Random Gaussian cubic surface Seed: 205 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0681 x*z^2 +0.362 y*z^2 +0.364 z^2 +0.105 x^2*z +0.0792 x*y*z -0.0115 x*z +0.123 y^2*z +0.213 y*z +0.0211 z +0.29 x^3 +0.0615 x^2*y +0.166 x^2 -0.353 x*y^2 +0.399 x*y -0.0626 x +0.184 y^3 -0.16 y^2 +0.434 y -0.0446 1
Affine cubic: f(x,y,z) = -0.0681 x*z^2 +0.362 y*z^2 +0.364 z^2 +0.105 x^2*z +0.0792 x*y*z -0.0115 x*z +0.123 y^2*z +0.213 y*z +0.0211 z +0.29 x^3 +0.0615 x^2*y +0.166 x^2 -0.353 x*y^2 +0.399 x*y -0.0626 x +0.184 y^3 -0.16 y^2 +0.434 y -0.0446 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].