Package org.hipparchus.geometry.euclidean.threed

Class Vector3D

java.lang.Object
org.hipparchus.geometry.euclidean.threed.Vector3D
All Implemented Interfaces:
Serializable, Point<Euclidean3D>, Vector<Euclidean3D,Vector3D>, Blendable<Vector<Euclidean3D,Vector3D>>
public class Vector3D extends Object implements Serializable, Vector<Euclidean3D,Vector3D>
This class implements vectors in a three-dimensional space.

Instance of this class are guaranteed to be immutable.

See Also:

  • Field Details

    • ZERO

      public static final Vector3D ZERO
      Null vector (coordinates: 0, 0, 0).

    • PLUS_I

      public static final Vector3D PLUS_I
      First canonical vector (coordinates: 1, 0, 0).

    • MINUS_I

      public static final Vector3D MINUS_I
      Opposite of the first canonical vector (coordinates: -1, 0, 0).

    • PLUS_J

      public static final Vector3D PLUS_J
      Second canonical vector (coordinates: 0, 1, 0).

    • MINUS_J

      public static final Vector3D MINUS_J
      Opposite of the second canonical vector (coordinates: 0, -1, 0).

    • PLUS_K

      public static final Vector3D PLUS_K
      Third canonical vector (coordinates: 0, 0, 1).

    • MINUS_K

      public static final Vector3D MINUS_K
      Opposite of the third canonical vector (coordinates: 0, 0, -1).

    • NaN

      public static final Vector3D NaN
      A vector with all coordinates set to NaN.

    • POSITIVE_INFINITY

      public static final Vector3D POSITIVE_INFINITY
      A vector with all coordinates set to positive infinity.

    • NEGATIVE_INFINITY

      public static final Vector3D NEGATIVE_INFINITY
      A vector with all coordinates set to negative infinity.

  • Constructor Details

    • Vector3D

      public Vector3D(double x, double y, double z)
      Simple constructor. Build a vector from its coordinates
      Parameters:
      x - abscissa
      y - ordinate
      z - height
      See Also:

    • Vector3D

      public Vector3D(double[] v) throws MathIllegalArgumentException
      Simple constructor. Build a vector from its coordinates
      Parameters:
      v - coordinates array
      Throws:
      MathIllegalArgumentException - if array does not have 3 elements
      See Also:

    • Vector3D

      public Vector3D(double alpha, double delta)
      Simple constructor. Build a vector from its azimuthal coordinates
      Parameters:
      alpha - azimuth (α) around Z (0 is +X, π/2 is +Y, π is -X and 3π/2 is -Y)
      delta - elevation (δ) above (XY) plane, from -π/2 to +π/2
      See Also:

    • Vector3D

      public Vector3D(double a, Vector3D u)
      Multiplicative constructor Build a vector from another one and a scale factor. The vector built will be a * u
      Parameters:
      a - scale factor
      u - base (unscaled) vector

    • Vector3D

      public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2)
      Linear constructor Build a vector from two other ones and corresponding scale factors. The vector built will be a1 * u1 + a2 * u2
      Parameters:
      a1 - first scale factor
      u1 - first base (unscaled) vector
      a2 - second scale factor
      u2 - second base (unscaled) vector

    • Vector3D

      public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2, double a3, Vector3D u3)
      Linear constructor Build a vector from three other ones and corresponding scale factors. The vector built will be a1 * u1 + a2 * u2 + a3 * u3
      Parameters:
      a1 - first scale factor
      u1 - first base (unscaled) vector
      a2 - second scale factor
      u2 - second base (unscaled) vector
      a3 - third scale factor
      u3 - third base (unscaled) vector

    • Vector3D

      public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2, double a3, Vector3D u3, double a4, Vector3D u4)
      Linear constructor Build a vector from four other ones and corresponding scale factors. The vector built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4
      Parameters:
      a1 - first scale factor
      u1 - first base (unscaled) vector
      a2 - second scale factor
      u2 - second base (unscaled) vector
      a3 - third scale factor
      u3 - third base (unscaled) vector
      a4 - fourth scale factor
      u4 - fourth base (unscaled) vector

  • Method Details

    • getX

      public double getX()
      Get the abscissa of the vector.
      Returns:
      abscissa of the vector
      See Also:

    • getY

      public double getY()
      Get the ordinate of the vector.
      Returns:
      ordinate of the vector
      See Also:

    • getZ

      public double getZ()
      Get the height of the vector.
      Returns:
      height of the vector
      See Also:

    • toArray

      public double[] toArray()
      Get the vector coordinates as a dimension 3 array.
      Returns:
      vector coordinates
      See Also:

    • getSpace

      public Space getSpace()
      Get the space to which the point belongs.
      Specified by:
      getSpace in interface Point<Euclidean3D>
      Returns:
      containing space

    • getZero

      public Vector3D getZero()
      Get the null vector of the vectorial space or origin point of the affine space.
      Specified by:
      getZero in interface Vector<Euclidean3D,Vector3D>
      Returns:
      null vector of the vectorial space or origin point of the affine space

    • getNorm1

      public double getNorm1()
      Get the L1 norm for the vector.
      Specified by:
      getNorm1 in interface Vector<Euclidean3D,Vector3D>
      Returns:
      L1 norm for the vector

    • getNorm

      public double getNorm()
      Get the L2 norm for the vector.
      Specified by:
      getNorm in interface Vector<Euclidean3D,Vector3D>
      Returns:
      Euclidean norm for the vector

    • getNormSq

      public double getNormSq()
      Get the square of the norm for the vector.
      Specified by:
      getNormSq in interface Vector<Euclidean3D,Vector3D>
      Returns:
      square of the Euclidean norm for the vector

    • getNormInf

      public double getNormInf()
      Get the L∞ norm for the vector.
      Specified by:
      getNormInf in interface Vector<Euclidean3D,Vector3D>
      Returns:
      L∞ norm for the vector

    • getAlpha

      public double getAlpha()
      Get the azimuth of the vector.
      Returns:
      azimuth (α) of the vector, between -π and +π
      See Also:

    • getDelta

      public double getDelta()
      Get the elevation of the vector.
      Returns:
      elevation (δ) of the vector, between -π/2 and +π/2
      See Also:

    • add

      public Vector3D add(Vector<Euclidean3D,Vector3D> v)
      Add a vector to the instance.
      Specified by:
      add in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      v - vector to add
      Returns:
      a new vector

    • add

      public Vector3D add(double factor, Vector<Euclidean3D,Vector3D> v)
      Add a scaled vector to the instance.
      Specified by:
      add in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      factor - scale factor to apply to v before adding it
      v - vector to add
      Returns:
      a new vector

    • subtract

      public Vector3D subtract(Vector<Euclidean3D,Vector3D> v)
      Subtract a vector from the instance.
      Specified by:
      subtract in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      v - vector to subtract
      Returns:
      a new vector

    • subtract

      public Vector3D subtract(double factor, Vector<Euclidean3D,Vector3D> v)
      Subtract a scaled vector from the instance.
      Specified by:
      subtract in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      factor - scale factor to apply to v before subtracting it
      v - vector to subtract
      Returns:
      a new vector

    • orthogonal

      public Vector3D orthogonal() throws MathRuntimeException
      Get a vector orthogonal to the instance.

      There are an infinite number of normalized vectors orthogonal to the instance. This method picks up one of them almost arbitrarily. It is useful when one needs to compute a reference frame with one of the axes in a predefined direction. The following example shows how to build a frame having the k axis aligned with the known vector u : 

      
   Vector3D k = u.normalize();
   Vector3D i = k.orthogonal();
   Vector3D j = Vector3D.crossProduct(k, i);
      Returns:
      a new normalized vector orthogonal to the instance
      Throws:
      MathRuntimeException - if the norm of the instance is null

    • angle

      public static double angle(Vector3D v1, Vector3D v2) throws MathRuntimeException
      Compute the angular separation between two vectors.

      This method computes the angular separation between two vectors using the dot product for well separated vectors and the cross product for almost aligned vectors. This allows to have a good accuracy in all cases, even for vectors very close to each other.

      Parameters:
      v1 - first vector
      v2 - second vector
      Returns:
      angular separation between v1 and v2
      Throws:
      MathRuntimeException - if either vector has a null norm

    • negate

      public Vector3D negate()
      Get the opposite of the instance.
      Specified by:
      negate in interface Vector<Euclidean3D,Vector3D>
      Returns:
      a new vector which is opposite to the instance

    • scalarMultiply

      public Vector3D scalarMultiply(double a)
      Multiply the instance by a scalar.
      Specified by:
      scalarMultiply in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      a - scalar
      Returns:
      a new vector

    • isNaN

      public boolean isNaN()
      Returns true if any coordinate of this point is NaN; false otherwise
      Specified by:
      isNaN in interface Point<Euclidean3D>
      Returns:
      true if any coordinate of this point is NaN; false otherwise

    • isInfinite

      public boolean isInfinite()
      Returns true if any coordinate of this vector is infinite and none are NaN; false otherwise
      Specified by:
      isInfinite in interface Vector<Euclidean3D,Vector3D>
      Returns:
      true if any coordinate of this vector is infinite and none are NaN; false otherwise

    • equals

      public boolean equals(Object other)
      Test for the equality of two 3D vectors.

      If all coordinates of two 3D vectors are exactly the same, and none are Double.NaN, the two 3D vectors are considered to be equal.

      NaN coordinates are considered to affect globally the vector and be equals to each other - i.e, if either (or all) coordinates of the 3D vector are equal to Double.NaN, the 3D vector is equal to NaN.

      Overrides:
      equals in class Object
      Parameters:
      other - Object to test for equality to this
      Returns:
      true if two 3D vector objects are equal, false if object is null, not an instance of Vector3D, or not equal to this Vector3D instance

    • equalsIeee754

      public boolean equalsIeee754(Object other)
      Test for the equality of two 3D vectors.

      If all coordinates of two 3D vectors are exactly the same, and none are NaN, the two 3D vectors are considered to be equal.

      In compliance with IEEE754 handling, if any coordinates of any of the two vectors are NaN, then the vectors are considered different. This implies that Vector3D.NaN.equals(Vector3D.NaN) returns false despite the instance is checked against itself.

      Parameters:
      other - Object to test for equality to this
      Returns:
      true if two 3D vector objects are equal, false if object is null, not an instance of Vector3D, or not equal to this Vector3D instance
      Since:
      2.1

    • hashCode

      public int hashCode()
      Get a hashCode for the 3D vector.

      All NaN values have the same hash code.

      Overrides:
      hashCode in class Object
      Returns:
      a hash code value for this object

    • dotProduct

      public double dotProduct(Vector<Euclidean3D,Vector3D> v)
      Compute the dot-product of the instance and another vector.

      The implementation uses specific multiplication and addition algorithms to preserve accuracy and reduce cancellation effects. It should be very accurate even for nearly orthogonal vectors.

      Specified by:
      dotProduct in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      v - second vector
      Returns:
      the dot product this.v
      See Also:

    • crossProduct

      public Vector3D crossProduct(Vector<Euclidean3D,Vector3D> v)
      Compute the cross-product of the instance with another vector.
      Parameters:
      v - other vector
      Returns:
      the cross product this ^ v as a new Vector3D

    • distance1

      public double distance1(Vector<Euclidean3D,Vector3D> v)
      Compute the distance between the instance and another vector according to the L1 norm.

      Calling this method is equivalent to calling: q.subtract(p).getNorm1() except that no intermediate vector is built

      Specified by:
      distance1 in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      v - second vector
      Returns:
      the distance between the instance and p according to the L1 norm

    • distance

      public double distance(Point<Euclidean3D> v)
      Compute the distance between the instance and another point.
      Specified by:
      distance in interface Point<Euclidean3D>
      Parameters:
      v - second point
      Returns:
      the distance between the instance and p

    • distanceInf

      public double distanceInf(Vector<Euclidean3D,Vector3D> v)
      Compute the distance between the instance and another vector according to the L∞ norm.

      Calling this method is equivalent to calling: q.subtract(p).getNormInf() except that no intermediate vector is built

      Specified by:
      distanceInf in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      v - second vector
      Returns:
      the distance between the instance and p according to the L∞ norm

    • distanceSq

      public double distanceSq(Vector<Euclidean3D,Vector3D> v)
      Compute the square of the distance between the instance and another vector.

      Calling this method is equivalent to calling: q.subtract(p).getNormSq() except that no intermediate vector is built

      Specified by:
      distanceSq in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      v - second vector
      Returns:
      the square of the distance between the instance and p

    • dotProduct

      public static double dotProduct(Vector3D v1, Vector3D v2)
      Compute the dot-product of two vectors.
      Parameters:
      v1 - first vector
      v2 - second vector
      Returns:
      the dot product v1.v2

    • crossProduct

      public static Vector3D crossProduct(Vector3D v1, Vector3D v2)
      Compute the cross-product of two vectors.
      Parameters:
      v1 - first vector
      v2 - second vector
      Returns:
      the cross product v1 ^ v2 as a new Vector

    • distance1

      public static double distance1(Vector3D v1, Vector3D v2)
      Compute the distance between two vectors according to the L1 norm.

      Calling this method is equivalent to calling: v1.subtract(v2).getNorm1() except that no intermediate vector is built

      Parameters:
      v1 - first vector
      v2 - second vector
      Returns:
      the distance between v1 and v2 according to the L1 norm

    • distance

      public static double distance(Vector3D v1, Vector3D v2)
      Compute the distance between two vectors according to the L2 norm.

      Calling this method is equivalent to calling: v1.subtract(v2).getNorm() except that no intermediate vector is built

      Parameters:
      v1 - first vector
      v2 - second vector
      Returns:
      the distance between v1 and v2 according to the L2 norm

    • distanceInf

      public static double distanceInf(Vector3D v1, Vector3D v2)
      Compute the distance between two vectors according to the L∞ norm.

      Calling this method is equivalent to calling: v1.subtract(v2).getNormInf() except that no intermediate vector is built

      Parameters:
      v1 - first vector
      v2 - second vector
      Returns:
      the distance between v1 and v2 according to the L∞ norm

    • distanceSq

      public static double distanceSq(Vector3D v1, Vector3D v2)
      Compute the square of the distance between two vectors.

      Calling this method is equivalent to calling: v1.subtract(v2).getNormSq() except that no intermediate vector is built

      Parameters:
      v1 - first vector
      v2 - second vector
      Returns:
      the square of the distance between v1 and v2

    • toString

      public String toString()
      Get a string representation of this vector.
      Overrides:
      toString in class Object
      Returns:
      a string representation of this vector

    • toString

      public String toString(NumberFormat format)
      Get a string representation of this vector.
      Specified by:
      toString in interface Vector<Euclidean3D,Vector3D>
      Parameters:
      format - the custom format for components
      Returns:
      a string representation of this vector