Describes functions for computing all the extrema
between a curve and a surface.
An ExtremaCurveSurface algorithm minimizes or
maximizes the distance between a point on the curve
and a point on the surface. Thus, it computes start
and end points of perpendiculars common to the
curve and the surface (an intersection point is not an
extremum except where the curve and the surface
are tangential at this point).
Solutions consist of pairs of points, and an extremum
is considered to be a segment joining the two points of a solution.
An ExtremaCurveSurface object provides a framework for:
More...

#include <GeomAPI_ExtremaCurveSurface.hxx>

Public Member Functions
	GeomAPI_ExtremaCurveSurface ()
	Constructs an empty algorithm for computing <br> extrema between a curve and a surface. Use an Init function to define the curve and the surface on which it is going to work. More...

	GeomAPI_ExtremaCurveSurface (const Handle< Geom_Curve > &Curve, const Handle< Geom_Surface > &Surface)
	Computes the extrema distances between the curve `and the surface <S>.` More...

	GeomAPI_ExtremaCurveSurface (const Handle< Geom_Curve > &Curve, const Handle< Geom_Surface > &Surface, const Quantity_Parameter Wmin, const Quantity_Parameter Wmax, const Quantity_Parameter Umin, const Quantity_Parameter Umax, const Quantity_Parameter Vmin, const Quantity_Parameter Vmax)
	Computes the extrema distances between the <br> curve <C> and the surface <S>. The solution <br> point are computed in the domain [Wmin,Wmax] of <br> the curve and in the domain [Umin,Umax] <br> [Vmin,Vmax] of the surface. <br> Warning Use the function NbExtrema to obtain the number of solutions. If this algorithm fails, NbExtrema returns 0. More...

void	Init (const Handle< Geom_Curve > &Curve, const Handle< Geom_Surface > &Surface)
	Computes the extrema distances between the curve `and the surface <S>.` More...

void	Init (const Handle< Geom_Curve > &Curve, const Handle< Geom_Surface > &Surface, const Quantity_Parameter Wmin, const Quantity_Parameter Wmax, const Quantity_Parameter Umin, const Quantity_Parameter Umax, const Quantity_Parameter Vmin, const Quantity_Parameter Vmax)
	Computes the extrema distances between the <br> curve <C> and the surface <S>. The solution <br> point are computed in the domain [Wmin,Wmax] of <br> the curve and in the domain [Umin,Umax] <br> [Vmin,Vmax] of the surface. <br> Warning Use the function NbExtrema to obtain the number of solutions. If this algorithm fails, NbExtrema returns 0. More...

Standard_Integer	NbExtrema () const
	Returns the number of extrema computed by this algorithm. <br> Note: if this algorithm fails, NbExtrema returns 0. More...

	operator Standard_Integer () const

void	Points (const Standard_Integer Index, gp_Pnt &P1, gp_Pnt &P2) const
	Returns the points P1 on the curve and P2 on the <br> surface, which are the ends of the extremum of index Index computed by this algorithm. Exceptions Standard_OutOfRange if Index is not in the range [ 1,NbExtrema ], where NbExtrema is the number of extrema computed by this algorithm. More...

void	Parameters (const Standard_Integer Index, Quantity_Parameter &W, Quantity_Parameter &U, Quantity_Parameter &V) const
	Returns the parameters W of the point on the curve, <br> and (U,V) of the point on the surface, which are the ends of the extremum of index Index computed by this algorithm. Exceptions Standard_OutOfRange if Index is not in the range [ 1,NbExtrema ], where NbExtrema is the number of extrema computed by this algorithm. More...

Quantity_Length	Distance (const Standard_Integer Index) const
	Computes the distance between the end points of the <br> extremum of index Index computed by this algorithm. Exceptions Standard_OutOfRange if index is not in the range [ 1,NbExtrema ], where NbExtrema is the number of extrema computed by this algorithm. More...

void	NearestPoints (gp_Pnt &PC, gp_Pnt &PS) const
	Returns the points PC on the curve and PS on the <br> surface, which are the ends of the shortest extremum computed by this algorithm. Exceptions - StdFail_NotDone if this algorithm fails. More...

void	LowerDistanceParameters (Quantity_Parameter &W, Quantity_Parameter &U, Quantity_Parameter &V) const
	Returns the parameters W of the point on the curve <br> and (U,V) of the point on the surface, which are the ends of the shortest extremum computed by this algorithm. Exceptions - StdFail_NotDone if this algorithm fails. More...

Quantity_Length	LowerDistance () const
	Computes the distance between the end points of the <br> shortest extremum computed by this algorithm. Exceptions - StdFail_NotDone if this algorithm fails. More...

	operator Standard_Real () const

const Extrema_ExtCS &	Extrema () const
	Returns the algorithmic object from Extrema More...

Detailed Description

Describes functions for computing all the extrema
between a curve and a surface.
An ExtremaCurveSurface algorithm minimizes or
maximizes the distance between a point on the curve
and a point on the surface. Thus, it computes start
and end points of perpendiculars common to the
curve and the surface (an intersection point is not an
extremum except where the curve and the surface
are tangential at this point).
Solutions consist of pairs of points, and an extremum
is considered to be a segment joining the two points of a solution.
An ExtremaCurveSurface object provides a framework for:

defining the construction of the extrema,
implementing the construction algorithm, and
consulting the results.
Warning
In some cases, the nearest points between a curve
and a surface do not correspond to one of the
computed extrema. Instead, they may be given by:
a point of a bounding curve of the surface and one of the following:
- its orthogonal projection on the curve,
- a limit point of the curve; or
a limit point of the curve and its projection on the surface; or
an intersection point between the curve and the surface.

Constructor & Destructor Documentation

GeomAPI_ExtremaCurveSurface::GeomAPI_ExtremaCurveSurface ( )

 Constructs an empty algorithm for computing <br>

extrema between a curve and a surface. Use an
Init function to define the curve and the surface on
which it is going to work.

GeomAPI_ExtremaCurveSurface::GeomAPI_ExtremaCurveSurface	(	const Handle< Geom_Curve > &	Curve,
		const Handle< Geom_Surface > &	Surface
	)

Computes the extrema distances between the
curve and the surface <S>.

GeomAPI_ExtremaCurveSurface::GeomAPI_ExtremaCurveSurface	(	const Handle< Geom_Curve > &	Curve,
		const Handle< Geom_Surface > &	Surface,
		const Quantity_Parameter	Wmin,
		const Quantity_Parameter	Wmax,
		const Quantity_Parameter	Umin,
		const Quantity_Parameter	Umax,
		const Quantity_Parameter	Vmin,
		const Quantity_Parameter	Vmax
	)

 Computes  the  extrema  distances  between  the <br>
     curve <C>  and the  surface  <S>.  The solution <br>
     point are computed in the domain [Wmin,Wmax] of <br>
     the  curve   and  in  the  domain   [Umin,Umax] <br>
     [Vmin,Vmax] of the surface. <br>

Warning
Use the function NbExtrema to obtain the number
of solutions. If this algorithm fails, NbExtrema returns 0.

Member Function Documentation

Quantity_Length GeomAPI_ExtremaCurveSurface::Distance ( const Standard_Integer Index ) const

 Computes the distance between the end points of the <br>

extremum of index Index computed by this algorithm.
Exceptions
Standard_OutOfRange if index is not in the range [
1,NbExtrema ], where NbExtrema is the
number of extrema computed by this algorithm.

const Extrema_ExtCS& GeomAPI_ExtremaCurveSurface::Extrema ( ) const

Returns the algorithmic object from Extrema

void GeomAPI_ExtremaCurveSurface::Init	(	const Handle< Geom_Curve > &	Curve,
		const Handle< Geom_Surface > &	Surface
	)

Computes the extrema distances between the
curve and the surface <S>.

void GeomAPI_ExtremaCurveSurface::Init	(	const Handle< Geom_Curve > &	Curve,
		const Handle< Geom_Surface > &	Surface,
		const Quantity_Parameter	Wmin,
		const Quantity_Parameter	Wmax,
		const Quantity_Parameter	Umin,
		const Quantity_Parameter	Umax,
		const Quantity_Parameter	Vmin,
		const Quantity_Parameter	Vmax
	)

 Computes  the  extrema  distances  between  the <br>
     curve <C>  and the  surface  <S>.  The solution <br>
     point are computed in the domain [Wmin,Wmax] of <br>
     the  curve   and  in  the  domain   [Umin,Umax] <br>
     [Vmin,Vmax] of the surface. <br>

Warning
Use the function NbExtrema to obtain the number
of solutions. If this algorithm fails, NbExtrema returns 0.

Quantity_Length GeomAPI_ExtremaCurveSurface::LowerDistance ( ) const

 Computes the distance between the end points of the <br>

shortest extremum computed by this algorithm.
Exceptions - StdFail_NotDone if this algorithm fails.

void GeomAPI_ExtremaCurveSurface::LowerDistanceParameters	(	Quantity_Parameter &	W,
		Quantity_Parameter &	U,
		Quantity_Parameter &	V
	)		const

 Returns the parameters W of the point on the curve <br>

and (U,V) of the point on the surface, which are the
ends of the shortest extremum computed by this algorithm.
Exceptions - StdFail_NotDone if this algorithm fails.

Standard_Integer GeomAPI_ExtremaCurveSurface::NbExtrema ( ) const

 Returns the number of extrema computed by this algorithm. <br>

Note: if this algorithm fails, NbExtrema returns 0.

void GeomAPI_ExtremaCurveSurface::NearestPoints	(	gp_Pnt &	PC,
		gp_Pnt &	PS
	)		const

 Returns the points PC on the curve and PS on the <br>

surface, which are the ends of the shortest extremum computed by this algorithm.
Exceptions - StdFail_NotDone if this algorithm fails.

GeomAPI_ExtremaCurveSurface::operator Standard_Integer ( ) const

GeomAPI_ExtremaCurveSurface::operator Standard_Real ( ) const

void GeomAPI_ExtremaCurveSurface::Parameters	(	const Standard_Integer	Index,
		Quantity_Parameter &	W,
		Quantity_Parameter &	U,
		Quantity_Parameter &	V
	)		const

 Returns the parameters W of the point on the curve, <br>

and (U,V) of the point on the surface, which are the
ends of the extremum of index Index computed by this algorithm.
Exceptions
Standard_OutOfRange if Index is not in the range [
1,NbExtrema ], where NbExtrema is the
number of extrema computed by this algorithm.

void GeomAPI_ExtremaCurveSurface::Points	(	const Standard_Integer	Index,
		gp_Pnt &	P1,
		gp_Pnt &	P2
	)		const

 Returns the points P1 on the curve and P2 on the <br>

surface, which are the ends of the extremum of index
Index computed by this algorithm.
Exceptions
Standard_OutOfRange if Index is not in the range [
1,NbExtrema ], where NbExtrema is the
number of extrema computed by this algorithm.

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

GeomAPI_ExtremaCurveSurface.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation