Enhanced unstructured points cloud subdivision applied for parallel Delaunay triangulation

Complex objects are omnipresent in different domains such as automotive, robotics, aeronautics, industrial design and medical. When such objects are no longer available, inexpensive similar or enhanced objects should be created; the Reverse Engineering is used to produce them from a points cloud by several methods. Delaunay triangulation is one of the oldest and most fundamental reconstruction methods. It consists of connecting the points to create the requested model. Three types of algorithms are used to build Delaunay triangulations: (i) Divide-and-conquer paradigm, (ii) Sweep line algorithms and (iii) Incremental insertion algorithms. With the appearance of machines with several processors, the Divide-and-conquer method has become very popular. It consists of splitting the points cloud into sub-clouds (partitions), triangulating the partitions independently of each other, and finally merging the sub-triangulations to obtain the solution. In this work, we are interested in the stage of splitting the points cloud. Several buckets or stripes splitting (partitioning) techniques have been proposed, such as octree and cells partitioning. So far, the best method for partitioning a points set into subsets with appropriate sizes has not been developed. To face this issue, this paper deals with partitioning the part space represented by the points cloud into regions via pooling points into sub-sets. For this purpose, the Basic K-means (BK) method and its derivative method, the Fast Global K-means (FGK), have been introduced for the first time in this research field. Obtained partitions, points sub-cloud, are divided over the processor cores. Independently, these partitions are further triangulated simultaneously by parallelizing the computations on several processors to improve the load balance and thus reduce the processing times. Finally, these methods are evaluated on a non-uniform points cloud to demonstrate their performances. Further, a comparative study is established to determine the most appropriate partitioning method. Results demonstrated that FGK achieved better performances in terms of partitions homogeneity, balanced workload at different processors, and consequently on the computation times compared to cell, octree and BK methods.