Random Gaussian cubic surface Seed: 315 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.111 x*z^2 +0.0122 y*z^2 -0.18 z^2 +0.164 x^2*z +0.319 x*y*z +0.114 x*z -0.271 y^2*z -0.417 y*z -0.0343 z -0.307 x^3 -0.132 x^2*y -0.134 x^2 +0.284 x*y^2 -0.255 x*y -0.46 x -0.194 y^3 +0.147 y^2 +0.138 y -0.00381 1
Affine cubic: f(x,y,z) = 0.111 x*z^2 +0.0122 y*z^2 -0.18 z^2 +0.164 x^2*z +0.319 x*y*z +0.114 x*z -0.271 y^2*z -0.417 y*z -0.0343 z -0.307 x^3 -0.132 x^2*y -0.134 x^2 +0.284 x*y^2 -0.255 x*y -0.46 x -0.194 y^3 +0.147 y^2 +0.138 y -0.00381 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].