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Java example source code file (SphericalPolygonsSetTest.java)

This example Java source code file (SphericalPolygonsSetTest.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.

Learn more about this Java project at its project page.

Java - Java tags/keywords

arcsset, circle, edge, enclosingball, list, regionfactory, s2point, sphericalpolygonsset, subcircle, test, unitsphererandomvectorgenerator, util, vector3d, vertex, well1024a

The SphericalPolygonsSetTest.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
 * this work for additional information regarding copyright ownership.
 * 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
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.geometry.spherical.twod;

import java.util.ArrayList;
import java.util.List;

import org.apache.commons.math3.geometry.enclosing.EnclosingBall;
import org.apache.commons.math3.geometry.euclidean.threed.Rotation;
import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.apache.commons.math3.geometry.partitioning.Region.Location;
import org.apache.commons.math3.geometry.partitioning.RegionFactory;
import org.apache.commons.math3.geometry.partitioning.SubHyperplane;
import org.apache.commons.math3.geometry.spherical.oned.ArcsSet;
import org.apache.commons.math3.geometry.spherical.oned.Sphere1D;
import org.apache.commons.math3.random.UnitSphereRandomVectorGenerator;
import org.apache.commons.math3.random.Well1024a;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;
import org.junit.Assert;
import org.junit.Test;

public class SphericalPolygonsSetTest {

    @Test
    public void testFullSphere() {
        SphericalPolygonsSet full = new SphericalPolygonsSet(1.0e-10);
        UnitSphereRandomVectorGenerator random =
                new UnitSphereRandomVectorGenerator(3, new Well1024a(0x852fd2a0ed8d2f6dl));
        for (int i = 0; i < 1000; ++i) {
            Vector3D v = new Vector3D(random.nextVector());
            Assert.assertEquals(Location.INSIDE, full.checkPoint(new S2Point(v)));
        }
        Assert.assertEquals(4 * FastMath.PI, new SphericalPolygonsSet(0.01, new S2Point[0]).getSize(), 1.0e-10);
        Assert.assertEquals(0, new SphericalPolygonsSet(0.01, new S2Point[0]).getBoundarySize(), 1.0e-10);
        Assert.assertEquals(0, full.getBoundaryLoops().size());
        Assert.assertTrue(full.getEnclosingCap().getRadius() > 0);
        Assert.assertTrue(Double.isInfinite(full.getEnclosingCap().getRadius()));
    }

    @Test
    public void testEmpty() {
        SphericalPolygonsSet empty =
            (SphericalPolygonsSet) new RegionFactory<Sphere2D>().getComplement(new SphericalPolygonsSet(1.0e-10));
        UnitSphereRandomVectorGenerator random =
                new UnitSphereRandomVectorGenerator(3, new Well1024a(0x76d9205d6167b6ddl));
        for (int i = 0; i < 1000; ++i) {
            Vector3D v = new Vector3D(random.nextVector());
            Assert.assertEquals(Location.OUTSIDE, empty.checkPoint(new S2Point(v)));
        }
        Assert.assertEquals(0, empty.getSize(), 1.0e-10);
        Assert.assertEquals(0, empty.getBoundarySize(), 1.0e-10);
        Assert.assertEquals(0, empty.getBoundaryLoops().size());
        Assert.assertTrue(empty.getEnclosingCap().getRadius() < 0);
        Assert.assertTrue(Double.isInfinite(empty.getEnclosingCap().getRadius()));
    }

    @Test
    public void testSouthHemisphere() {
        double tol = 0.01;
        double sinTol = FastMath.sin(tol);
        SphericalPolygonsSet south = new SphericalPolygonsSet(Vector3D.MINUS_K, tol);
        UnitSphereRandomVectorGenerator random =
                new UnitSphereRandomVectorGenerator(3, new Well1024a(0x6b9d4a6ad90d7b0bl));
        for (int i = 0; i < 1000; ++i) {
            Vector3D v = new Vector3D(random.nextVector());
            if (v.getZ() < -sinTol) {
                Assert.assertEquals(Location.INSIDE, south.checkPoint(new S2Point(v)));
            } else if (v.getZ() > sinTol) {
                Assert.assertEquals(Location.OUTSIDE, south.checkPoint(new S2Point(v)));
            } else {
                Assert.assertEquals(Location.BOUNDARY, south.checkPoint(new S2Point(v)));
            }
        }
        Assert.assertEquals(1, south.getBoundaryLoops().size());

        EnclosingBall<Sphere2D, S2Point> southCap = south.getEnclosingCap();
        Assert.assertEquals(0.0, S2Point.MINUS_K.distance(southCap.getCenter()), 1.0e-10);
        Assert.assertEquals(0.5 * FastMath.PI, southCap.getRadius(), 1.0e-10);

        EnclosingBall<Sphere2D, S2Point> northCap =
                ((SphericalPolygonsSet) new RegionFactory<Sphere2D>().getComplement(south)).getEnclosingCap();
        Assert.assertEquals(0.0, S2Point.PLUS_K.distance(northCap.getCenter()), 1.0e-10);
        Assert.assertEquals(0.5 * FastMath.PI, northCap.getRadius(), 1.0e-10);

    }

    @Test
    public void testPositiveOctantByIntersection() {
        double tol = 0.01;
        double sinTol = FastMath.sin(tol);
        RegionFactory<Sphere2D> factory = new RegionFactory();
        SphericalPolygonsSet plusX = new SphericalPolygonsSet(Vector3D.PLUS_I, tol);
        SphericalPolygonsSet plusY = new SphericalPolygonsSet(Vector3D.PLUS_J, tol);
        SphericalPolygonsSet plusZ = new SphericalPolygonsSet(Vector3D.PLUS_K, tol);
        SphericalPolygonsSet octant =
                (SphericalPolygonsSet) factory.intersection(factory.intersection(plusX, plusY), plusZ);
        UnitSphereRandomVectorGenerator random =
                new UnitSphereRandomVectorGenerator(3, new Well1024a(0x9c9802fde3cbcf25l));
        for (int i = 0; i < 1000; ++i) {
            Vector3D v = new Vector3D(random.nextVector());
            if ((v.getX() > sinTol) && (v.getY() > sinTol) && (v.getZ() > sinTol)) {
                Assert.assertEquals(Location.INSIDE, octant.checkPoint(new S2Point(v)));
            } else if ((v.getX() < -sinTol) || (v.getY() < -sinTol) || (v.getZ() < -sinTol)) {
                Assert.assertEquals(Location.OUTSIDE, octant.checkPoint(new S2Point(v)));
            } else {
                Assert.assertEquals(Location.BOUNDARY, octant.checkPoint(new S2Point(v)));
            }
        }

        List<Vertex> loops = octant.getBoundaryLoops();
        Assert.assertEquals(1, loops.size());
        boolean xPFound = false;
        boolean yPFound = false;
        boolean zPFound = false;
        boolean xVFound = false;
        boolean yVFound = false;
        boolean zVFound = false;
        Vertex first = loops.get(0);
        int count = 0;
        for (Vertex v = first; count == 0 || v != first; v = v.getOutgoing().getEnd()) {
            ++count;
            Edge e = v.getIncoming();
            Assert.assertTrue(v == e.getStart().getOutgoing().getEnd());
            xPFound = xPFound || e.getCircle().getPole().distance(Vector3D.PLUS_I) < 1.0e-10;
            yPFound = yPFound || e.getCircle().getPole().distance(Vector3D.PLUS_J) < 1.0e-10;
            zPFound = zPFound || e.getCircle().getPole().distance(Vector3D.PLUS_K) < 1.0e-10;
            Assert.assertEquals(0.5 * FastMath.PI, e.getLength(), 1.0e-10);
            xVFound = xVFound || v.getLocation().getVector().distance(Vector3D.PLUS_I) < 1.0e-10;
            yVFound = yVFound || v.getLocation().getVector().distance(Vector3D.PLUS_J) < 1.0e-10;
            zVFound = zVFound || v.getLocation().getVector().distance(Vector3D.PLUS_K) < 1.0e-10;
        }
        Assert.assertTrue(xPFound);
        Assert.assertTrue(yPFound);
        Assert.assertTrue(zPFound);
        Assert.assertTrue(xVFound);
        Assert.assertTrue(yVFound);
        Assert.assertTrue(zVFound);
        Assert.assertEquals(3, count);

        Assert.assertEquals(0.0,
                            ((S2Point) octant.getBarycenter()).distance(new S2Point(new Vector3D(1, 1, 1))),
                            1.0e-10);
        Assert.assertEquals(0.5 * FastMath.PI, octant.getSize(), 1.0e-10);

        EnclosingBall<Sphere2D, S2Point> cap = octant.getEnclosingCap();
        Assert.assertEquals(0.0, octant.getBarycenter().distance(cap.getCenter()), 1.0e-10);
        Assert.assertEquals(FastMath.acos(1.0 / FastMath.sqrt(3)), cap.getRadius(), 1.0e-10);

        EnclosingBall<Sphere2D, S2Point> reversedCap =
                ((SphericalPolygonsSet) factory.getComplement(octant)).getEnclosingCap();
        Assert.assertEquals(0, reversedCap.getCenter().distance(new S2Point(new Vector3D(-1, -1, -1))), 1.0e-10);
        Assert.assertEquals(FastMath.PI - FastMath.asin(1.0 / FastMath.sqrt(3)), reversedCap.getRadius(), 1.0e-10);

    }

    @Test
    public void testPositiveOctantByVertices() {
        double tol = 0.01;
        double sinTol = FastMath.sin(tol);
        SphericalPolygonsSet octant = new SphericalPolygonsSet(tol, S2Point.PLUS_I, S2Point.PLUS_J, S2Point.PLUS_K);
        UnitSphereRandomVectorGenerator random =
                new UnitSphereRandomVectorGenerator(3, new Well1024a(0xb8fc5acc91044308l));
        for (int i = 0; i < 1000; ++i) {
            Vector3D v = new Vector3D(random.nextVector());
            if ((v.getX() > sinTol) && (v.getY() > sinTol) && (v.getZ() > sinTol)) {
                Assert.assertEquals(Location.INSIDE, octant.checkPoint(new S2Point(v)));
            } else if ((v.getX() < -sinTol) || (v.getY() < -sinTol) || (v.getZ() < -sinTol)) {
                Assert.assertEquals(Location.OUTSIDE, octant.checkPoint(new S2Point(v)));
            } else {
                Assert.assertEquals(Location.BOUNDARY, octant.checkPoint(new S2Point(v)));
            }
        }
    }

    @Test
    public void testNonConvex() {
        double tol = 0.01;
        double sinTol = FastMath.sin(tol);
        RegionFactory<Sphere2D> factory = new RegionFactory();
        SphericalPolygonsSet plusX = new SphericalPolygonsSet(Vector3D.PLUS_I, tol);
        SphericalPolygonsSet plusY = new SphericalPolygonsSet(Vector3D.PLUS_J, tol);
        SphericalPolygonsSet plusZ = new SphericalPolygonsSet(Vector3D.PLUS_K, tol);
        SphericalPolygonsSet threeOctants =
                (SphericalPolygonsSet) factory.difference(plusZ, factory.intersection(plusX, plusY));

        UnitSphereRandomVectorGenerator random =
                new UnitSphereRandomVectorGenerator(3, new Well1024a(0x9c9802fde3cbcf25l));
        for (int i = 0; i < 1000; ++i) {
            Vector3D v = new Vector3D(random.nextVector());
            if (((v.getX() < -sinTol) || (v.getY() < -sinTol)) && (v.getZ() > sinTol)) {
                Assert.assertEquals(Location.INSIDE, threeOctants.checkPoint(new S2Point(v)));
            } else if (((v.getX() > sinTol) && (v.getY() > sinTol)) || (v.getZ() < -sinTol)) {
                Assert.assertEquals(Location.OUTSIDE, threeOctants.checkPoint(new S2Point(v)));
            } else {
                Assert.assertEquals(Location.BOUNDARY, threeOctants.checkPoint(new S2Point(v)));
            }
        }

        List<Vertex> loops = threeOctants.getBoundaryLoops();
        Assert.assertEquals(1, loops.size());
        boolean xPFound = false;
        boolean yPFound = false;
        boolean zPFound = false;
        boolean xVFound = false;
        boolean yVFound = false;
        boolean zVFound = false;
        Vertex first = loops.get(0);
        int count = 0;
        double sumPoleX = 0;
        double sumPoleY = 0;
        double sumPoleZ = 0;
        for (Vertex v = first; count == 0 || v != first; v = v.getOutgoing().getEnd()) {
            ++count;
            Edge e = v.getIncoming();
            Assert.assertTrue(v == e.getStart().getOutgoing().getEnd());
            if (e.getCircle().getPole().distance(Vector3D.MINUS_I) < 1.0e-10) {
                xPFound = true;
                sumPoleX += e.getLength();
            } else if (e.getCircle().getPole().distance(Vector3D.MINUS_J) < 1.0e-10) {
                yPFound = true;
                sumPoleY += e.getLength();
            } else {
                Assert.assertEquals(0.0, e.getCircle().getPole().distance(Vector3D.PLUS_K), 1.0e-10);
                zPFound = true;
                sumPoleZ += e.getLength();
            }
            xVFound = xVFound || v.getLocation().getVector().distance(Vector3D.PLUS_I) < 1.0e-10;
            yVFound = yVFound || v.getLocation().getVector().distance(Vector3D.PLUS_J) < 1.0e-10;
            zVFound = zVFound || v.getLocation().getVector().distance(Vector3D.PLUS_K) < 1.0e-10;
        }
        Assert.assertTrue(xPFound);
        Assert.assertTrue(yPFound);
        Assert.assertTrue(zPFound);
        Assert.assertTrue(xVFound);
        Assert.assertTrue(yVFound);
        Assert.assertTrue(zVFound);
        Assert.assertEquals(0.5 * FastMath.PI, sumPoleX, 1.0e-10);
        Assert.assertEquals(0.5 * FastMath.PI, sumPoleY, 1.0e-10);
        Assert.assertEquals(1.5 * FastMath.PI, sumPoleZ, 1.0e-10);

        Assert.assertEquals(1.5 * FastMath.PI, threeOctants.getSize(), 1.0e-10);

    }

    @Test
    public void testModeratlyComplexShape() {
        double tol = 0.01;
        List<SubHyperplane boundary = new ArrayList>();
        boundary.add(create(Vector3D.MINUS_J, Vector3D.PLUS_I,  Vector3D.PLUS_K,  tol, 0.0, 0.5 * FastMath.PI));
        boundary.add(create(Vector3D.MINUS_I, Vector3D.PLUS_K,  Vector3D.PLUS_J,  tol, 0.0, 0.5 * FastMath.PI));
        boundary.add(create(Vector3D.PLUS_K,  Vector3D.PLUS_J,  Vector3D.MINUS_I, tol, 0.0, 0.5 * FastMath.PI));
        boundary.add(create(Vector3D.MINUS_J, Vector3D.MINUS_I, Vector3D.MINUS_K, tol, 0.0, 0.5 * FastMath.PI));
        boundary.add(create(Vector3D.MINUS_I, Vector3D.MINUS_K, Vector3D.MINUS_J, tol, 0.0, 0.5 * FastMath.PI));
        boundary.add(create(Vector3D.PLUS_K,  Vector3D.MINUS_J, Vector3D.PLUS_I,  tol, 0.0, 0.5 * FastMath.PI));
        SphericalPolygonsSet polygon = new SphericalPolygonsSet(boundary, tol);

        Assert.assertEquals(Location.OUTSIDE, polygon.checkPoint(new S2Point(new Vector3D( 1,  1,  1).normalize())));
        Assert.assertEquals(Location.INSIDE,  polygon.checkPoint(new S2Point(new Vector3D(-1,  1,  1).normalize())));
        Assert.assertEquals(Location.INSIDE,  polygon.checkPoint(new S2Point(new Vector3D(-1, -1,  1).normalize())));
        Assert.assertEquals(Location.INSIDE,  polygon.checkPoint(new S2Point(new Vector3D( 1, -1,  1).normalize())));
        Assert.assertEquals(Location.OUTSIDE, polygon.checkPoint(new S2Point(new Vector3D( 1,  1, -1).normalize())));
        Assert.assertEquals(Location.OUTSIDE, polygon.checkPoint(new S2Point(new Vector3D(-1,  1, -1).normalize())));
        Assert.assertEquals(Location.INSIDE,  polygon.checkPoint(new S2Point(new Vector3D(-1, -1, -1).normalize())));
        Assert.assertEquals(Location.OUTSIDE, polygon.checkPoint(new S2Point(new Vector3D( 1, -1, -1).normalize())));

        Assert.assertEquals(MathUtils.TWO_PI, polygon.getSize(), 1.0e-10);
        Assert.assertEquals(3 * FastMath.PI, polygon.getBoundarySize(), 1.0e-10);

        List<Vertex> loops = polygon.getBoundaryLoops();
        Assert.assertEquals(1, loops.size());
        boolean pXFound = false;
        boolean mXFound = false;
        boolean pYFound = false;
        boolean mYFound = false;
        boolean pZFound = false;
        boolean mZFound = false;
        Vertex first = loops.get(0);
        int count = 0;
        for (Vertex v = first; count == 0 || v != first; v = v.getOutgoing().getEnd()) {
            ++count;
            Edge e = v.getIncoming();
            Assert.assertTrue(v == e.getStart().getOutgoing().getEnd());
            pXFound = pXFound || v.getLocation().getVector().distance(Vector3D.PLUS_I)  < 1.0e-10;
            mXFound = mXFound || v.getLocation().getVector().distance(Vector3D.MINUS_I) < 1.0e-10;
            pYFound = pYFound || v.getLocation().getVector().distance(Vector3D.PLUS_J)  < 1.0e-10;
            mYFound = mYFound || v.getLocation().getVector().distance(Vector3D.MINUS_J) < 1.0e-10;
            pZFound = pZFound || v.getLocation().getVector().distance(Vector3D.PLUS_K)  < 1.0e-10;
            mZFound = mZFound || v.getLocation().getVector().distance(Vector3D.MINUS_K) < 1.0e-10;
            Assert.assertEquals(0.5 * FastMath.PI, e.getLength(), 1.0e-10);
        }
        Assert.assertTrue(pXFound);
        Assert.assertTrue(mXFound);
        Assert.assertTrue(pYFound);
        Assert.assertTrue(mYFound);
        Assert.assertTrue(pZFound);
        Assert.assertTrue(mZFound);
        Assert.assertEquals(6, count);

    }

    @Test
    public void testSeveralParts() {
        double tol = 0.01;
        double sinTol = FastMath.sin(tol);
        List<SubHyperplane boundary = new ArrayList>();

        // first part: +X, +Y, +Z octant
        boundary.add(create(Vector3D.PLUS_J,  Vector3D.PLUS_K,  Vector3D.PLUS_I,  tol, 0.0, 0.5 * FastMath.PI));
        boundary.add(create(Vector3D.PLUS_K,  Vector3D.PLUS_I,  Vector3D.PLUS_J,  tol, 0.0, 0.5 * FastMath.PI));
        boundary.add(create(Vector3D.PLUS_I,  Vector3D.PLUS_J,  Vector3D.PLUS_K,  tol, 0.0, 0.5 * FastMath.PI));

        // first part: -X, -Y, -Z octant
        boundary.add(create(Vector3D.MINUS_J, Vector3D.MINUS_I, Vector3D.MINUS_K, tol, 0.0, 0.5 * FastMath.PI));
        boundary.add(create(Vector3D.MINUS_I, Vector3D.MINUS_K, Vector3D.MINUS_J, tol, 0.0, 0.5 * FastMath.PI));
        boundary.add(create(Vector3D.MINUS_K, Vector3D.MINUS_J, Vector3D.MINUS_I,  tol, 0.0, 0.5 * FastMath.PI));

        SphericalPolygonsSet polygon = new SphericalPolygonsSet(boundary, tol);

        UnitSphereRandomVectorGenerator random =
                new UnitSphereRandomVectorGenerator(3, new Well1024a(0xcc5ce49949e0d3ecl));
        for (int i = 0; i < 1000; ++i) {
            Vector3D v = new Vector3D(random.nextVector());
            if ((v.getX() < -sinTol) && (v.getY() < -sinTol) && (v.getZ() < -sinTol)) {
                Assert.assertEquals(Location.INSIDE, polygon.checkPoint(new S2Point(v)));
            } else if ((v.getX() < sinTol) && (v.getY() < sinTol) && (v.getZ() < sinTol)) {
                Assert.assertEquals(Location.BOUNDARY, polygon.checkPoint(new S2Point(v)));
            } else if ((v.getX() > sinTol) && (v.getY() > sinTol) && (v.getZ() > sinTol)) {
                Assert.assertEquals(Location.INSIDE, polygon.checkPoint(new S2Point(v)));
            } else if ((v.getX() > -sinTol) && (v.getY() > -sinTol) && (v.getZ() > -sinTol)) {
                Assert.assertEquals(Location.BOUNDARY, polygon.checkPoint(new S2Point(v)));
            } else {
                Assert.assertEquals(Location.OUTSIDE, polygon.checkPoint(new S2Point(v)));
            }
        }

        Assert.assertEquals(FastMath.PI, polygon.getSize(), 1.0e-10);
        Assert.assertEquals(3 * FastMath.PI, polygon.getBoundarySize(), 1.0e-10);

        // there should be two separate boundary loops
        Assert.assertEquals(2, polygon.getBoundaryLoops().size());

    }

    @Test
    public void testPartWithHole() {
        double tol = 0.01;
        double alpha = 0.7;
        S2Point center = new S2Point(new Vector3D(1, 1, 1));
        SphericalPolygonsSet hexa = new SphericalPolygonsSet(center.getVector(), Vector3D.PLUS_K, alpha, 6, tol);
        SphericalPolygonsSet hole  = new SphericalPolygonsSet(tol,
                                                              new S2Point(FastMath.PI / 6, FastMath.PI / 3),
                                                              new S2Point(FastMath.PI / 3, FastMath.PI / 3),
                                                              new S2Point(FastMath.PI / 4, FastMath.PI / 6));
        SphericalPolygonsSet hexaWithHole =
                (SphericalPolygonsSet) new RegionFactory<Sphere2D>().difference(hexa, hole);

        for (double phi = center.getPhi() - alpha + 0.1; phi < center.getPhi() + alpha - 0.1; phi += 0.07) {
            Location l = hexaWithHole.checkPoint(new S2Point(FastMath.PI / 4, phi));
            if (phi < FastMath.PI / 6 || phi > FastMath.PI / 3) {
                Assert.assertEquals(Location.INSIDE,  l);
            } else {
                Assert.assertEquals(Location.OUTSIDE, l);
            }
        }

        // there should be two separate boundary loops
        Assert.assertEquals(2, hexaWithHole.getBoundaryLoops().size());

        Assert.assertEquals(hexa.getBoundarySize() + hole.getBoundarySize(), hexaWithHole.getBoundarySize(), 1.0e-10);
        Assert.assertEquals(hexa.getSize() - hole.getSize(), hexaWithHole.getSize(), 1.0e-10);

    }

    @Test
    public void testConcentricSubParts() {
        double tol = 0.001;
        Vector3D center = new Vector3D(1, 1, 1);
        SphericalPolygonsSet hexaOut   = new SphericalPolygonsSet(center, Vector3D.PLUS_K, 0.9,  6, tol);
        SphericalPolygonsSet hexaIn    = new SphericalPolygonsSet(center, Vector3D.PLUS_K, 0.8,  6, tol);
        SphericalPolygonsSet pentaOut  = new SphericalPolygonsSet(center, Vector3D.PLUS_K, 0.7,  5, tol);
        SphericalPolygonsSet pentaIn   = new SphericalPolygonsSet(center, Vector3D.PLUS_K, 0.6,  5, tol);
        SphericalPolygonsSet quadriOut = new SphericalPolygonsSet(center, Vector3D.PLUS_K, 0.5,  4, tol);
        SphericalPolygonsSet quadriIn  = new SphericalPolygonsSet(center, Vector3D.PLUS_K, 0.4,  4, tol);
        SphericalPolygonsSet triOut    = new SphericalPolygonsSet(center, Vector3D.PLUS_K, 0.25, 3, tol);
        SphericalPolygonsSet triIn     = new SphericalPolygonsSet(center, Vector3D.PLUS_K, 0.15, 3, tol);

        RegionFactory<Sphere2D> factory = new RegionFactory();
        SphericalPolygonsSet hexa   = (SphericalPolygonsSet) factory.difference(hexaOut,   hexaIn);
        SphericalPolygonsSet penta  = (SphericalPolygonsSet) factory.difference(pentaOut,  pentaIn);
        SphericalPolygonsSet quadri = (SphericalPolygonsSet) factory.difference(quadriOut, quadriIn);
        SphericalPolygonsSet tri    = (SphericalPolygonsSet) factory.difference(triOut,    triIn);
        SphericalPolygonsSet concentric =
                (SphericalPolygonsSet) factory.union(factory.union(hexa, penta), factory.union(quadri, tri));

        // there should be two separate boundary loops
        Assert.assertEquals(8, concentric.getBoundaryLoops().size());

        Assert.assertEquals(hexaOut.getBoundarySize()   + hexaIn.getBoundarySize()   +
                            pentaOut.getBoundarySize()  + pentaIn.getBoundarySize()  +
                            quadriOut.getBoundarySize() + quadriIn.getBoundarySize() +
                            triOut.getBoundarySize()    + triIn.getBoundarySize(),
                            concentric.getBoundarySize(), 1.0e-10);
        Assert.assertEquals(hexaOut.getSize()   - hexaIn.getSize()   +
                            pentaOut.getSize()  - pentaIn.getSize()  +
                            quadriOut.getSize() - quadriIn.getSize() +
                            triOut.getSize()    - triIn.getSize(),
                            concentric.getSize(), 1.0e-10);

        // we expect lots of sign changes as we traverse all concentric rings
        double phi = new S2Point(center).getPhi();
        Assert.assertEquals(+0.207, concentric.projectToBoundary(new S2Point(-0.60,  phi)).getOffset(), 0.01);
        Assert.assertEquals(-0.048, concentric.projectToBoundary(new S2Point(-0.21,  phi)).getOffset(), 0.01);
        Assert.assertEquals(+0.027, concentric.projectToBoundary(new S2Point(-0.10,  phi)).getOffset(), 0.01);
        Assert.assertEquals(-0.041, concentric.projectToBoundary(new S2Point( 0.01,  phi)).getOffset(), 0.01);
        Assert.assertEquals(+0.049, concentric.projectToBoundary(new S2Point( 0.16,  phi)).getOffset(), 0.01);
        Assert.assertEquals(-0.038, concentric.projectToBoundary(new S2Point( 0.29,  phi)).getOffset(), 0.01);
        Assert.assertEquals(+0.097, concentric.projectToBoundary(new S2Point( 0.48,  phi)).getOffset(), 0.01);
        Assert.assertEquals(-0.022, concentric.projectToBoundary(new S2Point( 0.64,  phi)).getOffset(), 0.01);
        Assert.assertEquals(+0.072, concentric.projectToBoundary(new S2Point( 0.79,  phi)).getOffset(), 0.01);
        Assert.assertEquals(-0.022, concentric.projectToBoundary(new S2Point( 0.93,  phi)).getOffset(), 0.01);
        Assert.assertEquals(+0.091, concentric.projectToBoundary(new S2Point( 1.08,  phi)).getOffset(), 0.01);
        Assert.assertEquals(-0.037, concentric.projectToBoundary(new S2Point( 1.28,  phi)).getOffset(), 0.01);
        Assert.assertEquals(+0.051, concentric.projectToBoundary(new S2Point( 1.40,  phi)).getOffset(), 0.01);
        Assert.assertEquals(-0.041, concentric.projectToBoundary(new S2Point( 1.55,  phi)).getOffset(), 0.01);
        Assert.assertEquals(+0.027, concentric.projectToBoundary(new S2Point( 1.67,  phi)).getOffset(), 0.01);
        Assert.assertEquals(-0.044, concentric.projectToBoundary(new S2Point( 1.79,  phi)).getOffset(), 0.01);
        Assert.assertEquals(+0.201, concentric.projectToBoundary(new S2Point( 2.16,  phi)).getOffset(), 0.01);

    }

    @Test
    public void testGeographicalMap() {

        SphericalPolygonsSet continental = buildSimpleZone(new double[][] {
          { 51.14850,  2.51357 }, { 50.94660,  1.63900 }, { 50.12717,  1.33876 }, { 49.34737, -0.98946 },
          { 49.77634, -1.93349 }, { 48.64442, -1.61651 }, { 48.90169, -3.29581 }, { 48.68416, -4.59234 },
          { 47.95495, -4.49155 }, { 47.57032, -2.96327 }, { 46.01491, -1.19379 }, { 44.02261, -1.38422 },
          { 43.42280, -1.90135 }, { 43.03401, -1.50277 }, { 42.34338,  1.82679 }, { 42.47301,  2.98599 },
          { 43.07520,  3.10041 }, { 43.39965,  4.55696 }, { 43.12889,  6.52924 }, { 43.69384,  7.43518 },
          { 44.12790,  7.54959 }, { 45.02851,  6.74995 }, { 45.33309,  7.09665 }, { 46.42967,  6.50009 },
          { 46.27298,  6.02260 }, { 46.72577,  6.03738 }, { 47.62058,  7.46675 }, { 49.01778,  8.09927 },
          { 49.20195,  6.65822 }, { 49.44266,  5.89775 }, { 49.98537,  4.79922 }
        });
        SphericalPolygonsSet corsica = buildSimpleZone(new double[][] {
          { 42.15249,  9.56001 }, { 43.00998,  9.39000 }, { 42.62812,  8.74600 }, { 42.25651,  8.54421 },
          { 41.58361,  8.77572 }, { 41.38000,  9.22975 }
        });
        RegionFactory<Sphere2D> factory = new RegionFactory();
        SphericalPolygonsSet zone = (SphericalPolygonsSet) factory.union(continental, corsica);
        EnclosingBall<Sphere2D, S2Point> enclosing = zone.getEnclosingCap();
        Vector3D enclosingCenter = ((S2Point) enclosing.getCenter()).getVector();

        double step = FastMath.toRadians(0.1);
        for (Vertex loopStart : zone.getBoundaryLoops()) {
            int count = 0;
            for (Vertex v = loopStart; count == 0 || v != loopStart; v = v.getOutgoing().getEnd()) {
                ++count;
                for (int i = 0; i < FastMath.ceil(v.getOutgoing().getLength() / step); ++i) {
                    Vector3D p = v.getOutgoing().getPointAt(i * step);
                    Assert.assertTrue(Vector3D.angle(p, enclosingCenter) <= enclosing.getRadius());
                }
            }
        }

        S2Point supportPointA = s2Point(48.68416, -4.59234);
        S2Point supportPointB = s2Point(41.38000,  9.22975);
        Assert.assertEquals(enclosing.getRadius(), supportPointA.distance(enclosing.getCenter()), 1.0e-10);
        Assert.assertEquals(enclosing.getRadius(), supportPointB.distance(enclosing.getCenter()), 1.0e-10);
        Assert.assertEquals(0.5 * supportPointA.distance(supportPointB), enclosing.getRadius(), 1.0e-10);
        Assert.assertEquals(2, enclosing.getSupportSize());

        EnclosingBall<Sphere2D, S2Point> continentalInscribed =
                ((SphericalPolygonsSet) factory.getComplement(continental)).getEnclosingCap();
        Vector3D continentalCenter = ((S2Point) continentalInscribed.getCenter()).getVector();
        Assert.assertEquals(2.2, FastMath.toDegrees(FastMath.PI - continentalInscribed.getRadius()), 0.1);
        for (Vertex loopStart : continental.getBoundaryLoops()) {
            int count = 0;
            for (Vertex v = loopStart; count == 0 || v != loopStart; v = v.getOutgoing().getEnd()) {
                ++count;
                for (int i = 0; i < FastMath.ceil(v.getOutgoing().getLength() / step); ++i) {
                    Vector3D p = v.getOutgoing().getPointAt(i * step);
                    Assert.assertTrue(Vector3D.angle(p, continentalCenter) <= continentalInscribed.getRadius());
                }
            }
        }

        EnclosingBall<Sphere2D, S2Point> corsicaInscribed =
                ((SphericalPolygonsSet) factory.getComplement(corsica)).getEnclosingCap();
        Vector3D corsicaCenter = ((S2Point) corsicaInscribed.getCenter()).getVector();
        Assert.assertEquals(0.34, FastMath.toDegrees(FastMath.PI - corsicaInscribed.getRadius()), 0.01);
        for (Vertex loopStart : corsica.getBoundaryLoops()) {
            int count = 0;
            for (Vertex v = loopStart; count == 0 || v != loopStart; v = v.getOutgoing().getEnd()) {
                ++count;
                for (int i = 0; i < FastMath.ceil(v.getOutgoing().getLength() / step); ++i) {
                    Vector3D p = v.getOutgoing().getPointAt(i * step);
                    Assert.assertTrue(Vector3D.angle(p, corsicaCenter) <= corsicaInscribed.getRadius());
                }
            }
        }

    }

    private SubCircle create(Vector3D pole, Vector3D x, Vector3D y,
                             double tolerance, double ... limits) {
        RegionFactory<Sphere1D> factory = new RegionFactory();
        Circle circle = new Circle(pole, tolerance);
        Circle phased =
                (Circle) Circle.getTransform(new Rotation(circle.getXAxis(), circle.getYAxis(), x, y)).apply(circle);
        ArcsSet set = (ArcsSet) factory.getComplement(new ArcsSet(tolerance));
        for (int i = 0; i < limits.length; i += 2) {
            set = (ArcsSet) factory.union(set, new ArcsSet(limits[i], limits[i + 1], tolerance));
        }
        return new SubCircle(phased, set);
    }

    private SphericalPolygonsSet buildSimpleZone(double[][] points) {
        final S2Point[] vertices = new S2Point[points.length];
        for (int i = 0; i < points.length; ++i) {
            vertices[i] = s2Point(points[i][0], points[i][1]);
        }
        return new SphericalPolygonsSet(1.0e-10, vertices);
    }

    private S2Point s2Point(double latitude, double longitude) {
        return new S2Point(FastMath.toRadians(longitude), FastMath.toRadians(90.0 - latitude));
    }

}

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