Random Gaussian cubic surface Seed: 306 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.181 x*z^2 -0.113 y*z^2 -0.0563 z^2 -0.43 x^2*z +0.406 x*y*z -0.248 x*z +0.262 y^2*z +0.0488 y*z -0.0375 z -0.0299 x^3 -0.152 x^2*y -0.112 x^2 -0.145 x*y^2 +0.489 x*y -0.0527 x +0.147 y^3 +0.254 y^2 +0.284 y +0.0283 1
Affine cubic: f(x,y,z) = -0.181 x*z^2 -0.113 y*z^2 -0.0563 z^2 -0.43 x^2*z +0.406 x*y*z -0.248 x*z +0.262 y^2*z +0.0488 y*z -0.0375 z -0.0299 x^3 -0.152 x^2*y -0.112 x^2 -0.145 x*y^2 +0.489 x*y -0.0527 x +0.147 y^3 +0.254 y^2 +0.284 y +0.0283 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].