Random Gaussian cubic surface Seed: 420 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0977 x*z^2 -0.266 y*z^2 -0.355 z^2 -0.0867 x^2*z +0.077 x*y*z +0.00667 x*z +0.0665 y^2*z -0.335 y*z +0.281 z -0.106 x^3 +0.234 x^2*y -0.0624 x^2 -0.0697 x*y^2 -0.157 x*y +0.506 x +0.222 y^3 +0.302 y^2 -0.291 y +0.0594 1
Affine cubic: f(x,y,z) = -0.0977 x*z^2 -0.266 y*z^2 -0.355 z^2 -0.0867 x^2*z +0.077 x*y*z +0.00667 x*z +0.0665 y^2*z -0.335 y*z +0.281 z -0.106 x^3 +0.234 x^2*y -0.0624 x^2 -0.0697 x*y^2 -0.157 x*y +0.506 x +0.222 y^3 +0.302 y^2 -0.291 y +0.0594 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].