Fast and Efficient Calculations of Structural Invariants of Chirality

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 which are called ShapeDNA. And the five chiral invariants have three characteristics: 1) Three of the five chiral invariants decode the universal chirality index G0 in specified circumstance. 2) Three of them are proposed for the first time. 3) The five chiral invariants have low order (≤ 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.