I would very much like to see that scan. I would teach me a lot, I'm 
sure. My email address is myn### [at] hotmailcom.

Thank you.

Jaap Frank wrote:
> 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 
> 
>

Post a reply to this message