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Open CASCADE Technology
6.7.1
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Open CASCADE Technology
6.7.1
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BSplSLib B-spline surface Library <br>
This package provides an implementation of geometric
functions for rational and non rational, periodic and non
periodic B-spline surface computation.
this package uses the multi-dimensions splines methods
provided in the package BSplCLib.
In this package the B-spline surface is defined with :
. its control points : Array2OfPnt Poles
. its weights : Array2OfReal Weights
. its knots and their multiplicity in the two parametric
direction U and V : Array1OfReal UKnots, VKnots and
Array1OfInteger UMults, VMults.
. the degree of the normalized Spline functions :
UDegree, VDegree
. the Booleans URational, VRational to know if the weights
are constant in the U or V direction.
. the Booleans UPeriodic, VRational to know if the the
surface is periodic in the U or V direction.
Warnings : The bounds of UKnots and UMults should be the
same, the bounds of VKnots and VMults should be the same,
the bounds of Poles and Weights shoud be the same.
The Control points representation is :
Poles(Uorigin,Vorigin) ...................Poles(Uorigin,Vend)
. .
. .
Poles(Uend, Vorigin) .....................Poles(Uend, Vend)
For the double array the row indice corresponds to the
parametric U direction and the columns indice corresponds
to the parametric V direction.
KeyWords :
B-spline surface, Functions, Library
References :
. A survey of curve and surface 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
More...
#include <BSplSLib.hxx>
Static Public Member Functions | |
| static void | RationalDerivative (const Standard_Integer UDeg, const Standard_Integer VDeg, const Standard_Integer N, const Standard_Integer M, Standard_Real &Ders, Standard_Real &RDers, const Standard_Boolean All=Standard_True) |
this is a one dimensional function <br> typedef void (*EvaluatorFunction) ( | |
| static void | D0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P) |
| static void | D1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer Degree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv) |
| static void | D2 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv) |
| static void | D3 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv) |
| static void | DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Vec &Vn) |
| static void | Iso (const Standard_Real Param, const Standard_Boolean IsU, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Integer Degree, const Standard_Boolean Periodic, TColgp_Array1OfPnt &CPoles, TColStd_Array1OfReal &CWeights) |
| Computes the poles and weights of an isoparametric curve at parameter (UIso if <IsU> is True, VIso else). More... | |
| static void | Reverse (TColgp_Array2OfPnt &Poles, const Standard_Integer Last, const Standard_Boolean UDirection) |
| Reverses the array of poles. Last is the Index of the new first Row( Col) of Poles. On a non periodic surface 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 More... | |
| static void | HomogeneousD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, Standard_Real &W, gp_Pnt &P) |
Makes an homogeneous evaluation of Poles and Weights <br>
any and returns in P the Numerator value and <br>
in W the Denominator value if Weights are present <br>
otherwise returns 1.0e0 <br>
| |
| static void | HomogeneousD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, gp_Pnt &N, gp_Vec &Nu, gp_Vec &Nv, Standard_Real &D, Standard_Real &Du, Standard_Real &Dv) |
Makes an homogeneous evaluation of Poles and Weights <br>
any and returns in P the Numerator value and <br>
in W the Denominator value if Weights are present <br>
otherwise returns 1.0e0 <br>
| |
| static void | Reverse (TColStd_Array2OfReal &Weights, const Standard_Integer Last, const Standard_Boolean UDirection) |
| Reverses the array of weights. More... | |
| static Standard_Boolean | IsRational (const TColStd_Array2OfReal &Weights, const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer J1, const Standard_Integer J2, const Standard_Real Epsilon=0.0) |
| Returns False if all the weights of the array <Weights> in the area [I1,I2] * [J1,J2] are identic. Epsilon is used for comparing weights. If Epsilon is 0. the Epsilon of the first weight is used. More... | |
| static void | SetPoles (const TColgp_Array2OfPnt &Poles, TColStd_Array1OfReal &FP, const Standard_Boolean UDirection) |
| Copy in FP the coordinates of the poles. More... | |
| static void | SetPoles (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, TColStd_Array1OfReal &FP, const Standard_Boolean UDirection) |
| Copy in FP the coordinates of the poles. More... | |
| static void | GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array2OfPnt &Poles, const Standard_Boolean UDirection) |
| Get from FP the coordinates of the poles. More... | |
| static void | GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array2OfPnt &Poles, TColStd_Array2OfReal &Weights, const Standard_Boolean UDirection) |
| Get from FP the coordinates of the poles. More... | |
| static void | MovePoint (const Standard_Real U, const Standard_Real V, const gp_Vec &Displ, const Standard_Integer UIndex1, const Standard_Integer UIndex2, const Standard_Integer VIndex1, const Standard_Integer VIndex2, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean Rational, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, Standard_Integer &UFirstIndex, Standard_Integer &ULastIndex, Standard_Integer &VFirstIndex, Standard_Integer &VLastIndex, TColgp_Array2OfPnt &NewPoles) |
| Find the new poles which allows an old point (with a given u,v as parameters) to reach a new position UIndex1,UIndex2 indicate the range of poles we can move for U (1, UNbPoles-1) or (2, UNbPoles) -> no constraint for one side in U (2, UNbPoles-1) -> the ends are enforced for U don't enter (1,NbPoles) and (1,VNbPoles) -> error: rigid move if problem in BSplineBasis calculation, no change for the curve and UFirstIndex, VLastIndex = 0 VFirstIndex, VLastIndex = 0 More... | |
| static void | InsertKnots (const Standard_Boolean UDirection, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &AddKnots, const TColStd_Array1OfInteger &AddMults, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal &NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Epsilon, const Standard_Boolean Add=Standard_True) |
| static Standard_Boolean | RemoveKnot (const Standard_Boolean UDirection, const Standard_Integer Index, const Standard_Integer Mult, const Standard_Integer Degree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal &NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults, const Standard_Real Tolerance) |
| static void | IncreaseDegree (const Standard_Boolean UDirection, const Standard_Integer Degree, const Standard_Integer NewDegree, const Standard_Boolean Periodic, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal &NewWeights, TColStd_Array1OfReal &NewKnots, TColStd_Array1OfInteger &NewMults) |
| static void | Unperiodize (const Standard_Boolean UDirection, const Standard_Integer Degree, const TColStd_Array1OfInteger &Mults, const TColStd_Array1OfReal &Knots, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, TColStd_Array1OfInteger &NewMults, TColStd_Array1OfReal &NewKnots, TColgp_Array2OfPnt &NewPoles, TColStd_Array2OfReal &NewWeights) |
| static TColStd_Array2OfReal & | NoWeights () |
Used as argument for a non rational curve. <br> | |
| static void | BuildCache (const Standard_Real U, const Standard_Real V, const Standard_Real USpanDomain, const Standard_Real VSpanDomain, const Standard_Boolean UPeriodicFlag, const Standard_Boolean VPeriodicFlag, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Integer UIndex, const Standard_Integer VIndex, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, TColgp_Array2OfPnt &CachePoles, TColStd_Array2OfReal &CacheWeights) |
Perform the evaluation of the Taylor expansion <br>
of the Bspline normalized between 0 and 1. <br>
If rational computes the homogeneous Taylor expension <br>
for the numerator and stores it in CachePoles <br>
| |
| static void | CacheD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, gp_Pnt &Point) |
Perform the evaluation of the of the cache <br>
the parameter must be normalized between <br>
the 0 and 1 for the span. <br>
The Cache must be valid when calling this <br>
routine. Geom Package will insure that. <br>
and then multiplies by the weights <br>
this just evaluates the current point <br>
the CacheParameter is where the Cache was <br>
constructed the SpanLength is to normalize <br>
the polynomial in the cache to avoid bad conditioning <br>
effects <br>
| |
| static void | CoefsD0 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, gp_Pnt &Point) |
Calls CacheD0 for Bezier Surfaces Arrays computed with <br>
the method PolesCoefficients. <br>
Warning: To be used for BezierSurfaces ONLY!!! | |
| static void | CacheD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV) |
Perform the evaluation of the of the cache <br>
the parameter must be normalized between <br>
the 0 and 1 for the span. <br>
The Cache must be valid when calling this <br>
routine. Geom Package will insure that. <br>
and then multiplies by the weights <br>
this just evaluates the current point <br>
the CacheParameter is where the Cache was <br>
constructed the SpanLength is to normalize <br>
the polynomial in the cache to avoid bad conditioning <br>
effects <br>
| |
| static void | CoefsD1 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV) |
Calls CacheD0 for Bezier Surfaces Arrays computed with <br>
the method PolesCoefficients. <br>
Warning: To be used for BezierSurfaces ONLY!!! | |
| static void | CacheD2 (const Standard_Real U, const Standard_Real V, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Real UCacheParameter, const Standard_Real VCacheParameter, const Standard_Real USpanLenght, const Standard_Real VSpanLength, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV, gp_Vec &VecUU, gp_Vec &VecUV, gp_Vec &VecVV) |
Perform the evaluation of the of the cache <br>
the parameter must be normalized between <br>
the 0 and 1 for the span. <br>
The Cache must be valid when calling this <br>
routine. Geom Package will insure that. <br>
and then multiplies by the weights <br>
this just evaluates the current point <br>
the CacheParameter is where the Cache was <br>
constructed the SpanLength is to normalize <br>
the polynomial in the cache to avoid bad conditioning <br>
effects <br>
| |
| static void | CoefsD2 (const Standard_Real U, const Standard_Real V, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, gp_Pnt &Point, gp_Vec &VecU, gp_Vec &VecV, gp_Vec &VecUU, gp_Vec &VecUV, gp_Vec &VecVV) |
Calls CacheD0 for Bezier Surfaces Arrays computed with <br>
the method PolesCoefficients. <br>
Warning: To be used for BezierSurfaces ONLY!!! | |
| static void | PolesCoefficients (const TColgp_Array2OfPnt &Poles, TColgp_Array2OfPnt &CachePoles) |
| Warning! To be used for BezierSurfaces ONLY!!! More... | |
| static void | PolesCoefficients (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, TColgp_Array2OfPnt &CachePoles, TColStd_Array2OfReal &CacheWeights) |
Encapsulation of BuildCache to perform the <br>
evaluation of the Taylor expansion for beziersurfaces <br>
at parameters 0.,0.; <br>
Warning: To be used for BezierSurfaces ONLY!!! | |
| static void | Resolution (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean URat, const Standard_Boolean VRat, const Standard_Boolean UPer, const Standard_Boolean VPer, const Standard_Real Tolerance3D, Standard_Real &UTolerance, Standard_Real &VTolerance) |
| Given a tolerance in 3D space returns two tolerances, one in U one in V such that for all (u1,v1) and (u0,v0) in the domain of the surface f(u,v) we have : | u1 - u0 | < UTolerance and | v1 - v0 | < VTolerance we have |f (u1,v1) - f (u0,v0)| < Tolerance3D More... | |
| static void | Interpolate (const Standard_Integer UDegree, const Standard_Integer VDegree, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const TColStd_Array1OfReal &UParameters, const TColStd_Array1OfReal &VParameters, TColgp_Array2OfPnt &Poles, TColStd_Array2OfReal &Weights, Standard_Integer &InversionProblem) |
Performs the interpolation of the data points given in <br>
the Poles array in the form <br>
[1,...,RL][1,...,RC][1...PolesDimension] . The <br>
ColLength CL and the Length of UParameters must be the <br>
same. The length of VFlatKnots is VDegree + CL + 1. <br>
| |
| static void | Interpolate (const Standard_Integer UDegree, const Standard_Integer VDegree, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const TColStd_Array1OfReal &UParameters, const TColStd_Array1OfReal &VParameters, TColgp_Array2OfPnt &Poles, Standard_Integer &InversionProblem) |
Performs the interpolation of the data points given in <br>
the Poles array. <br>
The ColLength CL and the Length of UParameters must be <br>
the same. The length of VFlatKnots is VDegree + CL + 1. <br>
| |
| static void | FunctionMultiply (const BSplSLib_EvaluatorFunction &Function, const Standard_Integer UBSplineDegree, const Standard_Integer VBSplineDegree, const TColStd_Array1OfReal &UBSplineKnots, const TColStd_Array1OfReal &VBSplineKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UFlatKnots, const TColStd_Array1OfReal &VFlatKnots, const Standard_Integer UNewDegree, const Standard_Integer VNewDegree, TColgp_Array2OfPnt &NewNumerator, TColStd_Array2OfReal &NewDenominator, Standard_Integer &Status) |
this will multiply a given BSpline numerator N(u,v) <br>
and denominator D(u,v) defined by its <br>
U/VBSplineDegree and U/VBSplineKnots, and <br>
U/VMults. Its Poles and Weights are arrays which are <br>
coded as array2 of the form <br>
[1..UNumPoles][1..VNumPoles] by a function a(u,v) <br>
which is assumed to satisfy the following : 1. <br>
a(u,v) * N(u,v) and a(u,v) * D(u,v) is a polynomial <br>
BSpline that can be expressed exactly as a BSpline of <br>
degree U/VNewDegree on the knots U/VFlatKnots 2. the range <br>
of a(u,v) is the same as the range of N(u,v) <br>
or D(u,v) <br>
---Warning: it is the caller's responsability to <br>
insure that conditions 1. and 2. above are satisfied <br>
: no check whatsoever is made in this method -- <br>
Status will return 0 if OK else it will return the <br>
pivot index -- of the matrix that was inverted to <br>
compute the multiplied -- BSpline : the method used <br>
is interpolation at Schoenenberg -- points of <br>
a(u,v)* N(u,v) and a(u,v) * D(u,v) <br>
Status will return 0 if OK else it will return the pivot index | |
BSplSLib B-spline surface Library <br>
This package provides an implementation of geometric
functions for rational and non rational, periodic and non
periodic B-spline surface computation.
this package uses the multi-dimensions splines methods
provided in the package BSplCLib.
In this package the B-spline surface is defined with :
. its control points : Array2OfPnt Poles
. its weights : Array2OfReal Weights
. its knots and their multiplicity in the two parametric
direction U and V : Array1OfReal UKnots, VKnots and
Array1OfInteger UMults, VMults.
. the degree of the normalized Spline functions :
UDegree, VDegree
. the Booleans URational, VRational to know if the weights
are constant in the U or V direction.
. the Booleans UPeriodic, VRational to know if the the
surface is periodic in the U or V direction.
Warnings : The bounds of UKnots and UMults should be the
same, the bounds of VKnots and VMults should be the same,
the bounds of Poles and Weights shoud be the same.
The Control points representation is :
Poles(Uorigin,Vorigin) ...................Poles(Uorigin,Vend)
. .
. .
Poles(Uend, Vorigin) .....................Poles(Uend, Vend)
For the double array the row indice corresponds to the
parametric U direction and the columns indice corresponds
to the parametric V direction.
KeyWords :
B-spline surface, Functions, Library
References :
. A survey of curve and surface 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
|
static |
Perform the evaluation of the Taylor expansion <br>
of the Bspline normalized between 0 and 1. <br>
If rational computes the homogeneous Taylor expension <br>
for the numerator and stores it in CachePoles <br>
|
static |
Perform the evaluation of the of the cache <br>
the parameter must be normalized between <br>
the 0 and 1 for the span. <br>
The Cache must be valid when calling this <br>
routine. Geom Package will insure that. <br>
and then multiplies by the weights <br>
this just evaluates the current point <br>
the CacheParameter is where the Cache was <br>
constructed the SpanLength is to normalize <br>
the polynomial in the cache to avoid bad conditioning <br>
effects <br>
|
static |
Perform the evaluation of the of the cache <br>
the parameter must be normalized between <br>
the 0 and 1 for the span. <br>
The Cache must be valid when calling this <br>
routine. Geom Package will insure that. <br>
and then multiplies by the weights <br>
this just evaluates the current point <br>
the CacheParameter is where the Cache was <br>
constructed the SpanLength is to normalize <br>
the polynomial in the cache to avoid bad conditioning <br>
effects <br>
|
static |
Perform the evaluation of the of the cache <br>
the parameter must be normalized between <br>
the 0 and 1 for the span. <br>
The Cache must be valid when calling this <br>
routine. Geom Package will insure that. <br>
and then multiplies by the weights <br>
this just evaluates the current point <br>
the CacheParameter is where the Cache was <br>
constructed the SpanLength is to normalize <br>
the polynomial in the cache to avoid bad conditioning <br>
effects <br>
|
static |
Calls CacheD0 for Bezier Surfaces Arrays computed with <br>
the method PolesCoefficients. <br>
Warning: To be used for BezierSurfaces ONLY!!!
|
static |
Calls CacheD0 for Bezier Surfaces Arrays computed with <br>
the method PolesCoefficients. <br>
Warning: To be used for BezierSurfaces ONLY!!!
|
static |
Calls CacheD0 for Bezier Surfaces Arrays computed with <br>
the method PolesCoefficients. <br>
Warning: To be used for BezierSurfaces ONLY!!!
|
static |
|
static |
|
static |
|
static |
|
static |
|
static |
this will multiply a given BSpline numerator N(u,v) <br>
and denominator D(u,v) defined by its <br>
U/VBSplineDegree and U/VBSplineKnots, and <br>
U/VMults. Its Poles and Weights are arrays which are <br>
coded as array2 of the form <br>
[1..UNumPoles][1..VNumPoles] by a function a(u,v) <br>
which is assumed to satisfy the following : 1. <br>
a(u,v) * N(u,v) and a(u,v) * D(u,v) is a polynomial <br>
BSpline that can be expressed exactly as a BSpline of <br>
degree U/VNewDegree on the knots U/VFlatKnots 2. the range <br>
of a(u,v) is the same as the range of N(u,v) <br>
or D(u,v) <br>
---Warning: it is the caller's responsability to <br>
insure that conditions 1. and 2. above are satisfied <br>
: no check whatsoever is made in this method -- <br>
Status will return 0 if OK else it will return the <br>
pivot index -- of the matrix that was inverted to <br>
compute the multiplied -- BSpline : the method used <br>
is interpolation at Schoenenberg -- points of <br>
a(u,v)* N(u,v) and a(u,v) * D(u,v) <br>
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(u,v)*F(u,v)
–
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Get from FP the coordinates of the poles.
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Get from FP the coordinates of the poles.
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Makes an homogeneous evaluation of Poles and Weights <br>
any and returns in P the Numerator value and <br>
in W the Denominator value if Weights are present <br>
otherwise returns 1.0e0 <br>
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Makes an homogeneous evaluation of Poles and Weights <br>
any and returns in P the Numerator value and <br>
in W the Denominator value if Weights are present <br>
otherwise returns 1.0e0 <br>
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Performs the interpolation of the data points given in <br>
the Poles array in the form <br>
[1,...,RL][1,...,RC][1...PolesDimension] . The <br>
ColLength CL and the Length of UParameters must be the <br>
same. The length of VFlatKnots is VDegree + CL + 1. <br>
The RowLength RL and the Length of VParameters must be
the same. The length of VFlatKnots is Degree + RL + 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
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Performs the interpolation of the data points given in <br>
the Poles array. <br>
The ColLength CL and the Length of UParameters must be <br>
the same. The length of VFlatKnots is VDegree + CL + 1. <br>
The RowLength RL and the Length of VParameters must be
the same. The length of VFlatKnots is Degree + RL + 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
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Computes the poles and weights of an isoparametric
curve at parameter (UIso if <IsU> is True,
VIso else).
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Returns False if all the weights of the array <Weights>
in the area [I1,I2] * [J1,J2] are identic.
Epsilon is used for comparing weights.
If Epsilon is 0. the Epsilon of the first weight is used.
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Find the new poles which allows an old point (with a
given u,v as parameters) to reach a new position
UIndex1,UIndex2 indicate the range of poles we can
move for U
(1, UNbPoles-1) or (2, UNbPoles) -> no constraint
for one side in U
(2, UNbPoles-1) -> the ends are enforced for U
don't enter (1,NbPoles) and (1,VNbPoles)
-> error: rigid move
if problem in BSplineBasis calculation, no change
for the curve and
UFirstIndex, VLastIndex = 0
VFirstIndex, VLastIndex = 0
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Used as argument for a non rational curve. <br>
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Warning! To be used for BezierSurfaces ONLY!!!
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Encapsulation of BuildCache to perform the <br>
evaluation of the Taylor expansion for beziersurfaces <br>
at parameters 0.,0.; <br>
Warning: To be used for BezierSurfaces ONLY!!!
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this is a one dimensional function <br>
typedef void (*EvaluatorFunction) (
Standard_Integer // Derivative Request
Standard_Real * // StartEnd[2][2]
// [0] = U
// [1] = V
// [0] = start
// [1] = end
Standard_Real // UParameter
Standard_Real // VParamerer
Standard_Real & // Result
Standard_Integer &) ;// Error Code
serves to multiply a given vectorial BSpline by a function
//! Computes the derivatives of a ratio of
two-variables functions x(u,v) / w(u,v) at orders
<N,M>, x(u,v) is a vector in dimension
<3>.
<Ders> is an array containing the values of the
input derivatives from 0 to Min(<N>,<UDeg>), 0 to
Min(<M>,<VDeg>). For orders higher than
<UDeg,VDeg> the input derivatives are assumed to
be 0.
The <Ders> is a 2d array and the dimension of the
lines is always (<VDeg>+1) * (<3>+1), even
if <N> is smaller than <Udeg> (the derivatives
higher than <N> are not used).
Content of <Ders> :
x(i,j)[k] means : the composant k of x derivated
(i) times in u and (j) times in v.
... First line ...
x[1],x[2],...,x[3],w
x(0,1)[1],...,x(0,1)[3],w(1,0)
...
x(0,VDeg)[1],...,x(0,VDeg)[3],w(0,VDeg)
... Then second line ...
x(1,0)[1],...,x(1,0)[3],w(1,0)
x(1,1)[1],...,x(1,1)[3],w(1,1)
...
x(1,VDeg)[1],...,x(1,VDeg)[3],w(1,VDeg)
...
... Last line ...
x(UDeg,0)[1],...,x(UDeg,0)[3],w(UDeg,0)
x(UDeg,1)[1],...,x(UDeg,1)[3],w(UDeg,1)
...
x(Udeg,VDeg)[1],...,x(UDeg,VDeg)[3],w(Udeg,VDeg)
If <All> is false, only the derivative at order
<N,M> is computed. <RDers> is an array of length
3 which will contain the result :
x(1)/w , x(2)/w , ... derivated <N> <M> times
If <All> is true multiples derivatives are
computed. All the derivatives (i,j) with 0 <= i+j
<= Max(N,M) are computed. <RDers> is an array of
length 3 * (<N>+1) * (<M>+1) which will
contains :
x(1)/w , x(2)/w , ...
x(1)/w , x(2)/w , ... derivated <0,1> times
x(1)/w , x(2)/w , ... derivated <0,2> times
...
x(1)/w , x(2)/w , ... derivated <0,N> times
x(1)/w , x(2)/w , ... derivated <1,0> times
x(1)/w , x(2)/w , ... derivated <1,1> times
...
x(1)/w , x(2)/w , ... derivated <1,N> times
x(1)/w , x(2)/w , ... derivated <N,0> times
....
Warning: <RDers> must be dimensionned properly.
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Given a tolerance in 3D space returns two
tolerances, one in U one in V such that for
all (u1,v1) and (u0,v0) in the domain of
the surface f(u,v) we have :
| u1 - u0 | < UTolerance and
| v1 - v0 | < VTolerance
we have |f (u1,v1) - f (u0,v0)| < Tolerance3D
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Reverses the array of poles. Last is the Index of
the new first Row( Col) of Poles.
On a non periodic surface 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
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Reverses the array of weights.
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Copy in FP the coordinates of the poles.
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Copy in FP the coordinates of the poles.
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1.8.5