Random Gaussian cubic surface Seed: 273 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.224 x*z^2 +0.132 y*z^2 -0.15 z^2 +0.00136 x^2*z -0.375 x*y*z +0.145 x*z -0.245 y^2*z +0.153 y*z +0.0697 z +0.47 x^3 -0.236 x^2*y +0.3 x^2 -0.0729 x*y^2 +0.17 x*y -0.247 x +0.405 y^3 -0.0866 y^2 -0.164 y -0.0056 1
Affine cubic: f(x,y,z) = 0.224 x*z^2 +0.132 y*z^2 -0.15 z^2 +0.00136 x^2*z -0.375 x*y*z +0.145 x*z -0.245 y^2*z +0.153 y*z +0.0697 z +0.47 x^3 -0.236 x^2*y +0.3 x^2 -0.0729 x*y^2 +0.17 x*y -0.247 x +0.405 y^3 -0.0866 y^2 -0.164 y -0.0056 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].