Op 4-8-2022 om 12:36 schreef Bald Eagle:
> Thomas de Groot <tho### [at] degrootorg> wrote:
>> ...which reminds me to ask you (curiosity): how does
>>
>> #declare U = function (X, Y, Z) {(0.5 + atan2 (N(Z, X,Y,Z), N(X,
>> X,Y,Z))/(2*pi))}
>> #declare V = function (X, Y, Z) {(0.5 + asin(N(Y, X,Y,Z))/pi)}
>>
>> work? is puzzling, as far as atan2 and asin are concerned.
>>
>> --
>> Thomas
> 
> I don't have the file accessible to me ATM, but IIRC, the N() function is
> probably just a select () for whichever vector component is specified as the
> first argument. (*)
> 
> Then the atan2 returns an angle between -pi and pi, based on z and x.
> Dividing by tau gives values between -0.5 and 0.5, and then everything is
> shifted to between 0 and 1.
> 
> asin returns an angle between -pi/2 and pi/2.
> Dividing by pi gives values between -0.5 and 0.5, and then everything is shifted
> to between 0 and 1.
> 
> 
> (*) And the way THAT works, is taking the specified vector components and doing
> something like x*(-1) + y*0 + z*(2).  That should give you a -1, a 0, or a 2
> depending on which cardinal vector is specified.
> select () then returns one of three scalar values depending on what component it
> spits out.
> 


OK thanks. Sorry for diverting from the original post subject. I'll shut 
up now. :-)

-- 
Thomas

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