regina::NSnappedTwoSphere Class Reference
[Standard Triangulations and Subcomplexes]

Represents a 2-sphere made from two snapped 3-balls in a triangulation. More...

#include <nsnappedtwosphere.h>

Inheritance diagram for regina::NSnappedTwoSphere:

List of all members.

Public Member Functions
virtual	~NSnappedTwoSphere ()
	Destroys this snapped 2-sphere; note that the corresponding snapped 3-balls will also be destroyed.
NSnappedTwoSphere *	clone () const
	Returns a newly created clone of this structure.
const NSnappedBall *	getSnappedBall (int index) const
	Returns one of the two snapped 3-balls whose equators are joined.
void	reduceTriangulation () const
	Cuts along the 2-sphere and fills the two new boundary components with 3-balls.
NTriangulation *	getReducedTriangulation (const NTriangulation *original) const
	Makes a clone of this triangulation and reduces the clone as described by reduceTriangulation().
void	writeTextShort (std::ostream &out) const
	Writes this object in short text format to the given output stream.
Static Public Member Functions
static NSnappedTwoSphere *	formsSnappedTwoSphere (NTetrahedron *tet1, NTetrahedron *tet2)
	Determines if the two given tetrahedra together form a snapped 2-sphere.
static NSnappedTwoSphere *	formsSnappedTwoSphere (NSnappedBall *ball1, NSnappedBall *ball2)
	Determines if the two given snapped 3-balls together form a snapped 2-sphere.

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Detailed Description

Represents a 2-sphere made from two snapped 3-balls in a triangulation.

This occurs when two snapped 3-balls are glued together at their equators (note that this gluing does not have to extend to faces). Each 3-ball has a central disc (bounded by the 3-ball's equator and bisecting its internal edge), and these two discs together form an embedded 2-sphere in the triangulation.

This 2-sphere can be cut along and the two resulting 2-sphere boundaries filled in with 3-balls, and the resulting triangulation has the same number of tetrahedra as the original. If the snapped 2-sphere was separating, the resulting triangulation will contain the two terms of the corresponding connected sum.

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Constructor & Destructor Documentation

regina::NSnappedTwoSphere::~NSnappedTwoSphere

(

)

[inline, virtual]

Destroys this snapped 2-sphere; note that the corresponding snapped 3-balls will also be destroyed.

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Member Function Documentation

NSnappedTwoSphere* regina::NSnappedTwoSphere::clone

(

)

const

Returns a newly created clone of this structure.

Returns:

a newly created clone.

const NSnappedBall * regina::NSnappedTwoSphere::getSnappedBall

(

int

index

)

const [inline]

Returns one of the two snapped 3-balls whose equators are joined.

Parameters:

index

specifies which of the two 3-balls to return; this must be either 0 or 1.

Returns:

the corresponding snapped 3-ball.

void regina::NSnappedTwoSphere::reduceTriangulation

(

)

const

Cuts along the 2-sphere and fills the two new boundary components with 3-balls.

The number of tetrahedra in the triangulation will not change.

Note that if this 2-sphere is separating, this routine will effectively split the corresponding connected sum into its two original terms.

Todo:

Bug (urgent): This routine currently does nothing!

NTriangulation* regina::NSnappedTwoSphere::getReducedTriangulation

(

const NTriangulation *

original

)

const

Makes a clone of this triangulation and reduces the clone as described by reduceTriangulation().

The original triangulation containing this 2-sphere will not be modified. The clone will have no parent packet.

Todo:

Bug (urgent): This routine currently does nothing!

Parameters:

original

the triangulation in which this 2-sphere occurs.

Returns:

the newly created reduced triangulation.

static NSnappedTwoSphere* regina::NSnappedTwoSphere::formsSnappedTwoSphere	(	NTetrahedron *	tet1,
		NTetrahedron *	tet2
	)			[static]

Determines if the two given tetrahedra together form a snapped 2-sphere.

Precondition:

The two given tetrahedra are distinct.

Parameters:

	tet1	the first tetrahedron to examine.
	tet2	the second tetrahedron to examine.

Returns:

a newly created structure containing details of the snapped 2-sphere, or null if the given tetrahedra do not form a snapped 2-sphere.

static NSnappedTwoSphere* regina::NSnappedTwoSphere::formsSnappedTwoSphere	(	NSnappedBall *	ball1,
		NSnappedBall *	ball2
	)			[static]

Determines if the two given snapped 3-balls together form a snapped 2-sphere.

If this is the case, the snapped 3-balls stored in the structure returned will be clones of the original 3-balls, not the original 3-balls themselves.

Precondition:

The two given snapped 3-balls use distinct tetrahedra.

Parameters:

	ball1	the first snapped 3-ball to examine.
	ball2	the second snapped 3-ball to examine.

Returns:

a newly created structure containing details of the snapped 2-sphere, or null if the given snapped 3-balls do not form a snapped 2-sphere.

void regina::NSnappedTwoSphere::writeTextShort

(

std::ostream &

out

)

const [inline, virtual]

Writes this object in short text format to the given output stream.

The output should fit on a single line and no newline should be written.

Python:

The parameter out does not exist; standard output will be used.

Parameters:

out

the output stream to which to write.

Implements regina::ShareableObject.

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

• nsnappedtwosphere.h