Random Gaussian cubic surface Seed: 37 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.184 x*z^2 -0.0937 y*z^2 -0.269 z^2 +0.135 x^2*z +0.195 x*y*z +0.107 x*z -0.523 y^2*z -0.314 y*z +0.125 z +0.305 x^3 -0.306 x^2*y +0.198 x^2 +0.229 x*y^2 +0.00356 x*y -0.274 x -0.131 y^3 -0.074 y^2 +0.141 y +0.184 1
Affine cubic: f(x,y,z) = 0.184 x*z^2 -0.0937 y*z^2 -0.269 z^2 +0.135 x^2*z +0.195 x*y*z +0.107 x*z -0.523 y^2*z -0.314 y*z +0.125 z +0.305 x^3 -0.306 x^2*y +0.198 x^2 +0.229 x*y^2 +0.00356 x*y -0.274 x -0.131 y^3 -0.074 y^2 +0.141 y +0.184 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].