Random Gaussian cubic surface Seed: 247 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0149 x*z^2 -0.175 y*z^2 +0.366 z^2 -0.185 x^2*z +0.202 x*y*z +0.114 x*z +0.0289 y^2*z -0.0184 y*z -0.0103 z -0.0212 x^3 +0.143 x^2*y -0.109 x^2 -0.175 x*y^2 -0.167 x*y -0.0625 x -0.162 y^3 -0.315 y^2 +0.394 y +0.609 1
Affine cubic: f(x,y,z) = -0.0149 x*z^2 -0.175 y*z^2 +0.366 z^2 -0.185 x^2*z +0.202 x*y*z +0.114 x*z +0.0289 y^2*z -0.0184 y*z -0.0103 z -0.0212 x^3 +0.143 x^2*y -0.109 x^2 -0.175 x*y^2 -0.167 x*y -0.0625 x -0.162 y^3 -0.315 y^2 +0.394 y +0.609 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].