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)
  }

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