Random Gaussian cubic surface Seed: 238 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.154 x*z^2 -0.471 y*z^2 +0.216 z^2 +0.247 x^2*z -0.335 x*y*z -0.0991 x*z +0.0851 y^2*z +0.341 y*z -0.0913 z -0.151 x^3 +0.0758 x^2*y +0.128 x^2 +0.451 x*y^2 +0.0231 x*y -0.0735 x +0.0148 y^3 -0.0447 y^2 +0.363 y -0.0683 1
Affine cubic: f(x,y,z) = 0.154 x*z^2 -0.471 y*z^2 +0.216 z^2 +0.247 x^2*z -0.335 x*y*z -0.0991 x*z +0.0851 y^2*z +0.341 y*z -0.0913 z -0.151 x^3 +0.0758 x^2*y +0.128 x^2 +0.451 x*y^2 +0.0231 x*y -0.0735 x +0.0148 y^3 -0.0447 y^2 +0.363 y -0.0683 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].