Random Gaussian cubic surface Seed: 386 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.435 x*z^2 +0.359 y*z^2 +0.0884 z^2 -0.102 x^2*z -0.0909 x*y*z +0.142 x*z +0.00708 y^2*z -0.044 y*z +0.315 z -0.186 x^3 +0.257 x^2*y -0.0734 x^2 +0.202 x*y^2 -0.5 x*y +0.251 x -0.000968 y^3 -0.186 y^2 -0.155 y -0.123 1
Affine cubic: f(x,y,z) = -0.435 x*z^2 +0.359 y*z^2 +0.0884 z^2 -0.102 x^2*z -0.0909 x*y*z +0.142 x*z +0.00708 y^2*z -0.044 y*z +0.315 z -0.186 x^3 +0.257 x^2*y -0.0734 x^2 +0.202 x*y^2 -0.5 x*y +0.251 x -0.000968 y^3 -0.186 y^2 -0.155 y -0.123 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].