Random Gaussian cubic surface Seed: 76 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.126 x*z^2 +0.386 y*z^2 +0.216 z^2 +0.112 x^2*z +0.236 x*y*z -0.344 x*z +0.138 y^2*z +0.316 y*z +0.306 z -0.343 x^3 -0.196 x^2*y +0.1 x^2 +0.0725 x*y^2 -0.166 x*y +0.273 x -0.00841 y^3 -0.0303 y^2 -0.0959 y +0.325 1
Affine cubic: f(x,y,z) = -0.126 x*z^2 +0.386 y*z^2 +0.216 z^2 +0.112 x^2*z +0.236 x*y*z -0.344 x*z +0.138 y^2*z +0.316 y*z +0.306 z -0.343 x^3 -0.196 x^2*y +0.1 x^2 +0.0725 x*y^2 -0.166 x*y +0.273 x -0.00841 y^3 -0.0303 y^2 -0.0959 y +0.325 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].