#! /usr/bin/env python
#
def line_exp_perp_2d ( p1, p2, p3 ):

#*****************************************************************************80
#
## LINE_EXP_PERP_2D computes a line perpendicular to a line and through a point.
#
#  Discussion:
#
#    The explicit form of a line in 2D is:
#
#      ( P1, P2 ) = ( (X1,Y1), (X2,Y2) ).
#
#    The input point P3 should NOT lie on the line (P1,P2).  If it
#    does, then the output value P4 will equal P3.
#
#    P1-----P4-----------P2
#            |
#            |
#           P3
#
#    P4 is also the nearest point on the line (P1,P2) to the point P3.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    25 October 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, real P1(2), P2(2), two points on the line.
#
#    Input, real P3(2), a point (presumably not on the
#    line (P1,P2)), through which the perpendicular must pass.
#
#    Output, real P4(2), a point on the line (P1,P2),
#    such that the line (P3,P4) is perpendicular to the line (P1,P2).
#
#    Output, logical FLAG, is TRUE if the value could not be computed.
#
  import numpy as np

  bot = ( p2[0] - p1[0] ) ** 2 + ( p2[1] - p1[1] ) **2

  p4 = np.zeros ( 2 )

  if ( bot == 0.0 ):
    p4[0] = float ( 'inf' )
    p4[1] = float ( 'inf' )
    flag = 1
#
#  (P3-P1) dot (P2-P1) = Norm(P3-P1) * Norm(P2-P1) * Cos(Theta).
#
#  (P3-P1) dot (P2-P1) / Norm(P3-P1)**2 = normalized coordinate T
#  of the projection of (P3-P1) onto (P2-P1).
#
  t = ( ( p1[0] - p3[0] ) * ( p1[0] - p2[0] ) \
      + ( p1[1] - p3[1] ) * ( p1[1] - p2[1] ) ) / bot

  p4[0] = p1[0] + t * ( p2[0] - p1[0] )
  p4[1] = p1[1] + t * ( p2[1] - p1[1] )

  flag = 0

  return p4, flag