Random Gaussian cubic surface Seed: 286 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.231 x*z^2 +0.0758 y*z^2 +0.423 z^2 +0.154 x^2*z -0.0424 x*y*z +0.54 x*z -0.0426 y^2*z +0.0218 y*z +0.0425 z -0.114 x^3 +0.525 x^2*y +0.0143 x^2 +0.0374 x*y^2 -0.146 x*y -0.168 x -0.2 y^3 -0.0739 y^2 -0.15 y +0.182 1
Affine cubic: f(x,y,z) = 0.231 x*z^2 +0.0758 y*z^2 +0.423 z^2 +0.154 x^2*z -0.0424 x*y*z +0.54 x*z -0.0426 y^2*z +0.0218 y*z +0.0425 z -0.114 x^3 +0.525 x^2*y +0.0143 x^2 +0.0374 x*y^2 -0.146 x*y -0.168 x -0.2 y^3 -0.0739 y^2 -0.15 y +0.182 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].