The space-filling visualization model was first invented by Ben Shneiderman [28] for maximizing the utilization of display space in relational data (or graph) visualization, especially for tree visualization. It uses the concept of Enclosure which dismisses the "edges" in the graphic representation that are all too frequently used in traditional node-link based graph visualizations. Therefore, the major issue in graph visualization which is the edge crossing can be naturally solved through the adoption of a space filling approach. However in the past, the space-filling concept has not attracted much attention from researchers in the field of multidimensional visualization. Although the problem of 'edge crossing' has also occurred among polylines which are used as the basic visual elements in the parallel coordinates visualization, it is problematic if those 'edge crossings' among polylines are not evenly distributed on the display plate as visual clutter will occur. This problem could significantly reduce the human readability in terms of reviewing a particular region of the visualization. In this study, we propose a new Space-Filling Multidimensional Data Visualization (SFMDVis) that for the first-time introduces a space-filling approach into multidimensional data visualization. The main contributions are: (1) achieving the maximization of space utilization in multidimensional visualization (i.e. 100% of the display area is fully used), (2) eliminating visual clutter in SFMDVis through the use of the non-classic geometric primitive and (3) improving the quality of visualization for the visual perception of linear correlations among different variables as well as recognizing data patterns. To evaluate the quality of SFMDVis, we have conducted a usability study to measure the performance of SFMDVis in comparison with parallel coordinates and a scatterplot matrix for finding linear correlations and data patterns. The evaluation results have suggested that the accuracy of SFMDVis is better than both in terms of perceiving linear correlations and also that the SFMDVis is more efficient (less time is required) than both when recognizing data patterns. 2015 Elsevier Inc. (C) All rights reserved.