Random Gaussian cubic surface Seed: 100 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.271 x*z^2 +0.0678 y*z^2 +0.183 z^2 +0.127 x^2*z -0.225 x*y*z +0.251 x*z +0.164 y^2*z +0.165 y*z +0.174 z +0.259 x^3 +0.525 x^2*y -0.143 x^2 +0.0111 x*y^2 +0.411 x*y -0.313 x +0.0762 y^3 -0.161 y^2 -0.00464 y +0.111 1
Affine cubic: f(x,y,z) = -0.271 x*z^2 +0.0678 y*z^2 +0.183 z^2 +0.127 x^2*z -0.225 x*y*z +0.251 x*z +0.164 y^2*z +0.165 y*z +0.174 z +0.259 x^3 +0.525 x^2*y -0.143 x^2 +0.0111 x*y^2 +0.411 x*y -0.313 x +0.0762 y^3 -0.161 y^2 -0.00464 y +0.111 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].