Random Gaussian cubic surface Seed: 248 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0824 x*z^2 +0.341 y*z^2 -0.177 z^2 +0.0548 x^2*z +0.0514 x*y*z +0.264 x*z -0.206 y^2*z -0.227 y*z +0.314 z +0.37 x^3 -0.27 x^2*y +0.0759 x^2 +0.186 x*y^2 -0.0755 x*y +0.0189 x +0.194 y^3 +0.521 y^2 +0.0997 y +0.0534 1
Affine cubic: f(x,y,z) = 0.0824 x*z^2 +0.341 y*z^2 -0.177 z^2 +0.0548 x^2*z +0.0514 x*y*z +0.264 x*z -0.206 y^2*z -0.227 y*z +0.314 z +0.37 x^3 -0.27 x^2*y +0.0759 x^2 +0.186 x*y^2 -0.0755 x*y +0.0189 x +0.194 y^3 +0.521 y^2 +0.0997 y +0.0534 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].