Random Gaussian cubic surface Seed: 14 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.115 x*z^2 -0.162 y*z^2 -0.26 z^2 -0.483 x^2*z -0.0584 x*y*z +0.206 x*z +0.00547 y^2*z +0.0846 y*z +0.169 z -0.146 x^3 +0.438 x^2*y -0.145 x^2 +0.0617 x*y^2 +0.453 x*y -0.0189 x +0.0189 y^3 -0.0846 y^2 +0.0553 y -0.351 1
Affine cubic: f(x,y,z) = 0.115 x*z^2 -0.162 y*z^2 -0.26 z^2 -0.483 x^2*z -0.0584 x*y*z +0.206 x*z +0.00547 y^2*z +0.0846 y*z +0.169 z -0.146 x^3 +0.438 x^2*y -0.145 x^2 +0.0617 x*y^2 +0.453 x*y -0.0189 x +0.0189 y^3 -0.0846 y^2 +0.0553 y -0.351 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].