#!/usr/bin/perl -w

use strict;

use v5.10;

use Math::Trig;

my $oo;

for my $i (0..20) {

# construct a line on the X axis and a perpendicular bisector.

# make a point on the bisector 20 units from the intersection.

my $d = 20;

# let us cast rays from the point to the line

# let's say we want to sample a 20 degree area of the line.

# let's see how far apart the samples will be on the line given a

# fixed angle increment.

my $a = $i - 10; # we sample from 10° left to 10° right

my $o = $d * tan(deg2rad($a));

say +($oo - $o) . " X delta" if defined $oo;

$oo = $o;

}

say "notice that the distances between the sample points on the near frustum";

say "plane are not equidistant to each other. we need to correct for that.";

# construct a line and a perpendicular bisector.

# make a point on the bisector 20 units from the intersection.

my $d = 20;

# let us cast rays from the point to the line

# let's say we want to sample a 20 degree area of line.

# let's enforce a fixed distance between points on the instead of

# a fixed angle between sampled points.

my $s = $d * tan(deg2rad(-10));

my $o = $s / 10;

my $ot;

for (my $a = $s; $a < -$s; $a -= $o) {

my $t = rad2deg(atan2($a, $d));

say +($t - $ot) . " degree delta" if defined $ot;

$ot = $t;

}

say "notice that the *angles* between the sample points on the near frustum";

say "plane are now not the same, but the sample points on the near frustum";

say "are enforced to be equidistant to each other.";