Random Gaussian cubic surface Seed: 131 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0126 x*z^2 +0.225 y*z^2 -0.11 z^2 -0.0763 x^2*z +0.357 x*y*z +0.17 x*z -0.0544 y^2*z +0.145 y*z -0.0154 z +0.0138 x^3 +0.0728 x^2*y -0.231 x^2 -0.249 x*y^2 -0.00911 x*y +0.475 x +0.235 y^3 -0.0899 y^2 -0.453 y +0.369 1
Affine cubic: f(x,y,z) = -0.0126 x*z^2 +0.225 y*z^2 -0.11 z^2 -0.0763 x^2*z +0.357 x*y*z +0.17 x*z -0.0544 y^2*z +0.145 y*z -0.0154 z +0.0138 x^3 +0.0728 x^2*y -0.231 x^2 -0.249 x*y^2 -0.00911 x*y +0.475 x +0.235 y^3 -0.0899 y^2 -0.453 y +0.369 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].