Random Gaussian cubic surface Seed: 393 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0215 x*z^2 -0.097 y*z^2 +0.246 z^2 +0.488 x^2*z -0.322 x*y*z -0.0951 x*z -0.257 y^2*z -0.0864 y*z -0.0431 z +0.123 x^3 -0.0535 x^2*y -0.18 x^2 -0.379 x*y^2 -0.0362 x*y +0.422 x -0.334 y^3 -0.031 y^2 +0.0605 y +0.118 1
Affine cubic: f(x,y,z) = -0.0215 x*z^2 -0.097 y*z^2 +0.246 z^2 +0.488 x^2*z -0.322 x*y*z -0.0951 x*z -0.257 y^2*z -0.0864 y*z -0.0431 z +0.123 x^3 -0.0535 x^2*y -0.18 x^2 -0.379 x*y^2 -0.0362 x*y +0.422 x -0.334 y^3 -0.031 y^2 +0.0605 y +0.118 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].