Random Gaussian cubic surface Seed: 275 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.151 x*z^2 +0.296 y*z^2 +0.07 z^2 -0.0998 x^2*z +0.0188 x*y*z -0.087 x*z -0.149 y^2*z +0.0745 y*z +0.133 z +0.189 x^3 +0.0975 x^2*y +0.7 x^2 +0.286 x*y^2 -0.0147 x*y +0.109 x +0.0183 y^3 +0.0837 y^2 -0.377 y +0.205 1
Affine cubic: f(x,y,z) = -0.151 x*z^2 +0.296 y*z^2 +0.07 z^2 -0.0998 x^2*z +0.0188 x*y*z -0.087 x*z -0.149 y^2*z +0.0745 y*z +0.133 z +0.189 x^3 +0.0975 x^2*y +0.7 x^2 +0.286 x*y^2 -0.0147 x*y +0.109 x +0.0183 y^3 +0.0837 y^2 -0.377 y +0.205 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].