  A twisting system is one of the major tools to study graded algebras,
however, it is often difficult to construct a (non-algebraic) twisting system
if a graded algebra is given by generators and relations. In this paper, we
show that a twisted algebra of a geometric algebra is determined by a certain
automorphism of its point variety. As an application, we classify twisted
algebras of $3$-dimensional geometric Artin-Schelter regular algebras up to
graded algebra isomorphism.
