Random Gaussian cubic surface Seed: 397 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.232 x*z^2 -0.113 y*z^2 +0.155 z^2 +0.194 x^2*z +0.0379 x*y*z +0.473 x*z -0.167 y^2*z +0.318 y*z -0.0397 z -0.27 x^3 -0.19 x^2*y -0.124 x^2 -0.125 x*y^2 +0.276 x*y +0.00985 x -0.244 y^3 -0.217 y^2 +0.39 y +0.202 1
Affine cubic: f(x,y,z) = 0.232 x*z^2 -0.113 y*z^2 +0.155 z^2 +0.194 x^2*z +0.0379 x*y*z +0.473 x*z -0.167 y^2*z +0.318 y*z -0.0397 z -0.27 x^3 -0.19 x^2*y -0.124 x^2 -0.125 x*y^2 +0.276 x*y +0.00985 x -0.244 y^3 -0.217 y^2 +0.39 y +0.202 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].