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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/nspiralsolidtorus.h
* \brief Deals with spiralled solid tori in a triangulation.
*/
#ifndef __NSPIRALSOLIDTORUS_H
#ifndef __DOXYGEN
#define __NSPIRALSOLIDTORUS_H
#endif
#include "regina-core.h"
#include "maths/nperm4.h"
#include "subcomplex/nstandardtri.h"
namespace regina {
class NTetrahedron;
class NTriangulation;
/**
* \weakgroup subcomplex
* @{
*/
/**
* Represents a spiralled solid torus in a triangulation.
*
* A spiralled solid torus is created by placing tetrahedra one upon
* another in a spiralling fashion to form a giant loop.
*
* For each tetrahedron, label the vertices A, B, C and D. Draw the
* tetrahedron so that the vertices form an upward spiral in the order
* A-B-C-D, with D directly above A. Face BCD is on the top, face ABC
* is on the bottom and faces ABD and ACD are both vertical.
*
* When joining two tetrahedra, face BCD of the lower tetrahedron will
* be joined to face ABC of the upper tetrahedron. In this way the
* tetrahedra are placed one upon another to form a giant loop (which is
* closed up by placing the bottommost tetrahedron above the topmost
* tetrahedron in a similar fashion), forming a solid torus overall.
*
* In each tetrahedron, directed edges AB, BC and CD are <i>major edges</i>,
* directed edges AC and BD are <i>minor edges</i> and directed edge AD
* is an <i>axis edge</i>.
*
* The major edges all combined form a single longitude of the solid
* torus. Using this directed longitude, using the directed meridinal curve
* ACBA and assuming the spiralled solid torus contains \a n tetrahedra,
* the minor edges all combined form a (2, <i>n</i>) curve and
* the axis edges all combined form a (3, <i>n</i>) curve on the torus
* boundary.
*
* Note that all tetrahedra in the spiralled solid torus must be distinct
* and there must be at least one tetrahedron.
*
* Note also that class NTriSolidTorus represents a spiralled solid
* torus with precisely three tetrahedra. A spiralled solid torus with
* only one tetrahedron is in fact a (1,2,3) layered solid torus.
*
* All optional NStandardTriangulation routines are implemented for this
* class.
*/
class REGINA_API NSpiralSolidTorus : public NStandardTriangulation {
private:
unsigned long nTet;
/**< The number of tetrahedra in this spiralled solid torus. */
NTetrahedron** tet;
/**< The tetrahedra that make up this spiralled solid torus. */
NPerm4* vertexRoles;
/**< For tetrahedron \a i, <tt>vertexRoles[i]</tt> is a
permutation p chosen so that vertices A, B, C and D above
correspond to vertices p[0], p[1], p[2] and p[3]. */
public:
/**
* Destroys this spiralled solid torus.
*/
virtual ~NSpiralSolidTorus();
/**
* Returns a newly created clone of this structure.
*
* @return a newly created clone.
*/
NSpiralSolidTorus* clone() const;
/**
* Returns the number of tetrahedra in this spiralled solid torus.
*
* @return the number of tetrahedra.
*/
unsigned long getNumberOfTetrahedra() const;
/**
* Returns the requested tetrahedron in this spiralled solid torus.
* Tetrahedra are numbered from 0 to getNumberOfTetrahedra()-1
* inclusive, with tetrahedron <i>i</i>+1 being placed above
* tetrahedron <i>i</i>.
*
* @param index specifies which tetrahedron to return; this must
* be between 0 and getNumberOfTetrahedra()-1 inclusive.
* @return the requested tetrahedron.
*/
NTetrahedron* getTetrahedron(unsigned long index) const;
/**
* Returns a permutation represeting the role that each vertex
* of the requested tetrahedron plays in the solid torus.
* The permutation returned (call this <tt>p</tt>) maps 0, 1, 2 and
* 3 to the four vertices of tetrahedron \a index so that
* vertices <tt>p[0]</tt>, <tt>p[1]</tt>, <tt>p[2]</tt> and
* <tt>p[3]</tt> correspond to vertices A, B, C and D
* respectively as described in the general class notes.
*
* In particular, the directed edge from vertex
* <tt>p[0]</tt> to <tt>p[3]</tt> is an axis edge,
* directed edges <tt>p[0]</tt> to <tt>p[2]</tt> and
* <tt>p[1]</tt> to <tt>p[3]</tt> are minor edges and
* the directed path from vertices <tt>p[0]</tt> to <tt>p[1]</tt>
* to <tt>p[2]</tt> to <tt>p[3]</tt> follows the three
* major edges.
*
* See the general class notes for further details.
*
* @param index specifies which tetrahedron in the solid torus
* to examine; this must be between 0 and
* getNumberOfTetrahedra()-1 inclusive.
* @return a permutation representing the roles of the vertices
* of the requested tetrahedron.
*/
NPerm4 getVertexRoles(unsigned long index) const;
/**
* Reverses this spiralled solid torus.
* Tetrahedra 0, 1, 2, ..., getNumberOfTetrahedra()-1 will
* become tetrahedra getNumberOfTetrahedra()-1, ..., 2, 1, 0
* respectively. Note that this operation will change the
* vertex roles as well.
*
* The underlying triangulation is not changed; all that changes
* is how this spiralled solid torus is represented.
*/
void reverse();
/**
* Cycles this spiralled solid torus by the given number of
* tetrahedra.
* Tetrahedra <i>k</i>, <i>k</i>+1, <i>k</i>+2 and so on
* will become tetrahedra 0, 1, 2 and so on respectively.
* Note that this operation will not change the vertex roles.
*
* The underlying triangulation is not changed; all that changes
* is how this spiralled solid torus is represented.
*
* @param k the number of tetrahedra through which we should cycle.
*/
void cycle(unsigned long k);
/**
* Converts this spiralled solid torus into its canonical
* representation. The canonical representation of a spiralled
* solid torus is unique in a given triangulation.
*
* Tetrahedron 0 in the spiralled solid torus will be the
* tetrahedron with the lowest index in the triangulation, and
* under permutation <tt>getVertexRoles(0)</tt> the image of 0
* will be less than the image of 3.
*
* @param tri the triangulation in which this solid torus lives.
* @return \c true if and only if the representation of this
* spiralled solid torus was actually changed.
*/
bool makeCanonical(const NTriangulation* tri);
/**
* Determines whether this spiralled solid torus is in canonical
* form. Canonical form is described in detail in the
* description for makeCanonical().
*
* @param tri the triangulation in which this solid torus lives.
* @return \c true if and only if this spiralled solid torus is
* in canonical form.
*/
bool isCanonical(const NTriangulation* tri) const;
/**
* Determines if the given tetrahedron forms part of a
* spiralled solid torus with its vertices
* playing the given roles in the solid torus.
*
* Note that the boundary faces of the spiralled solid
* torus need not be boundary faces within the overall
* triangulation, i.e., they may be identified with each other
* or with faces of other tetrahedra.
*
* @param tet the tetrahedron to examine.
* @param useVertexRoles a permutation describing the role each
* tetrahedron vertex must play in the solid torus; this must be
* in the same format as the permutation returned by
* getVertexRoles().
* @return a newly created structure containing details of the
* solid torus with the given tetrahedron as tetrahedron 0, or
* \c null if the given tetrahedron is not part of a spiralled
* solid torus with the given vertex roles.
*/
static NSpiralSolidTorus* formsSpiralSolidTorus(NTetrahedron* tet,
NPerm4 useVertexRoles);
NManifold* getManifold() const;
NAbelianGroup* getHomologyH1() const;
std::ostream& writeName(std::ostream& out) const;
std::ostream& writeTeXName(std::ostream& out) const;
void writeTextLong(std::ostream& out) const;
private:
/**
* Creates a new partially initialised structure.
* Member \a nTet will be initialised and dynamic arrays
* \a tet and \a vertexRoles will be created.
*
* @param newNTet the number of tetrahedra in this spiralled
* solid torus; this must be strictly positive.
*/
NSpiralSolidTorus(unsigned long newNTet);
};
/*@}*/
// Inline functions for NSpiralSolidTorus
inline NSpiralSolidTorus::NSpiralSolidTorus(unsigned long newNTet) :
nTet(newNTet), tet(new NTetrahedron*[newNTet]),
vertexRoles(new NPerm4[newNTet]) {
}
inline NSpiralSolidTorus::~NSpiralSolidTorus() {
delete[] tet;
delete[] vertexRoles;
}
inline unsigned long NSpiralSolidTorus::getNumberOfTetrahedra() const {
return nTet;
}
inline NTetrahedron* NSpiralSolidTorus::getTetrahedron(unsigned long index)
const {
return tet[index];
}
inline NPerm4 NSpiralSolidTorus::getVertexRoles(unsigned long index) const {
return vertexRoles[index];
}
inline std::ostream& NSpiralSolidTorus::writeName(std::ostream& out) const {
return out << "Spiral(" << nTet << ')';
}
inline std::ostream& NSpiralSolidTorus::writeTeXName(std::ostream& out) const {
return out << "\\mathit{Spiral}(" << nTet << ')';
}
inline void NSpiralSolidTorus::writeTextLong(std::ostream& out) const {
out << nTet << "-tetrahedron spiralled solid torus";
}
} // namespace regina
#endif
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