Random Gaussian cubic surface Seed: 99 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0221 x*z^2 -0.124 y*z^2 +0.0135 z^2 +0.184 x^2*z -0.471 x*y*z +0.451 x*z -0.123 y^2*z -0.16 y*z -0.281 z +0.25 x^3 +0.181 x^2*y +0.334 x^2 +0.239 x*y^2 +0.0705 x*y +0.088 x +0.251 y^3 -0.235 y^2 -0.0123 y +0.102 1
Affine cubic: f(x,y,z) = 0.0221 x*z^2 -0.124 y*z^2 +0.0135 z^2 +0.184 x^2*z -0.471 x*y*z +0.451 x*z -0.123 y^2*z -0.16 y*z -0.281 z +0.25 x^3 +0.181 x^2*y +0.334 x^2 +0.239 x*y^2 +0.0705 x*y +0.088 x +0.251 y^3 -0.235 y^2 -0.0123 y +0.102 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].