Random Gaussian cubic surface Seed: 416 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0301 x*z^2 -0.412 y*z^2 +0.00869 z^2 -0.201 x^2*z -0.00416 x*y*z +0.0701 x*z -0.259 y^2*z -0.115 y*z +0.075 z -0.416 x^3 -0.262 x^2*y +0.0125 x^2 +0.485 x*y^2 -0.132 x*y +0.142 x +0.14 y^3 +0.356 y^2 +0.0502 y +0.183 1
Affine cubic: f(x,y,z) = -0.0301 x*z^2 -0.412 y*z^2 +0.00869 z^2 -0.201 x^2*z -0.00416 x*y*z +0.0701 x*z -0.259 y^2*z -0.115 y*z +0.075 z -0.416 x^3 -0.262 x^2*y +0.0125 x^2 +0.485 x*y^2 -0.132 x*y +0.142 x +0.14 y^3 +0.356 y^2 +0.0502 y +0.183 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].