Random Gaussian cubic surface Seed: 79 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.174 x*z^2 -0.205 y*z^2 +0.115 z^2 -0.148 x^2*z +0.363 x*y*z +0.00207 x*z -0.509 y^2*z +0.154 y*z -0.168 z +0.189 x^3 +0.157 x^2*y -0.132 x^2 +0.199 x*y^2 +0.00331 x*y +0.224 x +0.0697 y^3 -0.511 y^2 +0.00262 y -0.125 1
Affine cubic: f(x,y,z) = 0.174 x*z^2 -0.205 y*z^2 +0.115 z^2 -0.148 x^2*z +0.363 x*y*z +0.00207 x*z -0.509 y^2*z +0.154 y*z -0.168 z +0.189 x^3 +0.157 x^2*y -0.132 x^2 +0.199 x*y^2 +0.00331 x*y +0.224 x +0.0697 y^3 -0.511 y^2 +0.00262 y -0.125 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].