Random Gaussian cubic surface Seed: 168 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.118 x*z^2 +0.122 y*z^2 -0.0735 z^2 -0.147 x^2*z +0.169 x*y*z +0.0968 x*z +0.133 y^2*z -0.354 y*z -0.473 z +0.154 x^3 -0.234 x^2*y -0.0938 x^2 +0.144 x*y^2 -0.0293 x*y +0.213 x -0.459 y^3 +0.116 y^2 +0.266 y -0.3 1
Affine cubic: f(x,y,z) = -0.118 x*z^2 +0.122 y*z^2 -0.0735 z^2 -0.147 x^2*z +0.169 x*y*z +0.0968 x*z +0.133 y^2*z -0.354 y*z -0.473 z +0.154 x^3 -0.234 x^2*y -0.0938 x^2 +0.144 x*y^2 -0.0293 x*y +0.213 x -0.459 y^3 +0.116 y^2 +0.266 y -0.3 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].