Random Gaussian cubic surface Seed: 198 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.202 x*z^2 -0.316 y*z^2 +0.372 z^2 -0.568 x^2*z +0.131 x*y*z +0.0615 x*z +0.158 y^2*z -0.281 y*z -0.0477 z +0.282 x^3 -0.0556 x^2*y -0.115 x^2 -0.0801 x*y^2 -0.00389 x*y +0.162 x -0.29 y^3 -0.0776 y^2 +0.231 y +0.0138 1
Affine cubic: f(x,y,z) = -0.202 x*z^2 -0.316 y*z^2 +0.372 z^2 -0.568 x^2*z +0.131 x*y*z +0.0615 x*z +0.158 y^2*z -0.281 y*z -0.0477 z +0.282 x^3 -0.0556 x^2*y -0.115 x^2 -0.0801 x*y^2 -0.00389 x*y +0.162 x -0.29 y^3 -0.0776 y^2 +0.231 y +0.0138 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].