Random Gaussian cubic surface Seed: 175 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.112 x*z^2 +0.0208 y*z^2 +0.203 z^2 -0.0659 x^2*z +0.413 x*y*z +0.0693 x*z -0.143 y^2*z +0.126 y*z -0.0018 z -0.173 x^3 -0.224 x^2*y +0.0332 x^2 +0.111 x*y^2 +0.425 x*y -0.157 x +0.461 y^3 +0.415 y^2 -0.00457 y +0.213 1
Affine cubic: f(x,y,z) = 0.112 x*z^2 +0.0208 y*z^2 +0.203 z^2 -0.0659 x^2*z +0.413 x*y*z +0.0693 x*z -0.143 y^2*z +0.126 y*z -0.0018 z -0.173 x^3 -0.224 x^2*y +0.0332 x^2 +0.111 x*y^2 +0.425 x*y -0.157 x +0.461 y^3 +0.415 y^2 -0.00457 y +0.213 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].