Random Gaussian cubic surface Seed: 495 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.451 x*z^2 +0.268 y*z^2 +0.105 z^2 +0.41 x^2*z -0.222 x*y*z -0.05 x*z +0.0185 y^2*z +0.254 y*z +0.245 z +0.00786 x^3 -0.00346 x^2*y +0.125 x^2 +0.122 x*y^2 +0.306 x*y +0.0656 x -0.166 y^3 +0.149 y^2 -0.266 y +0.347 1
Affine cubic: f(x,y,z) = -0.451 x*z^2 +0.268 y*z^2 +0.105 z^2 +0.41 x^2*z -0.222 x*y*z -0.05 x*z +0.0185 y^2*z +0.254 y*z +0.245 z +0.00786 x^3 -0.00346 x^2*y +0.125 x^2 +0.122 x*y^2 +0.306 x*y +0.0656 x -0.166 y^3 +0.149 y^2 -0.266 y +0.347 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].