Random Gaussian cubic surface Seed: 62 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.263 x*z^2 -0.379 y*z^2 -0.121 z^2 -0.11 x^2*z -0.236 x*y*z -0.0749 x*z -0.0634 y^2*z -0.53 y*z -0.307 z -0.0539 x^3 -0.271 x^2*y -0.0957 x^2 +0.347 x*y^2 -0.269 x*y -0.0164 x +0.122 y^3 -0.104 y^2 -0.0327 y +0.124 1
Affine cubic: f(x,y,z) = -0.263 x*z^2 -0.379 y*z^2 -0.121 z^2 -0.11 x^2*z -0.236 x*y*z -0.0749 x*z -0.0634 y^2*z -0.53 y*z -0.307 z -0.0539 x^3 -0.271 x^2*y -0.0957 x^2 +0.347 x*y^2 -0.269 x*y -0.0164 x +0.122 y^3 -0.104 y^2 -0.0327 y +0.124 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].