Affine cubic: f(x,y,z) = 0.237 y*z^2 -0.354 z^2 +0.404 x^2*z -0.0609 x*y*z -0.135 x*z +0.164 y^2*z +0.093 y*z -0.202 z +0.129 x^3 -0.26 x^2*y +0.246 x^2 +0.0112 x*y^2 +0.0194 x*y -0.122 x +0.19 y^3 -0.106 y^2 -0.348 y -0.478 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].