Random Gaussian cubic surface Seed: 5 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.189 x*z^2 -0.312 y*z^2 -0.0586 z^2 +0.0992 x^2*z +0.268 x*y*z +0.0259 x*z -0.13 y^2*z -0.185 y*z +0.177 z +0.386 x^3 +0.0644 x^2*y -0.291 x^2 -0.226 x*y^2 +0.378 x*y +0.0479 x -0.409 y^3 -0.0197 y^2 -0.274 y -0.148 1
Affine cubic: f(x,y,z) = -0.189 x*z^2 -0.312 y*z^2 -0.0586 z^2 +0.0992 x^2*z +0.268 x*y*z +0.0259 x*z -0.13 y^2*z -0.185 y*z +0.177 z +0.386 x^3 +0.0644 x^2*y -0.291 x^2 -0.226 x*y^2 +0.378 x*y +0.0479 x -0.409 y^3 -0.0197 y^2 -0.274 y -0.148 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].