Random Gaussian cubic surface Seed: 153 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.428 x*z^2 +0.13 y*z^2 +0.192 z^2 +0.216 x^2*z +0.0184 x*y*z -0.315 x*z +0.0369 y^2*z +0.329 y*z -0.182 z +0.0411 x^3 +0.169 x^2*y -0.218 x^2 +0.26 x*y^2 -0.213 x*y -0.0194 x -0.311 y^3 +0.0342 y^2 -0.427 y +0.0465 1
Affine cubic: f(x,y,z) = 0.428 x*z^2 +0.13 y*z^2 +0.192 z^2 +0.216 x^2*z +0.0184 x*y*z -0.315 x*z +0.0369 y^2*z +0.329 y*z -0.182 z +0.0411 x^3 +0.169 x^2*y -0.218 x^2 +0.26 x*y^2 -0.213 x*y -0.0194 x -0.311 y^3 +0.0342 y^2 -0.427 y +0.0465 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].