Random Gaussian cubic surface Seed: 31 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.104 x*z^2 +0.0693 y*z^2 +0.159 z^2 -0.255 x^2*z +0.202 x*y*z +0.067 x*z +0.206 y^2*z +0.0715 y*z +0.305 z -0.246 x^3 +0.466 x^2*y +0.316 x^2 -0.157 x*y^2 +0.173 x*y +0.117 x -0.458 y^3 +0.156 y^2 -0.154 y -0.0656 1
Affine cubic: f(x,y,z) = -0.104 x*z^2 +0.0693 y*z^2 +0.159 z^2 -0.255 x^2*z +0.202 x*y*z +0.067 x*z +0.206 y^2*z +0.0715 y*z +0.305 z -0.246 x^3 +0.466 x^2*y +0.316 x^2 -0.157 x*y^2 +0.173 x*y +0.117 x -0.458 y^3 +0.156 y^2 -0.154 y -0.0656 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].