We study the problem of merging three-dimensional points that are nearby or coincident. We introduce a fast, efficient approach that uses data parallel techniques for execution in various shared-memory environments. Our technique incorporates a heuristic for efficiently clustering spatially close points together, which is one reason our method performs well against other methods. We then compare our approach against methods of a widely-used scientific visualization library accompanied by a performance study that shows our approach works well with different kinds of parallel hardware (many-core CPUs and NVIDIA GPUs) and data sets of various sizes