Random Gaussian cubic surface Seed: 196 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0265 x*z^2 +0.17 y*z^2 +0.378 z^2 -0.209 x^2*z -0.464 x*y*z +0.0648 x*z -0.372 y^2*z -0.145 y*z -0.348 z +0.296 x^3 -0.184 x^2*y +0.24 x^2 +0.0784 x*y^2 -0.12 x*y -0.146 x +0.108 y^3 -0.103 y^2 +0.199 y -0.0307 1
Affine cubic: f(x,y,z) = -0.0265 x*z^2 +0.17 y*z^2 +0.378 z^2 -0.209 x^2*z -0.464 x*y*z +0.0648 x*z -0.372 y^2*z -0.145 y*z -0.348 z +0.296 x^3 -0.184 x^2*y +0.24 x^2 +0.0784 x*y^2 -0.12 x*y -0.146 x +0.108 y^3 -0.103 y^2 +0.199 y -0.0307 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].