  Chirality plays an important role in physics, chemistry, biology, and other
fields. It describes an essential symmetry in structure. However, chirality
invariants are usually complicated in expression or difficult to evaluate. In
this paper, we present five general three-dimensional chirality invariants
based on the generating functions. And the five chiral invariants have four
characteristics:(1) They play an important role in the detection of symmetry,
especially in the treatment of 'false zero' problem. (2) Three of the five
chiral invariants decode an universal chirality index. (3) Three of them are
proposed for the first time. (4) The five chiral invariants have low order no
bigger than 4, brief expression, low time complexity O(n) and can act as
descriptors of three-dimensional objects in shape analysis. The five chiral
invariants give a geometric view to study the chiral invariants. And the
experiments show that the five chirality invariants are effective and
efficient, they can be used as a tool for symmetry detection or features in
shape analysis.
