Random Gaussian cubic surface Seed: 9 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.17 x*z^2 +0.0513 y*z^2 -0.35 z^2 +0.139 x^2*z +0.242 x*y*z -0.0956 x*z +0.0909 y^2*z +0.053 y*z -0.0833 z -0.182 x^3 -0.429 x^2*y +0.298 x^2 -0.0101 x*y^2 +0.533 x*y +0.175 x +0.0587 y^3 -0.139 y^2 +0.294 y -0.107 1
Affine cubic: f(x,y,z) = -0.17 x*z^2 +0.0513 y*z^2 -0.35 z^2 +0.139 x^2*z +0.242 x*y*z -0.0956 x*z +0.0909 y^2*z +0.053 y*z -0.0833 z -0.182 x^3 -0.429 x^2*y +0.298 x^2 -0.0101 x*y^2 +0.533 x*y +0.175 x +0.0587 y^3 -0.139 y^2 +0.294 y -0.107 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].