= Quadric surface
{title2=$x^TAx+b^Tx+c=0$}
A quadric surface in three-dimensional <Euclidean space> is the zero set of a real <polynomial> of degree two. Its quadratic part can be written with a <symmetric matrix> $A$, since the <antisymmetric matrix> part contributes zero to $x^TAx$. An <orthogonal diagonalization> and a <translation> expose its geometry: examples include an <ellipsoid>, an <elliptic cone>, and a <hyperboloid>. This affine geometric description allows singular surfaces such as a cone's vertex.
Back to article page
