document: An augmented spatial digital tree algorithm for contact detection in computational mechanics Based on the understanding of existing spatial digital tree-based contact detection approaches , and the alternating digital tree -LRB- ADT -RRB- algorithm in particular , a more efficient algorithm , termed the augmented spatial digital tree -LRB- ASDT -RRB- algorithm , is proposed in the present work . The ASDT algorithm adopts a different point representation scheme that uses only the lower comer vertex to represent a -LRB- hyper - -RRB- rectangle , with the upper comer vertex serving as the augmented information . Consequently , the ASDT algorithm can keep the working space the same as the original n-dimensional space and , in general , a much better balanced tree can be expected . This , together with the introduction of an additional bounding subregion for the rectangles associated with each tree node , makes it possible to significantly reduce the number of node visits in the region search , although each node visit may be slightly more expensive . Three examples arising in computational mechanics are presented to provide an assessment of the performance of the ASDT . The numerical results indicate that the ASDT is , at least , over 3.9 times faster than the ADT
doc_bio_tags: O B I I I I O B I O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: augmented spatial digital tree algorithm contact detection computational mechanics upper comer vertex
abstractive_keyphrases: alternating digital tree algorithm augmented data structure spatial binary tree-based contact detection approaches