<p>Data extraction algorithms on data hypercubes, or datacubes, are traditionally only capable of cutting boxes of data along the datacube axes. For many use cases however, this returns much more data than users actually need, leading to an unnecessary consumption of I/O resources. In this paper, we propose an alternative feature extraction technique, which carefully computes the indices of data points contained within user-requested shapes. This enables data storage systems to only read and return bytes useful to user applications from the datacube. Our main algorithm is based on high-dimensional computational geometry concepts and operates by successively reducing polytopes down to the points contained within them. We analyse this algorithm in detail before providing results about its performance and scalability. In particular, we show it is possible to achieve data reductions of up to 99% using this algorithm instead of current state of practice data extraction methods, such as meteorological field extractions from ECMWF’s FDB data store, where feature shapes are extracted a posteriori as a post-processing step. As we discuss later on, this novel extraction method will considerably help scale access to large petabyte size data hypercubes in a variety of scientific fields.</p>