Package org.apache.commons.math3.geometry.euclidean.threed

Examples of org.apache.commons.math3.geometry.euclidean.threed.Vector3D

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    @Test
    public void testSubSpace() {
        Circle circle = new Circle(new S2Point(1.2, 2.5), new S2Point(-4.3, 0), 1.0e-10);
        Assert.assertEquals(0.0, circle.toSubSpace(new S2Point(circle.getXAxis())).getAlpha(), 1.0e-10);
        Assert.assertEquals(0.5 * FastMath.PI, circle.toSubSpace(new S2Point(circle.getYAxis())).getAlpha(), 1.0e-10);
        Vector3D p = new Vector3D(1, 2, -4);
        Assert.assertEquals(circle.getPhase(p), circle.toSubSpace(new S2Point(p)).getAlpha(), 1.0e-10);
    }
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    @Test
    public void testSpace() {
        Circle circle = new Circle(new S2Point(1.2, 2.5), new S2Point(-4.3, 0), 1.0e-10);
        for (double alpha = 0; alpha < MathUtils.TWO_PI; alpha += 0.1) {
            Vector3D p = new Vector3D(FastMath.cos(alpha), circle.getXAxis(),
                                      FastMath.sin(alpha), circle.getYAxis());
            Vector3D q = circle.toSpace(new S1Point(alpha)).getVector();
            Assert.assertEquals(0.0, p.distance(q), 1.0e-10);
            Assert.assertEquals(0.5 * FastMath.PI, Vector3D.angle(circle.getPole(), q), 1.0e-10);
        }
    }
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    @Test
    public void testInsideArc() {
        RandomGenerator random = new Well1024a(0xbfd34e92231bbcfel);
        UnitSphereRandomVectorGenerator sphRandom = new UnitSphereRandomVectorGenerator(3, random);
        for (int i = 0; i < 100; ++i) {
            Circle c1 = new Circle(new Vector3D(sphRandom.nextVector()), 1.0e-10);
            Circle c2 = new Circle(new Vector3D(sphRandom.nextVector()), 1.0e-10);
            checkArcIsInside(c1, c2);
            checkArcIsInside(c2, c1);
        }
    }
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    public void testTransform() {
        RandomGenerator random = new Well1024a(0x16992fc4294bf2f1l);
        UnitSphereRandomVectorGenerator sphRandom = new UnitSphereRandomVectorGenerator(3, random);
        for (int i = 0; i < 100; ++i) {

            Rotation r = new Rotation(new Vector3D(sphRandom.nextVector()),
                                      FastMath.PI * random.nextDouble());
            Transform<Sphere2D, Sphere1D> t = Circle.getTransform(r);

            S2Point  p = new S2Point(new Vector3D(sphRandom.nextVector()));
            S2Point tp = (S2Point) t.apply(p);
            Assert.assertEquals(0.0, r.applyTo(p.getVector()).distance(tp.getVector()), 1.0e-10);

            Circle  c = new Circle(new Vector3D(sphRandom.nextVector()), 1.0e-10);
            Circle tc = (Circle) t.apply(c);
            Assert.assertEquals(0.0, r.applyTo(c.getPole()).distance(tc.getPole()),   1.0e-10);
            Assert.assertEquals(0.0, r.applyTo(c.getXAxis()).distance(tc.getXAxis()), 1.0e-10);
            Assert.assertEquals(0.0, r.applyTo(c.getYAxis()).distance(tc.getYAxis()), 1.0e-10);
            Assert.assertEquals(c.getTolerance(), ((Circle) t.apply(c)).getTolerance(), 1.0e-10);

            SubLimitAngle  sub = new LimitAngle(new S1Point(MathUtils.TWO_PI * random.nextDouble()),
                                                random.nextBoolean(), 1.0e-10).wholeHyperplane();
            Vector3D psub = c.getPointAt(((LimitAngle) sub.getHyperplane()).getLocation().getAlpha());
            SubLimitAngle tsub = (SubLimitAngle) t.apply(sub, c, tc);
            Vector3D ptsub = tc.getPointAt(((LimitAngle) tsub.getHyperplane()).getLocation().getAlpha());
            Assert.assertEquals(0.0, r.applyTo(psub).distance(ptsub), 1.0e-10);

        }
    }
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        // comparison with the result given by the formula :
        // qResult = (scalarA * scalarB - vectorA . vectorB) + (scalarA * vectorB + scalarB * vectorA + vectorA ^
        // vectorB)

        final Vector3D vectorA = new Vector3D(qA.getVectorPart());
        final Vector3D vectorB = new Vector3D(qB.getVectorPart());
        final Vector3D vectorResult = new Vector3D(qResult.getVectorPart());

        final double scalarPartRef = qA.getScalarPart() * qB.getScalarPart() - Vector3D.dotProduct(vectorA, vectorB);

        Assert.assertEquals(scalarPartRef, qResult.getScalarPart(), EPS);

        final Vector3D vectorPartRef = ((vectorA.scalarMultiply(qB.getScalarPart())).add(vectorB.scalarMultiply(qA
                .getScalarPart()))).add(Vector3D.crossProduct(vectorA, vectorB));
        final double norm = (vectorResult.subtract(vectorPartRef)).getNorm();

        Assert.assertEquals(0, norm, EPS);

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        // qResult = (- vectorQ . vector) + (scalarQ * vector + vectorQ ^ vector)

        final double[] vectorQ = quaternion.getVectorPart();
        final double[] vectorResultQxV = qResultQxV.getVectorPart();

        final double scalarPartRefQxV = -Vector3D.dotProduct(new Vector3D(vectorQ), new Vector3D(vector));
        Assert.assertEquals(scalarPartRefQxV, qResultQxV.getScalarPart(), EPS);

        final Vector3D vectorPartRefQxV = (new Vector3D(vector).scalarMultiply(quaternion.getScalarPart())).add(Vector3D
                .crossProduct(new Vector3D(vectorQ), new Vector3D(vector)));
        final double normQxV = (new Vector3D(vectorResultQxV).subtract(vectorPartRefQxV)).getNorm();
        Assert.assertEquals(0, normQxV, EPS);

        // Case : Product between a vector and a quaternion : VxQ

        final Quaternion qResultVxQ = Quaternion.multiply(new Quaternion(vector), quaternion);

        Assert.assertEquals(-19, qResultVxQ.getQ0(), EPS);
        Assert.assertEquals(13, qResultVxQ.getQ1(), EPS);
        Assert.assertEquals(21, qResultVxQ.getQ2(), EPS);
        Assert.assertEquals(3, qResultVxQ.getQ3(), EPS);

        final double[] vectorResultVxQ = qResultVxQ.getVectorPart();

        // comparison with the result given by the formula :
        // qResult = (- vector . vectorQ) + (scalarQ * vector + vector ^ vectorQ)

        final double scalarPartRefVxQ = -Vector3D.dotProduct(new Vector3D(vectorQ), new Vector3D(vector));
        Assert.assertEquals(scalarPartRefVxQ, qResultVxQ.getScalarPart(), EPS);

        final Vector3D vectorPartRefVxQ = (new Vector3D(vector).scalarMultiply(quaternion.getScalarPart())).add(Vector3D
                .crossProduct(new Vector3D(vector), new Vector3D(vectorQ)));
        final double normVxQ = (new Vector3D(vectorResultVxQ).subtract(vectorPartRefVxQ)).getNorm();
        Assert.assertEquals(0, normVxQ, EPS);
    }
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                {-3, 0, -9}
        }, new double[]{1, 1, 1});

        Optimum optimum = optimizer.optimize(problem.getBuilder().build());

        Plane span = new Plane(Vector3D.ZERO, new Vector3D(1, 2, -3), new Vector3D(2, 1, 0), TOl);
        double expected = FastMath.abs(span.getOffset(new Vector3D(1, 1, 1)));
        double actual = optimum.getResiduals().getNorm();

        //verify
        Assert.assertEquals(expected, actual, TOl);
    }
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    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());
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        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());
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        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)));
            }
        }
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Related Classes of org.apache.commons.math3.geometry.euclidean.threed.Vector3D

  • org.apache.commons.math3.analysis.differentiation.DerivativeStructure
  • org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction
  • org.apache.commons.math3.analysis.function.HarmonicOscillator
  • org.apache.commons.math3.analysis.function.Sin
  • org.apache.commons.math3.analysis.function.Sinc
  • org.apache.commons.math3.analysis.MultivariateFunction
  • org.apache.commons.math3.analysis.QuinticFunction
  • org.apache.commons.math3.analysis.solvers.BrentSolver
  • org.apache.commons.math3.analysis.UnivariateFunction
  • org.apache.commons.math3.complex.Complex
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