function x = blend_101 ( r, x0, x1 )

%*****************************************************************************80
%
%% blend_101() extends scalar endpoint data to a line.
%
%  Diagram:
%
%    0-----r-----1
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    22 October 2008
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    William Gordon,
%    Blending-Function Methods of Bivariate and Multivariate Interpolation
%    and Approximation,
%    SIAM Journal on Numerical Analysis,
%    Volume 8, Number 1, March 1971, pages 158-177.
%
%    William Gordon and Charles Hall,
%    Transfinite Element Methods: Blending-Function Interpolation over
%    Arbitrary Curved Element Domains,
%    Numerische Mathematik,
%    Volume 21, Number 1, 1973, pages 109-129.
%
%    William Gordon and Charles Hall,
%    Construction of Curvilinear Coordinate Systems and Application to
%    Mesh Generation,
%    International Journal of Numerical Methods in Engineering,
%    Volume 7, 1973, pages 461-477.
%
%    Joe Thompson, Bharat Soni, Nigel Weatherill,
%    Handbook of Grid Generation,
%    CRC Press, 1999.
%
%  Input:
%
%    real R, the coordinate where an interpolated
%    value is desired.
%
%    real X0, X1, the data values at the ends of the line.
%
%  Output:
%
%    real X, the interpolated data value at (R).
%
  x = ( 1.0 - r ) * x0  ...
    +         r   * x1;

  return
end
