Random Gaussian cubic surface Seed: 144 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.188 x*z^2 -0.207 y*z^2 -0.073 z^2 +0.237 x^2*z +0.0567 x*y*z +0.0943 x*z -0.307 y^2*z +0.281 y*z +0.468 z +0.207 x^3 -0.266 x^2*y +0.0694 x^2 +0.0743 x*y^2 +0.333 x*y +0.114 x +0.298 y^3 -0.243 y^2 -0.206 y -0.135 1
Affine cubic: f(x,y,z) = -0.188 x*z^2 -0.207 y*z^2 -0.073 z^2 +0.237 x^2*z +0.0567 x*y*z +0.0943 x*z -0.307 y^2*z +0.281 y*z +0.468 z +0.207 x^3 -0.266 x^2*y +0.0694 x^2 +0.0743 x*y^2 +0.333 x*y +0.114 x +0.298 y^3 -0.243 y^2 -0.206 y -0.135 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].