Symmetry Finding Algorithms

TL;DR: It is shown that symmetries of objects, and hence of closed boundaries, translate into simple structures in the invariant signature functions and are therefore, in principle, readily detectable.

TL;DR: The authors view symmetry as a continuous feature, and define a continuous symmetry measure (CSM) of shapes that is associated with the symmetric shape that is closest to the given one, enabling visual evaluation of the CSM.

TL;DR: A new method for symmetry detection, which uses the comparison of face loops has been devised, which proves to be an effective technique for the detection of symmetry, which also satisfies the requirements of the particular application.

TL;DR: A simple and efficient general algorithm for determining both rotational and involutional symmetries of polyhedra and it is shown that a slight modification of the symmetry detection algorithm can be used to solve the related conguity problem ofpolyhedra.

TL;DR: An algorithm is presented which finds all occurrences of one given string within another, in running time proportional to the sum of the lengths of the strings, showing that the set of concatenations of even palindromes, i.e., the language $\{\alpha \alpha ^R\}^*$, can be recognized in linear time.

TL;DR: All the apparently known lower bounds for linear decision trees are extended to bounded degree algebraic decision trees, thus answering the open questions raised by Steele and Yao [20].

TL;DR: The time bound for planar graph isomorphism is improved to O(|V|) time and the algorithm can be easily extended to partition a set of planar graphs into equivalence classes of isomorphic graphs in time linear in the total number of vertices in all graphs in the set.

TL;DR: Exact algorithms for detecting all rotational and involutional symmetries in point sets, polygons and polyhedra are described and are shown to be optimal in time complexity, within constants.