Random Gaussian cubic surface Seed: 474 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.23 x*z^2 -0.0574 y*z^2 +0.425 z^2 +0.000303 x^2*z -0.504 x*y*z +0.143 x*z +0.206 y*z -0.0854 z +0.129 x^3 +0.136 x^2*y +0.205 x^2 -0.361 x*y^2 -0.224 x*y -0.0451 x +0.0219 y^3 -0.0663 y^2 -0.417 y -0.02 1
Affine cubic: f(x,y,z) = 0.23 x*z^2 -0.0574 y*z^2 +0.425 z^2 +0.000303 x^2*z -0.504 x*y*z +0.143 x*z +0.206 y*z -0.0854 z +0.129 x^3 +0.136 x^2*y +0.205 x^2 -0.361 x*y^2 -0.224 x*y -0.0451 x +0.0219 y^3 -0.0663 y^2 -0.417 y -0.02 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].