Random Gaussian cubic surface Seed: 373 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.169 x*z^2 -0.108 y*z^2 -0.196 z^2 -0.218 x^2*z -0.467 x*y*z -0.0645 x*z +0.465 y^2*z +0.0408 y*z +0.066 z -0.011 x^3 +0.173 x^2*y -0.368 x^2 +0.195 x*y^2 -0.0754 x*y +0.0754 x +0.132 y^3 +0.337 y^2 -0.285 y +0.0527 1
Affine cubic: f(x,y,z) = 0.169 x*z^2 -0.108 y*z^2 -0.196 z^2 -0.218 x^2*z -0.467 x*y*z -0.0645 x*z +0.465 y^2*z +0.0408 y*z +0.066 z -0.011 x^3 +0.173 x^2*y -0.368 x^2 +0.195 x*y^2 -0.0754 x*y +0.0754 x +0.132 y^3 +0.337 y^2 -0.285 y +0.0527 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].