Random Gaussian cubic surface Seed: 304 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.263 x*z^2 -0.0784 y*z^2 -0.0169 z^2 +0.00624 x^2*z -0.109 x*y*z -0.134 x*z +0.0857 y^2*z -0.0192 y*z +0.264 z +0.0826 x^3 -0.0415 x^2*y +0.0263 x^2 +0.254 x*y^2 +0.169 x*y -0.273 x -0.0536 y^3 +0.399 y^2 +0.0638 y -0.689 1
Affine cubic: f(x,y,z) = -0.263 x*z^2 -0.0784 y*z^2 -0.0169 z^2 +0.00624 x^2*z -0.109 x*y*z -0.134 x*z +0.0857 y^2*z -0.0192 y*z +0.264 z +0.0826 x^3 -0.0415 x^2*y +0.0263 x^2 +0.254 x*y^2 +0.169 x*y -0.273 x -0.0536 y^3 +0.399 y^2 +0.0638 y -0.689 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].