Random Gaussian cubic surface Seed: 73 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.216 x*z^2 +0.154 y*z^2 -0.0753 z^2 +0.0584 x^2*z +0.0664 x*y*z -0.384 x*z +0.0989 y^2*z -0.191 y*z -0.246 z +0.22 x^3 -0.318 x^2*y -0.314 x^2 -0.166 x*y^2 +0.277 x*y +0.182 x -0.0329 y^3 +0.357 y^2 -0.15 y -0.354 1
Affine cubic: f(x,y,z) = -0.216 x*z^2 +0.154 y*z^2 -0.0753 z^2 +0.0584 x^2*z +0.0664 x*y*z -0.384 x*z +0.0989 y^2*z -0.191 y*z -0.246 z +0.22 x^3 -0.318 x^2*y -0.314 x^2 -0.166 x*y^2 +0.277 x*y +0.182 x -0.0329 y^3 +0.357 y^2 -0.15 y -0.354 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 15 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].