Fast and Efficient Calculations of Structural Invariants of Chirality
This work addresses the challenge of computing chirality invariants in fields like physics and chemistry, but it appears incremental as it builds on existing generating functions to propose new invariants.
The paper tackled the problem of complex and difficult-to-evaluate chirality invariants by presenting five general three-dimensional chirality invariants with low order (no bigger than 4), brief expression, and low time complexity O(n), which are shown to be effective and efficient in experiments for symmetry detection and shape analysis.
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.