Random Gaussian cubic surface Seed: 216 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0422 x*z^2 +0.412 y*z^2 +0.251 z^2 +0.2 x^2*z +0.121 x*y*z -0.302 x*z +0.119 y^2*z +0.322 y*z -0.045 z +0.166 x^3 +0.427 x^2*y +0.179 x^2 -0.0681 x*y^2 -0.473 x*y -0.153 x +0.0369 y^3 -0.0333 y^2 +0.0414 y -0.0426 1
Affine cubic: f(x,y,z) = 0.0422 x*z^2 +0.412 y*z^2 +0.251 z^2 +0.2 x^2*z +0.121 x*y*z -0.302 x*z +0.119 y^2*z +0.322 y*z -0.045 z +0.166 x^3 +0.427 x^2*y +0.179 x^2 -0.0681 x*y^2 -0.473 x*y -0.153 x +0.0369 y^3 -0.0333 y^2 +0.0414 y -0.0426 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].