Fast, optimal, and reproducible clustering algorithms for circular, periodic, or framed data. The algorithms introduced here are based on a core algorithm for optimal framed clustering the authors have developed (under review). The runtime of these algorithms is O(K N log^2 N), where K is the number of clusters and N is the number of circular data points. On a desktop computer using a single processor core, millions of data points can be grouped into a few clusters within seconds. One can apply the algorithms to characterize events along circular DNA molecules, circular RNA molecules, and circular genomes of bacteria, chloroplast, and mitochondria. One can also cluster climate data along any given longitude or latitude. Periodic data clustering can be formulated as circular clustering. The algorithms offer a general high-performance solution to circular, periodic, or framed data clustering.