// Quartic superellipsoids and supercylinders.

//  Coefficients of the general implicit quartic:
//
//    + a00 xxxx + a01 xxxy + a02 xxxz + a03 xxx  + a04 xxyy 
//    + a05 xxyz + a06 xxy  + a07 xxzz + a08 xxz  + a09 xx  
//    + a10 xyyy + a11 xyyz + a12 xyy  + a13 xyzz + a14 xyz  
//    + a15 xy   + a16 xzzz + a17 xzz  + a18 xz   + a19 x   
//    + a20 yyyy + a21 yyyz + a22 yyy  + a23 yyzz + a24 yyz  
//    + a25 yy   + a26 yzzz + a27 yzz  + a28 yz   + a29 y    
//    + a30 zzzz + a31 zzz  + a32 zz   + a33 z    + a34

// A fouth-power superellipsoid x^4 + y^4 + z^4 = 1
#declare super_ball = 
  poly
    { 4,
      < 1, 0, 0, 0, 0, 
        0, 0, 0, 0, 0, 
        0, 0, 0, 0, 0, 
        0, 0, 0, 0, 0,
        1, 0, 0, 0, 0, 
        0, 0, 0, 0, 0,
        1, 0, 0, 0, -1
      >
    }

// A fouth-power supercylinder x^4 + z^4 = 1
#declare super_cyl = 
  poly
    { 4,
      < 1, 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,
        1, 0, 0, 0, -1
      >
    }