Testing for uniformity in multidimensional data is important in exploratory pattern analysis, statistical pattern recognition, and image processing. The goal of this paper is to determine whether the data follow the uniform distribution over some compact convex set in K-dimensional space, called the sampling window. We first provide a simple, computationally efficient method for generating a uniformly distributed sample over a set which approximates the convex hul of the data. We then test for uniformity by comparing this generated sample to the data by using Friedman-Rafsky's minimal spanning tree (MST) based test. Experiments with both simulated and real data indicate that this MST-based test is useful in deciding if data are uniform.