Random Gaussian cubic surface Seed: 218 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.304 x*z^2 -0.23 y*z^2 +0.171 z^2 +0.0232 x^2*z +0.0584 x*y*z -0.0386 x*z +0.204 y^2*z -0.411 y*z -0.339 z -0.21 x^3 +0.265 x^2*y -0.376 x^2 -0.219 x*y^2 -0.0296 x*y -0.285 x +0.0414 y^3 +0.112 y^2 +0.145 y -0.272 1
Affine cubic: f(x,y,z) = 0.304 x*z^2 -0.23 y*z^2 +0.171 z^2 +0.0232 x^2*z +0.0584 x*y*z -0.0386 x*z +0.204 y^2*z -0.411 y*z -0.339 z -0.21 x^3 +0.265 x^2*y -0.376 x^2 -0.219 x*y^2 -0.0296 x*y -0.285 x +0.0414 y^3 +0.112 y^2 +0.145 y -0.272 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].