Last Update Dec. 7, 1997 　日本語はこちら

NUMERICAL SPACE / QUARTIC

POV-Ray's "quartic" defines 3 dimensional surfaces by 4th order equations. I'm not good at mathematics. But "quartic" is in my favor because it generates so curious surfaces. "quartic" is as follows,
"quartic { ＜a00, a01,... a34＞ }" means
a00 x^4 + a01 x^3 y + a02 x^3 z+ a03 x^3 + a04 x^2 y^2+
a05 x^2 y z+ a06 x^2 y + a07 x^2 z^2+a08 x^2 z+a09 x^2+
a10 x y^3+a11 x y^2 z+ a12 x y^2+a13 x y z^2+a14 x y z+
a15 x y + a16 x z^3 + a17 x z^2 + a18 x z + a19 x+
a20 y^4 + a21 y^3 z + a22 y^3+ a23 y^2 z^2 +a24 y^2 z+
a25 y^2 + a26 y z^3 + a27 y z^2 + a28 y z + a29 y+
a30 z^4 + a31 z^3 + a32 z^2 + a33 z + a34 = 0

I showed some images made by "quartic" on this page and I noted the main expression in the scene file of the images. Please try to generate the same shape on your personal computer.

 quartic { <0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0> rotate <30,0,0> } camera { location <-3, -3, -7> look_at <-1, -3, 0> angle 152 }

Illusion in Blue / 33k / Dec. 1997 / by Tsutomu Higo

 quartic { <0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0> } camera { ultra_wide_angle location <-1, 3, -5> look_at <0, -0.3, 0> angle 220 }

Two Curves / 18k / Dec. 1997 / by Tsutomu Higo

 quartic { <1,1,5,0,0,0,50,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0> } camera { ultra_wide_angle location <0.5, 0.4, 1.2> look_at <0, 0.25, 0> angle 360 }

Shiner in Shells / 39k / Dec. 1997 / by Tsutomu Higo

 quartic { <0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0> } camera { location <-1, 3, -5> look_at <0, -0.3, 0> angle 60 }

Cast Indigo / 24k / Dec. 1997 / by Tsutomu Higo

 quartic { <0,1,-1,0,0,0,0,0,0,0,0,0.2,0,0,0,0,0,0,0,3,0,0,0,0,0,0,1,0,0.1,0,0,4,0,0,-1> rotate <30,0,0> } camera { ultra_wide_angle location <10000, 0, 5000> look_at <-8000, 0, -10000> angle 200 }

Crashing Field / 26k / Dec. 1997 / by Tsutomu Higo