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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2011, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
/*! \file subcomplex/nblockedsfs.h
* \brief Supports closed Seifert fibred spaces that are triangulated using
* saturated blocks.
*/
#ifndef __NBLOCKEDSFS_H
#ifndef __DOXYGEN
#define __NBLOCKEDSFS_H
#endif
#include "regina-core.h"
#include "subcomplex/nstandardtri.h"
namespace regina {
class NSatBlock;
class NSatRegion;
/**
* \weakgroup subcomplex
* @{
*/
/**
* Represents a blocked Seifert fibred space. This is a particular type of
* triangulation of a closed Seifert fibred space, where this triangulation
* is formed from a single closed saturated region. A saturated region is
* in turn formed from saturated blocks by identifying their boundary annuli
* in pairs; see the NSatRegion class for details.
*
* Note that the routines writeName() and writeTeXName() do \e not
* offer enough information to uniquely identify the triangulation,
* since this essentially requires a 2-dimensional assembling of
* saturated blocks. For full detail, writeTextLong() may be used instead.
*
* The optional NStandardTriangulation routine getManifold() is
* implemented for this class, but getHomologyH1() is not.
*
* \testpart
*/
class REGINA_API NBlockedSFS : public NStandardTriangulation {
private:
NSatRegion* region_;
/**< The single saturated region that describes this entire
triangulation. */
public:
/**
* Destroys this structure and its constituent components.
*/
~NBlockedSFS();
/**
* Returns details of the single closed saturated region that
* fills this triangulation.
*
* @return the single saturated region.
*/
const NSatRegion& region() const;
/**
* Determines whether this triangulation is a plugged thin
* I-bundle or a plugged thick I-bundle. These structures are
* described in "Structures of small closed non-orientable
* 3-manifold triangulations", Benjamin A. Burton,
* J. Knot Theory Ramifications 16 (2007), 545--574.
*
* \ifacespython The argument \a name is not present. Instead,
* this routine returns a tuple of size two: the boolean usually
* returned from this function, and the string usually returned in
* the argument \a name.
*
* @param name used to return the name of the plugged thin/thick
* I-bundle, if the triangulation is of this form. If the
* triangulation is not of this form, this string is not touched.
* @return \c true if this triangulation is indeed a plugged thin
* I-bundle or a plugged thick I-bundle.
*/
bool isPluggedIBundle(std::string& name) const;
NManifold* getManifold() const;
std::ostream& writeName(std::ostream& out) const;
std::ostream& writeTeXName(std::ostream& out) const;
void writeTextLong(std::ostream& out) const;
/**
* Determines if the given triangulation is a blocked Seifert
* fibred space.
*
* @param tri the triangulation to examine.
* @return a newly created structure containing details of the
* blocked Seifert fibred space, or \c null if the given
* triangulation is not a blocked Seifert fibred space.
*/
static NBlockedSFS* isBlockedSFS(NTriangulation* tri);
private:
/**
* Constructs a new blocked Seifert fibred space, as described by
* the given saturated region. The new object will take ownership
* of the given region.
*
* Note that the new object must describe an existing triangulation.
*
* @param region the region describing this entire triangulation.
*/
NBlockedSFS(NSatRegion* region);
/**
* Attempts to identify the solid torus plugs in a plugged thin
* I-bundle or a plugged thick I-bundle. This routine is
* internal to isPluggedIBundle().
*
* It is assumed that the plugged thin/thick I-bundle has been
* completely identified, with the exception of the two solid
* torus plugs. Corresponding parameters describing the
* core I-bundle must be passed, along with two blocks that
* should correspond to the two plugs.
*
* If the two blocks are indeed solid torus plugs (either layered
* solid tori or Mobius bands), the full name of the plugged
* thin/thick I-bundle will be filled in and \c true will be
* returned. Note that this name may be normalised or otherwise
* modified to return a simpler set of parameters for the same
* triangulation. If either block is not a solid torus plug then
* \c false will be returned.
*
* @param thin \c true if the overall structure being identified
* is a plugged thin I-bundle, or \c false if it is a plugged
* thick I-bundle.
* @param id identifies the particular thin/thick twisted
* I-bundle into which the solid tori are plugged. This must be
* 1, 2, 3 or 4, to distinguish between the four thin twisted
* I-bundles or the four thick twisted I-bundles described in
* the paper "Structures of small closed non-orientable
* 3-manifold triangulations" (see isPluggedIBundle for details).
* @param name used to return the full parameterised name of this
* triangulation. If the two given blocks are not solid torus
* plugs, this string is not touched.
* @param torus0 the block that should provide the solid torus plug
* corresponding to the first pair of integers in the plugged
* thin/thick I-bundle parameters.
* @param horiz0 \c true if the first pair of integers in the
* plugged thin/thick I-bundle parameters should measure the
* number of times the meridinal curve cuts the vertical and
* horizontal edges of the adjacent block (not the block
* \a torus0, but its neighbour), or \c false if the vertical
* and diagonal edges should be used instead.
* @param torus1 the block that should provide the solid torus plug
* corresponding to the second pair of integers in the plugged
* thin/thick I-bundle parameters.
* @param horiz1 \c true if the second pair of integers in the
* plugged thin/thick I-bundle parameters should measure the
* number of times the meridinal curve cuts the vertical and
* horizontal edges of the adjacent block (not the block
* \a torus1, but its neighbour), or \c false if the vertical
* and diagonal edges should be used instead.
* @return \c true if the two given blocks are both solid torus
* plugs (either layered solid tori or Mobius bands), or \c false
* otherwise.
*/
static bool findPluggedTori(bool thin, int id, std::string& name,
const NSatBlock* torus0, bool horiz0,
const NSatBlock* torus1, bool horiz1);
};
/*@}*/
// Inline functions for NBlockedSFS
inline NBlockedSFS::NBlockedSFS(NSatRegion* region) : region_(region) {
}
inline const NSatRegion& NBlockedSFS::region() const {
return *region_;
}
} // namespace regina
#endif
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