# GeomAPI_PointsToBSplineSurface Class Reference

This class is used to approximate or interpolate a BSplineSurface passing through an Array2 of points, with a given continuity. Describes functions for building a BSpline surface which approximates or interpolates a set of points. A PointsToBSplineSurface object provides a framework for: More...

`#include <GeomAPI_PointsToBSplineSurface.hxx>`

## Public Member Functions

GeomAPI_PointsToBSplineSurface ()
Constructs an empty algorithm for approximation or interpolation of a surface. Use: More...

GeomAPI_PointsToBSplineSurface (const TColgp_Array2OfPnt &Points, const Standard_Integer DegMin=3, const Standard_Integer DegMax=8, const GeomAbs_Shape Continuity=GeomAbs_C2, const Standard_Real Tol3D=1.0e-3)
Approximates a BSpline Surface passing through an array of Points. The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D. More...

GeomAPI_PointsToBSplineSurface (const TColgp_Array2OfPnt &Points, const Approx_ParametrizationType ParType, const Standard_Integer DegMin=3, const Standard_Integer DegMax=8, const GeomAbs_Shape Continuity=GeomAbs_C2, const Standard_Real Tol3D=1.0e-3)
Approximates a BSpline Surface passing through an array of Points. The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D. More...

GeomAPI_PointsToBSplineSurface (const TColgp_Array2OfPnt &Points, const Standard_Real Weight1, const Standard_Real Weight2, const Standard_Real Weight3, const Standard_Integer DegMax=8, const GeomAbs_Shape Continuity=GeomAbs_C2, const Standard_Real Tol3D=1.0e-3)
Approximates a BSpline Surface passing through an array of points using variational smoothing algorithm, which tries to minimize additional criterium: Weight1*CurveLength + Weight2*Curvature + Weight3*Torsion. More...

GeomAPI_PointsToBSplineSurface (const TColStd_Array2OfReal &ZPoints, const Standard_Real X0, const Standard_Real dX, const Standard_Real Y0, const Standard_Real dY, const Standard_Integer DegMin=3, const Standard_Integer DegMax=8, const GeomAbs_Shape Continuity=GeomAbs_C2, const Standard_Real Tol3D=1.0e-3)
Approximates a BSpline Surface passing through an array of Points. More...

void Init (const TColgp_Array2OfPnt &Points, const Standard_Integer DegMin=3, const Standard_Integer DegMax=8, const GeomAbs_Shape Continuity=GeomAbs_C2, const Standard_Real Tol3D=1.0e-3)
Approximates a BSpline Surface passing through an array of Point. The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D. More...

void Interpolate (const TColgp_Array2OfPnt &Points, const Standard_Boolean thePeriodic=Standard_False)
Interpolates a BSpline Surface passing through an array of Point. The resulting BSpline will have the following properties: 1- his degree will be 3. 2- his continuity will be C2. More...

void Interpolate (const TColgp_Array2OfPnt &Points, const Approx_ParametrizationType ParType, const Standard_Boolean thePeriodic=Standard_False)
Interpolates a BSpline Surface passing through an array of Point. The resulting BSpline will have the following properties: 1- his degree will be 3. 2- his continuity will be C2. More...

void Init (const TColStd_Array2OfReal &ZPoints, const Standard_Real X0, const Standard_Real dX, const Standard_Real Y0, const Standard_Real dY, const Standard_Integer DegMin=3, const Standard_Integer DegMax=8, const GeomAbs_Shape Continuity=GeomAbs_C2, const Standard_Real Tol3D=1.0e-3)
Approximates a BSpline Surface passing through an array of Points. More...

void Interpolate (const TColStd_Array2OfReal &ZPoints, const Standard_Real X0, const Standard_Real dX, const Standard_Real Y0, const Standard_Real dY)
Interpolates a BSpline Surface passing through an array of Points. More...

void Init (const TColgp_Array2OfPnt &Points, const Approx_ParametrizationType ParType, const Standard_Integer DegMin=3, const Standard_Integer DegMax=8, const GeomAbs_Shape Continuity=GeomAbs_C2, const Standard_Real Tol3D=1.0e-3, const Standard_Boolean thePeriodic=Standard_False)
Approximates a BSpline Surface passing through an array of Point. The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D. More...

void Init (const TColgp_Array2OfPnt &Points, const Standard_Real Weight1, const Standard_Real Weight2, const Standard_Real Weight3, const Standard_Integer DegMax=8, const GeomAbs_Shape Continuity=GeomAbs_C2, const Standard_Real Tol3D=1.0e-3)
Approximates a BSpline Surface passing through an array of point using variational smoothing algorithm, which tries to minimize additional criterium: Weight1*CurveLength + Weight2*Curvature + Weight3*Torsion. More...

const Handle< Geom_BSplineSurface > & Surface () const
Returns the approximate BSpline Surface. More...

operator Handle< Geom_BSplineSurface > () const

Standard_Boolean IsDone () const

## Detailed Description

This class is used to approximate or interpolate a BSplineSurface passing through an Array2 of points, with a given continuity. Describes functions for building a BSpline surface which approximates or interpolates a set of points. A PointsToBSplineSurface object provides a framework for:

• defining the data of the BSpline surface to be built,
• implementing the approximation algorithm or the interpolation algorithm, and consulting the results. In fact, class contains 3 algorithms, 2 for approximation and 1 for interpolation. First approximation algorithm is based on usual least square criterium: minimization of square distance between samplimg points and result surface. Second approximation algorithm uses least square criterium and additional minimization of some local characteristic of surface (first, second and third partial derivative), which allows managing shape of surface. Interpolation algorithm produces surface, which passes through sampling points.

There is accordance between parametrization of result surface S(U, V) and indexes of array Points(i, j): first index corresponds U parameter of surface, second - V parameter of surface. So, points of any j-th column Points(*, j) represent any V isoline of surface, points of any i-th row Point(i, *) represent any U isoline of surface.

For each sampling point parameters U, V are calculated according to type of parametrization, which can be Approx_ChordLength, Approx_Centripetal or Approx_IsoParametric. Default value is Approx_ChordLength. For ChordLength parametrisation U(i) = U(i-1) + P(i).Distance(P(i-1)), For Centripetal type U(i) = U(i-1) + Sqrt(P(i).Distance(P(i-1))). Centripetal type can get better result for irregular distances between points.

Approximation and interpolation algorithms can build periodical surface along U direction, which corresponds columns of array Points(i, j), if corresponding parameter (thePeriodic, see comments below) of called methods is set to True. Algorithm uses first row Points(1, *) as periodic boundary, so to avoid getting wrong surface it is necessary to keep distance between corresponding points of first and last rows of Points: Points(1, *) != Points(Upper, *).

## ◆ GeomAPI_PointsToBSplineSurface() [1/5]

 GeomAPI_PointsToBSplineSurface::GeomAPI_PointsToBSplineSurface ( )

Constructs an empty algorithm for approximation or interpolation of a surface. Use:

• an Init function to define and build the BSpline surface by approximation, or
• an Interpolate function to define and build the BSpline surface by interpolation.

## ◆ GeomAPI_PointsToBSplineSurface() [2/5]

 GeomAPI_PointsToBSplineSurface::GeomAPI_PointsToBSplineSurface ( const TColgp_Array2OfPnt & Points, const Standard_Integer DegMin = `3`, const Standard_Integer DegMax = `8`, const GeomAbs_Shape Continuity = `GeomAbs_C2`, const Standard_Real Tol3D = `1.0e-3` )

Approximates a BSpline Surface passing through an array of Points. The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D.

## ◆ GeomAPI_PointsToBSplineSurface() [3/5]

 GeomAPI_PointsToBSplineSurface::GeomAPI_PointsToBSplineSurface ( const TColgp_Array2OfPnt & Points, const Approx_ParametrizationType ParType, const Standard_Integer DegMin = `3`, const Standard_Integer DegMax = `8`, const GeomAbs_Shape Continuity = `GeomAbs_C2`, const Standard_Real Tol3D = `1.0e-3` )

Approximates a BSpline Surface passing through an array of Points. The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D.

## ◆ GeomAPI_PointsToBSplineSurface() [4/5]

 GeomAPI_PointsToBSplineSurface::GeomAPI_PointsToBSplineSurface ( const TColgp_Array2OfPnt & Points, const Standard_Real Weight1, const Standard_Real Weight2, const Standard_Real Weight3, const Standard_Integer DegMax = `8`, const GeomAbs_Shape Continuity = `GeomAbs_C2`, const Standard_Real Tol3D = `1.0e-3` )

Approximates a BSpline Surface passing through an array of points using variational smoothing algorithm, which tries to minimize additional criterium: Weight1*CurveLength + Weight2*Curvature + Weight3*Torsion.

## ◆ GeomAPI_PointsToBSplineSurface() [5/5]

 GeomAPI_PointsToBSplineSurface::GeomAPI_PointsToBSplineSurface ( const TColStd_Array2OfReal & ZPoints, const Standard_Real X0, const Standard_Real dX, const Standard_Real Y0, const Standard_Real dY, const Standard_Integer DegMin = `3`, const Standard_Integer DegMax = `8`, const GeomAbs_Shape Continuity = `GeomAbs_C2`, const Standard_Real Tol3D = `1.0e-3` )

Approximates a BSpline Surface passing through an array of Points.

The points will be constructed as follow: P(i,j) = gp_Pnt( X0 + (i-1)*dX , Y0 + (j-1)*dY , ZPoints(i,j) )

The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D 4- the parametrization of the surface will verify: S->Value( U, V) = gp_Pnt( U, V, Z(U,V) );

## ◆ Init() [1/4]

 void GeomAPI_PointsToBSplineSurface::Init ( const TColgp_Array2OfPnt & Points, const Approx_ParametrizationType ParType, const Standard_Integer DegMin = `3`, const Standard_Integer DegMax = `8`, const GeomAbs_Shape Continuity = `GeomAbs_C2`, const Standard_Real Tol3D = `1.0e-3`, const Standard_Boolean thePeriodic = `Standard_False` )

Approximates a BSpline Surface passing through an array of Point. The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D.

## ◆ Init() [2/4]

 void GeomAPI_PointsToBSplineSurface::Init ( const TColgp_Array2OfPnt & Points, const Standard_Integer DegMin = `3`, const Standard_Integer DegMax = `8`, const GeomAbs_Shape Continuity = `GeomAbs_C2`, const Standard_Real Tol3D = `1.0e-3` )

Approximates a BSpline Surface passing through an array of Point. The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D.

## ◆ Init() [3/4]

 void GeomAPI_PointsToBSplineSurface::Init ( const TColgp_Array2OfPnt & Points, const Standard_Real Weight1, const Standard_Real Weight2, const Standard_Real Weight3, const Standard_Integer DegMax = `8`, const GeomAbs_Shape Continuity = `GeomAbs_C2`, const Standard_Real Tol3D = `1.0e-3` )

Approximates a BSpline Surface passing through an array of point using variational smoothing algorithm, which tries to minimize additional criterium: Weight1*CurveLength + Weight2*Curvature + Weight3*Torsion.

## ◆ Init() [4/4]

 void GeomAPI_PointsToBSplineSurface::Init ( const TColStd_Array2OfReal & ZPoints, const Standard_Real X0, const Standard_Real dX, const Standard_Real Y0, const Standard_Real dY, const Standard_Integer DegMin = `3`, const Standard_Integer DegMax = `8`, const GeomAbs_Shape Continuity = `GeomAbs_C2`, const Standard_Real Tol3D = `1.0e-3` )

Approximates a BSpline Surface passing through an array of Points.

The points will be constructed as follow: P(i,j) = gp_Pnt( X0 + (i-1)*dX , Y0 + (j-1)*dY , ZPoints(i,j) )

The resulting BSpline will have the following properties: 1- his degree will be in the range [Degmin,Degmax] 2- his continuity will be at least <Continuity> 3- the distance from the point <Points> to the BSpline will be lower to Tol3D 4- the parametrization of the surface will verify: S->Value( U, V) = gp_Pnt( U, V, Z(U,V) );

## ◆ Interpolate() [1/3]

 void GeomAPI_PointsToBSplineSurface::Interpolate ( const TColgp_Array2OfPnt & Points, const Approx_ParametrizationType ParType, const Standard_Boolean thePeriodic = `Standard_False` )

Interpolates a BSpline Surface passing through an array of Point. The resulting BSpline will have the following properties: 1- his degree will be 3. 2- his continuity will be C2.

## ◆ Interpolate() [2/3]

 void GeomAPI_PointsToBSplineSurface::Interpolate ( const TColgp_Array2OfPnt & Points, const Standard_Boolean thePeriodic = `Standard_False` )

Interpolates a BSpline Surface passing through an array of Point. The resulting BSpline will have the following properties: 1- his degree will be 3. 2- his continuity will be C2.

## ◆ Interpolate() [3/3]

 void GeomAPI_PointsToBSplineSurface::Interpolate ( const TColStd_Array2OfReal & ZPoints, const Standard_Real X0, const Standard_Real dX, const Standard_Real Y0, const Standard_Real dY )

Interpolates a BSpline Surface passing through an array of Points.

The points will be constructed as follow: P(i,j) = gp_Pnt( X0 + (i-1)*dX , Y0 + (j-1)*dY , ZPoints(i,j) )

The resulting BSpline will have the following properties: 1- his degree will be 3 2- his continuity will be C2. 4- the parametrization of the surface will verify: S->Value( U, V) = gp_Pnt( U, V, Z(U,V) );

## ◆ IsDone()

 Standard_Boolean GeomAPI_PointsToBSplineSurface::IsDone ( ) const

## ◆ operator Handle< Geom_BSplineSurface >()

 GeomAPI_PointsToBSplineSurface::operator Handle< Geom_BSplineSurface > ( ) const

## ◆ Surface()

 const Handle< Geom_BSplineSurface >& GeomAPI_PointsToBSplineSurface::Surface ( ) const

Returns the approximate BSpline Surface.

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