Random Gaussian cubic surface Seed: 372 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.151 x*z^2 +0.153 y*z^2 +0.135 z^2 +0.189 x^2*z +0.268 x*y*z +0.522 x*z +0.00778 y^2*z +0.0765 y*z +0.143 z +0.237 x^3 -0.0343 x^2*y +0.0328 x^2 +0.229 x*y^2 +0.0412 x*y -0.277 x +0.0726 y^3 -0.507 y^2 -0.188 y -0.206 1
Affine cubic: f(x,y,z) = 0.151 x*z^2 +0.153 y*z^2 +0.135 z^2 +0.189 x^2*z +0.268 x*y*z +0.522 x*z +0.00778 y^2*z +0.0765 y*z +0.143 z +0.237 x^3 -0.0343 x^2*y +0.0328 x^2 +0.229 x*y^2 +0.0412 x*y -0.277 x +0.0726 y^3 -0.507 y^2 -0.188 y -0.206 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].