🚀 go-pugleaf

In article <6790@internal.Apple.COM> desnoyer@apple.com (Peter
Desnoyers) writes: 
>In article <10946@saturn.ADS.COM> xanthian@saturn.ADS.COM (Metafont 
>Consultant Account) writes:
>> I see the idea of a modulus function that doesn't change if the axis
>> is shifted left or right by the mod base, rather than one that suffers
>> an ugly reflection at the origin, as inherently beautiful, in the math
>> sense.  It is also inherently more useful, in the graphics programming
>> sense.
>
>It is more than just pretty. The integers mod M has M elements, usually 
>represented as 0..M-1.  A modulo operator that results in {integers mod M} 
>having 2M-1 elements is either incorrectly named or incorrectly implemented.

[I knew I couldn't get away without drawing a picture; my words have
never been that clear...]

Peter,

It isn't the case, for the implementions I have seen that I considered
flawed, that the x mod 4 mapping looks like:

                                  3           3
                               2           2
                            1           1    
 0           0           0           0           0
         -1          -1
      -2          -2
   -3          -3

-8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8

but instead it looks like:

    3           3                 3           3
       2           2           2           2
          1           1     1           1    
 0           0           0           0           0

-8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8

when I need it to look like:

          3           3           3           3
       2           2           2           2
    1           1           1           1    
 0           0           0           0           0

-8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8

which latter is invarient under translations of the axis by multiples
of 4, the modulus base, a very desirable property for mapping a
rectangle onto a torus.
--
xanthian@ads.com xanthian@well.sf.ca.us (Kent Paul Dolan)
Again, my opinions, not the account furnishers'.