bilinear <- function ( x, y, z, newx, newy )

#*****************************************************************************80
#
## bilinear evaluates a bilinear interpolant.
#
#  Licensing:
#
#    Copyright 2016 James P. Howard, II
#
#    The computer code and data files on this web page are distributed under
#    https://opensource.org/licenses/BSD-2-Clause, the BSD-2-Clause license.
#
#  Modified:
#
#    27 February 2020
#
#  Author:
#
#    Original R code by James Howard;
#    Modifications by John Burkardt.
#
#  Reference:
#
#    James Howard,
#    Computational Methods for Numerical Analysis with R,
#    CRC Press, 2017,
#    ISBN13: 978-1-4987-2363-3.
#
{
  z1 <- ( x[2] - newx ) * z[1,1] + ( newx - x[1] ) * z[1,2]
  z1 <- z1 / ( x[2] - x[1] )
  z2 <- ( x[2] - newx ) * z[2,1] + ( newx - x[1] ) * z[2,2]
  z2 <- z2 / ( x[2] - x[1] )

  z <- ( y[2] - newy ) * z1 + ( newy - y[1] ) * z2
  z <- z / ( y[2] - y[1] )

  return ( z )
}