/*
              Persistence of Vision Raytracer Version 3.1
                      Steiner shapes include file
              Several cubic and quartic shape definitions
                          by Adam Coffman

 See the web site
 http://users.pfw.edu/CoffmanA/steinersurface.html
 for mathematical descriptions of these objects.
 Original file created March 31, 1999.
 Updated April 25, 1999.             
 Updated May 31, 2018 with new web address for Steiner Surfaces page.
*/


/* Steiner's Roman surface */
#declare Steiner_1 =
 quartic 
  {< 0,   0,   0,  0,  1,   0,   0,   1,   0,   0,
     0,   0,   0,  0,  1,   0,   0,   0,   0,   0,
     0,   0,   0,  1,  0,   0,   0,   0,   0,   0,
     0,   0,   0,  0,  0>
  }

/* Type 2 Steiner surface */
#declare Steiner_2 =
 quartic 
  {< 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 
     0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 
     0, 0, 0, 0, 0>
  }
                             
/* Type 2 Steiner surface
   (related to the previous quartic by a real projective linear
    transformation)
 */
#declare Steiner_2_b =                        
 quartic
  { < 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, -1, 
      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
      0, 0, 1, 0, 0>
  }

/* Steiner's Cross-cap surface */
#declare Steiner_3 =
 quartic 
  {< 4, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 
     0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 
     0, 0, 0, 0, 0>
  }

/* Type 4 Steiner surface */
#declare Steiner_4 =
 quartic 
  {< 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 
     0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
     -1, 0, 0, 0, 0>
  }

/* Type 5 Steiner surface */
#declare Steiner_5 =
 quartic 
  {< 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, 0, 0, 0, 0, 
     0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 
     0, 0, 0, 0, 0>
  }

/* Type 6 Steiner surface */
#declare Steiner_6 =
 quartic 
  {< 0,0,0,0,1,0,0,0,0,0,1,0,-2,2,0,0,0,0,0,0,
     1,0,-2,2,0,1,0,-2,0,0,1,0,0,0,0>
  }

/* Type 6 Steiner surface
   (related to the previous quartic by a real projective linear
    transformation)
 */
#declare Steiner_6_b =
 quartic 
  {< -5/4, 3, 0, 7/2, -5/2, 0, -11/2, -3, 0, -13/4, 1, 0, 5/2, 4, 0, 
     5/2, 0, 5, 0, 1, -1/4, 0, -1/2, -1, 0, -1/4, 0, -3, 0, 0, 
     -1, 0, -2, 0, 0>
  }

/* Type 7 Steiner surface
   (a ruled cubic)
 */
#declare Steiner_7 =
 cubic 
  {<0,0,0,0,1,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0>
  }

/* Whitney's umbrella */
#declare Steiner_8 =
 cubic 
  {<0,0,0,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0>
  }

/* Plucker's conoid */
#declare Steiner_8_b =
 cubic 
  {<0,0,-1,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0>
  }

/* Cayley's ruled cubic */
#declare Steiner_9 =
 cubic 
  {<0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,-1,0,0>
  }

/* Cayley's ruled cubic 
   (related to the previous cubic by a real projective linear
    transformation)
 */
#declare Steiner_9_b =
 cubic 
  {<0,0,0,0,0,1,0,-1,0,0,1,0,0,0,0,0,0,-1,0,0>
  }