) | `[static]`

static Standard_EXPORT void BSplCLib::BuildCache | ( | const Standard_Real | U,
|  | const Standard_Real | InverseOfSpanDomain,
|  | const Standard_Boolean | PeriodicFlag,
|  | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | TColgp_Array1OfPnt2d & | CachePoles,
|  | TColStd_Array1OfReal & | CacheWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::BuildCache | ( | const Standard_Real | U,
|  | const Standard_Real | InverseOfSpanDomain,
|  | const Standard_Boolean | PeriodicFlag,
|  | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | TColgp_Array1OfPnt & | CachePoles,
|  | TColStd_Array1OfReal & | CacheWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::BuildEval | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | Index,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | Standard_Real & | LP
| ) | `[static]`

static Standard_EXPORT void BSplCLib::BuildEval | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | Index,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | Standard_Real & | LP
| ) | `[static]`

static Standard_EXPORT void BSplCLib::BuildEval | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | Index,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | Standard_Real & | LP
| ) | `[static]`

static Standard_EXPORT void BSplCLib::BuildKnots | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | Index,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | Standard_Real & | LK
| ) | `[static]`

static Standard_EXPORT void BSplCLib::BuildSchoenbergPoints | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | TColStd_Array1OfReal & | Parameters
| ) | `[static]`

static Standard_EXPORT void BSplCLib::CacheD0 | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | CacheParameter,
|  | const Standard_Real | SpanLenght,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | Point
| ) | `[static]`

static Standard_EXPORT void BSplCLib::CacheD0 | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | CacheParameter,
|  | const Standard_Real | SpanLenght,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | Point
| ) | `[static]`

static Standard_EXPORT void BSplCLib::CacheD1 | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | CacheParameter,
|  | const Standard_Real | SpanLenght,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | Point,
|  | gp_Vec2d & | Vec
| ) | `[static]`

static Standard_EXPORT void BSplCLib::CacheD1 | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | CacheParameter,
|  | const Standard_Real | SpanLenght,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | Point,
|  | gp_Vec & | Vec
| ) | `[static]`

static Standard_EXPORT void BSplCLib::CacheD2 | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | CacheParameter,
|  | const Standard_Real | SpanLenght,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | Point,
|  | gp_Vec2d & | Vec1,
|  | gp_Vec2d & | Vec2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::CacheD2 | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | CacheParameter,
|  | const Standard_Real | SpanLenght,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | Point,
|  | gp_Vec & | Vec1,
|  | gp_Vec & | Vec2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::CacheD3 | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | CacheParameter,
|  | const Standard_Real | SpanLenght,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | Point,
|  | gp_Vec2d & | Vec1,
|  | gp_Vec2d & | Vec2,
|  | gp_Vec2d & | Vec3
| ) | `[static]`

static Standard_EXPORT void BSplCLib::CacheD3 | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | CacheParameter,
|  | const Standard_Real | SpanLenght,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | Point,
|  | gp_Vec & | Vec1,
|  | gp_Vec & | Vec2,
|  | gp_Vec & | Vec3
| ) | `[static]`

void BSplCLib::CoefsD0 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | Point
| ) | `[inline, static]`

void BSplCLib::CoefsD0 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | Point
| ) | `[inline, static]`

void BSplCLib::CoefsD1 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | Point,
|  | gp_Vec2d & | Vec
| ) | `[inline, static]`

void BSplCLib::CoefsD1 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | Point,
|  | gp_Vec & | Vec
| ) | `[inline, static]`

void BSplCLib::CoefsD2 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | Point,
|  | gp_Vec2d & | Vec1,
|  | gp_Vec2d & | Vec2
| ) | `[inline, static]`

void BSplCLib::CoefsD2 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | Point,
|  | gp_Vec & | Vec1,
|  | gp_Vec & | Vec2
| ) | `[inline, static]`

void BSplCLib::CoefsD3 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | Point,
|  | gp_Vec2d & | Vec1,
|  | gp_Vec2d & | Vec2,
|  | gp_Vec2d & | Vec3
| ) | `[inline, static]`

void BSplCLib::CoefsD3 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | Point,
|  | gp_Vec & | Vec1,
|  | gp_Vec & | Vec2,
|  | gp_Vec & | Vec3
| ) | `[inline, static]`

static Standard_EXPORT void BSplCLib::D0 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | P
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D0 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | P
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D0 | ( | const Standard_Real | U,
|  | const Standard_Integer | UIndex,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Pnt2d & | P
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D0 | ( | const Standard_Real | U,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Pnt & | P
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D0 | ( | const Standard_Real | U,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | Standard_Real & | P
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D1 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | P,
|  | gp_Vec2d & | V
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D1 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | P,
|  | gp_Vec & | V
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D1 | ( | const Standard_Real | U,
|  | const Standard_Integer | UIndex,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Pnt2d & | P,
|  | gp_Vec2d & | V
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D1 | ( | const Standard_Real | U,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Pnt & | P,
|  | gp_Vec & | V
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D1 | ( | const Standard_Real | U,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | Standard_Real & | P,
|  | Standard_Real & | V
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D2 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | P,
|  | gp_Vec2d & | V1,
|  | gp_Vec2d & | V2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D2 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | P,
|  | gp_Vec & | V1,
|  | gp_Vec & | V2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D2 | ( | const Standard_Real | U,
|  | const Standard_Integer | UIndex,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Pnt2d & | P,
|  | gp_Vec2d & | V1,
|  | gp_Vec2d & | V2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D2 | ( | const Standard_Real | U,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Pnt & | P,
|  | gp_Vec & | V1,
|  | gp_Vec & | V2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D2 | ( | const Standard_Real | U,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | Standard_Real & | P,
|  | Standard_Real & | V1,
|  | Standard_Real & | V2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D3 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | P,
|  | gp_Vec2d & | V1,
|  | gp_Vec2d & | V2,
|  | gp_Vec2d & | V3
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D3 | ( | const Standard_Real | U,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | P,
|  | gp_Vec & | V1,
|  | gp_Vec & | V2,
|  | gp_Vec & | V3
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D3 | ( | const Standard_Real | U,
|  | const Standard_Integer | UIndex,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Pnt2d & | P,
|  | gp_Vec2d & | V1,
|  | gp_Vec2d & | V2,
|  | gp_Vec2d & | V3
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D3 | ( | const Standard_Real | U,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Pnt & | P,
|  | gp_Vec & | V1,
|  | gp_Vec & | V2,
|  | gp_Vec & | V3
| ) | `[static]`

static Standard_EXPORT void BSplCLib::D3 | ( | const Standard_Real | U,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | Standard_Real & | P,
|  | Standard_Real & | V1,
|  | Standard_Real & | V2,
|  | Standard_Real & | V3
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Derivative | ( | const Standard_Integer | Degree,
|  | Standard_Real & | Knots,
|  | const Standard_Integer | Dimension,
|  | const Standard_Integer | Length,
|  | const Standard_Integer | Order,
|  | Standard_Real & | Poles
| ) | `[static]`

static Standard_EXPORT void BSplCLib::DN | ( | const Standard_Real | U,
|  | const Standard_Integer | N,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | P,
|  | gp_Vec2d & | VN
| ) | `[static]`

static Standard_EXPORT void BSplCLib::DN | ( | const Standard_Real | U,
|  | const Standard_Integer | N,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | P,
|  | gp_Vec & | VN
| ) | `[static]`

static Standard_EXPORT void BSplCLib::DN | ( | const Standard_Real | U,
|  | const Standard_Integer | N,
|  | const Standard_Integer | UIndex,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Vec2d & | V
| ) | `[static]`

static Standard_EXPORT void BSplCLib::DN | ( | const Standard_Real | U,
|  | const Standard_Integer | N,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | gp_Vec & | VN
| ) | `[static]`

static Standard_EXPORT void BSplCLib::DN | ( | const Standard_Real | U,
|  | const Standard_Integer | N,
|  | const Standard_Integer | Index,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | Standard_Real & | VN
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Eval | ( | const Standard_Real | U,
|  | const Standard_Boolean | PeriodicFlag,
|  | const Standard_Boolean | HomogeneousFlag,
|  | Standard_Integer & | ExtrapMode,
|  | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt2d & | Point,
|  | Standard_Real & | Weight
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Eval | ( | const Standard_Real | U,
|  | const Standard_Boolean | PeriodicFlag,
|  | const Standard_Boolean | HomogeneousFlag,
|  | Standard_Integer & | ExtrapMode,
|  | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | gp_Pnt & | Point,
|  | Standard_Real & | Weight
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Eval | ( | const Standard_Real | U,
|  | const Standard_Boolean | PeriodicFlag,
|  | const Standard_Integer | DerivativeRequest,
|  | Standard_Integer & | ExtrapMode,
|  | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | ArrayDimension,
|  | Standard_Real & | Poles,
|  | Standard_Real & | Weights,
|  | Standard_Real & | PolesResult,
|  | Standard_Real & | WeightsResult
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Eval | ( | const Standard_Real | U,
|  | const Standard_Boolean | PeriodicFlag,
|  | const Standard_Integer | DerivativeRequest,
|  | Standard_Integer & | ExtrapMode,
|  | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | ArrayDimension,
|  | Standard_Real & | Poles,
|  | Standard_Real & | Result
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Eval | ( | const Standard_Real | U,
|  | const Standard_Integer | Degree,
|  | Standard_Real & | Knots,
|  | const Standard_Integer | Dimension,
|  | Standard_Real & | Poles
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::EvalBsplineBasis | ( | const Standard_Integer | Side,
|  | const Standard_Integer | DerivativeOrder,
|  | const Standard_Integer | Order,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Real | Parameter,
|  | Standard_Integer & | FirstNonZeroBsplineIndex,
|  | math_Matrix & | BsplineBasis
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::FactorBandedMatrix | ( | math_Matrix & | Matrix,
|  | const Standard_Integer | UpperBandWidth,
|  | const Standard_Integer | LowerBandWidth,
|  | Standard_Integer & | PivotIndexProblem
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::FirstUKnotIndex | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfInteger & | Mults
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::FlatIndex | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | Index,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const Standard_Boolean | Periodic
| ) | `[static]`

static Standard_EXPORT void BSplCLib::FunctionMultiply | ( | const BSplCLib_EvaluatorFunction & | Function,
|  | const Standard_Integer | BSplineDegree,
|  | const TColStd_Array1OfReal & | BSplineFlatKnots,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | NewDegree,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | Standard_Integer & | Status
| ) | `[static]`

static Standard_EXPORT void BSplCLib::FunctionMultiply | ( | const BSplCLib_EvaluatorFunction & | Function,
|  | const Standard_Integer | BSplineDegree,
|  | const TColStd_Array1OfReal & | BSplineFlatKnots,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | NewDegree,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | Standard_Integer & | Status
| ) | `[static]`

static Standard_EXPORT void BSplCLib::FunctionMultiply | ( | const BSplCLib_EvaluatorFunction & | Function,
|  | const Standard_Integer | BSplineDegree,
|  | const TColStd_Array1OfReal & | BSplineFlatKnots,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | NewDegree,
|  | TColStd_Array1OfReal & | NewPoles,
|  | Standard_Integer & | Status
| ) | `[static]`

static Standard_EXPORT void BSplCLib::FunctionMultiply | ( | const BSplCLib_EvaluatorFunction & | Function,
|  | const Standard_Integer | BSplineDegree,
|  | const TColStd_Array1OfReal & | BSplineFlatKnots,
|  | const Standard_Integer | PolesDimension,
|  | Standard_Real & | Poles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | NewDegree,
|  | Standard_Real & | NewPoles,
|  | Standard_Integer & | Status
| ) | `[static]`

static Standard_EXPORT void BSplCLib::FunctionReparameterise | ( | const BSplCLib_EvaluatorFunction & | Function,
|  | const Standard_Integer | BSplineDegree,
|  | const TColStd_Array1OfReal & | BSplineFlatKnots,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | NewDegree,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | Standard_Integer & | Status
| ) | `[static]`

static Standard_EXPORT void BSplCLib::FunctionReparameterise | ( | const BSplCLib_EvaluatorFunction & | Function,
|  | const Standard_Integer | BSplineDegree,
|  | const TColStd_Array1OfReal & | BSplineFlatKnots,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | NewDegree,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | Standard_Integer & | Status
| ) | `[static]`

static Standard_EXPORT void BSplCLib::FunctionReparameterise | ( | const BSplCLib_EvaluatorFunction & | Function,
|  | const Standard_Integer | BSplineDegree,
|  | const TColStd_Array1OfReal & | BSplineFlatKnots,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | NewDegree,
|  | TColStd_Array1OfReal & | NewPoles,
|  | Standard_Integer & | Status
| ) | `[static]`

static Standard_EXPORT void BSplCLib::FunctionReparameterise | ( | const BSplCLib_EvaluatorFunction & | Function,
|  | const Standard_Integer | BSplineDegree,
|  | const TColStd_Array1OfReal & | BSplineFlatKnots,
|  | const Standard_Integer | PolesDimension,
|  | Standard_Real & | Poles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | NewDegree,
|  | Standard_Real & | NewPoles,
|  | Standard_Integer & | Status
| ) | `[static]`

static Standard_EXPORT void BSplCLib::GetPole | ( | const Standard_Integer | Index,
|  | const Standard_Integer | Length,
|  | const Standard_Integer | Depth,
|  | const Standard_Integer | Dimension,
|  | Standard_Real & | LocPoles,
|  | Standard_Integer & | Position,
|  | TColStd_Array1OfReal & | Pole
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Hunt | ( | const TColStd_Array1OfReal & | XX,
|  | const Standard_Real | X,
|  | Standard_Integer & | Iloc
| ) | `[static]`

static Standard_EXPORT void BSplCLib::IncreaseDegree | ( | const Standard_Integer | NewDegree,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::IncreaseDegree | ( | const Standard_Integer | NewDegree,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::IncreaseDegree | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | NewDegree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults
| ) | `[static]`

static Standard_EXPORT void BSplCLib::IncreaseDegree | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | NewDegree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults
| ) | `[static]`

static Standard_EXPORT void BSplCLib::IncreaseDegree | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | NewDegree,
|  | const Standard_Boolean | Periodic,
|  | const Standard_Integer | Dimension,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColStd_Array1OfReal & | NewPoles,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::IncreaseDegreeCountKnots | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | NewDegree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfInteger & | Mults
| ) | `[static]`

static Standard_EXPORT void BSplCLib::InsertKnot | ( | const Standard_Integer | UIndex,
|  | const Standard_Real | U,
|  | const Standard_Integer | UMult,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::InsertKnot | ( | const Standard_Integer | UIndex,
|  | const Standard_Real | U,
|  | const Standard_Integer | UMult,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::InsertKnots | ( | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColStd_Array1OfReal & | AddKnots,
|  | const TColStd_Array1OfInteger & | AddMults,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults,
|  | const Standard_Real | Epsilon,
|  | const Standard_Boolean | Add = `Standard_True`
| ) | `[static]`

static Standard_EXPORT void BSplCLib::InsertKnots | ( | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColStd_Array1OfReal & | AddKnots,
|  | const TColStd_Array1OfInteger & | AddMults,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults,
|  | const Standard_Real | Epsilon,
|  | const Standard_Boolean | Add = `Standard_True`
| ) | `[static]`

static Standard_EXPORT void BSplCLib::InsertKnots | ( | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const Standard_Integer | Dimension,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColStd_Array1OfReal & | AddKnots,
|  | const TColStd_Array1OfInteger & | AddMults,
|  | TColStd_Array1OfReal & | NewPoles,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults,
|  | const Standard_Real | Epsilon,
|  | const Standard_Boolean | Add = `Standard_True`
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Interpolate | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColStd_Array1OfReal & | Parameters,
|  | const TColStd_Array1OfInteger & | ContactOrderArray,
|  | const Standard_Integer | ArrayDimension,
|  | Standard_Real & | Poles,
|  | Standard_Real & | Weights,
|  | Standard_Integer & | InversionProblem
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Interpolate | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColStd_Array1OfReal & | Parameters,
|  | const TColStd_Array1OfInteger & | ContactOrderArray,
|  | const Standard_Integer | ArrayDimension,
|  | Standard_Real & | Poles,
|  | Standard_Integer & | InversionProblem
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Interpolate | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColStd_Array1OfReal & | Parameters,
|  | const TColStd_Array1OfInteger & | ContactOrderArray,
|  | TColgp_Array1OfPnt2d & | Poles,
|  | TColStd_Array1OfReal & | Weights,
|  | Standard_Integer & | InversionProblem
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Interpolate | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColStd_Array1OfReal & | Parameters,
|  | const TColStd_Array1OfInteger & | ContactOrderArray,
|  | TColgp_Array1OfPnt & | Poles,
|  | TColStd_Array1OfReal & | Weights,
|  | Standard_Integer & | InversionProblem
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Interpolate | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColStd_Array1OfReal & | Parameters,
|  | const TColStd_Array1OfInteger & | ContactOrderArray,
|  | TColgp_Array1OfPnt2d & | Poles,
|  | Standard_Integer & | InversionProblem
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Interpolate | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const TColStd_Array1OfReal & | Parameters,
|  | const TColStd_Array1OfInteger & | ContactOrderArray,
|  | TColgp_Array1OfPnt & | Poles,
|  | Standard_Integer & | InversionProblem
| ) | `[static]`

static Standard_EXPORT Standard_Boolean BSplCLib::IsRational | ( | const TColStd_Array1OfReal & | Weights,
|  | const Standard_Integer | I1,
|  | const Standard_Integer | I2,
|  | const Standard_Real | Epsilon = `0.0`
| ) | `[static]`

static Standard_EXPORT BSplCLib_KnotDistribution BSplCLib::KnotForm | ( | const TColStd_Array1OfReal & | Knots,
|  | const Standard_Integer | FromK1,
|  | const Standard_Integer | ToK2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Knots | ( | const TColStd_Array1OfReal & | KnotSeq,
|  | TColStd_Array1OfReal & | Knots,
|  | TColStd_Array1OfInteger & | Mults,
|  | const Standard_Boolean | Periodic = `Standard_False`
| ) | `[static]`

static Standard_EXPORT void BSplCLib::KnotSequence | ( | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | TColStd_Array1OfReal & | KnotSeq
| ) | `[static]`

static Standard_EXPORT void BSplCLib::KnotSequence | ( | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColStd_Array1OfReal & | KnotSeq
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::KnotSequenceLength | ( | const TColStd_Array1OfInteger & | Mults,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::KnotsLength | ( | const TColStd_Array1OfReal & | KnotSeq,
|  | const Standard_Boolean | Periodic = `Standard_False`
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::LastUKnotIndex | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfInteger & | Mults
| ) | `[static]`

static Standard_EXPORT void BSplCLib::LocateParameter | ( | const TColStd_Array1OfReal & | Knots,
|  | const Standard_Real | U,
|  | const Standard_Boolean | Periodic,
|  | const Standard_Integer | K1,
|  | const Standard_Integer | K2,
|  | Standard_Integer & | Index,
|  | Standard_Real & | NewU,
|  | const Standard_Real | Uf,
|  | const Standard_Real | Ue
| ) | `[static, private]`

static Standard_EXPORT void BSplCLib::LocateParameter | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const Standard_Real | U,
|  | const Standard_Boolean | Periodic,
|  | Standard_Integer & | Index,
|  | Standard_Real & | NewU
| ) | `[static]`

static Standard_EXPORT void BSplCLib::LocateParameter | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | Knots,
|  | const Standard_Real | U,
|  | const Standard_Boolean | IsPeriodic,
|  | const Standard_Integer | FromK1,
|  | const Standard_Integer | ToK2,
|  | Standard_Integer & | KnotIndex,
|  | Standard_Real & | NewU
| ) | `[static]`

static Standard_EXPORT void BSplCLib::LocateParameter | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const Standard_Real | U,
|  | const Standard_Boolean | IsPeriodic,
|  | const Standard_Integer | FromK1,
|  | const Standard_Integer | ToK2,
|  | Standard_Integer & | KnotIndex,
|  | Standard_Real & | NewU
| ) | `[static]`

Standard_Integer BSplCLib::MaxDegree | ( |  | ) | `[inline, static]`

static Standard_EXPORT Standard_Integer BSplCLib::MaxKnotMult | ( | const TColStd_Array1OfInteger & | Mults,
|  | const Standard_Integer | K1,
|  | const Standard_Integer | K2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::MergeBSplineKnots | ( | const Standard_Real | Tolerance,
|  | const Standard_Real | StartValue,
|  | const Standard_Real | EndValue,
|  | const Standard_Integer | Degree1,
|  | const TColStd_Array1OfReal & | Knots1,
|  | const TColStd_Array1OfInteger & | Mults1,
|  | const Standard_Integer | Degree2,
|  | const TColStd_Array1OfReal & | Knots2,
|  | const TColStd_Array1OfInteger & | Mults2,
|  | Standard_Integer & | NumPoles,
|  | Handle(TColStd_HArray1OfReal)& | NewKnots,
|  | Handle(TColStd_HArray1OfInteger)& | NewMults
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::MinKnotMult | ( | const TColStd_Array1OfInteger & | Mults,
|  | const Standard_Integer | K1,
|  | const Standard_Integer | K2
| ) | `[static]`

static Standard_EXPORT void BSplCLib::MovePoint | ( | const Standard_Real | U,
|  | const gp_Vec & | Displ,
|  | const Standard_Integer | Index1,
|  | const Standard_Integer | Index2,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Rational,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | Standard_Integer & | FirstIndex,
|  | Standard_Integer & | LastIndex,
|  | TColgp_Array1OfPnt & | NewPoles
| ) | `[static]`

static Standard_EXPORT void BSplCLib::MovePoint | ( | const Standard_Real | U,
|  | const gp_Vec2d & | Displ,
|  | const Standard_Integer | Index1,
|  | const Standard_Integer | Index2,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Rational,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | Standard_Integer & | FirstIndex,
|  | Standard_Integer & | LastIndex,
|  | TColgp_Array1OfPnt2d & | NewPoles
| ) | `[static]`

static Standard_EXPORT void BSplCLib::MovePointAndTangent | ( | const Standard_Real | U,
|  | const gp_Vec2d & | Delta,
|  | const gp_Vec2d & | DeltaDerivative,
|  | const Standard_Real | Tolerance,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Rational,
|  | const Standard_Integer | StartingCondition,
|  | const Standard_Integer | EndingCondition,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | Standard_Integer & | ErrorStatus
| ) | `[static]`

static Standard_EXPORT void BSplCLib::MovePointAndTangent | ( | const Standard_Real | U,
|  | const gp_Vec & | Delta,
|  | const gp_Vec & | DeltaDerivative,
|  | const Standard_Real | Tolerance,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Rational,
|  | const Standard_Integer | StartingCondition,
|  | const Standard_Integer | EndingCondition,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | Standard_Integer & | ErrorStatus
| ) | `[static]`

static Standard_EXPORT void BSplCLib::MovePointAndTangent | ( | const Standard_Real | U,
|  | const Standard_Integer | ArrayDimension,
|  | Standard_Real & | Delta,
|  | Standard_Real & | DeltaDerivative,
|  | const Standard_Real | Tolerance,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Rational,
|  | const Standard_Integer | StartingCondition,
|  | const Standard_Integer | EndingCondition,
|  | Standard_Real & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | Standard_Real & | NewPoles,
|  | Standard_Integer & | ErrorStatus
| ) | `[static]`

static Standard_EXPORT BSplCLib_MultDistribution BSplCLib::MultForm | ( | const TColStd_Array1OfInteger & | Mults,
|  | const Standard_Integer | FromK1,
|  | const Standard_Integer | ToK2
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::NbPoles | ( | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfInteger & | Mults
| ) | `[static]`

TColStd_Array1OfInteger & BSplCLib::NoMults | ( |  | ) | `[inline, static]`

TColStd_Array1OfReal & BSplCLib::NoWeights | ( |  | ) | `[inline, static]`

void BSplCLib::operator delete | ( | void * | anAddress | ) | `[inline]`

void* BSplCLib::operator new | ( | size_t | size | ) | `[inline]`

void* BSplCLib::operator new | ( | size_t | ,
|  | void * | anAddress
| ) | `[inline]`

static Standard_EXPORT Standard_Integer BSplCLib::PoleIndex | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | Index,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfInteger & | Mults
| ) | `[static]`

static Standard_EXPORT void BSplCLib::PolesCoefficients | ( | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | TColgp_Array1OfPnt & | CachePoles,
|  | TColStd_Array1OfReal & | CacheWeights
| ) | `[static]`

void BSplCLib::PolesCoefficients | ( | const TColgp_Array1OfPnt & | Poles,
|  | TColgp_Array1OfPnt & | CachePoles
| ) | `[inline, static]`

static Standard_EXPORT void BSplCLib::PolesCoefficients | ( | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | TColgp_Array1OfPnt2d & | CachePoles,
|  | TColStd_Array1OfReal & | CacheWeights
| ) | `[static]`

void BSplCLib::PolesCoefficients | ( | const TColgp_Array1OfPnt2d & | Poles,
|  | TColgp_Array1OfPnt2d & | CachePoles
| ) | `[inline, static]`

static Standard_EXPORT Standard_Boolean BSplCLib::PrepareInsertKnots | ( | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColStd_Array1OfReal & | AddKnots,
|  | const TColStd_Array1OfInteger & | AddMults,
|  | Standard_Integer & | NbPoles,
|  | Standard_Integer & | NbKnots,
|  | const Standard_Real | Epsilon,
|  | const Standard_Boolean | Add = `Standard_True`
| ) | `[static]`

static Standard_EXPORT void BSplCLib::PrepareTrimming | ( | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const Standard_Real | U1,
|  | const Standard_Real | U2,
|  | Standard_Integer & | NbKnots,
|  | Standard_Integer & | NbPoles
| ) | `[static]`

static Standard_EXPORT void BSplCLib::PrepareUnperiodize | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfInteger & | Mults,
|  | Standard_Integer & | NbKnots,
|  | Standard_Integer & | NbPoles
| ) | `[static]`

static Standard_EXPORT void BSplCLib::RaiseMultiplicity | ( | const Standard_Integer | KnotIndex,
|  | const Standard_Integer | Mult,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::RaiseMultiplicity | ( | const Standard_Integer | KnotIndex,
|  | const Standard_Integer | Mult,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT Standard_Boolean BSplCLib::RemoveKnot | ( | const Standard_Integer | Index,
|  | const Standard_Integer | Mult,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults,
|  | const Standard_Real | Tolerance
| ) | `[static]`

static Standard_EXPORT Standard_Boolean BSplCLib::RemoveKnot | ( | const Standard_Integer | Index,
|  | const Standard_Integer | Mult,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults,
|  | const Standard_Real | Tolerance
| ) | `[static]`

static Standard_EXPORT Standard_Boolean BSplCLib::RemoveKnot | ( | const Standard_Integer | Index,
|  | const Standard_Integer | Mult,
|  | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const Standard_Integer | Dimension,
|  | const TColStd_Array1OfReal & | Poles,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | TColStd_Array1OfReal & | NewPoles,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults,
|  | const Standard_Real | Tolerance
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Reparametrize | ( | const Standard_Real | U1,
|  | const Standard_Real | U2,
|  | TColStd_Array1OfReal & | Knots
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Resolution | ( | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const Standard_Integer | NumPoles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | Tolerance3D,
|  | Standard_Real & | UTolerance
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Resolution | ( | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const Standard_Integer | NumPoles,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | Tolerance3D,
|  | Standard_Real & | UTolerance
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Resolution | ( | Standard_Real & | PolesArray,
|  | const Standard_Integer | ArrayDimension,
|  | const Standard_Integer | NumPoles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Integer | Degree,
|  | const Standard_Real | Tolerance3D,
|  | Standard_Real & | UTolerance
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Reverse | ( | TColStd_Array1OfReal & | Weights,
|  | const Standard_Integer | Last
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Reverse | ( | TColgp_Array1OfPnt2d & | Poles,
|  | const Standard_Integer | Last
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Reverse | ( | TColgp_Array1OfPnt & | Poles,
|  | const Standard_Integer | Last
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Reverse | ( | TColStd_Array1OfInteger & | Mults | ) | `[static]`

static Standard_EXPORT void BSplCLib::Reverse | ( | TColStd_Array1OfReal & | Knots | ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::SolveBandedSystem | ( | const math_Matrix & | Matrix,
|  | const Standard_Integer | UpperBandWidth,
|  | const Standard_Integer | LowerBandWidth,
|  | const Standard_Boolean | HomogeneousFlag,
|  | TColgp_Array1OfPnt & | Array,
|  | TColStd_Array1OfReal & | Weights
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::SolveBandedSystem | ( | const math_Matrix & | Matrix,
|  | const Standard_Integer | UpperBandWidth,
|  | const Standard_Integer | LowerBandWidth,
|  | const Standard_Boolean | HomogenousFlag,
|  | TColgp_Array1OfPnt2d & | Array,
|  | TColStd_Array1OfReal & | Weights
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::SolveBandedSystem | ( | const math_Matrix & | Matrix,
|  | const Standard_Integer | UpperBandWidth,
|  | const Standard_Integer | LowerBandWidth,
|  | const Standard_Boolean | HomogenousFlag,
|  | const Standard_Integer | ArrayDimension,
|  | Standard_Real & | Array,
|  | Standard_Real & | Weights
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::SolveBandedSystem | ( | const math_Matrix & | Matrix,
|  | const Standard_Integer | UpperBandWidth,
|  | const Standard_Integer | LowerBandWidth,
|  | TColgp_Array1OfPnt & | Array
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::SolveBandedSystem | ( | const math_Matrix & | Matrix,
|  | const Standard_Integer | UpperBandWidth,
|  | const Standard_Integer | LowerBandWidth,
|  | TColgp_Array1OfPnt2d & | Array
| ) | `[static]`

static Standard_EXPORT Standard_Integer BSplCLib::SolveBandedSystem | ( | const math_Matrix & | Matrix,
|  | const Standard_Integer | UpperBandWidth,
|  | const Standard_Integer | LowerBandWidth,
|  | const Standard_Integer | ArrayDimension,
|  | Standard_Real & | Array
| ) | `[static]`

static Standard_EXPORT void BSplCLib::TangExtendToConstraint | ( | const TColStd_Array1OfReal & | FlatKnots,
|  | const Standard_Real | C1Coefficient,
|  | const Standard_Integer | NumPoles,
|  | Standard_Real & | Poles,
|  | const Standard_Integer | Dimension,
|  | const Standard_Integer | Degree,
|  | const TColStd_Array1OfReal & | ConstraintPoint,
|  | const Standard_Integer | Continuity,
|  | const Standard_Boolean | After,
|  | Standard_Integer & | NbPolesResult,
|  | Standard_Integer & | NbKnotsRsult,
|  | Standard_Real & | KnotsResult,
|  | Standard_Real & | PolesResult
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Trimming | ( | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const Standard_Real | U1,
|  | const Standard_Real | U2,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Trimming | ( | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | const Standard_Real | U1,
|  | const Standard_Real | U2,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Trimming | ( | const Standard_Integer | Degree,
|  | const Standard_Boolean | Periodic,
|  | const Standard_Integer | Dimension,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColStd_Array1OfReal & | Poles,
|  | const Standard_Real | U1,
|  | const Standard_Real | U2,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfInteger & | NewMults,
|  | TColStd_Array1OfReal & | NewPoles
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Unperiodize | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColgp_Array1OfPnt2d & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | TColStd_Array1OfInteger & | NewMults,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColgp_Array1OfPnt2d & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Unperiodize | ( | const Standard_Integer | Degree,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColgp_Array1OfPnt & | Poles,
|  | const TColStd_Array1OfReal & | Weights,
|  | TColStd_Array1OfInteger & | NewMults,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColgp_Array1OfPnt & | NewPoles,
|  | TColStd_Array1OfReal & | NewWeights
| ) | `[static]`

static Standard_EXPORT void BSplCLib::Unperiodize | ( | const Standard_Integer | Degree,
|  | const Standard_Integer | Dimension,
|  | const TColStd_Array1OfInteger & | Mults,
|  | const TColStd_Array1OfReal & | Knots,
|  | const TColStd_Array1OfReal & | Poles,
|  | TColStd_Array1OfInteger & | NewMults,
|  | TColStd_Array1OfReal & | NewKnots,
|  | TColStd_Array1OfReal & | NewPoles
| ) | `[static]`

The documentation for this class was generated from the following files:

- BSplCLib.hxx
- BSplCLib.lxx