Hello Shay,

"Shay" <n@n.n> schreef in bericht news:4c22b7da@news.povray.org...
> Thank you!
Your welcom.

>
> The formatting of your message is a bit skewed on my end,

I noticed when I read it back from the news side.
If you want I can do it in a word document, so there is no misunderstanding.

> but I will attempt to retrace your steps myself and check my work against 
> yours.
>
>  -Shay

If you are interested in the whole mathematical derivation,
then I can scan it for you, because I don't have it electronically.
It's hand written in a blank book with some other mathematical things
I did need. I didn't exaggerate that it takes some days. It's a colossal
derivation because you have to square a rather big equation twice
and then sort everything on A, B, a and b.
If you like to do it yourself, first try the normal torus, so you know
how to do that. The oval_oval_torus starts the same way, but half way
I subtracted two equations, otherwise you end up with a power 16 result.


I will reorganise the variables and powers for you so you can read it 
better:

Constants for their powers:
+t^4                       x^4y^4
+2t^2(B^2-a^2)     x^4y^2
+(B^2-a^2) ^2       x^4
+2t^6                     x^2y^6
+2t^4                     x^2y^4z^2
-2t^4{(A^2+B^2)+
           -3(B^2-a^2)}        x^2y^4
-2t^2{(A^2-a^2)+
           +(B^2-a^2)+
           -4(AB-a^2)}     x^2y^2z^2
+2t^2{(B^2-a^2)^2+
           -2(B^2-a^2)(A^2+a^2)}   x^2y^2
+2{(A^2-a^2)(B^2-a^2)+
        +2(A-B)^2a^2         x^2z^2
-2(B^2-a^2)^2(A^2+a^2)    x^2
+t^8  y^8
+2t^6  y^6z^2
+2t^6{(A^2-a^2)+(B^2-a^2)}  y^6
+t^4   y^4z^4
-2t^4{(A^2+B^2)-3(A^2-a^2)}  y^4z^2
+t^4{(A^2-a^2)^2+(B^2-a^2)^2+
          +4(A^2-a^2)(B^2-a^2)}  y^4
+2t^2(A^2-a^2)   y^2z^4
+2t^2{(A^2-a^2)^2+
            +2(A^2-a^2)(B^2+a^2)}  y^2z^2
+2t^2{(A^2-a^2)^2(B^2-a^2)+
            +(A^2-a^2)(B^2-a^2)^2}    y^2
+(A^2-a^2) ^2  z^4
-2(A^2-a^2)^2(B^2+a^2)   z^2
(B^2-a^2)^2(A^2-a^2)^2
The last one is the constant  or for power x^0y^0z^0 if you wish.

>> This equation works fine if the poly shape power 8 is possible, but for 
>> some reason today this is limited to power 7. There was a short period of 
>> time that power 15 was alowed, but alas, not in this times. For me it 
>> would be fine if this limitation is raised again.
>> In the short period that power 8 was alowed, it traces fine and not too 
>> slow. The slowing down happened with textures. Then it slowed down 
>> considerable. But I think that with our modern fast computers this is no 
>> problem anymore.
>>
>> You can still use this with the parametric Object, but then the shape is 
>> made out of triangles and is not the pure mathematic form.
>>
>> Maybe this mail causes that the max power is raised to 8 so this shape 
>> can be used in his pure mathematical form again.
>>
>> Jaap Frank

Because of this a request to Christof Lipka or Thorsten Froehlich;
Is it possible to raise the poly shape to power eight?
Power seven is just one power to low. If you mesh around with
these equations, then it always ends up with power four, eight or even 
sixteen.

Greetings,

Jaap Frank

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