cbezier <- function ( x, y, t )

#*****************************************************************************80
#
## cbezier computes a cubic Bezier curve.
#
#  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:
#
#    25 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.
#
{
  if ( length ( x ) != 4 || length ( y ) != 4 )
  {
    stop ( "cbezier: x and y must contain exactly 4 values!" )
  }
  newx <- ( 1.0 - t )^3 * x[1] + 3.0 * ( 1.0 - t )^2 * t * x[2] + 
          3.0 * ( 1 - t ) * t^2 * x[3] + t^3 * x[4]
  newy <- ( 1.0 - t )^3 * y[1] + 3.0 * ( 1.0 - t )^2 * t * y[2] + 
          3.0 * ( 1 - t ) * t^2 * y[3] + t^3 * y[4]

  return ( list ( x = newx, y = newy ) )
}