Random Gaussian cubic surface Seed: 158 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.375 x*z^2 +0.061 y*z^2 -0.241 z^2 -0.145 x^2*z +0.159 x*y*z -0.54 x*z +0.212 y^2*z -0.137 y*z +0.0297 z -0.257 x^3 +0.015 x^2*y -0.34 x^2 +0.0265 x*y^2 -0.169 x*y -0.0104 x +0.221 y^3 -0.294 y^2 +0.213 y -0.0594 1
Affine cubic: f(x,y,z) = 0.375 x*z^2 +0.061 y*z^2 -0.241 z^2 -0.145 x^2*z +0.159 x*y*z -0.54 x*z +0.212 y^2*z -0.137 y*z +0.0297 z -0.257 x^3 +0.015 x^2*y -0.34 x^2 +0.0265 x*y^2 -0.169 x*y -0.0104 x +0.221 y^3 -0.294 y^2 +0.213 y -0.0594 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].