Random Gaussian cubic surface Seed: 456 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.164 x*z^2 -0.388 y*z^2 +0.3 z^2 -0.00645 x^2*z -0.475 x*y*z -0.0347 x*z -0.121 y^2*z -0.0757 y*z -0.0534 z +0.355 x^3 +0.184 x^2*y +0.098 x^2 -0.0695 x*y^2 +0.107 x*y +0.339 x +0.184 y^3 +0.148 y^2 -0.158 y +0.318 1
Affine cubic: f(x,y,z) = 0.164 x*z^2 -0.388 y*z^2 +0.3 z^2 -0.00645 x^2*z -0.475 x*y*z -0.0347 x*z -0.121 y^2*z -0.0757 y*z -0.0534 z +0.355 x^3 +0.184 x^2*y +0.098 x^2 -0.0695 x*y^2 +0.107 x*y +0.339 x +0.184 y^3 +0.148 y^2 -0.158 y +0.318 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].