Package etomica.math.geometry

Class TruncatedOctahedron

java.lang.Object

etomica.math.geometry.Polytope

etomica.math.geometry.Polyhedron

etomica.math.geometry.TruncatedOctahedron

All Implemented Interfaces:

Shape

public class TruncatedOctahedron
extends Polyhedron

A truncated octahedron is an Archimedean, space-filling polyhedron with 24 vertices, 36 edges, and 14 faces. All edges are of the same length. Eight of the faces are regular hexagons, and six are squares.

See Also:

Serialized Form

Field Summary

Fields inherited from class etomica.math.geometry.Polyhedron

edges, faces

Fields inherited from class etomica.math.geometry.Polytope

D, embeddedSpace, hyperPlanes, position, vertices

Constructor Summary

Constructors

Constructor	Description
TruncatedOctahedron(Space embeddedSpace)	Constructs a truncated octahedron with vertices defined in the embedded space and with unit edge lengths.
TruncatedOctahedron(Space embeddedSpace, double edgeLength)	Constructs a truncated octahedron with vertices defined in the embedded space and with edge lengths equal to the given value.

Method Summary

Modifier and Type	Method	Description
boolean	contains(Vector v)	Returns true if the given vector lies inside the polytope, false otherwise.
double	getContainingCubeEdgeLength()	Returns the length of an edge of a cube in which the truncated octahedron is inscribed.
double	getEdgeLength()
double	getVolume()	Returns the (hyper)volume enclosed by the polytope.
void	setContainingCubeEdgeLength(double length)	Sets the size of the truncated octahedron in terms of the edge length of a cube that would contain it.
void	setEdgeLength(double edgeLength)	Specifies the common length of all edges of the truncated octahedron.
void	updateVertices()	The following defines the vertices that the truncated octahedron will have, based on Vector3D.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from class etomica.math.geometry.Polyhedron

distanceTo, getEdges, getFaces, getPerimeter, getSurfaceArea

Methods inherited from class etomica.math.geometry.Polytope

applyTranslationRotation, D, getEmbeddedSpace, getPosition, getVertexCount, getVertices, setPosition, toString

Constructor Detail

TruncatedOctahedron

public TruncatedOctahedron(Space embeddedSpace)

Constructs a truncated octahedron with vertices defined in the embedded space and with unit edge lengths.

TruncatedOctahedron

public TruncatedOctahedron(Space embeddedSpace,
                           double edgeLength)

Constructs a truncated octahedron with vertices defined in the embedded space and with edge lengths equal to the given value.

Method Detail

getEdgeLength

public double getEdgeLength()

Returns:

the common length of all edges of the truncated octahedron

setEdgeLength

public void setEdgeLength(double edgeLength)

Specifies the common length of all edges of the truncated octahedron.

Parameters:

edgeLength - the new length of all edges

getContainingCubeEdgeLength

public double getContainingCubeEdgeLength()

Returns the length of an edge of a cube in which the truncated octahedron is inscribed. This is the distance from one of the square faces of the truncated octahedron to the square face opposite it. It is equal to 2*sqrt(2)*edgeLength.

setContainingCubeEdgeLength

public void setContainingCubeEdgeLength(double length)

Sets the size of the truncated octahedron in terms of the edge length of a cube that would contain it.

updateVertices

public void updateVertices()

The following defines the vertices that the truncated octahedron will have, based on Vector3D. Edges are formed from the set of vertices by referring to the index of vertices[], and faces are formed by referring to the index of the edges[]. Thus it is essential that when constructing edges[], the first reference to each vertex must be sequential. For example, the first two edges might look something like this: vertices[0],vertices[1] and vertices[0], vertices[2]. Once the point vertices[0] has appeared for the first time, it may appear at any location in edges[] thereafter. However, the first two edges could not be vertices[0],vertices[2] and vertices[0],vertices[1], because vertices[2] was called before vertices[1] was called for the first time. This same logic applies to the ordering of the edges when defining the faces. The variable "n" has been incorporated into the definitions of the vertices so that the size of the truncated octahedron can be adjusted. The vertices have been numbered such that the faces are defined in terms of vertices as follows: (0,1,2,3), (0,4,5,6,7,8), (1,8,9,10,11,12), (2,12,13,14,15,16), (3,4,16,17,18,19), (5,19,20,21), (7,9,22,23), (11,13,24,25), (15,17,26,27), (6,21,23,28,29,30), (10,22,25,28,31,32), (14,24,27,32,33,34), (18,20,26,30,34,35), and (29,31,33,35). The physical order of the edges on each face does not need to be sequential. For example, when naming the edges of a square (let's call it faces[4]), the clockwise order of the edges could be edges[17],edges[5],edges[8],edges[3]. However, when listing the edges in faces[4], the order could be edges[3], edges[5], edges[8], edges[17]. This greatly simplifies the task of numbering vertices.

Specified by:

updateVertices in class Polytope

contains

public boolean contains(Vector v)

Description copied from class: Polytope

Returns true if the given vector lies inside the polytope, false otherwise.

Specified by:

contains in interface Shape

Specified by:

contains in class Polytope

getVolume

public double getVolume()

Description copied from class: Polytope

Returns the (hyper)volume enclosed by the polytope. So for a LineSegment instance, this is its length; for a polygon, it is the area; for a polyhedron, it is the volume.

Specified by:

getVolume in interface Shape

Specified by:

getVolume in class Polytope