A new 3D-border algorithm by neighbor finding

The authors propose a new algorithm for finding the three-dimensional border of linear octrees stored in a one dimensional array. A simple method is proposed to check whether an octant is a border octant. Then, the border finding procedure can be carried out node by node according to their location code ordering. In order to improve the performance of the algorithm, a new and efficient neighbor finding technique is proposed. The time complexity of the proposed neighbor finding method is analyzed and proved to be O(1) on the average. Compared with the existing border algorithms, the proposed algorithm has the following advantages: (1) no preprocessing is required to arrange the input data according to their grouping factors, (2) the border found is already a sorted sequence of border voxels with no extra sorting required, and (3) the average time complexity is improved from O(N log N) to O(N), where N is the number of nodes in the linear octree