Random Gaussian cubic surface Seed: 452 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0927 x*z^2 +0.119 y*z^2 -0.0867 z^2 +0.0349 x^2*z -0.295 x*y*z +0.171 x*z +0.554 y^2*z -0.158 y*z -0.236 z +0.177 x^3 -0.346 x^2*y -0.076 x^2 -0.21 x*y^2 +0.141 x*y +0.381 x -0.112 y^3 +0.0342 y^2 -0.136 y +0.259 1
Affine cubic: f(x,y,z) = -0.0927 x*z^2 +0.119 y*z^2 -0.0867 z^2 +0.0349 x^2*z -0.295 x*y*z +0.171 x*z +0.554 y^2*z -0.158 y*z -0.236 z +0.177 x^3 -0.346 x^2*y -0.076 x^2 -0.21 x*y^2 +0.141 x*y +0.381 x -0.112 y^3 +0.0342 y^2 -0.136 y +0.259 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].