Random Gaussian cubic surface Seed: 360 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.287 x*z^2 -0.0342 y*z^2 -0.102 z^2 -0.0241 x^2*z -0.376 x*y*z -0.0366 x*z +0.0217 y^2*z -0.125 y*z -0.0341 z +0.0584 x^3 -0.232 x^2*y +0.34 x^2 -0.0439 x*y^2 -0.398 x*y +0.129 x +0.433 y^3 -0.336 y^2 -0.0676 y -0.302 1
Affine cubic: f(x,y,z) = 0.287 x*z^2 -0.0342 y*z^2 -0.102 z^2 -0.0241 x^2*z -0.376 x*y*z -0.0366 x*z +0.0217 y^2*z -0.125 y*z -0.0341 z +0.0584 x^3 -0.232 x^2*y +0.34 x^2 -0.0439 x*y^2 -0.398 x*y +0.129 x +0.433 y^3 -0.336 y^2 -0.0676 y -0.302 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 7 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].