Random Gaussian cubic surface Seed: 110 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0672 x*z^2 +0.0363 y*z^2 +0.331 z^2 -0.00847 x^2*z -0.352 x*y*z -0.00247 x*z +0.139 y^2*z +0.322 y*z +0.501 z -0.361 x^3 -0.152 x^2*y -0.0425 x^2 +0.239 x*y^2 -0.0484 x*y -0.162 x -0.0596 y^3 -0.322 y^2 -0.167 y +0.104 1
Affine cubic: f(x,y,z) = 0.0672 x*z^2 +0.0363 y*z^2 +0.331 z^2 -0.00847 x^2*z -0.352 x*y*z -0.00247 x*z +0.139 y^2*z +0.322 y*z +0.501 z -0.361 x^3 -0.152 x^2*y -0.0425 x^2 +0.239 x*y^2 -0.0484 x*y -0.162 x -0.0596 y^3 -0.322 y^2 -0.167 y +0.104 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].