

On 14/10/2024 18:16, Bald Eagle wrote:
> I was experimenting with the mapping equations in:
>
> https://archive.bridgesmathart.org/2018/bridges201859.pdf
Really interesting article...
> and crashed POVRay (3.8) about 6 times.
>
> I'm guessing it has to do with trying to take square roots of something divided
> by 0, or 0/0.
> I haven't had a chance to scribble out a minimal .pov script to see what
> triggers it.
>
>
>
> I also was not able to get the mapping to work correctly  I'm guessing that I'm
> going to have to apply the _inverse_ of the mapping  but I'm out of practice,
> and can't see an easy way to go about that.
>
> Any suggestions?
I quickly did these two scenes.
I used the silly method that gives the images as attachments.
I don't know why you have crashes.
Here is some of my code :
 begin code 
#declare Sq = function(x) { x*x }
#declare fnDisc2Square = function(u,v) {
sgn(u*v)*sqrt(((Sq(u)Sq(v)+sqrt((Sq(u)+Sq(v))*(Sq(u)+Sq(v)+4*Sq(u)*Sq(v)*(Sq(u)+Sq(v)2)))))/(2*(Sq(u)+Sq(v)2)))
}
#declare fnSquare2Disc = function(x,y) {
sqrt((Sq(x)+Sq(y)(2*Sq(x)*Sq(y)))/((Sq(x)+Sq(y))*(1Sq(x)*Sq(y))))
}
#macro Disc2Square(U,V)
<fnDisc2Square(U,V)/V, fnDisc2Square(U,V)/U, 0.10>
#end
#macro Square2Disc(X,Y)
<fnSquare2Disc(X,Y)*X, fnSquare2Disc(X,Y)*Y, 0.10>
#end
 end code 
Values between 1 and 1 go through zero, but I don't have any crashes.
I don't know if this will help you..

Kurtz le pirate
Compagnie de la banquise
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Attachments:
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Download 'disc2square.png' (440 KB)
Preview of image 'square2disc.png'
Preview of image 'disc2square.png'

