Random Gaussian cubic surface Seed: 213 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0585 x*z^2 -0.243 y*z^2 -0.0603 z^2 +0.12 x^2*z +0.0241 x*y*z -0.44 x*z +0.266 y^2*z +0.436 y*z +0.0377 z -0.229 x^3 -0.26 x^2*y -0.253 x^2 +0.201 x*y^2 +0.00809 x*y -0.164 x -0.316 y^3 -0.316 y^2 +0.106 y +0.0377 1
Affine cubic: f(x,y,z) = 0.0585 x*z^2 -0.243 y*z^2 -0.0603 z^2 +0.12 x^2*z +0.0241 x*y*z -0.44 x*z +0.266 y^2*z +0.436 y*z +0.0377 z -0.229 x^3 -0.26 x^2*y -0.253 x^2 +0.201 x*y^2 +0.00809 x*y -0.164 x -0.316 y^3 -0.316 y^2 +0.106 y +0.0377 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].