Random Gaussian cubic surface Seed: 313 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0231 x*z^2 +0.265 y*z^2 -0.085 z^2 +0.0681 x^2*z -0.54 x*y*z -0.136 x*z +0.269 y^2*z -0.311 y*z +0.0465 z +0.266 x^3 -0.0476 x^2*y +0.212 x^2 -0.134 x*y^2 -0.382 x*y +0.215 x +0.225 y^3 +0.141 y^2 -0.0801 y -0.176 1
Affine cubic: f(x,y,z) = -0.0231 x*z^2 +0.265 y*z^2 -0.085 z^2 +0.0681 x^2*z -0.54 x*y*z -0.136 x*z +0.269 y^2*z -0.311 y*z +0.0465 z +0.266 x^3 -0.0476 x^2*y +0.212 x^2 -0.134 x*y^2 -0.382 x*y +0.215 x +0.225 y^3 +0.141 y^2 -0.0801 y -0.176 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].