// Last edited on 2000-11-14 18:17:25 by stolfi

/*
  Coefficients of an 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 superelliptic ellipsoid  x^4 + z^4 + z^4 = 1
#declare lac_superlip =
 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
    >
    sturm
  }
// A superelliptic infinite cylinder x^4 + z^4 = 1
#declare lac_superlipcyl =
 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
    >
    sturm
  }

// A superelliptic finite cylinder (length 2 in Y direction)
#declare lac_superliprod =
  intersection{
    object{lac_superlipcyl}
    plane {<00, +1, 00>,  1}
    plane {<00, -1, 00>,  1}
    bounded_by {box{<-1,-1,-1>, <+1,+1,+1>}}
  }