Random Gaussian cubic surface Seed: 97 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0667 x*z^2 +0.297 y*z^2 -0.109 z^2 -0.252 x^2*z -0.326 x*y*z -0.235 x*z -0.124 y^2*z -0.346 y*z +0.258 z -0.341 x^3 +0.277 x^2*y -0.118 x^2 -0.138 x*y^2 -0.443 x*y +0.0781 x +0.191 y^3 +0.0179 y^2 -0.0319 y -0.0606 1
Affine cubic: f(x,y,z) = -0.0667 x*z^2 +0.297 y*z^2 -0.109 z^2 -0.252 x^2*z -0.326 x*y*z -0.235 x*z -0.124 y^2*z -0.346 y*z +0.258 z -0.341 x^3 +0.277 x^2*y -0.118 x^2 -0.138 x*y^2 -0.443 x*y +0.0781 x +0.191 y^3 +0.0179 y^2 -0.0319 y -0.0606 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].