org.apache.commons.math4.geometry.euclidean.twod

## Class PolygonsSet

• All Implemented Interfaces:
Region<Euclidean2D>

public class PolygonsSet
extends AbstractRegion<Euclidean2D,Euclidean1D>
This class represents a 2D region: a set of polygons.
Since:
3.0

• ### Nested classes/interfaces inherited from interface org.apache.commons.math4.geometry.partitioning.Region

Region.Location
• ### Constructor Summary

Constructors
Constructor and Description
PolygonsSet(BSPTree<Euclidean2D> tree, double tolerance)
Build a polygons set from a BSP tree.
PolygonsSet(Collection<SubHyperplane<Euclidean2D>> boundary, double tolerance)
Build a polygons set from a Boundary REPresentation (B-rep).
PolygonsSet(double tolerance)
Build a polygons set representing the whole plane.
PolygonsSet(double xMin, double xMax, double yMin, double yMax, double tolerance)
Build a parallellepipedic box.
PolygonsSet(double hyperplaneThickness, Vector2D... vertices)
Build a polygon from a simple list of vertices.
• ### Method Summary

All Methods
Modifier and Type Method and Description
PolygonsSet buildNew(BSPTree<Euclidean2D> tree)
Build a region using the instance as a prototype.
protected void computeGeometricalProperties()
Compute some geometrical properties.
Vector2D[][] getVertices()
Get the vertices of the polygon.
• ### Methods inherited from class org.apache.commons.math4.geometry.partitioning.AbstractRegion

applyTransform, checkPoint, checkPoint, checkPoint, checkPoint, contains, copySelf, getBarycenter, getBoundarySize, getSize, getTolerance, getTree, intersection, isEmpty, isEmpty, isFull, isFull, projectToBoundary, setBarycenter, setBarycenter, setSize
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### PolygonsSet

public PolygonsSet(double tolerance)
Build a polygons set representing the whole plane.
Parameters:
tolerance - tolerance below which points are considered identical
Since:
3.3
• #### PolygonsSet

public PolygonsSet(BSPTree<Euclidean2D> tree,
double tolerance)
Build a polygons set from a BSP tree.

The leaf nodes of the BSP tree must have a Boolean attribute representing the inside status of the corresponding cell (true for inside cells, false for outside cells). In order to avoid building too many small objects, it is recommended to use the predefined constants Boolean.TRUE and Boolean.FALSE

This constructor is aimed at expert use, as building the tree may be a difficult task. It is not intended for general use and for performances reasons does not check thoroughly its input, as this would require walking the full tree each time. Failing to provide a tree with the proper attributes, will therefore generate problems like NullPointerException or ClassCastException only later on. This limitation is known and explains why this constructor is for expert use only. The caller does have the responsibility to provided correct arguments.

Parameters:
tree - inside/outside BSP tree representing the region
tolerance - tolerance below which points are considered identical
Since:
3.3
• #### PolygonsSet

public PolygonsSet(Collection<SubHyperplane<Euclidean2D>> boundary,
double tolerance)
Build a polygons set from a Boundary REPresentation (B-rep).

The boundary is provided as a collection of sub-hyperplanes. Each sub-hyperplane has the interior part of the region on its minus side and the exterior on its plus side.

The boundary elements can be in any order, and can form several non-connected sets (like for example polygons with holes or a set of disjoint polygons considered as a whole). In fact, the elements do not even need to be connected together (their topological connections are not used here). However, if the boundary does not really separate an inside open from an outside open (open having here its topological meaning), then subsequent calls to the checkPoint method will not be meaningful anymore.

If the boundary is empty, the region will represent the whole space.

Parameters:
boundary - collection of boundary elements, as a collection of SubHyperplane objects
tolerance - tolerance below which points are considered identical
Since:
3.3
• #### PolygonsSet

public PolygonsSet(double xMin,
double xMax,
double yMin,
double yMax,
double tolerance)
Build a parallellepipedic box.
Parameters:
xMin - low bound along the x direction
xMax - high bound along the x direction
yMin - low bound along the y direction
yMax - high bound along the y direction
tolerance - tolerance below which points are considered identical
Since:
3.3
• #### PolygonsSet

public PolygonsSet(double hyperplaneThickness,
Vector2D... vertices)
Build a polygon from a simple list of vertices.

The boundary is provided as a list of points considering to represent the vertices of a simple loop. The interior part of the region is on the left side of this path and the exterior is on its right side.

This constructor does not handle polygons with a boundary forming several disconnected paths (such as polygons with holes).

For cases where this simple constructor applies, it is expected to be numerically more robust than the general constructor using subhyperplanes.

If the list is empty, the region will represent the whole space.

Polygons with thin pikes or dents are inherently difficult to handle because they involve lines with almost opposite directions at some vertices. Polygons whose vertices come from some physical measurement with noise are also difficult because an edge that should be straight may be broken in lots of different pieces with almost equal directions. In both cases, computing the lines intersections is not numerically robust due to the almost 0 or almost π angle. Such cases need to carefully adjust the hyperplaneThickness parameter. A too small value would often lead to completely wrong polygons with large area wrongly identified as inside or outside. Large values are often much safer. As a rule of thumb, a value slightly below the size of the most accurate detail needed is a good value for the hyperplaneThickness parameter.

Parameters:
hyperplaneThickness - tolerance below which points are considered to belong to the hyperplane (which is therefore more a slab)
vertices - vertices of the simple loop boundary
• ### Method Detail

• #### buildNew

public PolygonsSet buildNew(BSPTree<Euclidean2D> tree)
Build a region using the instance as a prototype.

This method allow to create new instances without knowing exactly the type of the region. It is an application of the prototype design pattern.

The leaf nodes of the BSP tree must have a Boolean attribute representing the inside status of the corresponding cell (true for inside cells, false for outside cells). In order to avoid building too many small objects, it is recommended to use the predefined constants Boolean.TRUE and Boolean.FALSE. The tree also must have either null internal nodes or internal nodes representing the boundary as specified in the getTree method).

Specified by:
buildNew in interface Region<Euclidean2D>
Specified by:
buildNew in class AbstractRegion<Euclidean2D,Euclidean1D>
Parameters:
tree - inside/outside BSP tree representing the new region
Returns:
the built region
• #### computeGeometricalProperties

protected void computeGeometricalProperties()
Compute some geometrical properties.

The properties to compute are the barycenter and the size.

Specified by:
computeGeometricalProperties in class AbstractRegion<Euclidean2D,Euclidean1D>
• #### getVertices

public Vector2D[][] getVertices()
Get the vertices of the polygon.

The polygon boundary can be represented as an array of loops, each loop being itself an array of vertices.

In order to identify open loops which start and end by infinite edges, the open loops arrays start with a null point. In this case, the first non null point and the last point of the array do not represent real vertices, they are dummy points intended only to get the direction of the first and last edge. An open loop consisting of a single infinite line will therefore be represented by a three elements array with one null point followed by two dummy points. The open loops are always the first ones in the loops array.

If the polygon has no boundary at all, a zero length loop array will be returned.

All line segments in the various loops have the inside of the region on their left side and the outside on their right side when moving in the underlying line direction. This means that closed loops surrounding finite areas obey the direct trigonometric orientation.

Returns:
vertices of the polygon, organized as oriented boundary loops with the open loops first (the returned value is guaranteed to be non-null)