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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_Array1OfRealNoWeights ()
 Used as argument for a non rational curve.

.
static TColStd_Array1OfIntegerNoMults ()
 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:
Generated on Mon Aug 25 13:12:03 2008 for OpenCASCADE by  doxygen 1.4.1