Class RhombBoundary

java.lang.Object

RhombBoundary

All Implemented Interfaces:

java.io.Serializable

public class RhombBoundary
extends java.lang.Object
implements java.io.Serializable

A class representing a patch of rhombic tiles. This is equivalent to a pseudoline arrangement. Here the pseudolines are represented by Yarns and their intersections by SimpleRhombs. Each SimpleRhomb corresponds to a rhomb, and each Yarn to a sequence of rhombs, each of which shares an edge with the last, and all of which have two edges in the same family of parallel edges. This class contains methods for creating and modifying such arrangements.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static int	BATCH_SIZE Number of permutations we create before stopping to output interim results.
static long	serialVersionUID For serialization.
static int	WORK_UNIT_LENGTH Number of permutations in a WorkUnit.

Constructor Summary

Constructors

Constructor and Description
RhombBoundary(int[] angles, boolean sym) Public constructor.

Method Summary

Methods

Modifier and Type	Method and Description
static void	allValid(int[] i, boolean sym) Check all permutations of an input list for compatibility with all rhombs.
static void	allValid(int[] i, boolean sym, java.util.List<java.util.List<java.lang.Integer>> rule) Check all permutations of an input list for compatibility with all rhombs.
static void	allValid(int[] i, boolean sym, java.util.List<java.util.List<java.lang.Integer>> rule, int[] pre, int[] suf) Check all permutations of an input list for compatibility with all rhombs.
Point	base(int i) Find the base of the rhomb at the boundary subedge with this index.
java.lang.String	boundaryString() Output the angles in termini in reverse order, replacing 2*Point.N() with 0.
void	collapse(Rhomb j) Remove the rhomb represented by j, if it is on the edge.
static RhombBoundary	createPrototile(int i) Public static factory method.
static RhombBoundary	createRhombBoundary(int even, int[] angles) Public static factory method.
static RhombBoundary	createRhombBoundary(int even, int[] angles1, int[] angles2) Public static factory method.
static RhombBoundary	createRhombBoundary(int even, int[] angles1, int[] angles2, boolean sym) Public static factory method.
static RhombBoundary	createStarBoundary(int[] i) Public static factory method.
static RhombBoundary	createSymmetricRhombBoundary(int even, int[] angles) Public static factory method.
static RhombBoundary	createTriangleBoundary(int[] a1, int[] a2, int[] a3, int[] triangle) Public static factory method.
boolean	equals(java.lang.Object obj) Currently broken.
java.util.List<Hex>	flipTriple(Hex t) Flip one of the Triples.
java.lang.String	gapString() Output a list of subrhombs in gap-readable format.
static void	gapString(int[] i1, int[] i2, boolean ref, java.lang.String fileName) Output a gap file with a full complement of substitutions rules.
static void	gapString(int[] i, java.lang.String fileName) Output a gap file with a full complement of substitutions rules.
static void	gapString(int[] i1, java.lang.String[] saveFiles, java.lang.String outName) Output a gap file with a full complement of substitutions rules.
java.util.List<Rhomb>	getEdgeRhombs() Getter method.
java.util.List<Rhomb>	getJoins() Getter method.
java.util.List<Hex>	getTriples() Getter method.
int	hashCode() Currently broken.
static void	main(java.lang.String[] args) For testing.
static java.lang.String	matrixString(int[][] i1) Convert a two-dimensional array of ints to a String.
int	numTriples() How many Triples are there?
void	postscriptString(java.lang.String fileName) Write all of the Rhombs to a postscript file.
static java.util.List<RhombBoundary>	prototileList() Public static factory method.
static int[]	reverse(int[] i) Create the reverse of an array of ints.
void	setEdgeJoins() Fill the list of all rhombs that have two edges on the boundary.
void	setJoins() Set the Joins of all the Yarns.
RhombBoundary	simplify() Produce a RhombBoundary representing the same data, but with simpler fields.
static int[][]	substitutionMatrix(int[] i1) Produce a substitution matrix for the set of all rhombic prototiles with the given edge sequence.
int[]	tileNumbers() Get the number of tiles of each type.
java.lang.String	toString() Output a String.
boolean	valid() Check for the validity of the crossings.
static java.lang.String	vectorString(int[] i) Represent an integer vector as a String.
int[][][]	yarnDump() Output two lists of lists: the first is a list of pairs of boundary indices, indicating the boundary segments to which each Yarn is connected.
java.lang.String	yarnString() Output the results of yarnDump() as a String.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Field Detail

serialVersionUID

public static final long serialVersionUID

For serialization.

See Also:

Constant Field Values

WORK_UNIT_LENGTH

public static final int WORK_UNIT_LENGTH

Number of permutations in a WorkUnit.

See Also:

Constant Field Values

BATCH_SIZE

public static final int BATCH_SIZE

Number of permutations we create before stopping to output interim results.

See Also:

Constant Field Values

Constructor Detail

RhombBoundary

public RhombBoundary(int[] angles,
             boolean sym)

Public constructor.

Parameters:

angles - A list of angle differences. These should be integers between -N/2 and +N/2. They correspond to the angles (expressed as integer multiples of pi/Point.N()) of a sequence of unit-length line segments that constitute the boundary of the patch.

sym - Tells us if the patch should be made symmetric under a mirror reflection. This means that we change the signs of the angles on opposite sides to make indentations exdentations and exdentaions indentations.

Method Detail

setJoins

public void setJoins()

Set the Joins of all the Yarns.

setEdgeJoins

public void setEdgeJoins()

Fill the list of all rhombs that have two edges on the boundary. Clear this list first, as it might be out of date.

flipTriple

public java.util.List<Hex> flipTriple(Hex t)

Flip one of the Triples. A Triple is a hexagon consisting of three rhombs, any two of which meet at a common edge. This method shifts each rhombs across to the side of the hexagon opposite where it currently is.

Parameters:

t - The triple we flip.

Returns:

A List of all Triples that are created or destroyed by this flip.

collapse

public void collapse(Rhomb j)

Remove the rhomb represented by j, if it is on the edge. Careful! We assume that j is on the edge, but we don't check.

Parameters:

j - The join representing the rhomb that we wish to remove.

getJoins

public java.util.List<Rhomb> getJoins()

Getter method.

Returns:

A list of all the Joins inside this boundary.

getTriples

public java.util.List<Hex> getTriples()

Getter method.

Returns:

A list of all the Triples inside this boundary.

getEdgeRhombs

public java.util.List<Rhomb> getEdgeRhombs()

Getter method.

Returns:

A list of all the Joins inside this boundary that represent rhombs having two or more edges on the boundary.

numTriples

public int numTriples()

How many Triples are there?

Returns:

The number of Triples.

createRhombBoundary

public static RhombBoundary createRhombBoundary(int even,
                                int[] angles)

Public static factory method. Calls createRhombBoundary(int,int[],int[],boolean) with angles repeated twice and with the boolean variable sym set to false.

Parameters:

even - One of the angles of the big rhomb that we create, expressed as an integer multiple of pi/Point.N().

angles - A sequence of angle differences that determines the shape of the four edges of the rhomb.

Returns:

A RhombBoundary created by applying the sequence angles to each edge of the rhomb that has angles even*pi/Point.N() and (Point.N()-even)*pi/Point.N(). It will probably not be tiled symmetrically.

createSymmetricRhombBoundary

public static RhombBoundary createSymmetricRhombBoundary(int even,
                                         int[] angles)

Public static factory method. Same as createRhombBoundary(int,int[]) except it symmetrizes the boundary. This entails reversing the edge shapes on opposite sides.

createRhombBoundary

public static RhombBoundary createRhombBoundary(int even,
                                int[] angles1,
                                int[] angles2)

Public static factory method. Calls createRhombBoundary(int,int[],int[],boolean) with the boolean variable sym set to false.

Parameters:

even - One of the angles of the big rhomb that we create, expressed as an integer multiple of pi/Point.N().

angles1 - A sequence of angle differences that determines the shape of the top and left edges of the rhomb.

angles2 - A sequence of angle differences that determines the shape of the bottom and right edges of the rhomb.

Returns:

A RhombBoundary created by applying the sequences angles1 and angles2 to the top and left (respectively bottom and right) edges of the rhomb that has angles even*pi/N and (N-even)*pi/N.

createRhombBoundary

public static RhombBoundary createRhombBoundary(int even,
                                int[] angles1,
                                int[] angles2,
                                boolean sym)

Public static factory method. This is the root method that many of the others call. It builds a rhomb boundary for the inflated rhomb with angles even*pi/Point.N() and (N-even)*pi/N.

Parameters:

even - One of the angles of the big rhomb that we create, expressed as an integer multiple of pi/N.

angles1 - A sequence of angle differences that determines the shape of the top and left edges of the rhomb.

angles2 - A sequence of angle differences that determines the shape of the bottom and right edges of the rhomb.

sym - Tells us whether or not to symmetrize. When we symmetrize we reverse the edge shapes on opposite sides. This should only be done if angles1 and angles2 are the same.

Returns:

A RhombBoundary created by applying the sequences angles1 and angles2 to the top and left (respectively bottom and right) edges of the rhomb that has angles even*pi/N and (N-even)*pi/N.

createTriangleBoundary

public static RhombBoundary createTriangleBoundary(int[] a1,
                                   int[] a2,
                                   int[] a3,
                                   int[] triangle)

Public static factory method. This creates the boundary of a triangle with distorted edges, and then tiles it with rhombs.

Parameters:

a1 - A sequence of angle differences that determines the shape of the first edge of the triangle.

a2 - A sequence of angle differences that determines the shape of the second edge of the triangle.

a3 - A sequence of angle differences that determines the shape of the third edge of the triangle.

triangle - A list of three integers that represent the angles of the triangle, expressed as integer multiples of pi/Point.N().

Returns:

A triangle with edges distorted according to a1, a2, and a3, tiled with rhombs.

createStarBoundary

public static RhombBoundary createStarBoundary(int[] i)

Public static factory method. This creates the boundary of a region with 2*Point.N()-fold rotational symmetry. Each edge of this region is constructed using edge sequence i. There are no checks to make sure that i is well-formed.

Parameters:

i - A sequence of angle differences that determines the shape of the first edge of the region.

Returns:

A planar region with 2*N-fold rotational symmetry tiled with rhombs. with rhombs.

createPrototile

public static RhombBoundary createPrototile(int i)

Public static factory method. This creates the boundary of a basic prototile with the given type, plus 1.

Parameters:

i - The type of the prototile that is created (less 1).

Returns:

The canonical prototile of type i+1.

prototileList

public static java.util.List<RhombBoundary> prototileList()

Public static factory method. This creates a list of all the prototiles, each in canonical position.

Returns:

A list of RhombBoundaries, each containing one prototile.

simplify

public RhombBoundary simplify()

Produce a RhombBoundary representing the same data, but with simpler fields.

Returns:

Another RhombBoundary that uses SimpleRhomb instead of Join and SimpleHex instead of Triple.

valid

public boolean valid()

Check for the validity of the crossings.

Returns:

true if any two Yarns that cross are valid (see Yarn.valid()).

toString

public java.lang.String toString()

Output a String.

Overrides:

toString in class java.lang.Object

Returns:

A String representing this RhombBoundary. List all the Yarns and their crossings.

equals

public boolean equals(java.lang.Object obj)

Currently broken. Any two RhombBoundaries are equal.

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Currently broken.

Overrides:

hashCode in class java.lang.Object

Returns:

19.

base

public Point base(int i)

Find the base of the rhomb at the boundary subedge with this index. We have a set of prototile rhombs that all have a vertex at the origin. This vertex has an even angle on it, with two edges emanating from it in the positive orientation. One of those edges lies on the positive x-axis. All of the rhombs in a tiling represented by a RhombBoundary are obtained from these prototiles by rotation and translation. This method takes a rhomb in a tiling, and tells us which of its vertices is the image of the origin under the transformation that carries the associated prototile onto it.

Parameters:

i - An index of an element in the Terminus list.

Returns:

The base vertex of the rhomb in this tiling that has an edge on Terminus number i.

gapString

public java.lang.String gapString()

Output a list of subrhombs in gap-readable format.

Returns:

A String containing gap-readable representations of all the rhombs in this tiling.

gapString

public static void gapString(int[] i1,
             int[] i2,
             boolean ref,
             java.lang.String fileName)

Output a gap file with a full complement of substitutions rules. This method constructs a bunch of RhombBoundaries using edge sequences i1 and i2, then calls gapString() on each of them to produce its associated substitution rule. It writes all of these substitution rules, with appropriate preamble, to the file called fileName.

Parameters:

i1 - The edge sequence for the top and left edges of the rhombs.

i2 - The edge sequence for the bottom and right edges of the rhombs.

ref - Tells us whether or not we're making different substitution rules for the reflected versions of the prototiles. This is deprecated.

fileName - The name of the file to which we write the gap output.

postscriptString

public void postscriptString(java.lang.String fileName)

Write all of the Rhombs to a postscript file.

Parameters:

fileName - The name of the file to which we write the postscript output.

gapString

public static void gapString(int[] i1,
             java.lang.String[] saveFiles,
             java.lang.String outName)

Output a gap file with a full complement of substitutions rules. Read the rules from a list of saved files. Order matters. The saved files represent inflated rhombs, and must be entered in order of decreasing even angles. Writes the results to a gap-readable file.

Parameters:

i1 - An edge sequence. It is only used to compute the inflation matrix, not to make substitution rules. It should match the inflation factors for the rhombs in the saved files, but we don't enforce this.

saveFiles - A list of names of saved .rb files containing serialized RhombBoundaries.

outName - The name of the output file.

gapString

public static void gapString(int[] i,
             java.lang.String fileName)

Output a gap file with a full complement of substitutions rules. Same as gapString(int[],int[],boolean,String), except the boolean variable ref is set to false, and the same edge sequence i is input for both i1 and i2.

reverse

public static int[] reverse(int[] i)

Create the reverse of an array of ints.

Parameters:

i - The array that we want to reverse.

Returns:

The reverse of i.

allValid

public static void allValid(int[] i,
            boolean sym,
            java.util.List<java.util.List<java.lang.Integer>> rule,
            int[] pre,
            int[] suf)

Check all permutations of an input list for compatibility with all rhombs. sym tells us whether or not to symmetrize the boundaries. This method writes to stdout all permutations of i that yield valid tilings for each inflated prototile.

Parameters:

i - The seed that we use to produce edge sequences. All edge sequences are obtained by permuting i and then applying rule to replace symbols.

sym - Tells us whether or not to symmetrize the RhombBoundaries that we construct.

rule - A list of lists. The nth entry tells us how to replace the number n wherever it appears in the sequence i, or any of its permutations.

pre - A list of ints to prepend to each permutation.

suf - A list of ints to append to each permutation.

allValid

public static void allValid(int[] i,
            boolean sym,
            java.util.List<java.util.List<java.lang.Integer>> rule)

Check all permutations of an input list for compatibility with all rhombs. This is the same as allValid(int[],boolean,List,int[],int[]), except it does not involve a prefix or suffix. sym tells us whether or not to symmetrize the boundaries. This method writes to stdout all permutations of i that yield valid tilings for each inflated prototile.

Parameters:

i - The seed that we use to produce edge sequences. All edge sequences are obtained by permuting i and then applying rule to replace symbols.

sym - Tells us whether or not to symmetrize the RhombBoundaries that we construct.

rule - A list of lists. The nth entry tells us how to replace the number n wherever it appears in the sequence i, or any of its permutations.

allValid

public static void allValid(int[] i,
            boolean sym)

Check all permutations of an input list for compatibility with all rhombs. This is the same as allValid(int[],boolean,List), except it does not involve a substitution. This method writes to stdout all permutations of i that yield valid tilings for each inflated prototile.

Parameters:

i - The seed that we use to produce edge sequences. All edge sequences are obtained by permuting i. symbols.

sym - Tells us whether or not to symmetrize the RhombBoundaries that we construct.

vectorString

public static java.lang.String vectorString(int[] i)

Represent an integer vector as a String.

Parameters:

i - The integer vector for which we produce a String representation.

Returns:

A String containing the elements of i, separated by commas and enclosed in square brackets.

tileNumbers

public int[] tileNumbers()

Get the number of tiles of each type.

Returns:

An int array, the ith entry of which is the number of rhombs of type i appearing in this tiling.

substitutionMatrix

public static int[][] substitutionMatrix(int[] i1)

Produce a substitution matrix for the set of all rhombic prototiles with the given edge sequence. The substituted rhombs are RhombBoundaries constructed using createRhombBoundary(int,int[]).

Returns:

An Point.N()/2 x N/2 int matrix, the (i,j)th entry of which is the number of tiles of type i appearing in the substituted image of tile j.

matrixString

public static java.lang.String matrixString(int[][] i1)

Convert a two-dimensional array of ints to a String.

Parameters:

i1 - a matrix of ints that we represent as a String.

Returns:

A string containing all the entries of i1. Rows are separated by newlines; columns are represented by commas.

yarnDump

public int[][][] yarnDump()

Output two lists of lists: the first is a list of pairs of boundary indices, indicating the boundary segments to which each Yarn is connected. The second is a list of lists of indices. Each list contains the indices of the Yarns that the Yarn at that position crosses.

Returns:

Two arrays of ints, the first boundary indices for all the Yarns, the second containing crossing lists for all the Yarns.

yarnString

public java.lang.String yarnString()

Output the results of yarnDump() as a String.

Returns:

A String representing all of the Yarn intersection data.

boundaryString

public java.lang.String boundaryString()

Output the angles in termini in reverse order, replacing 2*Point.N() with 0.

Returns:

The angles in termini in reverse order, replacing 2*N with 0.

main

public static void main(java.lang.String[] args)

For testing.