Random Gaussian cubic surface Seed: 51 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.137 x*z^2 -0.149 y*z^2 +0.0192 z^2 +0.299 x^2*z -0.0773 x*y*z -0.263 x*z -0.191 y^2*z +0.424 y*z -0.0837 z -0.283 x^3 -0.0722 x^2*y +0.0712 x^2 +0.0686 x*y^2 +0.445 x*y -0.0457 x -0.369 y^3 +0.36 y^2 +0.0685 y +0.0716 1
Affine cubic: f(x,y,z) = -0.137 x*z^2 -0.149 y*z^2 +0.0192 z^2 +0.299 x^2*z -0.0773 x*y*z -0.263 x*z -0.191 y^2*z +0.424 y*z -0.0837 z -0.283 x^3 -0.0722 x^2*y +0.0712 x^2 +0.0686 x*y^2 +0.445 x*y -0.0457 x -0.369 y^3 +0.36 y^2 +0.0685 y +0.0716 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].