"waggy" <hon### [at] handbasketorg> schreef in bericht 
news:web.4c27982b751c630af99d05c80@news.povray.org...
> Jaap Frank wrote:
>>[snip]
>> 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.
>>
> A power 8 poly works fine in 3.7beta35.  (I don't have 3.6 installed in a
> convenient computer right now.)
>
> Beautiful work!
>
> ~waggy
>
> #local a=1;
> #local b=1;
> #local A=4; // Major radius of the swept elipse
> #local B=2; // Minor radius of the swept elipse
> #local tratio=a/b;
>
> #local c21=   pow(tratio,4);//ok
> #local c20= 2*pow(tratio,2)*(B*B-a*a);//ok
> #local c19=   pow(B*B-a*a,2);//ok
> #local c18= 2*pow(tratio,6) ;//ok
> #local c17= 2*pow(tratio,4);//ok
> #local c16=-2*pow(tratio,4)*( A*A+B*B -3*(B*B-a*a) );//ok
> #local c15=-2*pow(tratio,2)*( A*A-a*a +B*B-a*a -4*(A*B-a*a) );//ok
> #local c14= 2*pow(tratio,2)*( pow(B*B-a*a,2) -2*(B*B-a*a)*(A*A+a*a) );//ok
> #local c13= 2*(  (A*A-a*a) * (B*B-a*a) +2*pow(A-B,2)*a*a  )  ;//ok? 
> unclear
> where closing paren goes
> #local c12=-2*pow(B*B-a*a,2)*(A*A+a*a);//ok
> #local c11=   pow(tratio,8);//ok
> #local c10= 2*pow(tratio,6);//ok
> #local c9 = 2*pow(tratio,6)*((A*A-a*a)+(B*B-a*a));//ok
> #local c8 =   pow(tratio,4) ;//ok
> #local c7 =-2*pow(tratio,4)*( (A*A+B*B)-3*(A*A-a*a) );//ok
> #local c6 =   pow(tratio,4)*( pow((A*A-a*a),2) +pow((B*B-a*a),2)
> +4*(A*A-a*a)*(B*B-a*a) );//ok
> #local c5 = 2*pow(tratio,2)*(A*A-a*a);//ok
> #local c4 = 2*pow(tratio,2)*( pow(A*A-a*a,2) +2*(A*A-a*a)*(B*B+a*a) );//ok
> #local c3 = 2*pow(tratio,2)*( pow(A*A-a*a,2)*(B*B-a*a) +
> (A*A-a*a)*pow(B*B-a*a,2) );//ok
> #local c2 =   pow(A*A-a*a ,2);//ok
> #local c1 =-2*pow(A*A-a*a,2)*(B*B+a*a);//ok
> #local c0 =   pow(B*B-a*a,2)*pow(A*A-a*a,2) ;//ok
>
> //powers check out ok.
> #declare oval_oval_torus = function(x,y,z) {
>   c21* pow(x,4)*pow(y,4)
>  +c20* pow(x,4)*pow(y,2)
>  +c19* pow(x,4)
>  +c18* pow(x,2)*pow(y,6)
>  +c17* pow(x,2)*pow(y,4)*pow(z,2)
>  +c16* pow(x,2)*pow(y,4)
>  +c15* pow(x,2)*pow(y,2)*pow(z,2)
>  +c14* pow(x,2)*pow(y,2)
>  +c13* pow(x,2)*pow(z,2)
>  +c12* pow(x,2)
>  +c11* pow(y,8)
>  +c10* pow(y,6)*pow(z,2)
>  +c9 * pow(y,6)
>  +c8 * pow(y,4)*pow(z,4)
>  +c7 * pow(y,4)*pow(z,2)
>  +c6 * pow(y,4)
>  +c5 * pow(y,2)*pow(z,4)
>  +c4 * pow(y,2)*pow(z,2)
>  +c3 * pow(y,2)
>  +c2 * pow(z,4)
>  +c1 * pow(z,2)
>  +c0
>  }
> poly {8,
> <0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
>  0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
>  c21,0, 0, 0, 0, c20,  0, 0, 0,
>  0, 0, 0, 0, 0, c19,  0, 0, 0,
>  0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
>  0, 0,   0, 0,   0, 0, 0, 0, c18, 0,
>  0, c17, 0, c16, 0, 0, 0, 0, 0, 0,
>  c15,0, c14, 0,   0, 0,   0, 0, 0, 0,
>  0, 0, 0, c13,   0, c12, 0, 0, 0, 0,
>  0, 0, 0, 0, 0,  0, 0,   0, 0, 0, 0,
>  0, 0, 0, 0, 0, 0, 0,   0, 0, 0, 0,
>  0, 0, 0,  0, 0,  0, 0,  0, 0, 0, c11,
>  0, 0, c10, 0, c9, 0, 0, 0, 0, c8, 0,
>  c7, 0, c6, 0, 0,  0, 0, 0, 0, 0, 0,
>  c5, 0, c4, 0, c3, 0, 0, 0, 0, 0, 0,
>  0, 0, 0, 0, 0, 0, c2, 0, c1, 0, c0>
>  sturm // Using strum isn't that much slower, and seems nicer.
>  texture {
>    pigment {
>      color rgb <0.8,0.8,1.0>
>    }
>    finish{
>      diffuse 0.3
>      ambient 0.0
>      specular 0.6
>      reflection { 0.8 metallic }
>      conserve_energy
>    }
>  }
>  //rotate 90*x
>  //translate y*((A+B+a+b)/2 +0.5)
>  }
>
>
Wow, I didn.t try it in the beta's. That is excellent!
Now I can go further with things from the nineties!

Jaap Frank

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