Random Gaussian cubic surface Seed: 71 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0197 x*z^2 +0.209 y*z^2 -0.0444 z^2 -0.0359 x^2*z +0.203 x*y*z +0.206 x*z +0.139 y^2*z -0.574 y*z -0.23 z -0.124 x^3 +0.299 x^2*y +0.0184 x^2 -0.159 x*y^2 +0.152 x*y +0.132 x -0.461 y^3 +0.219 y^2 -0.171 y +0.0859 1
Affine cubic: f(x,y,z) = 0.0197 x*z^2 +0.209 y*z^2 -0.0444 z^2 -0.0359 x^2*z +0.203 x*y*z +0.206 x*z +0.139 y^2*z -0.574 y*z -0.23 z -0.124 x^3 +0.299 x^2*y +0.0184 x^2 -0.159 x*y^2 +0.152 x*y +0.132 x -0.461 y^3 +0.219 y^2 -0.171 y +0.0859 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].