Random Gaussian cubic surface Seed: 78 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.157 x*z^2 +0.0919 y*z^2 -0.0887 z^2 -0.254 x^2*z +0.165 x*y*z -0.0798 x*z +0.0108 y^2*z +0.168 y*z +0.588 z -0.112 x^3 +0.123 x^2*y +0.206 x^2 +0.062 x*y^2 +0.266 x*y +0.394 x +0.235 y^3 +0.116 y^2 +0.328 y +0.105 1
Affine cubic: f(x,y,z) = -0.157 x*z^2 +0.0919 y*z^2 -0.0887 z^2 -0.254 x^2*z +0.165 x*y*z -0.0798 x*z +0.0108 y^2*z +0.168 y*z +0.588 z -0.112 x^3 +0.123 x^2*y +0.206 x^2 +0.062 x*y^2 +0.266 x*y +0.394 x +0.235 y^3 +0.116 y^2 +0.328 y +0.105 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].