Package org.robwork.sdurw_geometry

Class HyperSphere

  • public class HyperSphere
extends java.lang.Object
    A hyper-sphere of K dimensions.

    Functions are provided to create (almost) uniform distribution of points on a hyper-sphere as
    shown in [1].

    The distribution of points is illustrated below for 2 and 3 dimensional hyper-spheres.
    Notice that the tessellation is best when \delta is small.

    Distribution of points for K=2 and K=3.

    [1] Lovisolo, L., and E. A. B. Da Silva. "Uniform distribution of points on a hyper-sphere
    with applications to vector bit-plane encoding." IEE Proceedings-Vision, Image and Signal
    Processing 148.3 (2001): 187-193.

    • Constructor Summary

      Constructors 
      Constructor Description
      HyperSphere​(long dimensions)
      Construct a hyper-sphere of unit size.
      HyperSphere​(long cPtr, boolean cMemoryOwn)  

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double area()
      Calculate the surface area of a hyper-sphere.

      Calculated for even dimensionality as \frac{K \pi^{K/2}}{(K/2)!}

      Calculated for odd dimensionality as \frac{K 2^K \pi^{(K-1)/2}}{K!}
      void delete()  
      static long getCPtr​(HyperSphere obj)  
      long getDimensions()
      Get the number of dimensions of the hyper-sphere.
      SWIGTYPE_p_std__vectorT_Eigen__VectorXd_t uniformDistributionCartesian​(double delta)
      Create a uniform distribution in Cartesian coordinates.

      This uses #uniformDistributionSpherical and maps the spherical coordinates to Cartesian
      coordinates.
      SWIGTYPE_p_std__vectorT_Eigen__VectorXd_t uniformDistributionSpherical​(double delta)
      Create a uniform distribution in spherical coordinates.

      This implements the algorithm in [1], section 2.1, for dimensions 2 \leq K \leq 6.
      double volume()
      The volume of a hyper-sphere.

      Calculated for even dimensionality as \frac{\pi^{K/2}}{(K/2)!}

      Calculated for odd dimensionality as \frac{2 (2 \pi)^{(K-1)/2}}{K!!}
      where the double factorial for odd K means 1 \cdot 3 \cdot 5 \dots K

      • Methods inherited from class java.lang.Object

        equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Constructor Detail

      • HyperSphere

        public HyperSphere​(long cPtr,
                   boolean cMemoryOwn)

      • HyperSphere

        public HyperSphere​(long dimensions)
        Construct a hyper-sphere of unit size.
        Parameters:
        dimensions - [in] the number of dimensions.

    • Method Detail

      • getCPtr

        public static long getCPtr​(HyperSphere obj)

      • delete

        public void delete()

      • uniformDistributionCartesian

        public SWIGTYPE_p_std__vectorT_Eigen__VectorXd_t uniformDistributionCartesian​(double delta)
        Create a uniform distribution in Cartesian coordinates.

        This uses #uniformDistributionSpherical and maps the spherical coordinates to Cartesian
        coordinates. The mapping is documented in [1], section 2.1.

        Parameters:
        delta - [in] the resolution.
        Returns:
        unit vectors, [x_1 x_2 \dots x_K]^T , in Cartesian coordinates with
        dimension K.
        Note: This function is only implemented for 2 \leq K \leq 6 .

      • uniformDistributionSpherical

        public SWIGTYPE_p_std__vectorT_Eigen__VectorXd_t uniformDistributionSpherical​(double delta)
        Create a uniform distribution in spherical coordinates.

        This implements the algorithm in [1], section 2.1, for dimensions 2 \leq K \leq 6.

        Parameters:
        delta - [in] the resolution.
        Returns:
        list of vectors, [\theta_1 \theta_2 \dots \theta_{K-1}]^T , in spherical
        coordinates with dimension K-1.
        Note: This function is only implemented for 2 \leq K \leq 6 .

      • getDimensions

        public long getDimensions()
        Get the number of dimensions of the hyper-sphere.
        Returns:
        the number of dimensions, 2 \leq K \leq 6 .

      • area

        public double area()
        Calculate the surface area of a hyper-sphere.

        Calculated for even dimensionality as \frac{K \pi^{K/2}}{(K/2)!}

        Calculated for odd dimensionality as \frac{K 2^K \pi^{(K-1)/2}}{K!}

        Returns:
        the surface area.

      • volume

        public double volume()
        The volume of a hyper-sphere.

        Calculated for even dimensionality as \frac{\pi^{K/2}}{(K/2)!}

        Calculated for odd dimensionality as \frac{2 (2 \pi)^{(K-1)/2}}{K!!}
        where the double factorial for odd K means 1 \cdot 3 \cdot 5 \dots K

        Returns:
        the volume.