Shell Programming and Scripting

#  cat generate-points
#!/bin/bash -p
nawk -v MinX=$1 -v MinY=$2 -v MaxX=$3 -v MaxY=$4 -v Points=$5 '
{
  StepX=(MaxX-MinX)/(Points-1);
  StepY=(MaxY-MinY)/(Points-1);
  for(y=0;y<Points;y++) {
    X=MinX+StepX*y;
    Y=MinY+StepY*y;
    printf("%0.2f %0.2f\n",X,Y)
  }
  exit;
}
' <$0

which produces e.g. :

#  ./generate-points 455989.0 8673453.4 283957.6 8691250.1 7

455989.00 8673453.40
427317.10 8676419.52
398645.20 8679385.63
369973.30 8682351.75
341301.40 8685317.87
312629.50 8688283.98
283957.60 8691250.10

$
$
$ cat lerp.pl
#!/usr/bin/perl -w
# ==============================================================================
# For the end points: P1 = (x0,y0) and P2 = (x1,y1), the linear interpolant
# equation is: y = y0 + (x - x0)*((y1 - y0)/(x1 - x0)).
# In this program, (x0,y0) = ($xstart,$ystart) and (x1,y1) = ($xend,$yend).
# ==============================================================================
@x = ();                  # array to store x-coordinates
@y = ();                  # array to store y-coordinates
$total = 6918;            # total no. of equidistant points, including endpoints
$xstart = 455989.0;       # x0
$xend = 283957.6;         # x1
$ystart = 8673453.4;      # y0
$yend = 8691250.1;        # y1
$iter = $xstart;          # the iterator variable
$incr = (($xstart - $xend)/($total - 1));  # increment per iteration
$i = 0;                   # array index
$yvalue = 0;              # calculated value of y-coordinate
# populate arrays
while ($iter >= $xend) {
  push @x, $iter;
  # calculate y-coordinate
  # y = y0 + (x - x0)*((y1 - y0)/(x1 - x0))
  $yvalue = $ystart + ($iter - $xstart)*(($yend - $ystart)/($xend - $xstart));
  push @y, $yvalue;
  $iter -= $incr;
}
# display
printf("%4s  %9s  %10s  %9s  %9s\n","No.","x-coord","y-coord",
                                    "delta-x","delta-y");
printf("%4s  %9s  %10s  %9s  %9s\n","-"x4,"-"x9,"-"x10,"-"x9,"-"x9);
foreach $elem (@x) {
  printf("%4d  %9.2f  %10.2f  %9.2f  %9.2f\n",$i+1,$elem,$y[$i],
                                              $i == 0 ? 0 : $x[$i]-$x[$i-1],
                                              $i == 0 ? 0 : $y[$i]-$y[$i-1]);
  $i++;
}
$
$
$ perl lerp.pl
 No.    x-coord     y-coord    delta-x    delta-y
----  ---------  ----------  ---------  ---------
   1  455989.00  8673453.40       0.00       0.00
   2  455964.13  8673455.97     -24.87       2.57
   3  455939.26  8673458.55     -24.87       2.57
   4  455914.39  8673461.12     -24.87       2.57
   5  455889.52  8673463.69     -24.87       2.57
   6  455864.65  8673466.26     -24.87       2.57
   7  455839.78  8673468.84     -24.87       2.57
   8  455814.90  8673471.41     -24.87       2.57
   9  455790.03  8673473.98     -24.87       2.57
  10  455765.16  8673476.56     -24.87       2.57
...
...
 998  431192.80  8676018.57     -24.87       2.57
 999  431167.93  8676021.15     -24.87       2.57
1000  431143.06  8676023.72     -24.87       2.57
1001  431118.19  8676026.29     -24.87       2.57
1002  431093.32  8676028.87     -24.87       2.57
...
...
1998  406321.99  8678591.47     -24.87       2.57
1999  406297.12  8678594.04     -24.87       2.57
2000  406272.25  8678596.61     -24.87       2.57
2001  406247.38  8678599.19     -24.87       2.57
2002  406222.51  8678601.76     -24.87       2.57
...
...
2998  381451.18  8681164.36     -24.87       2.57
2999  381426.31  8681166.93     -24.87       2.57
3000  381401.44  8681169.51     -24.87       2.57
3001  381376.57  8681172.08     -24.87       2.57
3002  381351.70  8681174.65     -24.87       2.57
...
...
3998  356580.37  8683737.25     -24.87       2.57
3999  356555.50  8683739.83     -24.87       2.57
4000  356530.63  8683742.40     -24.87       2.57
4001  356505.76  8683744.97     -24.87       2.57
4002  356480.89  8683747.54     -24.87       2.57
...
...
4998  331709.56  8686310.15     -24.87       2.57
4999  331684.69  8686312.72     -24.87       2.57
5000  331659.82  8686315.29     -24.87       2.57
5001  331634.94  8686317.86     -24.87       2.57
5002  331610.07  8686320.44     -24.87       2.57
...
...
5998  306838.75  8688883.04     -24.87       2.57
5999  306813.88  8688885.61     -24.87       2.57
6000  306789.00  8688888.18     -24.87       2.57
6001  306764.13  8688890.76     -24.87       2.57
6002  306739.26  8688893.33     -24.87       2.57
...
...
6915  284032.21  8691242.38     -24.87       2.57
6916  284007.34  8691244.95     -24.87       2.57
6917  283982.47  8691247.53     -24.87       2.57
6918  283957.60  8691250.10     -24.87       2.57
$
$