Examples of org.apache.commons.math.geometry.Vector3D

Package org.apache.commons.math.geometry

Examples of org.apache.commons.math.geometry.Vector3D

org.apache.commons.math.geometry.Vector3D
This class implements vectors in a three-dimensional space.
Instance of this class are guaranteed to be immutable.
@version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $ @since 1.2


  }


  public void testAxisAngle() {


    Rotation r = new Rotation(new Vector3D(10, 10, 10), 2 * Math.PI / 3);
    checkVector(r.applyTo(Vector3D.PLUS_I), Vector3D.PLUS_J);
    checkVector(r.applyTo(Vector3D.PLUS_J), Vector3D.PLUS_K);
    checkVector(r.applyTo(Vector3D.PLUS_K), Vector3D.PLUS_I);
    double s = 1 / Math.sqrt(3);
    checkVector(r.getAxis(), new Vector3D(s, s, s));
    checkAngle(r.getAngle(), 2 * Math.PI / 3);


    try {
      new Rotation(new Vector3D(0, 0, 0), 2 * Math.PI / 3);
      fail("an exception should have been thrown");
    } catch (ArithmeticException e) {
    } catch (Exception e) {
      fail("unexpected exception");
    }


    r = new Rotation(Vector3D.PLUS_K, 1.5 * Math.PI);
    checkVector(r.getAxis(), new Vector3D(0, 0, -1));
    checkAngle(r.getAngle(), 0.5 * Math.PI);


    r = new Rotation(Vector3D.PLUS_J, Math.PI);
    checkVector(r.getAxis(), Vector3D.PLUS_J);
    checkAngle(r.getAngle(), Math.PI);

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    assertEquals(-1, Vector3D.dotProduct(r.getAxis(), reverted.getAxis()), 1.0e-12);
  }


  public void testVectorOnePair() {


    Vector3D u = new Vector3D(3, 2, 1);
    Vector3D v = new Vector3D(-4, 2, 2);
    Rotation r = new Rotation(u, v);
    checkVector(r.applyTo(u.scalarMultiply(v.getNorm())), v.scalarMultiply(u.getNorm()));


    checkAngle(new Rotation(u, u.negate()).getAngle(), Math.PI);


    try {
        new Rotation(u, Vector3D.ZERO);

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  }


  public void testVectorTwoPairs() {


    Vector3D u1 = new Vector3D(3, 0, 0);
    Vector3D u2 = new Vector3D(0, 5, 0);
    Vector3D v1 = new Vector3D(0, 0, 2);
    Vector3D v2 = new Vector3D(-2, 0, 2);
    Rotation r = new Rotation(u1, u2, v1, v2);
    checkVector(r.applyTo(Vector3D.PLUS_I), Vector3D.PLUS_K);
    checkVector(r.applyTo(Vector3D.PLUS_J), Vector3D.MINUS_I);


    r = new Rotation(u1, u2, u1.negate(), u2.negate());
    Vector3D axis = r.getAxis();
    if (Vector3D.dotProduct(axis, Vector3D.PLUS_K) > 0) {
      checkVector(axis, Vector3D.PLUS_K);
    } else {
      checkVector(axis, Vector3D.MINUS_K);
    }
    checkAngle(r.getAngle(), Math.PI);


    double sqrt = Math.sqrt(2) / 2;
    r = new Rotation(Vector3D.PLUS_I,  Vector3D.PLUS_J,
                     new Vector3D(0.5, 0.5,  sqrt),
                     new Vector3D(0.5, 0.5, -sqrt));
    checkRotation(r, sqrt, 0.5, 0.5, 0);


    r = new Rotation(u1, u2, u1, Vector3D.crossProduct(u1, u2));
    checkRotation(r, sqrt, -sqrt, 0, 0);

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        }
      }
    }


    checkVector(r.applyTo(Vector3D.PLUS_I),
                new Vector3D(m3[0][0], m3[1][0], m3[2][0]));
    checkVector(r.applyTo(Vector3D.PLUS_J),
                new Vector3D(m3[0][1], m3[1][1], m3[2][1]));
    checkVector(r.applyTo(Vector3D.PLUS_K),
                new Vector3D(m3[0][2], m3[1][2], m3[2][2]));


    double[][] m4 = { { 1.0,  0.0,  0.0 },
                      { 0.0, -1.0,  0.0 },
                      { 0.0,  0.0, -1.0 } };
    r = new Rotation(m4, 1.0e-7);

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  }


  public void testQuaternion() {


    Rotation r1 = new Rotation(new Vector3D(2, -3, 5), 1.7);
    double n = 23.5;
    Rotation r2 = new Rotation(n * r1.getQ0(), n * r1.getQ1(),
                               n * r1.getQ2(), n * r1.getQ3(),
                               true);
    for (double x = -0.9; x < 0.9; x += 0.2) {
      for (double y = -0.9; y < 0.9; y += 0.2) {
        for (double z = -0.9; z < 0.9; z += 0.2) {
          Vector3D u = new Vector3D(x, y, z);
          checkVector(r2.applyTo(u), r1.applyTo(u));
        }
      }
    }

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  }


  public void testCompose() {


    Rotation r1 = new Rotation(new Vector3D(2, -3, 5), 1.7);
    Rotation r2 = new Rotation(new Vector3D(-1, 3, 2), 0.3);
    Rotation r3 = r2.applyTo(r1);


    for (double x = -0.9; x < 0.9; x += 0.2) {
      for (double y = -0.9; y < 0.9; y += 0.2) {
        for (double z = -0.9; z < 0.9; z += 0.2) {
          Vector3D u = new Vector3D(x, y, z);
          checkVector(r2.applyTo(r1.applyTo(u)), r3.applyTo(u));
        }
      }
    }

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  }


  public void testComposeInverse() {


    Rotation r1 = new Rotation(new Vector3D(2, -3, 5), 1.7);
    Rotation r2 = new Rotation(new Vector3D(-1, 3, 2), 0.3);
    Rotation r3 = r2.applyInverseTo(r1);


    for (double x = -0.9; x < 0.9; x += 0.2) {
      for (double y = -0.9; y < 0.9; y += 0.2) {
        for (double z = -0.9; z < 0.9; z += 0.2) {
          Vector3D u = new Vector3D(x, y, z);
          checkVector(r2.applyInverseTo(r1.applyTo(u)), r3.applyTo(u));
        }
      }
    }

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  }


  public void testApplyInverseTo() {


    Rotation r = new Rotation(new Vector3D(2, -3, 5), 1.7);
    for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
      for (double phi = -1.55; phi < 1.55; phi += 0.2) {
          Vector3D u = new Vector3D(Math.cos(lambda) * Math.cos(phi),
                                    Math.sin(lambda) * Math.cos(phi),
                                    Math.sin(phi));
          r.applyInverseTo(r.applyTo(u));
          checkVector(u, r.applyInverseTo(r.applyTo(u)));
          checkVector(u, r.applyTo(r.applyInverseTo(u)));
      }
    }


    r = Rotation.IDENTITY;
    for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
      for (double phi = -1.55; phi < 1.55; phi += 0.2) {
          Vector3D u = new Vector3D(Math.cos(lambda) * Math.cos(phi),
                                    Math.sin(lambda) * Math.cos(phi),
                                    Math.sin(phi));
          checkVector(u, r.applyInverseTo(r.applyTo(u)));
          checkVector(u, r.applyTo(r.applyInverseTo(u)));
      }
    }


    r = new Rotation(Vector3D.PLUS_K, Math.PI);
    for (double lambda = 0; lambda < 6.2; lambda += 0.2) {
      for (double phi = -1.55; phi < 1.55; phi += 0.2) {
          Vector3D u = new Vector3D(Math.cos(lambda) * Math.cos(phi),
                                    Math.sin(lambda) * Math.cos(phi),
                                    Math.sin(phi));
          checkVector(u, r.applyInverseTo(r.applyTo(u)));
          checkVector(u, r.applyTo(r.applyInverseTo(u)));
      }

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  }


  public void testAxisAngle() {


    Rotation r = new Rotation(new Vector3D(10, 10, 10), 2 * Math.PI / 3);
    checkVector(r.applyTo(Vector3D.plusI), Vector3D.plusJ);
    checkVector(r.applyTo(Vector3D.plusJ), Vector3D.plusK);
    checkVector(r.applyTo(Vector3D.plusK), Vector3D.plusI);
    double s = 1 / Math.sqrt(3);
    checkVector(r.getAxis(), new Vector3D(s, s, s));
    checkAngle(r.getAngle(), 2 * Math.PI / 3);


    try {
      new Rotation(new Vector3D(0, 0, 0), 2 * Math.PI / 3);
      fail("an exception should have been thrown");
    } catch (ArithmeticException e) {
    } catch (Exception e) {
      fail("unexpected exception");
    }


    r = new Rotation(Vector3D.plusK, 1.5 * Math.PI);
    checkVector(r.getAxis(), new Vector3D(0, 0, -1));
    checkAngle(r.getAngle(), 0.5 * Math.PI);


    r = new Rotation(Vector3D.plusJ, Math.PI);
    checkVector(r.getAxis(), Vector3D.plusJ);
    checkAngle(r.getAngle(), Math.PI);

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    assertEquals(-1, Vector3D.dotProduct(r.getAxis(), reverted.getAxis()), 1.0e-12);
  }


  public void testVectorOnePair() {


    Vector3D u = new Vector3D(3, 2, 1);
    Vector3D v = new Vector3D(-4, 2, 2);
    Rotation r = new Rotation(u, v);
    checkVector(r.applyTo(u.scalarMultiply(v.getNorm())), v.scalarMultiply(u.getNorm()));


    checkAngle(new Rotation(u, u.negate()).getAngle(), Math.PI);


    try {
        new Rotation(u, new Vector3D());
        fail("an exception should have been thrown");
      } catch (IllegalArgumentException e) {
        // expected behavior
      } catch (Exception e) {
        fail("unexpected exception");

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Related Classes of org.apache.commons.math.geometry.Vector3D

org.apache.commons.math.geometry.RotationTest

org.apache.commons.math.geometry.Vector3DTest

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