Random Gaussian cubic surface Seed: 395 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.183 x*z^2 +0.0738 y*z^2 +0.0361 z^2 +0.133 x^2*z -0.232 x*y*z +0.234 x*z -0.172 y^2*z +0.326 y*z +0.303 z +0.505 x^3 +0.177 x^2*y -0.19 x^2 -0.181 x*y^2 -0.0117 x*y -0.117 x -0.438 y^3 +0.0945 y^2 -0.15 y -0.117 1
Affine cubic: f(x,y,z) = -0.183 x*z^2 +0.0738 y*z^2 +0.0361 z^2 +0.133 x^2*z -0.232 x*y*z +0.234 x*z -0.172 y^2*z +0.326 y*z +0.303 z +0.505 x^3 +0.177 x^2*y -0.19 x^2 -0.181 x*y^2 -0.0117 x*y -0.117 x -0.438 y^3 +0.0945 y^2 -0.15 y -0.117 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].