Points on a circle primitive

[Tim Gould]

Hi all,

Below is a perl script to take a bunch of angles and convert them to points on the edge of a circle primitve (ie. a 16 or 48 point polygon). The comments up top describe how to use it. It's designed to make generating rims on the bottom of curved parts relatively easy when there's only a few segments required and hand-coding makes more sense than using Philo's wonderful toys.

Tim

Code:

#! /usr/bin/perl
# ang2point.pl [-r RAD] [-t THICK] [-s SEGS] ang1 ang2 ... angn
#
# RAD defaults to 20
# THICK defaults to none
# SEGS defaults to 16
#
# Projects the angles onto a circular primitive of radius RAD
# with SEGS segments. If THICK is specified it also shows the
# points on an inner radius of RAD-THICK
#
# It scales the radius at each angle to ensure it lies on the
# SEG-sided polygon that approximates the circle.
#

use POSIX;

$rad=20;
$segs=16;
@angs=();
$thick=0;

for ($ia=0; $ia<=$#ARGV; $ia++) {
    $opt=lc($ARGV[$ia]);
    if ($opt eq '-r') {
    $ia++;
    $rad=$ARGV[$ia];
    } elsif ($opt eq '-t') {
    $ia++;
    $thick=$ARGV[$ia];
    } elsif ($opt eq '-s') {
    $ia++;
    $segs=$ARGV[$ia];
    } else {
    push @angs, $opt;
    }
}

$nang=$#angs+1;
print "0 // ang2point.pl ".join(' ', @ARGV)."\n";
print "0 // Calculating $nang points at outer radius $rad on $segs segments\n";
if ($thick>0) {
    $radp=$rad-$thick;
    print "0 // Also calculating inner radius $radp\n";
}

@reffs=();
@rieffs=();

$kk=3.141592635/180;
foreach $ang (@angs) {
    $f=$ang/360;
    $a0=floor($f*$segs)/$segs*360;
    $ar=$ang-$a0;
    #print "$a0 + $ar\n";

    $c0=cos($kk*$a0);
    $s0=sin($kk*$a0);
    $cf=cos($kk*($a0+360/$segs));
    $sf=sin($kk*($a0+360/$segs));

    $ct=cos($kk*$ang);
    $st=sin($kk*$ang);

    $scale=($c0*$sf-$s0*$cf)/(($sf-$s0)*$ct-($cf-$c0)*$st);
    $reff=$scale*$rad;
    $rieff=$scale*($rad-$thick);
    #print "Effective radius $reff\n";
    push @reffs, $reff;
    push @rieffs, $rieff;
}

@pts=();
@ipts=();
foreach $ia (0..$#angs) {
    $x=$reffs[$ia]*cos($kk*$angs[$ia]);
    $z=$reffs[$ia]*sin($kk*$angs[$ia]);
    push @pts, sprintf("0 // Point %2d: %.3f 0 %.3f\n",
               $ia+1, $x, $z);
    if ($thick>0) {
    $x=$rieffs[$ia]*cos($kk*$angs[$ia]);
    $z=$rieffs[$ia]*sin($kk*$angs[$ia]);
    push @ipts, sprintf("0 // Inner point %2d: %.3f 0 %.3f\n",
                $ia+1, $x, $z);
    }
}

print @pts;
print @ipts;