Random Gaussian cubic surface Seed: 86 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.347 x*z^2 -0.0536 y*z^2 +0.141 z^2 +0.152 x^2*z -0.17 x*y*z +0.107 x*z +0.0831 y^2*z +0.0232 y*z +0.047 z -0.283 x^3 -0.0287 x^2*y -0.0459 x^2 +0.337 x*y^2 +0.0195 x*y -0.515 x +0.25 y^3 +0.355 y^2 -0.00745 y +0.364 1
Affine cubic: f(x,y,z) = -0.347 x*z^2 -0.0536 y*z^2 +0.141 z^2 +0.152 x^2*z -0.17 x*y*z +0.107 x*z +0.0831 y^2*z +0.0232 y*z +0.047 z -0.283 x^3 -0.0287 x^2*y -0.0459 x^2 +0.337 x*y^2 +0.0195 x*y -0.515 x +0.25 y^3 +0.355 y^2 -0.00745 y +0.364 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].