Random Gaussian cubic surface Seed: 83 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.398 x*z^2 -0.114 y*z^2 -0.011 z^2 +0.106 x^2*z -0.28 x*y*z +0.322 x*z +0.0589 y^2*z -0.144 y*z -0.414 z -0.181 x^3 +0.19 x^2*y +0.147 x^2 +0.24 x*y^2 -0.14 x*y +0.205 x -0.0533 y^3 +0.392 y^2 +0.0263 y -0.27 1
Affine cubic: f(x,y,z) = -0.398 x*z^2 -0.114 y*z^2 -0.011 z^2 +0.106 x^2*z -0.28 x*y*z +0.322 x*z +0.0589 y^2*z -0.144 y*z -0.414 z -0.181 x^3 +0.19 x^2*y +0.147 x^2 +0.24 x*y^2 -0.14 x*y +0.205 x -0.0533 y^3 +0.392 y^2 +0.0263 y -0.27 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 7 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].