# GeomConvert_BSplineSurfaceKnotSplitting Class Reference

An algorithm to determine isoparametric curves along which a BSpline surface should be split in order to obtain patches of the same continuity. The continuity order is given at the construction time. It is possible to compute the surface patches corresponding to the splitting with the method of package SplitBSplineSurface. For a B-spline surface the discontinuities are localised at the knot values. Between two knots values the B-spline is infinitely continuously differentiable. For each parametric direction at a knot of range index the continuity in this direction is equal to : Degree - Mult (Index) where Degree is the degree of the basis B-spline functions and Mult the multiplicity of the knot of range Index in the given direction. If for your computation you need to have B-spline surface with a minima of continuity it can be interesting to know between which knot values, a B-spline patch, has a continuity of given order. This algorithm computes the indexes of the knots where you should split the surface, to obtain patches with a constant continuity given at the construction time. If you just want to compute the local derivatives on the surface you don't need to create the BSpline patches, you can use the functions LocalD1, LocalD2, LocalD3, LocalDN of the class BSplineSurface from package Geom. More...

`#include <GeomConvert_BSplineSurfaceKnotSplitting.hxx>`

## Public Member Functions

GeomConvert_BSplineSurfaceKnotSplitting (const Handle< Geom_BSplineSurface > &BasisSurface, const Standard_Integer UContinuityRange, const Standard_Integer VContinuityRange)
Determines the u- and v-isoparametric curves along which the BSpline surface BasisSurface should be split in order to obtain patches with a degree of continuity equal to UContinuityRange in the u parametric direction, and to VContinuityRange in the v parametric direction. These isoparametric curves are defined by parameters, which are BasisSurface knot values in the u or v parametric direction. They are identified by indices in the BasisSurface knots table in the corresponding parametric direction. Use the available interrogation functions to access computed values, followed by the global function SplitBSplineSurface (provided by the package GeomConvert) to split the surface. Exceptions Standard_RangeError if UContinuityRange or VContinuityRange is less than zero. More...

Standard_Integer NbUSplits () const
Returns the number of u-isoparametric curves along which the analysed BSpline surface should be split in order to obtain patches with the continuity required by this framework. The parameters which define these curves are knot values in the corresponding parametric direction. Note that the four curves which bound the surface are counted among these splitting curves. More...

Standard_Integer NbVSplits () const
Returns the number of v-isoparametric curves along which the analysed BSpline surface should be split in order to obtain patches with the continuity required by this framework. The parameters which define these curves are knot values in the corresponding parametric direction. Note that the four curves which bound the surface are counted among these splitting curves. More...

void Splitting (TColStd_Array1OfInteger &USplit, TColStd_Array1OfInteger &VSplit) const
Loads the USplit and VSplit tables with the split knots values computed in this framework. Each value in these tables is an index in the knots table corresponding to the u or v parametric direction of the BSpline surface analysed by this algorithm. The USplit and VSplit values are given in ascending order and comprise the indices of the knots which give the first and last isoparametric curves of the surface in the corresponding parametric direction. Use two consecutive values from the USplit table and two consecutive values from the VSplit table as arguments of the global function SplitBSplineSurface (provided by the package GeomConvert) to split the surface. Exceptions Standard_DimensionError if: More...

Standard_Integer USplitValue (const Standard_Integer UIndex) const
Returns the split knot of index UIndex to the split knots table for the u parametric direction computed in this framework. The returned value is an index in the knots table relative to the u parametric direction of the BSpline surface analysed by this algorithm. Note: If UIndex is equal to 1, or to the number of split knots for the u parametric direction computed in this framework, the corresponding knot gives the parameter of one of the bounding curves of the surface. Exceptions Standard_RangeError if UIndex is less than 1 or greater than the number of split knots for the u parametric direction computed in this framework. More...

Standard_Integer VSplitValue (const Standard_Integer VIndex) const
Returns the split knot of index VIndex to the split knots table for the v parametric direction computed in this framework. The returned value is an index in the knots table relative to the v parametric direction of the BSpline surface analysed by this algorithm. Note: If UIndex is equal to 1, or to the number of split knots for the v parametric direction computed in this framework, the corresponding knot gives the parameter of one of the bounding curves of the surface. Exceptions Standard_RangeError if VIndex is less than 1 or greater than the number of split knots for the v parametric direction computed in this framework. More...

## Detailed Description

An algorithm to determine isoparametric curves along which a BSpline surface should be split in order to obtain patches of the same continuity. The continuity order is given at the construction time. It is possible to compute the surface patches corresponding to the splitting with the method of package SplitBSplineSurface. For a B-spline surface the discontinuities are localised at the knot values. Between two knots values the B-spline is infinitely continuously differentiable. For each parametric direction at a knot of range index the continuity in this direction is equal to : Degree - Mult (Index) where Degree is the degree of the basis B-spline functions and Mult the multiplicity of the knot of range Index in the given direction. If for your computation you need to have B-spline surface with a minima of continuity it can be interesting to know between which knot values, a B-spline patch, has a continuity of given order. This algorithm computes the indexes of the knots where you should split the surface, to obtain patches with a constant continuity given at the construction time. If you just want to compute the local derivatives on the surface you don't need to create the BSpline patches, you can use the functions LocalD1, LocalD2, LocalD3, LocalDN of the class BSplineSurface from package Geom.

## Constructor & Destructor Documentation

 GeomConvert_BSplineSurfaceKnotSplitting::GeomConvert_BSplineSurfaceKnotSplitting ( const Handle< Geom_BSplineSurface > & BasisSurface, const Standard_Integer UContinuityRange, const Standard_Integer VContinuityRange )

Determines the u- and v-isoparametric curves along which the BSpline surface BasisSurface should be split in order to obtain patches with a degree of continuity equal to UContinuityRange in the u parametric direction, and to VContinuityRange in the v parametric direction. These isoparametric curves are defined by parameters, which are BasisSurface knot values in the u or v parametric direction. They are identified by indices in the BasisSurface knots table in the corresponding parametric direction. Use the available interrogation functions to access computed values, followed by the global function SplitBSplineSurface (provided by the package GeomConvert) to split the surface. Exceptions Standard_RangeError if UContinuityRange or VContinuityRange is less than zero.

## Member Function Documentation

 Standard_Integer GeomConvert_BSplineSurfaceKnotSplitting::NbUSplits ( ) const

Returns the number of u-isoparametric curves along which the analysed BSpline surface should be split in order to obtain patches with the continuity required by this framework. The parameters which define these curves are knot values in the corresponding parametric direction. Note that the four curves which bound the surface are counted among these splitting curves.

 Standard_Integer GeomConvert_BSplineSurfaceKnotSplitting::NbVSplits ( ) const

Returns the number of v-isoparametric curves along which the analysed BSpline surface should be split in order to obtain patches with the continuity required by this framework. The parameters which define these curves are knot values in the corresponding parametric direction. Note that the four curves which bound the surface are counted among these splitting curves.

 void GeomConvert_BSplineSurfaceKnotSplitting::Splitting ( TColStd_Array1OfInteger & USplit, TColStd_Array1OfInteger & VSplit ) const

Loads the USplit and VSplit tables with the split knots values computed in this framework. Each value in these tables is an index in the knots table corresponding to the u or v parametric direction of the BSpline surface analysed by this algorithm. The USplit and VSplit values are given in ascending order and comprise the indices of the knots which give the first and last isoparametric curves of the surface in the corresponding parametric direction. Use two consecutive values from the USplit table and two consecutive values from the VSplit table as arguments of the global function SplitBSplineSurface (provided by the package GeomConvert) to split the surface. Exceptions Standard_DimensionError if:

• the array USplit was not created with the following bounds:
• 1 , and
• the number of split knots in the u parametric direction computed in this framework (as given by the function NbUSplits); or
• the array VSplit was not created with the following bounds:
• 1 , and
• the number of split knots in the v parametric direction computed in this framework (as given by the function NbVSplits).
 Standard_Integer GeomConvert_BSplineSurfaceKnotSplitting::USplitValue ( const Standard_Integer UIndex ) const

Returns the split knot of index UIndex to the split knots table for the u parametric direction computed in this framework. The returned value is an index in the knots table relative to the u parametric direction of the BSpline surface analysed by this algorithm. Note: If UIndex is equal to 1, or to the number of split knots for the u parametric direction computed in this framework, the corresponding knot gives the parameter of one of the bounding curves of the surface. Exceptions Standard_RangeError if UIndex is less than 1 or greater than the number of split knots for the u parametric direction computed in this framework.

 Standard_Integer GeomConvert_BSplineSurfaceKnotSplitting::VSplitValue ( const Standard_Integer VIndex ) const

Returns the split knot of index VIndex to the split knots table for the v parametric direction computed in this framework. The returned value is an index in the knots table relative to the v parametric direction of the BSpline surface analysed by this algorithm. Note: If UIndex is equal to 1, or to the number of split knots for the v parametric direction computed in this framework, the corresponding knot gives the parameter of one of the bounding curves of the surface. Exceptions Standard_RangeError if VIndex is less than 1 or greater than the number of split knots for the v parametric direction computed in this framework.

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