Constructor Detail

• Pnt

  public Pnt(double... coords)

  Constructor.

  Parameters:

  coords - the coordinates

Method Detail

• toString

  public String toString()

• equals

  public boolean equals(Object other)

• hashCode

  public int hashCode()

• coord

  public double coord(int i)

  Parameters:

  i - the index of the coordinate.

  Returns:

  the specified coordinate of this Pnt

  Throws:

  ArrayIndexOutOfBoundsException - for bad coordinate

• dimension

  public int dimension()

  Returns:

  this Pnt's dimension.

• dimCheck

  public int dimCheck(Pnt p)

  Check that dimensions match.

  Parameters:

  p - the Pnt to check (against this Pnt)

  Returns:

  the dimension of the Pnts

  Throws:

  IllegalArgumentException - if dimension fail to match

• extend

  public Pnt extend(double... coords)

  Create a new Pnt by adding additional coordinates to this Pnt.

  Parameters:

  coords - the new coordinates (added on the right end)

  Returns:

  a new Pnt with the additional coordinates

• dot

  public double dot(Pnt p)

  Dot product.

  Parameters:

  p - the other Pnt

  Returns:

  dot product of this Pnt and p

• magnitude

  public double magnitude()

  Magnitude (as a vector).

  Returns:

  the Euclidean length of this vector

• subtract

  public Pnt subtract(Pnt p)

  Subtract.

  Parameters:

  p - the other Pnt

  Returns:

  a new Pnt = this - p

• add

  public Pnt add(Pnt p)

  Add.

  Parameters:

  p - the other Pnt

  Returns:

  a new Pnt = this + p

• angle

  public double angle(Pnt p)

  Angle (in radians) between two Pnts (treated as vectors).

  Parameters:

  p - the other Pnt

  Returns:

  the angle (in radians) between the two Pnts

• bisector

  public Pnt bisector(Pnt point)

  Perpendicular bisector of two Pnts. Works in any dimension. The coefficients are returned as a Pnt of one higher dimension (e.g., (A,B,C,D) for an equation of the form Ax + By + Cz + D = 0).

  Parameters:

  point - the other point

  Returns:

  the coefficients of the perpendicular bisector

• toString

  public static String toString(Pnt[] matrix)

  Create a String for a matrix.

  Parameters:

  matrix - the matrix (an array of Pnts)

  Returns:

  a String represenation of the matrix

• determinant

  public static double determinant(Pnt[] matrix)

  Compute the determinant of a matrix (array of Pnts). This is not an efficient implementation, but should be adequate for low dimension.

  Parameters:

  matrix - the matrix as an array of Pnts

  Returns:

  the determinnant of the input matrix

  Throws:

  IllegalArgumentException - if dimensions are wrong

• cross

  public static Pnt cross(Pnt[] matrix)

  Compute generalized cross-product of the rows of a matrix. The result is a Pnt perpendicular (as a vector) to each row of the matrix. This is not an efficient implementation, but should be adequate for low dimension.

  Parameters:

  matrix - the matrix of Pnts (one less row than the Pnt dimension)

  Returns:

  a Pnt perpendicular to each row Pnt

  Throws:

  IllegalArgumentException - if matrix is wrong shape

• content

  public static double content(Pnt[] simplex)

  Determine the signed content (i.e., area or volume, etc.) of a simplex.

  Parameters:

  simplex - the simplex (as an array of Pnts)

  Returns:

  the signed content of the simplex

• relation

  public int[] relation(Pnt[] simplex)

  Relation between this Pnt and a simplex (represented as an array of Pnts). Result is an array of signs, one for each vertex of the simplex, indicating the relation between the vertex, the vertex's opposite facet, and this Pnt.

     -1 means Pnt is on same side of facet
      0 means Pnt is on the facet
     +1 means Pnt is on opposite side of facet
   

  Parameters:

  simplex - an array of Pnts representing a simplex

  Returns:

  an array of signs showing relation between this Pnt and simplex

  Throws:

  IllegalArgumentException - if the simplex is degenerate

• isOutside

  public Pnt isOutside(Pnt[] simplex)

  Test if this Pnt is outside of simplex.

  Parameters:

  simplex - the simplex (an array of Pnts)

  Returns:

  simplex Pnt that "witnesses" outsideness (or null if not outside)

• isOn

  public Pnt isOn(Pnt[] simplex)

  Test if this Pnt is on a simplex.

  Parameters:

  simplex - the simplex (an array of Pnts)

  Returns:

  the simplex Pnt that "witnesses" on-ness (or null if not on)

• isInside

  public boolean isInside(Pnt[] simplex)

  Test if this Pnt is inside a simplex.

  Parameters:

  simplex - the simplex (an arary of Pnts)

  Returns:

  true iff this Pnt is inside simplex.

• vsCircumcircle

  public int vsCircumcircle(Pnt[] simplex)

  Test relation between this Pnt and circumcircle of a simplex.

  Parameters:

  simplex - the simplex (as an array of Pnts)

  Returns:

  -1, 0, or +1 for inside, on, or outside of circumcircle

• circumcenter

  public static Pnt circumcenter(Pnt[] simplex)

  Circumcenter of a simplex.

  Parameters:

  simplex - the simplex (as an array of Pnts)

  Returns:

  the circumcenter (a Pnt) of simplex