Random Gaussian cubic surface Seed: 454 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.271 x*z^2 -0.18 y*z^2 -0.0763 z^2 +0.0899 x^2*z -0.272 x*y*z -0.162 x*z -0.268 y^2*z +0.164 y*z +0.131 z +0.124 x^3 +0.653 x^2*y -0.118 x^2 +0.222 x*y^2 -0.222 x*y +0.149 x +0.216 y^3 -0.148 y^2 -0.0541 y +0.126 1
Affine cubic: f(x,y,z) = 0.271 x*z^2 -0.18 y*z^2 -0.0763 z^2 +0.0899 x^2*z -0.272 x*y*z -0.162 x*z -0.268 y^2*z +0.164 y*z +0.131 z +0.124 x^3 +0.653 x^2*y -0.118 x^2 +0.222 x*y^2 -0.222 x*y +0.149 x +0.216 y^3 -0.148 y^2 -0.0541 y +0.126 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].