Random Gaussian cubic surface Seed: 327 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0278 x*z^2 -0.12 y*z^2 -0.198 z^2 -0.0272 x^2*z +0.0687 x*y*z -0.201 x*z +0.336 y^2*z +0.139 y*z +0.00628 z +0.22 x^3 +0.451 x^2*y -0.17 x^2 -0.0243 x*y^2 +0.201 x*y +0.0367 x -0.038 y^3 -0.654 y^2 -0.12 y -0.00344 1
Affine cubic: f(x,y,z) = 0.0278 x*z^2 -0.12 y*z^2 -0.198 z^2 -0.0272 x^2*z +0.0687 x*y*z -0.201 x*z +0.336 y^2*z +0.139 y*z +0.00628 z +0.22 x^3 +0.451 x^2*y -0.17 x^2 -0.0243 x*y^2 +0.201 x*y +0.0367 x -0.038 y^3 -0.654 y^2 -0.12 y -0.00344 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].