Random Gaussian cubic surface Seed: 186 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0567 x*z^2 -0.0634 y*z^2 +0.342 z^2 +0.25 x^2*z +0.182 x*y*z -0.187 x*z +0.0214 y^2*z +0.0286 y*z -0.434 z -0.00198 x^3 +0.0808 x^2*y +0.0564 x^2 -0.0182 x*y^2 -0.306 x*y -0.202 x -0.186 y^3 -0.377 y^2 +0.0248 y -0.485 1
Affine cubic: f(x,y,z) = -0.0567 x*z^2 -0.0634 y*z^2 +0.342 z^2 +0.25 x^2*z +0.182 x*y*z -0.187 x*z +0.0214 y^2*z +0.0286 y*z -0.434 z -0.00198 x^3 +0.0808 x^2*y +0.0564 x^2 -0.0182 x*y^2 -0.306 x*y -0.202 x -0.186 y^3 -0.377 y^2 +0.0248 y -0.485 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].