Random Gaussian cubic surface Seed: 15 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.332 x*z^2 -0.217 y*z^2 +0.0915 z^2 -0.122 x^2*z +0.122 x*y*z +0.187 x*z -0.335 y^2*z +0.236 y*z -0.138 z +0.486 x^3 +0.169 x^2*y -0.125 x^2 +0.0468 x*y^2 +0.0499 x*y +0.0765 x +0.324 y^3 +0.124 y^2 +0.386 y +0.147 1
Affine cubic: f(x,y,z) = -0.332 x*z^2 -0.217 y*z^2 +0.0915 z^2 -0.122 x^2*z +0.122 x*y*z +0.187 x*z -0.335 y^2*z +0.236 y*z -0.138 z +0.486 x^3 +0.169 x^2*y -0.125 x^2 +0.0468 x*y^2 +0.0499 x*y +0.0765 x +0.324 y^3 +0.124 y^2 +0.386 y +0.147 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].