Random Gaussian cubic surface Seed: 147 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.339 x*z^2 +0.147 y*z^2 +0.0154 z^2 -0.0925 x^2*z -0.0798 x*y*z +0.0914 x*z +0.181 y^2*z -0.0896 y*z -0.0722 z -0.563 x^3 +0.144 x^2*y +0.5 x^2 -0.00302 x*y^2 -0.32 x*y -0.199 x -0.114 y^3 +0.135 y^2 +0.129 y -0.127 1
Affine cubic: f(x,y,z) = -0.339 x*z^2 +0.147 y*z^2 +0.0154 z^2 -0.0925 x^2*z -0.0798 x*y*z +0.0914 x*z +0.181 y^2*z -0.0896 y*z -0.0722 z -0.563 x^3 +0.144 x^2*y +0.5 x^2 -0.00302 x*y^2 -0.32 x*y -0.199 x -0.114 y^3 +0.135 y^2 +0.129 y -0.127 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].