Random Gaussian cubic surface Seed: 95 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0462 x*z^2 -0.0564 y*z^2 +0.477 z^2 +0.0272 x^2*z -0.117 x*y*z +0.317 x*z +0.195 y^2*z +0.0578 y*z +0.127 z -0.244 x^3 +0.00671 x^2*y -0.019 x^2 -0.613 x*y^2 +0.249 x*y +0.124 x +0.0467 y^3 +0.215 y^2 -0.163 y +0.0834 1
Affine cubic: f(x,y,z) = -0.0462 x*z^2 -0.0564 y*z^2 +0.477 z^2 +0.0272 x^2*z -0.117 x*y*z +0.317 x*z +0.195 y^2*z +0.0578 y*z +0.127 z -0.244 x^3 +0.00671 x^2*y -0.019 x^2 -0.613 x*y^2 +0.249 x*y +0.124 x +0.0467 y^3 +0.215 y^2 -0.163 y +0.0834 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].