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# Java example source code file (SphericalPolygonsSet.java)

This example Java source code file (SphericalPolygonsSet.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

## Java - Java tags/keywords

arraylist, bsptree, circle, edge, edgesbuilder, enclosingball, list, propertiescomputer, rotation, s2point, spheregenerator, sphericalpolygonsset, util, vector3d, vertex

## The SphericalPolygonsSet.java Java example source code

/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements.  See the NOTICE file distributed with
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License.  You may obtain a copy of the License at
*
*
* Unless required by applicable law or agreed to in writing, software
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
*/
package org.apache.commons.math3.geometry.spherical.twod;

import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Iterator;
import java.util.List;

import org.apache.commons.math3.exception.MathIllegalStateException;
import org.apache.commons.math3.geometry.enclosing.EnclosingBall;
import org.apache.commons.math3.geometry.enclosing.WelzlEncloser;
import org.apache.commons.math3.geometry.euclidean.threed.Euclidean3D;
import org.apache.commons.math3.geometry.euclidean.threed.Rotation;
import org.apache.commons.math3.geometry.euclidean.threed.RotationConvention;
import org.apache.commons.math3.geometry.euclidean.threed.SphereGenerator;
import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.apache.commons.math3.geometry.partitioning.AbstractRegion;
import org.apache.commons.math3.geometry.partitioning.BSPTree;
import org.apache.commons.math3.geometry.partitioning.BoundaryProjection;
import org.apache.commons.math3.geometry.partitioning.RegionFactory;
import org.apache.commons.math3.geometry.partitioning.SubHyperplane;
import org.apache.commons.math3.geometry.spherical.oned.Sphere1D;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;

/** This class represents a region on the 2-sphere: a set of spherical polygons.
* @since 3.3
*/
public class SphericalPolygonsSet extends AbstractRegion<Sphere2D, Sphere1D> {

/** Boundary defined as an array of closed loops start vertices. */
private List<Vertex> loops;

/** Build a polygons set representing the whole real 2-sphere.
* @param tolerance below which points are consider to be identical
*/
public SphericalPolygonsSet(final double tolerance) {
super(tolerance);
}

/** Build a polygons set representing a hemisphere.
* @param pole pole of the hemisphere (the pole is in the inside half)
* @param tolerance below which points are consider to be identical
*/
public SphericalPolygonsSet(final Vector3D pole, final double tolerance) {
super(new BSPTree<Sphere2D>(new Circle(pole, tolerance).wholeHyperplane(),
new BSPTree<Sphere2D>(Boolean.FALSE),
new BSPTree<Sphere2D>(Boolean.TRUE),
null),
tolerance);
}

/** Build a polygons set representing a regular polygon.
* @param center center of the polygon (the center is in the inside half)
* @param meridian point defining the reference meridian for first polygon vertex
* @param outsideRadius distance of the vertices to the center
* @param n number of sides of the polygon
* @param tolerance below which points are consider to be identical
*/
public SphericalPolygonsSet(final Vector3D center, final Vector3D meridian,
final double outsideRadius, final int n,
final double tolerance) {
}

/** Build a polygons set from a BSP tree.
* <p>The leaf nodes of the BSP tree must have a
* {@code 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
* {@code Boolean.TRUE} and {@code Boolean.FALSE}</p>
* @param tree inside/outside BSP tree representing the region
* @param tolerance below which points are consider to be identical
*/
public SphericalPolygonsSet(final BSPTree<Sphere2D> tree, final double tolerance) {
super(tree, tolerance);
}

/** Build a polygons set from a Boundary REPresentation (B-rep).
* <p>The boundary is provided as a collection of {@link
* SubHyperplane sub-hyperplanes}. Each sub-hyperplane has the
* interior part of the region on its minus side and the exterior on
* its plus side.</p>
* <p>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
* org.apache.commons.math3.geometry.partitioning.Region#checkPoint(org.apache.commons.math3.geometry.Point)
* checkPoint} method will not be meaningful anymore.</p>
* <p>If the boundary is empty, the region will represent the whole
* space.</p>
* @param boundary collection of boundary elements, as a
* collection of {@link SubHyperplane SubHyperplane} objects
* @param tolerance below which points are consider to be identical
*/
public SphericalPolygonsSet(final Collection<SubHyperplane boundary, final double tolerance) {
super(boundary, tolerance);
}

/** Build a polygon from a simple list of vertices.
* <p>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.</p>
* <p>This constructor does not handle polygons with a boundary
* forming several disconnected paths (such as polygons with holes).</p>
* <p>For cases where this simple constructor applies, it is expected to
* be numerically more robust than the {@link #SphericalPolygonsSet(Collection,
* double) general constructor} using {@link SubHyperplane subhyperplanes}.</p>
* <p>If the list is empty, the region will represent the whole
* space.</p>
* <p>
* Polygons with thin pikes or dents are inherently difficult to handle because
* they involve circles 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
* circles intersections is not numerically robust due to the almost 0 or almost
* π angle. Such cases need to carefully adjust the {@code 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 {@code hyperplaneThickness}
* parameter.
* </p>
* @param hyperplaneThickness tolerance below which points are considered to
* belong to the hyperplane (which is therefore more a slab)
* @param vertices vertices of the simple loop boundary
*/
public SphericalPolygonsSet(final double hyperplaneThickness, final S2Point ... vertices) {
super(verticesToTree(hyperplaneThickness, vertices), hyperplaneThickness);
}

/** Build the vertices representing a regular polygon.
* @param center center of the polygon (the center is in the inside half)
* @param meridian point defining the reference meridian for first polygon vertex
* @param outsideRadius distance of the vertices to the center
* @param n number of sides of the polygon
* @return vertices array
*/
private static S2Point[] createRegularPolygonVertices(final Vector3D center, final Vector3D meridian,
final double outsideRadius, final int n) {
final S2Point[] array = new S2Point[n];
final Rotation r0 = new Rotation(Vector3D.crossProduct(center, meridian),
array[0] = new S2Point(r0.applyTo(center));

final Rotation r = new Rotation(center, MathUtils.TWO_PI / n, RotationConvention.VECTOR_OPERATOR);
for (int i = 1; i < n; ++i) {
array[i] = new S2Point(r.applyTo(array[i - 1].getVector()));
}

return array;
}

/** Build the BSP tree of a polygons set from a simple list of vertices.
* <p>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.</p>
* <p>This constructor does not handle polygons with a boundary
* forming several disconnected paths (such as polygons with holes).</p>
* <p>This constructor handles only polygons with edges strictly shorter
* than $$\pi$$. If longer edges are needed, they need to be broken up
* in smaller sub-edges so this constraint holds.</p>
* <p>For cases where this simple constructor applies, it is expected to
* be numerically more robust than the {@link #PolygonsSet(Collection) general
* constructor} using {@link SubHyperplane subhyperplanes}.</p>
* @param hyperplaneThickness tolerance below which points are consider to
* belong to the hyperplane (which is therefore more a slab)
* @param vertices vertices of the simple loop boundary
* @return the BSP tree of the input vertices
*/
private static BSPTree<Sphere2D> verticesToTree(final double hyperplaneThickness,
final S2Point ... vertices) {

final int n = vertices.length;
if (n == 0) {
// the tree represents the whole space
return new BSPTree<Sphere2D>(Boolean.TRUE);
}

// build the vertices
final Vertex[] vArray = new Vertex[n];
for (int i = 0; i < n; ++i) {
vArray[i] = new Vertex(vertices[i]);
}

// build the edges
List<Edge> edges = new ArrayList(n);
Vertex end = vArray[n - 1];
for (int i = 0; i < n; ++i) {

// get the endpoints of the edge
final Vertex start = end;
end = vArray[i];

// get the circle supporting the edge, taking care not to recreate it
// if it was already created earlier due to another edge being aligned
// with the current one
Circle circle = start.sharedCircleWith(end);
if (circle == null) {
circle = new Circle(start.getLocation(), end.getLocation(), hyperplaneThickness);
}

// create the edge and store it
Vector3D.angle(start.getLocation().getVector(),
end.getLocation().getVector()),
circle));

// check if another vertex also happens to be on this circle
for (final Vertex vertex : vArray) {
if (vertex != start && vertex != end &&
FastMath.abs(circle.getOffset(vertex.getLocation())) <= hyperplaneThickness) {
vertex.bindWith(circle);
}
}

}

// build the tree top-down
final BSPTree<Sphere2D> tree = new BSPTree();
insertEdges(hyperplaneThickness, tree, edges);

return tree;

}

/** Recursively build a tree by inserting cut sub-hyperplanes.
* @param hyperplaneThickness tolerance below which points are considered to
* belong to the hyperplane (which is therefore more a slab)
* @param node current tree node (it is a leaf node at the beginning
* of the call)
* @param edges list of edges to insert in the cell defined by this node
* (excluding edges not belonging to the cell defined by this node)
*/
private static void insertEdges(final double hyperplaneThickness,
final BSPTree<Sphere2D> node,
final List<Edge> edges) {

// find an edge with an hyperplane that can be inserted in the node
int index = 0;
Edge inserted = null;
while (inserted == null && index < edges.size()) {
inserted = edges.get(index++);
if (!node.insertCut(inserted.getCircle())) {
inserted = null;
}
}

if (inserted == null) {
// no suitable edge was found, the node remains a leaf node
// we need to set its inside/outside boolean indicator
final BSPTree<Sphere2D> parent = node.getParent();
if (parent == null || node == parent.getMinus()) {
node.setAttribute(Boolean.TRUE);
} else {
node.setAttribute(Boolean.FALSE);
}
return;
}

// we have split the node by inserting an edge as a cut sub-hyperplane
// distribute the remaining edges in the two sub-trees
final List<Edge> outsideList = new ArrayList();
final List<Edge> insideList  = new ArrayList();
for (final Edge edge : edges) {
if (edge != inserted) {
edge.split(inserted.getCircle(), outsideList, insideList);
}
}

// recurse through lower levels
if (!outsideList.isEmpty()) {
insertEdges(hyperplaneThickness, node.getPlus(), outsideList);
} else {
node.getPlus().setAttribute(Boolean.FALSE);
}
if (!insideList.isEmpty()) {
insertEdges(hyperplaneThickness, node.getMinus(),  insideList);
} else {
node.getMinus().setAttribute(Boolean.TRUE);
}

}

/** {@inheritDoc} */
@Override
public SphericalPolygonsSet buildNew(final BSPTree<Sphere2D> tree) {
return new SphericalPolygonsSet(tree, getTolerance());
}

/** {@inheritDoc}
* @exception MathIllegalStateException if the tolerance setting does not allow to build
* a clean non-ambiguous boundary
*/
@Override
protected void computeGeometricalProperties() throws MathIllegalStateException {

final BSPTree<Sphere2D> tree = getTree(true);

if (tree.getCut() == null) {

// the instance has a single cell without any boundaries

if (tree.getCut() == null && (Boolean) tree.getAttribute()) {
// the instance covers the whole space
setSize(4 * FastMath.PI);
setBarycenter(new S2Point(0, 0));
} else {
setSize(0);
setBarycenter(S2Point.NaN);
}

} else {

// the instance has a boundary
final PropertiesComputer pc = new PropertiesComputer(getTolerance());
tree.visit(pc);
setSize(pc.getArea());
setBarycenter(pc.getBarycenter());

}

}

/** Get the boundary loops of the polygon.
* <p>The polygon boundary can be represented as a list of closed loops,
* each loop being given by exactly one of its vertices. From each loop
* start vertex, one can follow the loop by finding the outgoing edge,
* then the end vertex, then the next outgoing edge ... until the start
* vertex of the loop (exactly the same instance) is found again once
* the full loop has been visited.</p>
* <p>If the polygon has no boundary at all, a zero length loop
* array will be returned.</p>
* <p>If the polygon is a simple one-piece polygon, then the returned
* array will contain a single vertex.
* </p>
* <p>All edges in the various loops have the inside of the region on
* their left side (i.e. toward their pole) and the outside on their
* right side (i.e. away from their pole) when moving in the underlying
* circle direction. This means that the closed loops obey the direct
* trigonometric orientation.</p>
* @return boundary of the polygon, organized as an unmodifiable list of loops start vertices.
* @exception MathIllegalStateException if the tolerance setting does not allow to build
* a clean non-ambiguous boundary
* @see Vertex
* @see Edge
*/
public List<Vertex> getBoundaryLoops() throws MathIllegalStateException {

if (loops == null) {
if (getTree(false).getCut() == null) {
loops = Collections.emptyList();
} else {

// sort the arcs according to their start point
final BSPTree<Sphere2D> root = getTree(true);
final EdgesBuilder visitor = new EdgesBuilder(root, getTolerance());
root.visit(visitor);
final List<Edge> edges = visitor.getEdges();

// convert the list of all edges into a list of start vertices
loops = new ArrayList<Vertex>();
while (!edges.isEmpty()) {

// this is an edge belonging to a new loop, store it
Edge edge = edges.get(0);
final Vertex startVertex = edge.getStart();

// remove all remaining edges in the same loop
do {

// remove one edge
for (final Iterator<Edge> iterator = edges.iterator(); iterator.hasNext();) {
if (iterator.next() == edge) {
iterator.remove();
break;
}
}

// go to next edge following the boundary loop
edge = edge.getEnd().getOutgoing();

} while (edge.getStart() != startVertex);

}

}
}

return Collections.unmodifiableList(loops);

}

/** Get a spherical cap enclosing the polygon.
* <p>
* This method is intended as a first test to quickly identify points
* that are guaranteed to be outside of the region, hence performing a full
* only if the point status remains undecided after the quick check. It is
* is therefore mostly useful to speed up computation for small polygons with
* complex shapes (say a country boundary on Earth), as the spherical cap will
* be small and hence will reliably identify a large part of the sphere as outside,
* whereas the full check can be more computing intensive. A typical use case is
* therefore:
* </p>
* <pre>
*   // compute region, plus an enclosing spherical cap
*   SphericalPolygonsSet complexShape = ...;
*   EnclosingBall<Sphere2D, S2Point> cap = complexShape.getEnclosingCap();
*
*   // check lots of points
*   for (Vector3D p : points) {
*
*     final Location l;
*     if (cap.contains(p)) {
*       // we cannot be sure where the point is
*       // we need to perform the full computation
*       l = complexShape.checkPoint(v);
*     } else {
*       // no need to do further computation,
*       // we already know the point is outside
*       l = Location.OUTSIDE;
*     }
*
*     // use l ...
*
*   }
* </pre>
* <p>
* In the special cases of empty or whole sphere polygons, special
* spherical caps are returned, with angular radius set to negative
* or positive infinity so the {@link
* EnclosingBall#contains(org.apache.commons.math3.geometry.Point) ball.contains(point)}
* method return always false or true.
* </p>
* <p>
* This method is <em>not guaranteed to return the smallest enclosing cap.
* </p>
* @return a spherical cap enclosing the polygon
*/
public EnclosingBall<Sphere2D, S2Point> getEnclosingCap() {

// handle special cases first
if (isEmpty()) {
return new EnclosingBall<Sphere2D, S2Point>(S2Point.PLUS_K, Double.NEGATIVE_INFINITY);
}
if (isFull()) {
return new EnclosingBall<Sphere2D, S2Point>(S2Point.PLUS_K, Double.POSITIVE_INFINITY);
}

// as the polygons is neither empty nor full, it has some boundaries and cut hyperplanes
final BSPTree<Sphere2D> root = getTree(false);
if (isEmpty(root.getMinus()) && isFull(root.getPlus())) {
// the polygon covers an hemisphere, and its boundary is one 2π long edge
final Circle circle = (Circle) root.getCut().getHyperplane();
return new EnclosingBall<Sphere2D, S2Point>(new S2Point(circle.getPole()).negate(),
0.5 * FastMath.PI);
}
if (isFull(root.getMinus()) && isEmpty(root.getPlus())) {
// the polygon covers an hemisphere, and its boundary is one 2π long edge
final Circle circle = (Circle) root.getCut().getHyperplane();
return new EnclosingBall<Sphere2D, S2Point>(new S2Point(circle.getPole()),
0.5 * FastMath.PI);
}

// gather some inside points, to be used by the encloser
final List<Vector3D> points = getInsidePoints();

// extract points from the boundary loops, to be used by the encloser as well
final List<Vertex> boundary = getBoundaryLoops();
for (final Vertex loopStart : boundary) {
int count = 0;
for (Vertex v = loopStart; count == 0 || v != loopStart; v = v.getOutgoing().getEnd()) {
++count;
}
}

// find the smallest enclosing 3D sphere
final SphereGenerator generator = new SphereGenerator();
final WelzlEncloser<Euclidean3D, Vector3D> encloser =
new WelzlEncloser<Euclidean3D, Vector3D>(getTolerance(), generator);
EnclosingBall<Euclidean3D, Vector3D> enclosing3D = encloser.enclose(points);
final Vector3D[] support3D = enclosing3D.getSupport();

// convert to 3D sphere to spherical cap
final double h = enclosing3D.getCenter().getNorm();
if (h < getTolerance()) {
// the 3D sphere is centered on the unit sphere and covers it
// fall back to a crude approximation, based only on outside convex cells
EnclosingBall<Sphere2D, S2Point> enclosingS2 =
new EnclosingBall<Sphere2D, S2Point>(S2Point.PLUS_K, Double.POSITIVE_INFINITY);
for (Vector3D outsidePoint : getOutsidePoints()) {
final S2Point outsideS2 = new S2Point(outsidePoint);
final BoundaryProjection<Sphere2D> projection = projectToBoundary(outsideS2);
if (FastMath.PI - projection.getOffset() < enclosingS2.getRadius()) {
enclosingS2 = new EnclosingBall<Sphere2D, S2Point>(outsideS2.negate(),
FastMath.PI - projection.getOffset(),
(S2Point) projection.getProjected());
}
}
return enclosingS2;
}
final S2Point[] support = new S2Point[support3D.length];
for (int i = 0; i < support3D.length; ++i) {
support[i] = new S2Point(support3D[i]);
}

final EnclosingBall<Sphere2D, S2Point> enclosingS2 =
new EnclosingBall<Sphere2D, S2Point>(new S2Point(enclosing3D.getCenter()),
FastMath.acos((1 + h * h - r * r) / (2 * h)),
support);

return enclosingS2;

}

/** Gather some inside points.
* @return list of points known to be strictly in all inside convex cells
*/
private List<Vector3D> getInsidePoints() {
final PropertiesComputer pc = new PropertiesComputer(getTolerance());
getTree(true).visit(pc);
return pc.getConvexCellsInsidePoints();
}

/** Gather some outside points.
* @return list of points known to be strictly in all outside convex cells
*/
private List<Vector3D> getOutsidePoints() {
final SphericalPolygonsSet complement =
(SphericalPolygonsSet) new RegionFactory<Sphere2D>().getComplement(this);
final PropertiesComputer pc = new PropertiesComputer(getTolerance());
complement.getTree(true).visit(pc);
return pc.getConvexCellsInsidePoints();
}

}


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