Random Gaussian cubic surface Seed: 61 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.116 x*z^2 -0.215 y*z^2 +0.216 z^2 -0.23 x^2*z -0.363 x*y*z +0.133 x*z +0.171 y^2*z -0.193 y*z -0.115 z +0.567 x^3 -0.207 x^2*y -0.103 x^2 +0.24 x*y^2 +0.152 x*y +0.328 x +0.167 y^3 -0.0831 y^2 +0.0241 y -0.112 1
Affine cubic: f(x,y,z) = -0.116 x*z^2 -0.215 y*z^2 +0.216 z^2 -0.23 x^2*z -0.363 x*y*z +0.133 x*z +0.171 y^2*z -0.193 y*z -0.115 z +0.567 x^3 -0.207 x^2*y -0.103 x^2 +0.24 x*y^2 +0.152 x*y +0.328 x +0.167 y^3 -0.0831 y^2 +0.0241 y -0.112 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].