next surface previous surface 2D curves 3D curves surfaces fractals polyhedra

BISPHERICAL ALGEBRAIC SURFACE



An algebraic surface is said to be bispherical if the umbilics (i.e. the points at infinity of the complex sphere with zero radius ) form a double line, in the complex projective completion of the space.
The necessary and sufficient condition is that the polynomial composed of the terms with highest degree n of its Cartesian equation be divisible by and that the polynomial composed of the terms of with degree n - 1 be divisible by .

The bispherical quartics are the Darboux cyclides.
 
 
next surface previous surface 2D curves 3D curves surfaces fractals polyhedra

© Robert FERRÉOL 2017