Random Gaussian cubic surface Seed: 152 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.261 x*z^2 -0.0129 y*z^2 -0.211 z^2 +0.0386 x^2*z -0.17 x*y*z +0.112 x*z -0.0695 y^2*z -0.735 y*z +0.0714 z +0.138 x^3 +0.0914 x^2*y +0.0424 x^2 +0.0936 x*y^2 +0.326 x*y -0.125 x -0.222 y^3 -0.193 y^2 -0.105 y -0.191 1
Affine cubic: f(x,y,z) = -0.261 x*z^2 -0.0129 y*z^2 -0.211 z^2 +0.0386 x^2*z -0.17 x*y*z +0.112 x*z -0.0695 y^2*z -0.735 y*z +0.0714 z +0.138 x^3 +0.0914 x^2*y +0.0424 x^2 +0.0936 x*y^2 +0.326 x*y -0.125 x -0.222 y^3 -0.193 y^2 -0.105 y -0.191 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].