Random Gaussian cubic surface Seed: 436 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0141 x*z^2 +0.221 y*z^2 +0.151 z^2 +0.42 x^2*z -0.364 x*y*z -0.0903 x*z -0.0273 y^2*z +0.339 y*z +0.0842 z +0.0473 x^3 -0.226 x^2*y -0.151 x^2 +0.125 x*y^2 +0.281 x*y +0.176 x -0.45 y^3 -0.167 y^2 +0.223 y +0.081 1
Affine cubic: f(x,y,z) = -0.0141 x*z^2 +0.221 y*z^2 +0.151 z^2 +0.42 x^2*z -0.364 x*y*z -0.0903 x*z -0.0273 y^2*z +0.339 y*z +0.0842 z +0.0473 x^3 -0.226 x^2*y -0.151 x^2 +0.125 x*y^2 +0.281 x*y +0.176 x -0.45 y^3 -0.167 y^2 +0.223 y +0.081 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].