Random Gaussian cubic surface Seed: 442 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.205 x*z^2 +0.0907 y*z^2 -0.366 z^2 -0.155 x^2*z +0.198 x*y*z +0.253 x*z -0.00104 y^2*z +0.367 y*z +0.312 z -0.0468 x^3 +0.0749 x^2*y +0.297 x^2 +0.152 x*y^2 +0.227 x*y +0.0193 x +0.4 y^3 -0.122 y^2 -0.329 y +0.0493 1
Affine cubic: f(x,y,z) = -0.205 x*z^2 +0.0907 y*z^2 -0.366 z^2 -0.155 x^2*z +0.198 x*y*z +0.253 x*z -0.00104 y^2*z +0.367 y*z +0.312 z -0.0468 x^3 +0.0749 x^2*y +0.297 x^2 +0.152 x*y^2 +0.227 x*y +0.0193 x +0.4 y^3 -0.122 y^2 -0.329 y +0.0493 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].