Random Gaussian cubic surface Seed: 298 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0381 x*z^2 +0.454 y*z^2 +0.251 z^2 -0.168 x^2*z +0.119 x*y*z -0.135 x*z +0.105 y^2*z -0.0757 y*z -0.164 z +0.0817 x^3 +0.393 x^2*y -0.298 x^2 -0.0931 x*y^2 -0.0216 x*y +0.192 x -0.246 y^3 -0.181 y^2 -0.456 y +0.169 1
Affine cubic: f(x,y,z) = 0.0381 x*z^2 +0.454 y*z^2 +0.251 z^2 -0.168 x^2*z +0.119 x*y*z -0.135 x*z +0.105 y^2*z -0.0757 y*z -0.164 z +0.0817 x^3 +0.393 x^2*y -0.298 x^2 -0.0931 x*y^2 -0.0216 x*y +0.192 x -0.246 y^3 -0.181 y^2 -0.456 y +0.169 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 15 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].