Class Vector3D

  • All Implemented Interfaces:
    java.io.Serializable

    public class Vector3D
    extends java.lang.Object
    implements java.io.Serializable
    This class implements vectors in a three-dimensional space.

    Instance of this class are guaranteed to be immutable.

    Since:
    1.2
    Version:
    $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 août 2010) $
    See Also:
    Serialized Form
    • Field Summary

      Fields 
      Modifier and Type Field Description
      static Vector3D MINUS_I
      Opposite of the first canonical vector (coordinates: -1, 0, 0).
      static Vector3D MINUS_J
      Opposite of the second canonical vector (coordinates: 0, -1, 0).
      static Vector3D MINUS_K
      Opposite of the third canonical vector (coordinates: 0, 0, -1).
      static Vector3D NaN
      A vector with all coordinates set to NaN.
      static Vector3D NEGATIVE_INFINITY
      A vector with all coordinates set to negative infinity.
      static Vector3D PLUS_I
      First canonical vector (coordinates: 1, 0, 0).
      static Vector3D PLUS_J
      Second canonical vector (coordinates: 0, 1, 0).
      static Vector3D PLUS_K
      Third canonical vector (coordinates: 0, 0, 1).
      static Vector3D POSITIVE_INFINITY
      A vector with all coordinates set to positive infinity.
      static Vector3D ZERO
      Null vector (coordinates: 0, 0, 0).
    • Constructor Summary

      Constructors 
      Constructor Description
      Vector3D​(double alpha, double delta)
      Simple constructor.
      Vector3D​(double x, double y, double z)
      Simple constructor.
      Vector3D​(double a, Vector3D u)
      Multiplicative constructor Build a vector from another one and a scale factor.
      Vector3D​(double a1, Vector3D u1, double a2, Vector3D u2)
      Linear constructor Build a vector from two other ones and corresponding scale factors.
      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.
      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.
    • Field Detail

      • 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 Detail

      • 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:
        getX(), getY(), getZ()
      • 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:
        getAlpha(), getDelta()
      • 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 Detail

      • getNorm1

        public double getNorm1()
        Get the L1 norm for the vector.
        Returns:
        L1 norm for the vector
      • getNorm

        public double getNorm()
        Get the L2 norm for the vector.
        Returns:
        euclidian norm for the vector
      • getNormSq

        public double getNormSq()
        Get the square of the norm for the vector.
        Returns:
        square of the euclidian norm for the vector
      • getNormInf

        public double getNormInf()
        Get the L norm for the vector.
        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:
        Vector3D(double, double)
      • getDelta

        public double getDelta()
        Get the elevation of the vector.
        Returns:
        elevation (δ) of the vector, between -π/2 and +π/2
        See Also:
        Vector3D(double, double)
      • add

        public Vector3D add​(Vector3D v)
        Add a vector to the instance.
        Parameters:
        v - vector to add
        Returns:
        a new vector
      • add

        public Vector3D add​(double factor,
                            Vector3D v)
        Add a scaled vector to the instance.
        Parameters:
        factor - scale factor to apply to v before adding it
        v - vector to add
        Returns:
        a new vector
      • subtract

        public Vector3D subtract​(Vector3D v)
        Subtract a vector from the instance.
        Parameters:
        v - vector to subtract
        Returns:
        a new vector
      • subtract

        public Vector3D subtract​(double factor,
                                 Vector3D v)
        Subtract a scaled vector from the instance.
        Parameters:
        factor - scale factor to apply to v before subtracting it
        v - vector to subtract
        Returns:
        a new vector
      • normalize

        public Vector3D normalize()
        Get a normalized vector aligned with the instance.
        Returns:
        a new normalized vector
        Throws:
        java.lang.ArithmeticException - if the norm is zero
      • orthogonal

        public Vector3D orthogonal()
        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:
        java.lang.ArithmeticException - if the norm of the instance is null
      • angle

        public static double angle​(Vector3D v1,
                                   Vector3D v2)
        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:
        java.lang.ArithmeticException - if either vector has a null norm
      • negate

        public Vector3D negate()
        Get the opposite of the instance.
        Returns:
        a new vector which is opposite to the instance
      • scalarMultiply

        public Vector3D scalarMultiply​(double a)
        Multiply the instance by a scalar
        Parameters:
        a - scalar
        Returns:
        a new vector
      • isNaN

        public boolean isNaN()
        Returns true if any coordinate of this vector is NaN; false otherwise
        Returns:
        true if any coordinate of this vector is NaN; false otherwise
      • isInfinite

        public boolean isInfinite()
        Returns true if any coordinate of this vector is infinite and none are NaN; false otherwise
        Returns:
        true if any coordinate of this vector is infinite and none are NaN; false otherwise
      • equals

        public boolean equals​(java.lang.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 java.lang.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
      • hashCode

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

        All NaN values have the same hash code.

        Overrides:
        hashCode in class java.lang.Object
        Returns:
        a hash code value for this object
      • 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 java.lang.String toString()
        Get a string representation of this vector.
        Overrides:
        toString in class java.lang.Object
        Returns:
        a string representation of this vector