Mapped Regular Pavings

Abstract: Regular pavings are based on the concept of using tree structures to represent partitions of root boxes. Regular pavings can be extended into mapped regular pavings where root boxes are mapped tofunctions or sets, which can be used for ecient algorithms in simulations, calculations and other applications. The algorithms rely on a binary tree structures which makes them ecient and intuitive touse. Mapped regular pavings are exible in how precise the approximation is and at the same time balance that with the memory usage. Increasing the partitioning of the root box will increase the precisionof the approximation but will also require a tree with more branches, requiring more memory and longer computations.