Random Gaussian cubic surface Seed: 164 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.301 x*z^2 +0.144 y*z^2 -0.387 z^2 +0.181 x^2*z +0.127 x*y*z -0.262 x*z -0.0719 y^2*z -0.0991 y*z +0.463 z -0.224 x^3 -0.141 x^2*y -0.31 x^2 -0.000508 x*y^2 +0.213 x*y -0.13 x -0.0347 y^3 +0.211 y^2 +0.226 y +0.259 1
Affine cubic: f(x,y,z) = 0.301 x*z^2 +0.144 y*z^2 -0.387 z^2 +0.181 x^2*z +0.127 x*y*z -0.262 x*z -0.0719 y^2*z -0.0991 y*z +0.463 z -0.224 x^3 -0.141 x^2*y -0.31 x^2 -0.000508 x*y^2 +0.213 x*y -0.13 x -0.0347 y^3 +0.211 y^2 +0.226 y +0.259 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 15 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].