The recent emergence of LiDAR scanning technology has resulted in the availability of very large three dimensional point cloud data sets. An example of such a data set is the AHN2 data set, which contains a high-density point cloud for the Netherlands. The direct visualization of these point cloud data sets is important because it provides the first step in understanding them. However, the size of these data sets prevents them from simply being displayed, let alone from being explored interactively. As such, they present a challenge in visualization. In this thesis, we describe the methods used by earlier works to beat this challenge. These methods involve the use of space driven spatial data structures to provide efficient out-of-core access to the point cloud data set, and the alleviation of one or more of the bottlenecks in the point cloud visualization pipeline to improve interactiveness. Choosing to use a different approach, we present a method to interactively visualize these point cloud data sets using the concept of visualization on a budget. We reduce the complexity of a point cloud visualization by using continuous level-of-detail, and we minimize its impact on the effectiveness of the visualization by using a point analogue of visual importance, for which we present a metric. The complexity of the visualization is automatically adapted to maintain interactiveness. As a result, the visualization always consists of those points that, for a given metric, best represent the point cloud data set for the required interactiveness. We present a prototype toolchain that includes the implementation of our method and demonstrate its performance on a variety of point cloud data sets. We describe its performance characteristics and present a preliminary user study for the method. We evaluate initial results and conclude that our method works, and propose the development of a better metric that does not require user intervention. We end by showing that the prototype toolchain can be used to continue research on this promising method.