A four-dimensional Menger Sponge. More...

#include <Sponge.h>

Inheritance diagram for Sponge:

Collaboration diagram for Sponge:

Public Member Functions
	Sponge (unsigned _level=1, unsigned _distance=2, double _rad=0.8, VecMath::Vector< 4 > _center=VecMath::Vector< 4 >(0., 0., 0., 0.))
	Sponge constructor.
virtual	~Sponge ()
	Sponge destructor.
virtual std::string	getFunctionName () const
virtual void	Transform (const VecMath::Rotation< 4 > &R, const VecMath::Vector< 4 > &T, const VecMath::Vector< 4 > &scale)
	Transforms a Sponge.
virtual void	Project (double ScrW, double CamW, bool DepthCue4D)
	Projects a Sponge into three-space.
virtual void	Draw (UI::View *view)
	Draw the projected Sponge (onto screen or into GL list, as it is)
virtual void	SetParameters (const ParameterMap &parms)
	Set parameters to the Displayable.
virtual void	ReInit (double, double, double, double, double, double, double, double, double)
	Rebuild the Sponge if the parameters have changed.
virtual std::string	description ()
Protected Member Functions
virtual void	Initialize ()
	This function actually creates the hypersponge.
virtual unsigned long	MemRequired (unsigned)
	return the approximate amount of memory needed to display a sponge of current `level` and given `distance`
Protected Attributes
unsigned	Level
	Level of the hypersponge.
std::vector< Hypercube * >	List
	List of sub-sponges (see Initialize())
int	distance
	max. distance (see Initialize())
double	rad
	radius, more correctly size, of the sponge
VecMath::Vector< 4 >	center
	center of the sponge

Detailed Description

A four-dimensional Menger Sponge.

A Menger Sponge in three dimensions is a fractal produced by subdividing a cube and taking away parts of the cube which get subsequentally smaller. The level parameter controls how often this process is repeated, i.e. how many holes there are in the final object.

A four-dimensional Menger Sponge is created analogously from a hypercube.

The fractal can be further controlled by the distance parameter:

distance = 0: Only the innermost cube is removed, resulting in a four-dimensional foam with connected body and disjoint holes.
distance = 1: the innermost and the next to innermost cubes are removed, which results in a foam in three dimensions, but has holes in the four-dimensional structure.
distance = 2: the holes reach the surface of the cube, resulting in a sponge structure - both the holes and the cubes ("curd") are connected.
distance = 3: only the corners of the hypercube remain, resulting in dust - the "curd" is disjoint, the holes are connected.

Constructor & Destructor Documentation

Sponge::Sponge	(	unsigned	_level = `1`,
		unsigned	_distance = `2`,
		double	_rad = `0.8`,
		VecMath::Vector< 4 >	_center = `VecMath::Vector<4>(0., 0.,0., 0.)`
	)

Sponge constructor.

Construct a Hypersponge of level level.

Parameters:

_level	hypersponge level
_distance	distance of subcubes to center to be counted as part of the fractal = 0: solid hypercube = 1: foam = 2: sponge = 3: dust >= 4: nothing
_rad	side_length/2
_center	center
_level	Level of recursion used in creating the Sponge
_distance	see Initialize()
_rad	Size of the Sponge - `_rad` is half the side length
_center	Center point of the Sponge

References Displayable::declareParameter(), and Initialize().

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Member Function Documentation

virtual std::string Sponge::description ( ) [inline, virtual]

Returns:: A string with a description of the Hypersponge object

Reimplemented from Hypercube.

References std::ends(), and Level.

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void Sponge::Draw ( UI::View * view ) [virtual]

Draw the projected Sponge (onto screen or into GL list, as it is)

Draws all sub-sponges, recursively.

Reimplemented from Hypercube.

References UI::View::commitDraw(), Level, List, and std::vector< _Tp, _Alloc >::size().

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virtual std::string Sponge::getFunctionName ( ) const [inline, virtual]

Returns:: The name of the Displayable in cleartext

Reimplemented from Hypercube.

void Sponge::Initialize ( void ) [protected, virtual]

This function actually creates the hypersponge.

It views it as an assembly of $ 3^4 $ smaller sponges, slicing the sponge in three sub-sponges in every one of the four dimensions, and then taking away some of the resulting 81 smaller sub-sponges.

if the parameter distance is zero, it only removes the sub-sponge with distance 0 from the center, i.e. the one at the center.
if the parameter distance is one, it only removes the sub-sponges with distance <= 1, amounting to nine removed sub-sponges. The three- dimensional surface of the hypercube enveloping the sponge is not breached, because the surface of a hypercube is two units away from the center, instead of one unit, as in 3D.
if distance = 2, the holes reach the hypercubes surface, giving an object analogous to the three-dimensional Menger Sponge.
if distance = 3, only the 16 corners of the hypercube remain, giving four-dimensional fractal dust.

If the level of the sponge is 1, the sub-sponges are hypercubes. Otherwise, they are Hypersponges with a level reduced by 1.

Reimplemented from Hypercube.

References abs(), center, std::cerr, distance, std::endl(), Loki::SingletonHolder< T, CreationPolicy >::Instance(), Level, List, Displayable::MemRequired(), std::vector< _Tp, _Alloc >::push_back(), and rad.

Referenced by Sponge().

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unsigned long Sponge::MemRequired ( unsigned distance ) [protected, virtual]

return the approximate amount of memory needed to display a sponge of current level and given distance

Todo:: uses hardcoded and experimentally found value for memory per hypercube

Parameters:

distance see Initialize()

Returns:: approx. mem required

References Level, and pow().

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void Sponge::Project	(	double	scr_w,
		double	cam_w,
		bool	depthcue4d
	)		`[virtual]`

Projects a Sponge into three-space.

The projection is achieved by projecting all constituting sub-sponges.

Parameters:

scr_w	w coordinate of screen
cam_w	w coordinate of camera
depthcue4d	wheter to use hyperfog/dc

Reimplemented from VertexHolder< 4, 1, double >.

References List, and std::vector< _Tp, _Alloc >::size().

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virtual void Sponge::SetParameters ( const ParameterMap & ) [inline, virtual]

Set parameters to the Displayable.

Todo:: This function is only there to provide an interface, and it's not abstract so that Displayable s which don't have Parameters don't need to reimplement an unneeded method. But the present implementation does not make sense.

Reimplemented from Hypercube.

References std::map< _Key, _Tp, _Compare, _Alloc >::begin(), std::cerr, distance, std::map< _Key, _Tp, _Compare, _Alloc >::end(), Level, rad, Displayable::setParameter(), and ParameterMap::toString().

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