IntersectionMatrix.java
/*
* Copyright (c) 2016 Vivid Solutions.
*
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License 2.0
* and Eclipse Distribution License v. 1.0 which accompanies this distribution.
* The Eclipse Public License is available at http://www.eclipse.org/legal/epl-v20.html
* and the Eclipse Distribution License is available at
*
* http://www.eclipse.org/org/documents/edl-v10.php.
*/
package org.locationtech.jts.geom;
/**
* Models a <b>Dimensionally Extended Nine-Intersection Model (DE-9IM)</b> matrix.
* DE-9IM matrix values (such as "212FF1FF2")
* specify the topological relationship between two {@link Geometry}s.
* This class can also represent matrix patterns (such as "T*T******")
* which are used for matching instances of DE-9IM matrices.
* <p>
* DE-9IM matrices are 3x3 matrices with integer entries.
* The matrix indices {0,1,2} represent the topological locations
* that occur in a geometry (Interior, Boundary, Exterior).
* These are provided by the constants
* {@link Location#INTERIOR}, {@link Location#BOUNDARY}, and {@link Location#EXTERIOR}.
* <p>
* When used to specify the topological relationship between two geometries,
* the matrix entries represent the possible dimensions of each intersection:
* {@link Dimension#A} = 2, {@link Dimension#L} = 1, {@link Dimension#P} = 0 and {@link Dimension#FALSE} = -1.
* When used to represent a matrix pattern entries can have the additional values
* {@link Dimension#TRUE} {"T") and {@link Dimension#DONTCARE} ("*").
* <p>
* For a description of the DE-9IM and the spatial predicates derived from it,
* see the following references:
* <ul>
* <li><i><a href="http://www.opengis.org/techno/specs.htm">
* OGC 99-049 OpenGIS Simple Features Specification for SQL</a></i>
* , Section 2.1.13</li>
* <li><i><a href="http://portal.opengeospatial.org/files/?artifact_id=25355">
* OGC 06-103r4 OpenGIS Implementation Standard for Geographic information - Simple feature access - Part 1: Common architecture</a></i>
* , Section 6.1.15 (which provides some further details on certain predicate specifications).
* </li>
* <li>Wikipedia article on <a href="https://en.wikipedia.org/wiki/DE-9IM">DE-9IM</a></li>
* </ul>
* <p>
* Methods are provided to:
* <UL>
* <LI>set and query the elements of the matrix in a convenient fashion
* <LI>convert to and from the standard string representation (specified in
* SFS Section 2.1.13.2).
* <LI>test if a matrix matches a given pattern string.
* <li>test if a matrix (possibly with geometry dimensions) matches a standard named spatial predicate
* </UL>
*
*@version 1.7
*/
public class IntersectionMatrix implements Cloneable {
/**
* Internal representation of this <code>IntersectionMatrix</code>.
*/
private int[][] matrix;
/**
* Creates an <code>IntersectionMatrix</code> with <code>FALSE</code>
* dimension values.
*/
public IntersectionMatrix() {
matrix = new int[3][3];
setAll(Dimension.FALSE);
}
/**
* Creates an <code>IntersectionMatrix</code> with the given dimension
* symbols.
*
*@param elements a String of nine dimension symbols in row major order
*/
public IntersectionMatrix(String elements) {
this();
set(elements);
}
/**
* Creates an <code>IntersectionMatrix</code> with the same elements as
* <code>other</code>.
*
*@param other an <code>IntersectionMatrix</code> to copy
*/
public IntersectionMatrix(IntersectionMatrix other) {
this();
matrix[Location.INTERIOR][Location.INTERIOR] = other.matrix[Location.INTERIOR][Location.INTERIOR];
matrix[Location.INTERIOR][Location.BOUNDARY] = other.matrix[Location.INTERIOR][Location.BOUNDARY];
matrix[Location.INTERIOR][Location.EXTERIOR] = other.matrix[Location.INTERIOR][Location.EXTERIOR];
matrix[Location.BOUNDARY][Location.INTERIOR] = other.matrix[Location.BOUNDARY][Location.INTERIOR];
matrix[Location.BOUNDARY][Location.BOUNDARY] = other.matrix[Location.BOUNDARY][Location.BOUNDARY];
matrix[Location.BOUNDARY][Location.EXTERIOR] = other.matrix[Location.BOUNDARY][Location.EXTERIOR];
matrix[Location.EXTERIOR][Location.INTERIOR] = other.matrix[Location.EXTERIOR][Location.INTERIOR];
matrix[Location.EXTERIOR][Location.BOUNDARY] = other.matrix[Location.EXTERIOR][Location.BOUNDARY];
matrix[Location.EXTERIOR][Location.EXTERIOR] = other.matrix[Location.EXTERIOR][Location.EXTERIOR];
}
/**
* Adds one matrix to another.
* Addition is defined by taking the maximum dimension value of each position
* in the summand matrices.
*
* @param im the matrix to add
*/
public void add(IntersectionMatrix im)
{
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
setAtLeast(i, j, im.get(i, j));
}
}
}
/**
* Tests if the dimension value matches <tt>TRUE</tt>
* (i.e. has value 0, 1, 2 or TRUE).
*
*@param actualDimensionValue a number that can be stored in the <code>IntersectionMatrix</code>
* . Possible values are <code>{TRUE, FALSE, DONTCARE, 0, 1, 2}</code>.
*@return true if the dimension value matches TRUE
*/
public static boolean isTrue(int actualDimensionValue) {
if (actualDimensionValue >= 0 || actualDimensionValue == Dimension.TRUE) {
return true;
}
return false;
}
/**
* Tests if the dimension value satisfies the dimension symbol.
*
*@param actualDimensionValue a number that can be stored in the <code>IntersectionMatrix</code>
* . Possible values are <code>{TRUE, FALSE, DONTCARE, 0, 1, 2}</code>.
*@param requiredDimensionSymbol a character used in the string
* representation of an <code>IntersectionMatrix</code>. Possible values
* are <code>{T, F, * , 0, 1, 2}</code>.
*@return true if the dimension symbol matches
* the dimension value
*/
public static boolean matches(int actualDimensionValue, char requiredDimensionSymbol) {
if (requiredDimensionSymbol == Dimension.SYM_DONTCARE) {
return true;
}
if (requiredDimensionSymbol == Dimension.SYM_TRUE && (actualDimensionValue >= 0 || actualDimensionValue
== Dimension.TRUE)) {
return true;
}
if (requiredDimensionSymbol == Dimension.SYM_FALSE && actualDimensionValue == Dimension.FALSE) {
return true;
}
if (requiredDimensionSymbol == Dimension.SYM_P && actualDimensionValue == Dimension.P) {
return true;
}
if (requiredDimensionSymbol == Dimension.SYM_L && actualDimensionValue == Dimension.L) {
return true;
}
if (requiredDimensionSymbol == Dimension.SYM_A && actualDimensionValue == Dimension.A) {
return true;
}
return false;
}
/**
* Tests if each of the actual dimension symbols in a matrix string satisfies the
* corresponding required dimension symbol in a pattern string.
*
*@param actualDimensionSymbols nine dimension symbols to validate.
* Possible values are <code>{T, F, * , 0, 1, 2}</code>.
*@param requiredDimensionSymbols nine dimension symbols to validate
* against. Possible values are <code>{T, F, * , 0, 1, 2}</code>.
*@return true if each of the required dimension
* symbols encompass the corresponding actual dimension symbol
*/
public static boolean matches(String actualDimensionSymbols, String requiredDimensionSymbols) {
IntersectionMatrix m = new IntersectionMatrix(actualDimensionSymbols);
return m.matches(requiredDimensionSymbols);
}
/**
* Changes the value of one of this <code>IntersectionMatrix</code>s
* elements.
*
*@param row the row of this <code>IntersectionMatrix</code>,
* indicating the interior, boundary or exterior of the first <code>Geometry</code>
*@param column the column of this <code>IntersectionMatrix</code>,
* indicating the interior, boundary or exterior of the second <code>Geometry</code>
*@param dimensionValue the new value of the element
*/
public void set(int row, int column, int dimensionValue) {
matrix[row][column] = dimensionValue;
}
/**
* Changes the elements of this <code>IntersectionMatrix</code> to the
* dimension symbols in <code>dimensionSymbols</code>.
*
*@param dimensionSymbols nine dimension symbols to which to set this <code>IntersectionMatrix</code>
* s elements. Possible values are <code>{T, F, * , 0, 1, 2}</code>
*/
public void set(String dimensionSymbols) {
for (int i = 0; i < dimensionSymbols.length(); i++) {
int row = i / 3;
int col = i % 3;
matrix[row][col] = Dimension.toDimensionValue(dimensionSymbols.charAt(i));
}
}
/**
* Changes the specified element to <code>minimumDimensionValue</code> if the
* element is less.
*
*@param row the row of this <code>IntersectionMatrix</code>
* , indicating the interior, boundary or exterior of the first <code>Geometry</code>
*@param column the column of this <code>IntersectionMatrix</code>
* , indicating the interior, boundary or exterior of the second <code>Geometry</code>
*@param minimumDimensionValue the dimension value with which to compare the
* element. The order of dimension values from least to greatest is
* <code>{DONTCARE, TRUE, FALSE, 0, 1, 2}</code>.
*/
public void setAtLeast(int row, int column, int minimumDimensionValue) {
if (matrix[row][column] < minimumDimensionValue) {
matrix[row][column] = minimumDimensionValue;
}
}
/**
* If row >= 0 and column >= 0, changes the specified element to <code>minimumDimensionValue</code>
* if the element is less. Does nothing if row <0 or column < 0.
*
*@param row the row of this <code>IntersectionMatrix</code>
* , indicating the interior, boundary or exterior of the first <code>Geometry</code>
*@param column the column of this <code>IntersectionMatrix</code>
* , indicating the interior, boundary or exterior of the second <code>Geometry</code>
*@param minimumDimensionValue the dimension value with which to compare the
* element. The order of dimension values from least to greatest is
* <code>{DONTCARE, TRUE, FALSE, 0, 1, 2}</code>.
*/
public void setAtLeastIfValid(int row, int column, int minimumDimensionValue) {
if (row >= 0 && column >= 0) {
setAtLeast(row, column, minimumDimensionValue);
}
}
/**
* For each element in this <code>IntersectionMatrix</code>, changes the
* element to the corresponding minimum dimension symbol if the element is
* less.
*
*@param minimumDimensionSymbols nine dimension symbols with which to
* compare the elements of this <code>IntersectionMatrix</code>. The
* order of dimension values from least to greatest is <code>{DONTCARE, TRUE, FALSE, 0, 1, 2}</code>
* .
*/
public void setAtLeast(String minimumDimensionSymbols) {
for (int i = 0; i < minimumDimensionSymbols.length(); i++) {
int row = i / 3;
int col = i % 3;
setAtLeast(row, col, Dimension.toDimensionValue(minimumDimensionSymbols.charAt(i)));
}
}
/**
* Changes the elements of this <code>IntersectionMatrix</code> to <code>dimensionValue</code>
* .
*
*@param dimensionValue the dimension value to which to set this <code>IntersectionMatrix</code>
* s elements. Possible values <code>{TRUE, FALSE, DONTCARE, 0, 1, 2}</code>
* .
*/
public void setAll(int dimensionValue) {
for (int ai = 0; ai < 3; ai++) {
for (int bi = 0; bi < 3; bi++) {
matrix[ai][bi] = dimensionValue;
}
}
}
/**
* Returns the value of one of this matrix
* entries.
* The value of the provided index is one of the
* values from the {@link Location} class.
* The value returned is a constant
* from the {@link Dimension} class.
*
*@param row the row of this <code>IntersectionMatrix</code>, indicating
* the interior, boundary or exterior of the first <code>Geometry</code>
*@param column the column of this <code>IntersectionMatrix</code>,
* indicating the interior, boundary or exterior of the second <code>Geometry</code>
*@return the dimension value at the given matrix position.
*/
public int get(int row, int column) {
return matrix[row][column];
}
/**
* Tests if this matrix matches <code>[FF*FF****]</code>.
*
*@return <code>true</code> if the two <code>Geometry</code>s related by
* this matrix are disjoint
*/
public boolean isDisjoint() {
return
matrix[Location.INTERIOR][Location.INTERIOR] == Dimension.FALSE &&
matrix[Location.INTERIOR][Location.BOUNDARY] == Dimension.FALSE &&
matrix[Location.BOUNDARY][Location.INTERIOR] == Dimension.FALSE &&
matrix[Location.BOUNDARY][Location.BOUNDARY] == Dimension.FALSE;
}
/**
* Tests if <code>isDisjoint</code> returns false.
*
*@return <code>true</code> if the two <code>Geometry</code>s related by
* this matrix intersect
*/
public boolean isIntersects() {
return ! isDisjoint();
}
/**
* Tests if this matrix matches
* <code>[FT*******]</code>, <code>[F**T*****]</code> or <code>[F***T****]</code>.
*
*@param dimensionOfGeometryA the dimension of the first <code>Geometry</code>
*@param dimensionOfGeometryB the dimension of the second <code>Geometry</code>
*@return <code>true</code> if the two <code>Geometry</code>
* s related by this matrix touch; Returns false
* if both <code>Geometry</code>s are points.
*/
public boolean isTouches(int dimensionOfGeometryA, int dimensionOfGeometryB) {
if (dimensionOfGeometryA > dimensionOfGeometryB) {
//no need to get transpose because pattern matrix is symmetrical
return isTouches(dimensionOfGeometryB, dimensionOfGeometryA);
}
if ((dimensionOfGeometryA == Dimension.A && dimensionOfGeometryB == Dimension.A) ||
(dimensionOfGeometryA == Dimension.L && dimensionOfGeometryB == Dimension.L) ||
(dimensionOfGeometryA == Dimension.L && dimensionOfGeometryB == Dimension.A) ||
(dimensionOfGeometryA == Dimension.P && dimensionOfGeometryB == Dimension.A) ||
(dimensionOfGeometryA == Dimension.P && dimensionOfGeometryB == Dimension.L)) {
return matrix[Location.INTERIOR][Location.INTERIOR] == Dimension.FALSE &&
(isTrue(matrix[Location.INTERIOR][Location.BOUNDARY])
|| isTrue(matrix[Location.BOUNDARY][Location.INTERIOR])
|| isTrue(matrix[Location.BOUNDARY][Location.BOUNDARY]));
}
return false;
}
/**
* Tests whether this geometry crosses the
* specified geometry.
* <p>
* The <code>crosses</code> predicate has the following equivalent definitions:
* <ul>
* <li>The geometries have some but not all interior points in common.
* <li>The DE-9IM Intersection Matrix for the two geometries matches
* <ul>
* <li><code>[T*T******]</code> (for P/L, P/A, and L/A situations)
* <li><code>[T*****T**]</code> (for L/P, L/A, and A/L situations)
* <li><code>[0********]</code> (for L/L situations)
* </ul>
* </ul>
* For any other combination of dimensions this predicate returns <code>false</code>.
* <p>
* The SFS defined this predicate only for P/L, P/A, L/L, and L/A situations.
* JTS extends the definition to apply to L/P, A/P and A/L situations as well.
* This makes the relation symmetric.
*
*@param dimensionOfGeometryA the dimension of the first <code>Geometry</code>
*@param dimensionOfGeometryB the dimension of the second <code>Geometry</code>
*@return <code>true</code> if the two <code>Geometry</code>s
* related by this matrix cross.
*/
public boolean isCrosses(int dimensionOfGeometryA, int dimensionOfGeometryB) {
if ((dimensionOfGeometryA == Dimension.P && dimensionOfGeometryB == Dimension.L) ||
(dimensionOfGeometryA == Dimension.P && dimensionOfGeometryB == Dimension.A) ||
(dimensionOfGeometryA == Dimension.L && dimensionOfGeometryB == Dimension.A)) {
return isTrue(matrix[Location.INTERIOR][Location.INTERIOR]) &&
isTrue(matrix[Location.INTERIOR][Location.EXTERIOR]);
}
if ((dimensionOfGeometryA == Dimension.L && dimensionOfGeometryB == Dimension.P) ||
(dimensionOfGeometryA == Dimension.A && dimensionOfGeometryB == Dimension.P) ||
(dimensionOfGeometryA == Dimension.A && dimensionOfGeometryB == Dimension.L)) {
return isTrue(matrix[Location.INTERIOR][Location.INTERIOR]) &&
isTrue(matrix[Location.EXTERIOR][Location.INTERIOR]);
}
if (dimensionOfGeometryA == Dimension.L && dimensionOfGeometryB == Dimension.L) {
return matrix[Location.INTERIOR][Location.INTERIOR] == 0;
}
return false;
}
/**
* Tests whether this matrix matches <code>[T*F**F***]</code>.
*
*@return <code>true</code> if the first <code>Geometry</code> is within
* the second
*/
public boolean isWithin() {
return isTrue(matrix[Location.INTERIOR][Location.INTERIOR]) &&
matrix[Location.INTERIOR][Location.EXTERIOR] == Dimension.FALSE &&
matrix[Location.BOUNDARY][Location.EXTERIOR] == Dimension.FALSE;
}
/**
* Tests whether this matrix matches [T*****FF*[.
*
*@return <code>true</code> if the first <code>Geometry</code> contains the
* second
*/
public boolean isContains() {
return isTrue(matrix[Location.INTERIOR][Location.INTERIOR]) &&
matrix[Location.EXTERIOR][Location.INTERIOR] == Dimension.FALSE &&
matrix[Location.EXTERIOR][Location.BOUNDARY] == Dimension.FALSE;
}
/**
* Tests if this matrix matches
* <code>[T*****FF*]</code>
* or <code>[*T****FF*]</code>
* or <code>[***T**FF*]</code>
* or <code>[****T*FF*]</code>
*
*@return <code>true</code> if the first <code>Geometry</code> covers the
* second
*/
public boolean isCovers() {
boolean hasPointInCommon =
isTrue(matrix[Location.INTERIOR][Location.INTERIOR])
|| isTrue(matrix[Location.INTERIOR][Location.BOUNDARY])
|| isTrue(matrix[Location.BOUNDARY][Location.INTERIOR])
|| isTrue(matrix[Location.BOUNDARY][Location.BOUNDARY]);
return hasPointInCommon &&
matrix[Location.EXTERIOR][Location.INTERIOR] == Dimension.FALSE &&
matrix[Location.EXTERIOR][Location.BOUNDARY] == Dimension.FALSE;
}
/**
*Tests if this matrix matches
* <code>[T*F**F***]</code>
* or <code>[*TF**F***]</code>
* or <code>[**FT*F***]</code>
* or <code>[**F*TF***]</code>
*
*@return <code>true</code> if the first <code>Geometry</code>
* is covered by the second
*/
public boolean isCoveredBy() {
boolean hasPointInCommon =
isTrue(matrix[Location.INTERIOR][Location.INTERIOR])
|| isTrue(matrix[Location.INTERIOR][Location.BOUNDARY])
|| isTrue(matrix[Location.BOUNDARY][Location.INTERIOR])
|| isTrue(matrix[Location.BOUNDARY][Location.BOUNDARY]);
return hasPointInCommon &&
matrix[Location.INTERIOR][Location.EXTERIOR] == Dimension.FALSE &&
matrix[Location.BOUNDARY][Location.EXTERIOR] == Dimension.FALSE;
}
/**
* Tests whether the argument dimensions are equal and
* this matrix matches the pattern <tt>[T*F**FFF*]</tt>.
* <p>
* <b>Note:</b> This pattern differs from the one stated in
* <i>Simple feature access - Part 1: Common architecture</i>.
* That document states the pattern as <tt>[TFFFTFFFT]</tt>. This would
* specify that
* two identical <tt>POINT</tt>s are not equal, which is not desirable behaviour.
* The pattern used here has been corrected to compute equality in this situation.
*
*@param dimensionOfGeometryA the dimension of the first <code>Geometry</code>
*@param dimensionOfGeometryB the dimension of the second <code>Geometry</code>
*@return <code>true</code> if the two <code>Geometry</code>s
* related by this matrix are equal; the
* <code>Geometry</code>s must have the same dimension to be equal
*/
public boolean isEquals(int dimensionOfGeometryA, int dimensionOfGeometryB) {
if (dimensionOfGeometryA != dimensionOfGeometryB) {
return false;
}
return isTrue(matrix[Location.INTERIOR][Location.INTERIOR]) &&
matrix[Location.INTERIOR][Location.EXTERIOR] == Dimension.FALSE &&
matrix[Location.BOUNDARY][Location.EXTERIOR] == Dimension.FALSE &&
matrix[Location.EXTERIOR][Location.INTERIOR] == Dimension.FALSE &&
matrix[Location.EXTERIOR][Location.BOUNDARY] == Dimension.FALSE;
}
/**
* Tests if this matrix matches
* <UL>
* <LI><tt>[T*T***T**]</tt> (for two points or two surfaces)
* <LI><tt>[1*T***T**]</tt> (for two curves)
* </UL>.
*
*@param dimensionOfGeometryA the dimension of the first <code>Geometry</code>
*@param dimensionOfGeometryB the dimension of the second <code>Geometry</code>
*@return <code>true</code> if the two <code>Geometry</code>s
* related by this matrix overlap. For this
* function to return <code>true</code>, the <code>Geometry</code>s must
* be two points, two curves or two surfaces.
*/
public boolean isOverlaps(int dimensionOfGeometryA, int dimensionOfGeometryB) {
if ((dimensionOfGeometryA == Dimension.P && dimensionOfGeometryB == Dimension.P) ||
(dimensionOfGeometryA == Dimension.A && dimensionOfGeometryB == Dimension.A)) {
return isTrue(matrix[Location.INTERIOR][Location.INTERIOR])
&& isTrue(matrix[Location.INTERIOR][Location.EXTERIOR])
&& isTrue(matrix[Location.EXTERIOR][Location.INTERIOR]);
}
if (dimensionOfGeometryA == Dimension.L && dimensionOfGeometryB == Dimension.L) {
return matrix[Location.INTERIOR][Location.INTERIOR] == 1
&& isTrue(matrix[Location.INTERIOR][Location.EXTERIOR])
&& isTrue(matrix[Location.EXTERIOR][Location.INTERIOR]);
}
return false;
}
/**
* Tests whether this matrix matches the given matrix pattern.
*
*@param pattern A pattern containing nine dimension symbols with which to
* compare the entries of this matrix. Possible
* symbol values are <code>{T, F, * , 0, 1, 2}</code>.
*@return <code>true</code> if this matrix matches the pattern
*/
public boolean matches(String pattern) {
if (pattern.length() != 9) {
throw new IllegalArgumentException("Should be length 9: " + pattern);
}
for (int ai = 0; ai < 3; ai++) {
for (int bi = 0; bi < 3; bi++) {
if (!matches(matrix[ai][bi], pattern.charAt(3 * ai +
bi))) {
return false;
}
}
}
return true;
}
/**
* Transposes this IntersectionMatrix.
*
*@return this <code>IntersectionMatrix</code> as a convenience
*/
public IntersectionMatrix transpose() {
int temp = matrix[1][0];
matrix[1][0] = matrix[0][1];
matrix[0][1] = temp;
temp = matrix[2][0];
matrix[2][0] = matrix[0][2];
matrix[0][2] = temp;
temp = matrix[2][1];
matrix[2][1] = matrix[1][2];
matrix[1][2] = temp;
return this;
}
/**
* Returns a nine-character <code>String</code> representation of this <code>IntersectionMatrix</code>
* .
*
*@return the nine dimension symbols of this <code>IntersectionMatrix</code>
* in row-major order.
*/
public String toString() {
StringBuilder builder = new StringBuilder("123456789");
for (int ai = 0; ai < 3; ai++) {
for (int bi = 0; bi < 3; bi++) {
builder.setCharAt(3 * ai + bi, Dimension.toDimensionSymbol(matrix[ai][bi]));
}
}
return builder.toString();
}
}