Random Gaussian cubic surface Seed: 236 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.131 x*z^2 +0.324 y*z^2 +0.0599 z^2 +0.437 x^2*z -0.0593 x*y*z -0.283 x*z -0.314 y^2*z -0.246 y*z +0.126 z -0.173 x^3 +0.0411 x^2*y +0.312 x^2 +0.2 x*y^2 +0.33 x*y -0.224 x -0.14 y^3 +0.126 y^2 +0.00455 y -0.247 1
Affine cubic: f(x,y,z) = 0.131 x*z^2 +0.324 y*z^2 +0.0599 z^2 +0.437 x^2*z -0.0593 x*y*z -0.283 x*z -0.314 y^2*z -0.246 y*z +0.126 z -0.173 x^3 +0.0411 x^2*y +0.312 x^2 +0.2 x*y^2 +0.33 x*y -0.224 x -0.14 y^3 +0.126 y^2 +0.00455 y -0.247 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].