Random Gaussian cubic surface Seed: 129 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.00909 x*z^2 -0.395 y*z^2 -0.077 z^2 -0.057 x^2*z +0.138 x*y*z -0.0883 x*z -0.056 y^2*z -0.173 y*z -0.177 z +0.137 x^3 +0.199 x^2*y +0.429 x^2 +0.0755 x*y^2 +0.0248 x*y +0.169 x +0.325 y^3 -0.0651 y^2 -0.589 y -0.0991 1
Affine cubic: f(x,y,z) = 0.00909 x*z^2 -0.395 y*z^2 -0.077 z^2 -0.057 x^2*z +0.138 x*y*z -0.0883 x*z -0.056 y^2*z -0.173 y*z -0.177 z +0.137 x^3 +0.199 x^2*y +0.429 x^2 +0.0755 x*y^2 +0.0248 x*y +0.169 x +0.325 y^3 -0.0651 y^2 -0.589 y -0.0991 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].