Random Gaussian cubic surface Seed: 20 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.104 x*z^2 +0.349 y*z^2 +0.405 z^2 +0.092 x^2*z +0.12 x*y*z -0.142 x*z -0.265 y^2*z -0.261 y*z -0.29 z +0.27 x^3 -0.0163 x^2*y +0.0372 x^2 -0.186 x*y^2 -0.316 x*y -0.349 x -0.244 y^3 +0.174 y^2 +0.00535 y -0.133 1
Affine cubic: f(x,y,z) = -0.104 x*z^2 +0.349 y*z^2 +0.405 z^2 +0.092 x^2*z +0.12 x*y*z -0.142 x*z -0.265 y^2*z -0.261 y*z -0.29 z +0.27 x^3 -0.0163 x^2*y +0.0372 x^2 -0.186 x*y^2 -0.316 x*y -0.349 x -0.244 y^3 +0.174 y^2 +0.00535 y -0.133 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].