Fast and Efficient Calculations of Structural Invariants of Chirality

Abstract: 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.