  We introduce the notion of the twisted Segre product $A\circ_\psi B$ of
$\mathbb Z$-graded algebras $A$ and $B$ with respect to a twisting map $\psi$.
It is proved that if $A$ and $B$ are noetherian Koszul Artin-Schelter regular
algebras and $\psi$ is a twisting map such that the twisted Segre product
$A\circ_\psi B$ is noetherian, then $A\circ_\psi B$ is a noncommutative graded
isolated singularity. To prove this result, the notion of densely (bi-)graded
algebras is introduced. Moreover, we show that the twisted Segre product
$A\circ_\psi B$ of $A=k[u,v]$ and $B=k[x,y]$ with respect to a diagonal
twisting map $\psi$ is a noncommutative quadric surface (so in particular it is
noetherian), and we compute the stable category of graded maximal
Cohen-Macaulay modules over it.
