On 11 Feb 98 15:12:17 GMT, "Tristan Wibberley"
<tri### [at] compaqcom> wrote:

>Look at how the 4th order goes
>extend to 5th
>
>The numbers give which power of each of x, y and z are in each term.
>To extend further, count down in base n (eg 6th order use base 6) from n00
>to get each term.

Not quite.  For example, there is no 440 term.  Only terms 
of order 6 or less are included.  Also, of course, you must 
include 600, 060, and 006, which are not legal numbers in 
base 6.  So the real answer is: count down (base 10) from 
777, and only include numbers where the sum of the digits 
is equal to or less than the order of the polynomial you're 
generating.  Of course, there are easier and more efficient
ways to do it.

Here's a perl program that will generate the terms in 
the correct order, suitable for including in a POV file.
to use it on Unix, just call it "coeffs", make it mode 700,
and type "coeffs 6 >coeffs.out" to create a file called 
"coeffs.out" containing the definition for a poly of order 
6.  Under Windows, you'll have to type 
"perl coeffs 6 >coeffs.out" and make sure perl.exe is in
your path somewhere.  To find a recent port of Perl for
your machine, see http://cpan.perl.org/ports/

Programmers in other languages, feel free to borrow this 
and rewrite it for the Perl-deprived.  Windows and Mac
users, hop over to povray.binaries.utilities and grab
the template file I'll post over there shortly.

----------- cut here ------>8==========
#!/usr/bin/perl -w

use strict;
 
my $order = $ARGV[0];
print "poly { $order, <\n";
for ( my $x=$order; $x >= 0; $x-- ) {
  for ( my $y=$order-$x; $y >= 0; $y-- ) {
    for ( my $z=$order-$y-$x; $z >= 0; $z-- ) {
      print '  0';
      if ($x+$y+$z) {
        print ', /* ';
        print 'x' if ($x);
        print $x if ($x>1);
        print 'y' if ($y);
        print $y if ($y>1);
        print 'z' if ($z);
        print $z if ($z>1);
        print ' */';
      }
    print "\n";
    }
  }
}

print "> }\n";
----------- cut here ------>8==========

Here's a sample of the output, for order 3:

poly { 3, <
  0, /* x3 */
  0, /* x2y */
  0, /* x2z */
  0, /* x2 */
  0, /* xy2 */
  0, /* xyz */
  0, /* xy */
  0, /* xz2 */
  0, /* xz */
  0, /* x */
  0, /* y3 */
  0, /* y2z */
  0, /* y2 */
  0, /* yz2 */
  0, /* yz */
  0, /* y */
  0, /* z3 */
  0, /* z2 */
  0, /* z */
  0
> }

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