Random Gaussian cubic surface Seed: 422 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.462 x*z^2 +0.121 y*z^2 +0.153 z^2 -0.397 x^2*z -0.0553 x*y*z +0.219 x*z -0.196 y^2*z -0.0721 y*z +0.0434 z +0.119 x^3 +0.127 x^2*y +0.223 x^2 -0.116 x*y^2 +0.219 x*y -0.0575 x +0.278 y^3 -0.192 y^2 +0.457 y -0.165 1
Affine cubic: f(x,y,z) = 0.462 x*z^2 +0.121 y*z^2 +0.153 z^2 -0.397 x^2*z -0.0553 x*y*z +0.219 x*z -0.196 y^2*z -0.0721 y*z +0.0434 z +0.119 x^3 +0.127 x^2*y +0.223 x^2 -0.116 x*y^2 +0.219 x*y -0.0575 x +0.278 y^3 -0.192 y^2 +0.457 y -0.165 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].