Random Gaussian cubic surface Seed: 199 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.15 x*z^2 +0.112 y*z^2 -0.231 z^2 -0.00686 x^2*z -0.0978 x*y*z -0.172 x*z -0.0109 y^2*z -0.204 y*z -0.411 z +0.115 x^3 -0.334 x^2*y +0.122 x^2 -0.0343 x*y^2 +0.362 x*y -0.35 x +0.171 y^3 +0.446 y^2 +0.17 y -0.101 1
Affine cubic: f(x,y,z) = 0.15 x*z^2 +0.112 y*z^2 -0.231 z^2 -0.00686 x^2*z -0.0978 x*y*z -0.172 x*z -0.0109 y^2*z -0.204 y*z -0.411 z +0.115 x^3 -0.334 x^2*y +0.122 x^2 -0.0343 x*y^2 +0.362 x*y -0.35 x +0.171 y^3 +0.446 y^2 +0.17 y -0.101 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].