Random Gaussian cubic surface Seed: 193 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0358 x*z^2 +0.00438 y*z^2 +0.195 z^2 +0.0309 x^2*z -0.139 x*y*z +0.274 x*z +0.358 y^2*z +0.618 y*z +0.43 z +0.113 x^3 +0.0538 x^2*y +0.000501 x^2 +0.0712 x*y^2 -0.275 x*y -0.0464 x -0.198 y^3 -0.0416 y^2 -0.076 y +0.161 1
Affine cubic: f(x,y,z) = -0.0358 x*z^2 +0.00438 y*z^2 +0.195 z^2 +0.0309 x^2*z -0.139 x*y*z +0.274 x*z +0.358 y^2*z +0.618 y*z +0.43 z +0.113 x^3 +0.0538 x^2*y +0.000501 x^2 +0.0712 x*y^2 -0.275 x*y -0.0464 x -0.198 y^3 -0.0416 y^2 -0.076 y +0.161 1
Shadow: the quartic B(x,y)^2 - 4 A(x,y) C(x,y) = 0 is drawn on the z=-4 xy-plane in the same 3D scene. The translucent ruled curtain rises upward from the shadow to the ramification curve where the lifted point has z >= -2 and lies above the displayed projection plane. The 3 real projected lines on the xy-plane are bitangents found from the projective lines on the cubic surface. Same-color transparent line projection cones are included but hidden by default; use the page toggle to show them.
Viewing box: axis ranges are [-4, 4].