Random Gaussian cubic surface Seed: 173 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.236 x*z^2 -0.0207 y*z^2 +0.0551 z^2 -0.428 x^2*z -0.316 x*y*z -0.0335 x*z +0.202 y^2*z +0.236 y*z +0.0528 z -0.5 x^3 +0.122 x^2*y -0.112 x^2 -0.0367 x*y^2 +0.248 x*y +0.0271 x +0.25 y^3 +0.322 y^2 +0.0104 y +0.223 1
Affine cubic: f(x,y,z) = 0.236 x*z^2 -0.0207 y*z^2 +0.0551 z^2 -0.428 x^2*z -0.316 x*y*z -0.0335 x*z +0.202 y^2*z +0.236 y*z +0.0528 z -0.5 x^3 +0.122 x^2*y -0.112 x^2 -0.0367 x*y^2 +0.248 x*y +0.0271 x +0.25 y^3 +0.322 y^2 +0.0104 y +0.223 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].