-- Created on: 1991-08-09
-- Created by: Jean Claude VAUTHIER
-- Copyright (c) 1991-1999 Matra Datavision
-- Copyright (c) 1999-2012 OPEN CASCADE SAS
--
-- The content of this file is subject to the Open CASCADE Technology Public
-- License Version 6.5 (the "License"). You may not use the content of this file
-- except in compliance with the License. Please obtain a copy of the License
-- at http://www.opencascade.org and read it completely before using this file.
--
-- The Initial Developer of the Original Code is Open CASCADE S.A.S., having its
-- main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France.
--
-- The Original Code and all software distributed under the License is
-- distributed on an "AS IS" basis, without warranty of any kind, and the
-- Initial Developer hereby disclaims all such warranties, including without
-- limitation, any warranties of merchantability, fitness for a particular
-- purpose or non-infringement. Please see the License for the specific terms
-- and conditions governing the rights and limitations under the License.
--Modified : RLE Aug 1993 Major modifications.
-- 15-Mar-95 xab : added cache mecanism to speed up
-- evaluation
-- 25-Mar-95 xab : added Lagrange evaluator
-- mei : modified 08-Jun-95 : added method MovePoint
-- xab : modified 11-Mar-96 : added method MovePointAndTangent
-- xab : modified 18-Mar-97 : added method to reparameterise a bspline
-- jct : modified 15-Apr-97 : added method to extend a bspline
package BSplCLib
---Purpose: 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
--
-- Warnings :
-- The bounds of Poles and Weights should be the same.
-- The bounds of Knots and Mults should be the same.
--
-- Weights can be a null reference (BSplCLib::NoWeights())
-- the curve is non rational.
--
-- Mults can be a null reference (BSplCLib::NoMults())
-- the knots are "flat" knots.
--
-- KeyWords :
-- B-spline curve, Functions, Library
--
-- References :
-- . A survey of curves and surfaces methods in CADG Wolfgang
-- BOHM CAGD 1 (1984)
-- . On de Boor-like algorithms and blossoming Wolfgang BOEHM
-- cagd 5 (1988)
-- . Blossoming and knot insertion algorithms for B-spline curves
-- Ronald N. GOLDMAN
-- . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA
-- . Curves and Surfaces for Computer Aided Geometric Design,
-- a practical guide Gerald Farin
uses TColStd, gp, TColgp, math, GeomAbs
is
imported EvaluatorFunction ;
---Purpose: this is a one dimensional function
-- typedef void (*EvaluatorFunction) (
-- Standard_Integer // Derivative Request
-- Standard_Real * // StartEnd[2]
-- Standard_Real // Parameter
-- Standard_Real & // Result
-- Standard_Integer &) ;// Error Code
-- serves to multiply a given vectorial BSpline by a function
enumeration KnotDistribution is NonUniform, Uniform;
---Purpose: This enumeration describes the repartition of the
-- knots sequence. If all the knots differ by the
-- same positive constant from the preceding knot the
-- "KnotDistribution" is else it is
--
enumeration MultDistribution is NonConstant, Constant, QuasiConstant;
---Purpose: This enumeration describes the form of the
-- sequence of mutiplicities. MultDistribution is :
--
-- Constant if all the multiplicities have the same
-- value.
--
-- QuasiConstant if all the internal knots have the
-- same multiplicity and if the first and last knot
-- have a different multiplicity.
--
-- NonConstant in other cases.
-------------------------------------------------------------
-------------------------------------------------------------
---------- ----------
---------- Knots and Multiplicities ----------
---------- ----------
-------------------------------------------------------------
-------------------------------------------------------------
Hunt (XX : in Array1OfReal from TColStd;
X : in Real;
Iloc : in out Integer);
---Purpose: 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.
--
---References : Numerical Recipes in C (William H.Press, Brian
-- P. Flannery, Saul A. Teukolsky, William T.
-- Vetterling)
FirstUKnotIndex (Degree : Integer;
Mults : Array1OfInteger from TColStd)
returns Integer;
---Purpose: Computes the index of the knots value which gives
-- the start point of the curve.
LastUKnotIndex (Degree : Integer;
Mults : Array1OfInteger from TColStd)
returns Integer;
---Purpose: Computes the index of the knots value which gives
-- the end point of the curve.
FlatIndex (Degree : Integer;
Index : Integer;
Mults : Array1OfInteger from TColStd;
Periodic : Boolean)
returns Integer;
---Purpose: Computes the index of the flats knots sequence
-- corresponding to in the knots sequence
-- which multiplicities are .
LocateParameter (Degree : Integer;
Knots : Array1OfReal from TColStd;
Mults : Array1OfInteger from TColStd;
U : Real;
IsPeriodic : Boolean;
FromK1 : Integer;
ToK2 : Integer;
KnotIndex : in out Integer;
NewU : in out Real);
---Purpose: 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"
LocateParameter (Degree : Integer;
Knots : Array1OfReal from TColStd;
U : Real;
IsPeriodic : Boolean;
FromK1 : Integer;
ToK2 : Integer;
KnotIndex : in out Integer;
NewU : in out Real);
---Purpose: 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"
LocateParameter (Knots : Array1OfReal from TColStd;
U : Real;
Periodic : Boolean;
K1,K2 : Integer;
Index : in out Integer;
NewU : in out Real;
Uf,Ue : Real)
is private;
---Level: Internal
LocateParameter (Degree : Integer;
Knots : Array1OfReal from TColStd;
Mults : Array1OfInteger from TColStd;
U : Real;
Periodic : Boolean;
Index : in out Integer;
NewU : in out Real);
---Level: Internal
MaxKnotMult (Mults : Array1OfInteger from TColStd;
K1, K2 : Integer)
returns Integer;
---Purpose: Finds the greatest multiplicity in a set of knots
-- between K1 and K2. Mults is the multiplicity
-- associated with each knot value.
MinKnotMult (Mults : Array1OfInteger from TColStd;
K1, K2 : Integer)
returns Integer;
---Purpose: Finds the lowest multiplicity in a set of knots
-- between K1 and K2. Mults is the multiplicity
-- associated with each knot value.
NbPoles(Degree : Integer;
Periodic : Boolean;
Mults : Array1OfInteger from TColStd)
returns Integer;
---Purpose: 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.
KnotSequenceLength(Mults : Array1OfInteger from TColStd;
Degree : Integer;
Periodic : Boolean)
returns Integer;
---Purpose: 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
KnotSequence (Knots : Array1OfReal from TColStd;
Mults : Array1OfInteger from TColStd;
KnotSeq : in out Array1OfReal from TColStd);
KnotSequence (Knots : Array1OfReal from TColStd;
Mults : Array1OfInteger from TColStd;
Degree : Integer;
Periodic : Boolean;
KnotSeq : in out Array1OfReal from TColStd);
---Purpose: 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)
KnotsLength( KnotSeq : Array1OfReal from TColStd;
Periodic : Boolean = Standard_False)
returns Integer;
---Purpose: Returns the length of the sequence of knots (and
-- Mults) without repetition.
Knots( KnotSeq : Array1OfReal from TColStd;
Knots : out Array1OfReal from TColStd;
Mults : out Array1OfInteger from TColStd;
Periodic : Boolean = Standard_False);
---Purpose: Computes the sequence of knots Knots without
-- repetition of the knots of multiplicity greater
-- than 1.
--
-- Length of and must be
-- KnotsLength(KnotSequence,Periodic)
KnotForm (Knots : Array1OfReal from TColStd;
FromK1, ToK2 : Integer)
returns KnotDistribution;
---Purpose: 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 .
MultForm (Mults : Array1OfInteger from TColStd;
FromK1, ToK2 : Integer)
returns MultDistribution;
---Purpose:
-- Analyses the distribution of multiplicities between
-- the knot FromK1 and the Knot ToK2.
KnotAnalysis (Degree : Integer;
Periodic : Boolean;
CKnots : Array1OfReal from TColStd;
CMults : Array1OfInteger from TColStd;
KnotForm : out BSplKnotDistribution from GeomAbs;
MaxKnotMult: out Integer);
---Purpose: Analyzes the array of knots.
-- Returns the form and the maximum knot multiplicity.
Reparametrize (U1, U2 : Real;
Knots : in out Array1OfReal from TColStd);
---Purpose:
-- 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.
Reverse (Knots : in out Array1OfReal from TColStd);
---Purpose: Reverses the array knots to become the knots
-- sequence of the reversed curve.
Reverse (Mults : in out Array1OfInteger from TColStd);
---Purpose: Reverses the array of multiplicities.
Reverse (Poles : in out Array1OfPnt from TColgp;
Last : Integer);
---Purpose: 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)
Reverse (Poles : in out Array1OfPnt2d from TColgp;
Last : Integer);
---Purpose: Reverses the array of poles.
Reverse (Weights : in out Array1OfReal from TColStd;
Last : Integer);
---Purpose: Reverses the array of poles.
IsRational(Weights : Array1OfReal from TColStd;
I1,I2 : Integer;
Epsilon : Real = 0.0) returns Boolean;
---Purpose:
-- Returns False if all the weights of the array
-- between I1 an I2 are identic. Epsilon is used for
-- comparing weights. If Epsilon is 0. the Epsilon of the
-- first weight is used.
MaxDegree returns Integer;
---Purpose: returns the degree maxima for a BSplineCurve.
---C++: inline
Eval(U : Real;
Degree : Integer;
Knots : in out Real;
Dimension : Integer;
Poles : in out Real);
---Purpose: Perform the Boor algorithm to evaluate a point at
-- parameter __, with and .
--
-- Poles is an array of Reals of size
--
-- * +1
--
-- Containing the poles. At the end contains
-- the current point.
BoorScheme(U : Real;
Degree : Integer;
Knots : in out Real;
Dimension : Integer;
Poles : in out Real;
Depth : Integer;
Length : Integer);
---Purpose: Performs the Boor Algorithm at parameter ____ with
-- the given and the array of on the
-- poles of dimension . The schema
-- is computed until level on a basis of
-- poles.
--
-- * Knots is an array of reals of length :
--
-- +
--
-- * Poles is an array of reals of length :
--
-- (2 * + 1) *
--
-- 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).
AntiBoorScheme(U : Real;
Degree : Integer;
Knots : in out Real;
Dimension : Integer;
Poles : in out Real;
Depth : Integer;
Length : Integer;
Tolerance : Real) returns Boolean;
---Purpose: 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 False is
-- returned.
Derivative(Degree : Integer;
Knots : in out Real;
Dimension : Integer;
Length : Integer;
Order : Integer;
Poles : in out Real);
---Purpose: Computes the poles of the BSpline giving the
-- derivatives of 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).
Bohm(U : Real;
Degree : Integer;
N : Integer;
Knots : in out Real;
Dimension : Integer;
Poles : in out Real);
---Purpose: Performs the Bohm Algorithm at parameter ____. This
-- algorithm computes the value and all the derivatives
-- up to order N (N <= Degree).
--
-- is the original array of poles.
--
-- The result in is the value and the
-- derivatives. Poles[0] is the value, Poles[Degree]
-- is the last derivative.
NoWeights returns Array1OfReal from TColStd;
---Purpose: Used as argument for a non rational curve.
--
---C++: return &
---C++: inline
NoMults returns Array1OfInteger from TColStd;
---Purpose: Used as argument for a flatknots evaluation.
--
---C++: return &
---C++: inline
BuildKnots(Degree, Index : Integer;
Periodic : Boolean;
Knots : Array1OfReal from TColStd;
Mults : Array1OfInteger from TColStd;
LK : in out Real);
---Purpose: Stores in LK the usefull knots for the BoorSchem
-- on the span Knots(Index) - Knots(Index+1)
PoleIndex (Degree, Index : Integer;
Periodic : Boolean;
Mults : Array1OfInteger from TColStd)
returns Integer;
---Purpose: 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().
BuildEval(Degree,Index : Integer;
Poles : Array1OfReal from TColStd;
Weights : Array1OfReal from TColStd;
LP : in out Real);
BuildEval(Degree,Index : Integer;
Poles : Array1OfPnt from TColgp;
Weights : Array1OfReal from TColStd;
LP : in out Real);
BuildEval(Degree,Index : Integer;
Poles : Array1OfPnt2d from TColgp;
Weights : Array1OfReal from TColStd;
LP : in out Real);
---Purpose: Copy in the poles and weights for the Eval
-- scheme. starting from Poles(Poles.Lower()+Index)
BuildBoor(Index,Length,Dimension : Integer;
Poles : Array1OfReal from TColStd;
LP : in out Real);
---Purpose: Copy in poles for Boor scheme.
-- Starting from * , copy
-- poles.
BoorIndex(Index, Length, Depth : Integer)
returns Integer;
---Purpose: Returns the index in the Boor result array of the
-- poles . If the Boor algorithm was perform
-- with and .
GetPole(Index,Length,Depth,Dimension : Integer;
LocPoles : in out Real;
Position : in out Integer;
Pole : in out Array1OfReal from TColStd);
---Purpose: Copy the pole at position in the Boor
-- scheme of dimension to in
-- the array . is updated.
PrepareInsertKnots (
Degree : in Integer;
Periodic : in Boolean;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
AddKnots : in Array1OfReal from TColStd;
AddMults : in Array1OfInteger from TColStd;
NbPoles : out Integer;
NbKnots : out Integer;
Epsilon : in Real;
Add : in Boolean = Standard_True)
returns Boolean;
---Purpose: Returns in the new number of poles
-- and knots if the sequence of knots is inserted in the sequence .
--
-- 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.
InsertKnots (
Degree : in Integer;
Periodic : in Boolean;
Dimension : in Integer;
Poles : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
AddKnots : in Array1OfReal from TColStd;
AddMults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfReal from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
Epsilon : in Real;
Add : in Boolean = Standard_True);
InsertKnots (
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
AddKnots : in Array1OfReal from TColStd;
AddMults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt from TColgp;
NewWeights : out Array1OfReal from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
Epsilon : in Real;
Add : in Boolean = Standard_True);
InsertKnots (
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
AddKnots : in Array1OfReal from TColStd;
AddMults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt2d from TColgp;
NewWeights : out Array1OfReal from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
Epsilon : in Real;
Add : in Boolean = Standard_True);
---Purpose: Insert a sequence of knots with
-- multiplicities . 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
-- and .
--
-- 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.
InsertKnot (
UIndex : in Integer;
U : in Real;
UMult : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt from TColgp;
NewWeights : out Array1OfReal from TColStd);
InsertKnot (
UIndex : in Integer;
U : in Real;
UMult : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt2d from TColgp;
NewWeights : out Array1OfReal from TColStd);
---Purpose: 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.
RaiseMultiplicity (
KnotIndex : in Integer;
Mult : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt from TColgp;
NewWeights : out Array1OfReal from TColStd);
RaiseMultiplicity (
KnotIndex : in Integer;
Mult : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt2d from TColgp;
NewWeights : out Array1OfReal from TColStd);
---Purpose: Raise the multiplicity of knot to .
--
-- The new control points are returned. Knots and Mults are
-- not updated.
RemoveKnot (
Index : in Integer;
Mult : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Dimension : in Integer;
Poles : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfReal from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
Tolerance : Real) returns Boolean;
RemoveKnot (
Index : in Integer;
Mult : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt from TColgp;
NewWeights : out Array1OfReal from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
Tolerance : Real) returns Boolean;
RemoveKnot (
Index : in Integer;
Mult : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt2d from TColgp;
NewWeights : out Array1OfReal from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
Tolerance : Real) returns Boolean;
---Purpose: Decrement the multiplicity of
-- to . If 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.
IncreaseDegreeCountKnots (Degree, NewDegree : Integer;
Periodic : Boolean;
Mults : Array1OfInteger from TColStd)
returns Integer;
---Purpose: Returns the number of knots of a curve with
-- multiplicities after elevating the degree from
-- to . See the IncreaseDegree method
-- for more comments.
IncreaseDegree (Degree,
NewDegree : in Integer;
Periodic : in Boolean;
Dimension : in Integer;
Poles : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : in out Array1OfReal from TColStd;
NewKnots : in out Array1OfReal from TColStd;
NewMults : in out Array1OfInteger from TColStd);
IncreaseDegree (Degree,
NewDegree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : in out Array1OfPnt from TColgp;
NewWeights : in out Array1OfReal from TColStd;
NewKnots : in out Array1OfReal from TColStd;
NewMults : in out Array1OfInteger from TColStd);
IncreaseDegree (Degree,
NewDegree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
NewPoles : in out Array1OfPnt2d from TColgp;
NewWeights : in out Array1OfReal from TColStd;
NewKnots : in out Array1OfReal from TColStd;
NewMults : in out Array1OfInteger from TColStd);
IncreaseDegree (NewDegree : in Integer;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
NewPoles : in out Array1OfPnt from TColgp;
NewWeights : in out Array1OfReal from TColStd);
---Warning: To be used for Beziercurves ONLY!!!
IncreaseDegree (NewDegree : in Integer;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
NewPoles : in out Array1OfPnt2d from TColgp;
NewWeights : in out Array1OfReal from TColStd);
---Purpose: Increase the degree of a bspline (or bezier) curve
-- of dimension form to
-- .
--
-- 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.\
--
---Warning: To be used for Beziercurves ONLY!!!
PrepareUnperiodize (Degree : in Integer from Standard;
Mults : in Array1OfInteger from TColStd;
NbKnots : out Integer from Standard;
NbPoles : out Integer from Standard);
---Purpose: Set in and the number of Knots and
-- Poles of the NotPeriodic Curve identical at the
-- periodic curve with a degree , a
-- knots-distribution with Multiplicities .
Unperiodize (Degree : in Integer from Standard;
Dimension : in Integer from Standard;
Mults : in Array1OfInteger from TColStd;
Knots : in Array1OfReal from TColStd;
Poles : in Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewPoles : out Array1OfReal from TColStd);
Unperiodize (Degree : in Integer from Standard;
Mults : in Array1OfInteger from TColStd;
Knots : in Array1OfReal from TColStd;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewPoles : out Array1OfPnt from TColgp;
NewWeights: out Array1OfReal from TColStd);
Unperiodize (Degree : in Integer from Standard;
Mults : in Array1OfInteger from TColStd;
Knots : in Array1OfReal from TColStd;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
NewKnots : out Array1OfReal from TColStd;
NewPoles : out Array1OfPnt2d from TColgp;
NewWeights: out Array1OfReal from TColStd);
PrepareTrimming (Degree : in Integer from Standard;
Periodic: in Boolean from Standard;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
U1 : in Real from Standard;
U2 : in Real from Standard;
NbKnots : out Integer from Standard;
NbPoles : out Integer from Standard);
---Purpose: Set in and the number of Knots and
-- Poles of the curve resulting of the trimming of the
-- BSplinecurve definded with , ,
Trimming (Degree : in Integer from Standard;
Periodic : in Boolean from Standard;
Dimension : in Integer from Standard;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
Poles : in Array1OfReal from TColStd;
U1 : in Real from Standard;
U2 : in Real from Standard;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
NewPoles : out Array1OfReal from TColStd);
Trimming (Degree : in Integer from Standard;
Periodic : in Boolean from Standard;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
U1 : in Real from Standard;
U2 : in Real from Standard;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt from TColgp;
NewWeights : out Array1OfReal from TColStd);
Trimming (Degree : in Integer from Standard;
Periodic : in Boolean from Standard;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
U1 : in Real from Standard;
U2 : in Real from Standard;
NewKnots : out Array1OfReal from TColStd;
NewMults : out Array1OfInteger from TColStd;
NewPoles : out Array1OfPnt2d from TColgp;
NewWeights : out Array1OfReal from TColStd);
-------------------------------------------------------------
-------------------------------------------------------------
---------- ----------
---------- Curve Evaluations ----------
---------- ----------
-------------------------------------------------------------
-------------------------------------------------------------
D0(U : in Real;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfReal from TColStd;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Real);
D0(U : in Real;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Pnt from gp);
D0(U : in Real;
UIndex : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Pnt2d from gp);
D0(U : in Real;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt from gp);
---Warning: To be used for Beziercurves ONLY!!!
D0(U : in Real;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt2d from gp);
---Warning: To be used for Beziercurves ONLY!!!
D1(U : in Real;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfReal from TColStd;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Real;
V : out Real);
D1(U : in Real;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Pnt from gp;
V : out Vec from gp);
D1(U : in Real;
UIndex : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Pnt2d from gp;
V : out Vec2d from gp);
D1(U : in Real;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt from gp;
V : out Vec from gp);
---Warning: To be used for Beziercurves ONLY!!!
D1(U : in Real;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt2d from gp;
V : out Vec2d from gp);
---Warning: To be used for Beziercurves ONLY!!!
D2(U : in Real;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfReal from TColStd;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Real;
V1,V2 : out Real);
D2(U : in Real;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Pnt from gp;
V1,V2 : out Vec from gp);
D2(U : in Real;
UIndex : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Pnt2d from gp;
V1,V2 : out Vec2d from gp);
D2(U : in Real;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt from gp;
V1,V2 : out Vec from gp);
---Warning: To be used for Beziercurves ONLY!!!
D2(U : in Real;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt2d from gp;
V1,V2 : out Vec2d from gp);
---Warning: To be used for Beziercurves ONLY!!!
D3(U : in Real;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfReal from TColStd;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Real;
V1,V2,V3 : out Real);
D3(U : in Real;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Pnt from gp;
V1,V2,V3 : out Vec from gp);
D3(U : in Real;
UIndex : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
P : out Pnt2d from gp;
V1,V2,V3 : out Vec2d from gp);
D3(U : in Real;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt from gp;
V1,V2,V3 : out Vec from gp);
---Warning: To be used for Beziercurves ONLY!!!
D3(U : in Real;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt2d from gp;
V1,V2,V3 : out Vec2d from gp);
---Warning: To be used for Beziercurves ONLY!!!
DN(U : in Real;
N : in Integer;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfReal from TColStd;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
VN : out Real);
DN(U : in Real;
N : in Integer;
Index : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
VN : out Vec from gp);
DN(U : in Real;
N : in Integer;
UIndex : in Integer;
Degree : in Integer;
Periodic : in Boolean;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
Knots : in Array1OfReal from TColStd;
Mults : in Array1OfInteger from TColStd;
V : out Vec2d from gp);
DN(U : in Real;
N : in Integer;
Poles : in Array1OfPnt from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt from gp;
VN : out Vec from gp);
---Warning: To be used for Beziercurves ONLY!!!
DN(U : in Real;
N : in Integer;
Poles : in Array1OfPnt2d from TColgp;
Weights : in Array1OfReal from TColStd;
P : out Pnt2d from gp;
VN : out Vec2d from gp);
---Purpose: 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 is the the localization of the
-- parameter in the knot sequence. If is out
-- of range the correct value will be searched.
--
--
-- VERY IMPORTANT!!!
-- USE BSplCLib::NoWeights() as Weights argument for non
-- rational curves computations.
---Warning: To be used for Beziercurves ONLY!!!
EvalBsplineBasis(Side : in Integer ;
DerivativeOrder : in Integer ;
Order : in Integer ;
FlatKnots : Array1OfReal from TColStd ;
Parameter : in Real ;
FirstNonZeroBsplineIndex : in out Integer ;
BsplineBasis : in out Matrix from math)
returns Integer ;
---Purpose: 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
BuildBSpMatrix(Parameters : in Array1OfReal from TColStd;
OrderArray : in Array1OfInteger from TColStd;
FlatKnots : in Array1OfReal from TColStd;
Degree : in Integer;
Matrix : in out Matrix from math;
UpperBandWidth : out Integer ;
LowerBandWidth : out Integer) returns Integer ;
---Purpose: 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
FactorBandedMatrix(Matrix : in out Matrix from math ;
UpperBandWidth : in Integer ;
LowerBandWidth : in Integer ;
PivotIndexProblem : out Integer) returns Integer ;
---Purpose: 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
SolveBandedSystem (Matrix : in Matrix from math ;
UpperBandWidth : in Integer ;
LowerBandWidth : in Integer ;
ArrayDimension : in Integer ;
Array : in out Real)
returns Integer ;
---Purpose: 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
SolveBandedSystem (Matrix : in Matrix from math ;
UpperBandWidth : in Integer ;
LowerBandWidth : in Integer ;
Array : in out Array1OfPnt2d from TColgp)
returns Integer ;
---Purpose: 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
SolveBandedSystem (Matrix : in Matrix from math ;
UpperBandWidth : in Integer ;
LowerBandWidth : in Integer ;
Array : in out Array1OfPnt from TColgp)
returns Integer ;
---Purpose: 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
SolveBandedSystem (Matrix : in Matrix from math ;
UpperBandWidth : in Integer ;
LowerBandWidth : in Integer ;
HomogenousFlag : in Boolean ;
ArrayDimension : Integer ;
Array : in out Real ;
Weights : in out Real )
returns Integer ;
SolveBandedSystem (Matrix : in Matrix from math ;
UpperBandWidth : in Integer ;
LowerBandWidth : in Integer ;
HomogenousFlag : in Boolean ;
Array : in out Array1OfPnt2d from TColgp;
Weights : in out Array1OfReal from TColStd )
returns Integer ;
---Purpose: 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.
SolveBandedSystem (Matrix : in Matrix from math ;
UpperBandWidth : in Integer ;
LowerBandWidth : in Integer ;
HomogeneousFlag : in Boolean ;
Array : in out Array1OfPnt from TColgp;
Weights : in out Array1OfReal from TColStd )
returns Integer ;
---Purpose: 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.
MergeBSplineKnots(Tolerance : Real from Standard ;
StartValue : Real from Standard ;
EndValue : Real from Standard ;
Degree1 : Integer from Standard ;
Knots1 : Array1OfReal from TColStd ;
Mults1 : Array1OfInteger from TColStd ;
Degree2 : Integer from Standard ;
Knots2 : Array1OfReal from TColStd ;
Mults2 : Array1OfInteger from TColStd ;
NumPoles : in out Integer ;
NewKnots : in out HArray1OfReal from TColStd ;
NewMults : in out HArray1OfInteger from TColStd) ;
---Purpose: Merges two knot vector by setting the starting and
-- ending values to StartValue and EndValue
FunctionReparameterise(Function : EvaluatorFunction from BSplCLib ;
BSplineDegree : Integer ;
BSplineFlatKnots : Array1OfReal from TColStd ;
PolesDimension : Integer ;
Poles : in out Real ;
FlatKnots : Array1OfReal from TColStd ;
NewDegree : Integer ;
NewPoles : in out Real ;
Status : in out Integer) ;
---Purpose: 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:
--
-- 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))
FunctionReparameterise(
Function : EvaluatorFunction from BSplCLib ;
BSplineDegree : Integer ;
BSplineFlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfReal from TColStd ;
FlatKnots : Array1OfReal from TColStd ;
NewDegree : Integer ;
NewPoles : in out Array1OfReal from TColStd ;
Status : in out Integer) ;
---Purpose: 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:
--
-- 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))
FunctionReparameterise( Function : EvaluatorFunction from BSplCLib ;
BSplineDegree : Integer ;
BSplineFlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfPnt from TColgp ;
FlatKnots : Array1OfReal from TColStd ;
NewDegree : Integer ;
NewPoles : in out Array1OfPnt from TColgp ;
Status : in out Integer) ;
---Purpose: 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))
FunctionReparameterise(
Function : EvaluatorFunction from BSplCLib ;
BSplineDegree : Integer ;
BSplineFlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfPnt2d from TColgp ;
FlatKnots : Array1OfReal from TColStd ;
NewDegree : Integer ;
NewPoles : in out Array1OfPnt2d from TColgp ;
Status : in out Integer) ;
---Purpose: 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))
FunctionMultiply(Function : EvaluatorFunction from BSplCLib ;
BSplineDegree : Integer ;
BSplineFlatKnots : Array1OfReal from TColStd ;
PolesDimension : Integer ;
Poles : in out Real ;
FlatKnots : Array1OfReal from TColStd ;
NewDegree : Integer ;
NewPoles : in out Real ;
Status : in out Integer) ;
---Purpose: 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)
FunctionMultiply(Function : EvaluatorFunction from BSplCLib ;
BSplineDegree : Integer ;
BSplineFlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfReal from TColStd ;
FlatKnots : Array1OfReal from TColStd ;
NewDegree : Integer ;
NewPoles : in out Array1OfReal from TColStd ;
Status : in out Integer) ;
---Purpose: 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)
FunctionMultiply(Function : EvaluatorFunction from BSplCLib ;
BSplineDegree : Integer ;
BSplineFlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfPnt2d from TColgp ;
FlatKnots : Array1OfReal from TColStd ;
NewDegree : Integer ;
NewPoles : in out Array1OfPnt2d from TColgp ;
Status : in out Integer) ;
---Purpose: 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)
FunctionMultiply(Function : EvaluatorFunction from BSplCLib ;
BSplineDegree : Integer ;
BSplineFlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfPnt from TColgp ;
FlatKnots : Array1OfReal from TColStd ;
NewDegree : Integer ;
NewPoles : in out Array1OfPnt from TColgp ;
Status : in out Integer) ;
---Purpose: 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)
Eval(U : Real;
PeriodicFlag : Boolean ;
DerivativeRequest : Integer ;
ExtrapMode : in out Integer ;
Degree : Integer;
FlatKnots : Array1OfReal from TColStd ;
ArrayDimension : Integer ;
Poles : in out Real ;
Result : in out Real) ;
---Purpose: Perform the De Boor algorithm to evaluate a point at
-- parameter ____, with and .
--
-- Poles is an array of Reals of size
--
-- * +1
--
-- Containing the poles. At the end 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
Eval(U : Real;
PeriodicFlag : Boolean ;
DerivativeRequest : Integer ;
ExtrapMode : in out Integer ;
Degree : Integer;
FlatKnots : Array1OfReal from TColStd ;
ArrayDimension : Integer ;
Poles : in out Real ;
Weights : in out Real ;
PolesResult : in out Real ;
WeightsResult : in out Real) ;
---Purpose: Perform the De Boor algorithm to evaluate a point at
-- parameter ____, with and .
-- 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: and must be dimensionned
-- properly.
Eval(U : Real;
PeriodicFlag : Boolean ;
HomogeneousFlag : Boolean ;
ExtrapMode : in out Integer ;
Degree : Integer;
FlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfPnt from TColgp;
Weights : Array1OfReal from TColStd ;
Point : out Pnt from gp ;
Weight : in out Real) ;
---Purpose: Perform the evaluation of the Bspline Basis
-- and then multiplies by the weights
-- this just evaluates the current point
Eval(U : Real;
PeriodicFlag : Boolean ;
HomogeneousFlag : Boolean ;
ExtrapMode : in out Integer ;
Degree : Integer;
FlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfPnt2d from TColgp;
Weights : Array1OfReal from TColStd ;
Point : out Pnt2d from gp ;
Weight : in out Real) ;
---Purpose: Perform the evaluation of the Bspline Basis
-- and then multiplies by the weights
-- this just evaluates the current point
--
TangExtendToConstraint(FlatKnots : Array1OfReal from TColStd ;
C1Coefficient : Real ;
NumPoles : in Integer ;
Poles : in out Real ;
Dimension : Integer ;
Degree : Integer ;
ConstraintPoint : Array1OfReal from TColStd ;
Continuity : Integer ;
After : Boolean ;
NbPolesResult : in out Integer ;
NbKnotsRsult : in out Integer ;
KnotsResult : in out Real ;
PolesResult : in out Real) ;
---Purpose: Extend a BSpline nD using the tangency map
-- is the coefficient of reparametrisation
-- must be equal to 1, 2 or 3.
-- must be greater or equal than + 1.
--
-- Warning: and must be dimensionned
-- properly.
CacheD0(U : Real;
Degree : Integer;
CacheParameter : Real;
SpanLenght : Real;
Poles : Array1OfPnt from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt from gp) ;
---Purpose: 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
CacheD0(U : Real;
Degree : Integer;
CacheParameter : Real;
SpanLenght : Real;
Poles : Array1OfPnt2d from TColgp;
Weights : Array1OfReal from TColStd ;
Point : out Pnt2d from gp) ;
---Purpose: 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
CoefsD0(U : Real;
Poles : Array1OfPnt from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt from gp) ;
---Purpose: Calls CacheD0 for Bezier Curves Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for Beziercurves ONLY!!!
---C++: inline
CoefsD0(U : Real;
Poles : Array1OfPnt2d from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt2d from gp) ;
---Purpose: Calls CacheD0 for Bezier Curves Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for Beziercurves ONLY!!!
---C++: inline
CacheD1(U : Real;
Degree : Integer;
CacheParameter: Real;
SpanLenght : Real;
Poles : Array1OfPnt from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt from gp ;
Vec : out Vec from gp) ;
---Purpose: 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
CacheD1(U : Real;
Degree : Integer;
CacheParameter : Real;
SpanLenght : Real;
Poles : Array1OfPnt2d from TColgp;
Weights : Array1OfReal from TColStd ;
Point : out Pnt2d from gp ;
Vec : out Vec2d from gp) ;
---Purpose: 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
CoefsD1(U : Real;
Poles : Array1OfPnt from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt from gp;
Vec : out Vec from gp) ;
---Purpose: Calls CacheD1 for Bezier Curves Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for Beziercurves ONLY!!!
---C++: inline
CoefsD1(U : Real;
Poles : Array1OfPnt2d from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt2d from gp;
Vec : out Vec2d from gp) ;
---Purpose: Calls CacheD1 for Bezier Curves Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for Beziercurves ONLY!!!
---C++: inline
CacheD2(U : Real;
Degree : Integer;
CacheParameter : Real;
SpanLenght : Real;
Poles : Array1OfPnt from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt from gp ;
Vec1,Vec2 : out Vec from gp) ;
---Purpose: 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
CacheD2(U : Real;
Degree : Integer;
CacheParameter : Real;
SpanLenght : Real;
Poles : Array1OfPnt2d from TColgp;
Weights : Array1OfReal from TColStd ;
Point : out Pnt2d from gp ;
Vec1,Vec2 : out Vec2d from gp) ;
---Purpose: 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
CoefsD2(U : Real;
Poles : Array1OfPnt from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt from gp;
Vec1,Vec2 : out Vec from gp) ;
---Purpose: Calls CacheD1 for Bezier Curves Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for Beziercurves ONLY!!!
---C++: inline
CoefsD2(U : Real;
Poles : Array1OfPnt2d from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt2d from gp;
Vec1,Vec2 : out Vec2d from gp) ;
---Purpose: Calls CacheD1 for Bezier Curves Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for Beziercurves ONLY!!!
---C++: inline
CacheD3(U : Real;
Degree : Integer;
CacheParameter : Real;
SpanLenght : Real;
Poles : Array1OfPnt from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt from gp ;
Vec1,Vec2,Vec3 : out Vec from gp) ;
---Purpose: 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
CacheD3(U : Real;
Degree : Integer;
CacheParameter : Real;
SpanLenght : Real;
Poles : Array1OfPnt2d from TColgp;
Weights : Array1OfReal from TColStd ;
Point : out Pnt2d from gp ;
Vec1,Vec2,Vec3 : out Vec2d from gp) ;
---Purpose: 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
CoefsD3(U : Real;
Poles : Array1OfPnt from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt from gp;
Vec1,Vec2,Vec3: out Vec from gp) ;
---Purpose: Calls CacheD1 for Bezier Curves Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for Beziercurves ONLY!!!
---C++: inline
CoefsD3(U : Real;
Poles : Array1OfPnt2d from TColgp ;
Weights : Array1OfReal from TColStd ;
Point : out Pnt2d from gp;
Vec1,Vec2,Vec3: out Vec2d from gp) ;
---Purpose: Calls CacheD1 for Bezier Curves Arrays computed with
-- the method PolesCoefficients.
-- Warning: To be used for Beziercurves ONLY!!!
---C++: inline
BuildCache(U : Real;
InverseOfSpanDomain : Real;
PeriodicFlag : Boolean ;
Degree : Integer;
FlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfPnt from TColgp;
Weights : Array1OfReal from TColStd ;
CachePoles : in out Array1OfPnt from TColgp;
CacheWeights : in out Array1OfReal from TColStd) ;
---Purpose: 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
BuildCache(U : Real;
InverseOfSpanDomain : Real;
PeriodicFlag : Boolean ;
Degree : Integer;
FlatKnots : Array1OfReal from TColStd ;
Poles : Array1OfPnt2d from TColgp;
Weights : Array1OfReal from TColStd ;
CachePoles : in out Array1OfPnt2d from TColgp;
CacheWeights : in out Array1OfReal from TColStd) ;
---Purpose: 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
PolesCoefficients(Poles : Array1OfPnt2d from TColgp;
CachePoles : in out Array1OfPnt2d from TColgp);
---Warning: To be used for Beziercurves ONLY!!!
---C++: inline
PolesCoefficients(Poles : Array1OfPnt2d from TColgp;
Weights : Array1OfReal from TColStd ;
CachePoles : in out Array1OfPnt2d from TColgp;
CacheWeights : in out Array1OfReal from TColStd) ;
---Warning: To be used for Beziercurves ONLY!!!
PolesCoefficients(Poles : Array1OfPnt from TColgp;
CachePoles : in out Array1OfPnt from TColgp);
---Warning: To be used for Beziercurves ONLY!!!
---C++: inline
PolesCoefficients(Poles : Array1OfPnt from TColgp;
Weights : Array1OfReal from TColStd ;
CachePoles : in out Array1OfPnt from TColgp;
CacheWeights : in out Array1OfReal from TColStd) ;
---Purpose: Encapsulation of BuildCache to perform the
-- evaluation of the Taylor expansion for beziercurves
-- at parameter 0.
-- Warning: To be used for Beziercurves ONLY!!!
FlatBezierKnots (Degree: Integer) returns Real;
---Purpose: Returns pointer to statically allocated array representing
-- flat knots for bezier curve of the specified degree.
-- Raises OutOfRange if Degree > MaxDegree()
---C++: return const &
BuildSchoenbergPoints(Degree : Integer ;
FlatKnots : Array1OfReal from TColStd ;
Parameters : in out Array1OfReal from TColStd) ;
---Purpose: builds the Schoenberg points from the flat knot
-- used to interpolate a BSpline since the
-- BSpline matrix is invertible.
Interpolate(Degree : Integer ;
FlatKnots : Array1OfReal from TColStd ;
Parameters : Array1OfReal from TColStd ;
ContactOrderArray : Array1OfInteger from TColStd ;
Poles : in out Array1OfPnt from TColgp ;
InversionProblem : out Integer) ;
---Purpose: 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
Interpolate(Degree : Integer ;
FlatKnots : Array1OfReal from TColStd ;
Parameters : Array1OfReal from TColStd ;
ContactOrderArray : Array1OfInteger from TColStd ;
Poles : in out Array1OfPnt2d from TColgp ;
InversionProblem : out Integer) ;
---Purpose: 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
Interpolate(Degree : Integer ;
FlatKnots : Array1OfReal from TColStd ;
Parameters : Array1OfReal from TColStd ;
ContactOrderArray : Array1OfInteger from TColStd ;
Poles : in out Array1OfPnt from TColgp ;
Weights : in out Array1OfReal from TColStd ;
InversionProblem : out Integer) ;
---Purpose: 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
--
--
Interpolate(Degree : Integer ;
FlatKnots : Array1OfReal from TColStd ;
Parameters : Array1OfReal from TColStd ;
ContactOrderArray : Array1OfInteger from TColStd ;
Poles : in out Array1OfPnt2d from TColgp ;
Weights : in out Array1OfReal from TColStd ;
InversionProblem : out Integer) ;
---Purpose: 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
Interpolate(Degree : Integer ;
FlatKnots : Array1OfReal from TColStd ;
Parameters : Array1OfReal from TColStd ;
ContactOrderArray : Array1OfInteger from TColStd ;
ArrayDimension : Integer ;
Poles : in out Real ;
InversionProblem : out Integer) ;
---Purpose: 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
--
Interpolate(Degree : Integer ;
FlatKnots : Array1OfReal from TColStd ;
Parameters : Array1OfReal from TColStd ;
ContactOrderArray : Array1OfInteger from TColStd ;
ArrayDimension : Integer ;
Poles : in out Real ;
Weights : in out Real ;
InversionProblem : out Integer) ;
MovePoint(U : Real; -- parameter of the point
Displ : Vec2d from gp; -- translation vector of the point
Index1 : Integer; -- first movable pole
Index2 : Integer; -- last movable pole
Degree : Integer;
Rational : Boolean;
Poles : Array1OfPnt2d from TColgp;
Weights : Array1OfReal from TColStd;
FlatKnots : Array1OfReal from TColStd;
FirstIndex : in out Integer; -- first pole modified
LastIndex : in out Integer; -- last pole modified
NewPoles : in out Array1OfPnt2d from TColgp); -- new poles
---Purpose: 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
MovePoint(U : Real; -- parameter of the point
Displ : Vec from gp; -- translation vector of the point
Index1 : Integer; -- first movable pole
Index2 : Integer; -- last movable pole
Degree : Integer;
Rational : Boolean;
Poles : Array1OfPnt from TColgp;
Weights : Array1OfReal from TColStd;
FlatKnots : Array1OfReal from TColStd;
FirstIndex : in out Integer; -- first pole modified
LastIndex : in out Integer; -- last pole modified
NewPoles : in out Array1OfPnt from TColgp); -- new poles
---Purpose: 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
MovePointAndTangent(U : Real ;
ArrayDimension : Integer ;
Delta : in out Real ;
DeltaDerivative : in out Real ;
Tolerance : Real ;
Degree : Integer ;
Rational : Boolean ;
StartingCondition : Integer ;
EndingCondition : Integer ;
Poles : in out Real ;
Weights : Array1OfReal from TColStd;
FlatKnots : Array1OfReal from TColStd;
NewPoles : in out Real ;
ErrorStatus : in out Integer) ;
---Purpose: 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.
MovePointAndTangent(U : Real ;
Delta : Vec from gp ;
DeltaDerivative : Vec from gp ;
Tolerance : Real ;
Degree : Integer ;
Rational : Boolean ;
StartingCondition : Integer ;
EndingCondition : Integer ;
Poles : Array1OfPnt from TColgp ;
Weights : Array1OfReal from TColStd;
FlatKnots : Array1OfReal from TColStd;
NewPoles : in out Array1OfPnt from TColgp ;
ErrorStatus : in out Integer) ;
---Purpose: 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.
MovePointAndTangent(U : Real ;
Delta : Vec2d from gp ;
DeltaDerivative : Vec2d from gp ;
Tolerance : Real ;
Degree : Integer ;
Rational : Boolean ;
StartingCondition : Integer ;
EndingCondition : Integer ;
Poles : Array1OfPnt2d from TColgp ;
Weights : Array1OfReal from TColStd ;
FlatKnots : Array1OfReal from TColStd ;
NewPoles : in out Array1OfPnt2d from TColgp ;
ErrorStatus : in out Integer) ;
---Purpose: 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.
Resolution( PolesArray : in out Real ;
ArrayDimension : Integer ;
NumPoles : Integer ;
Weights : in Array1OfReal from TColStd;
FlatKnots : in Array1OfReal from TColStd;
Degree : in Integer;
Tolerance3D : Real from Standard ;
UTolerance : out Real from Standard) ;
---Purpose:
-- 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
Resolution( Poles : in Array1OfPnt from TColgp ;
Weights : in Array1OfReal from TColStd ;
NumPoles : in Integer from Standard ;
FlatKnots : in Array1OfReal from TColStd ;
Degree : in Integer from Standard ;
Tolerance3D : Real from Standard ;
UTolerance : out Real from Standard) ;
---Purpose:
-- 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
Resolution( Poles : in Array1OfPnt2d from TColgp ;
Weights : in Array1OfReal from TColStd ;
NumPoles : in Integer from Standard ;
FlatKnots : in Array1OfReal from TColStd ;
Degree : in Integer ;
Tolerance3D : Real from Standard ;
UTolerance : out Real from Standard) ;
---Purpose:
-- 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
end BSplCLib;
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