James T. Klosowski

Efficient collision detection using bounding volume hierarchies of k-DOPs

Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at real-time rates. Applications such as haptic force feedback can require over 1000 collision queries per second. We develop and analyze a method, based on bounding-volume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a discrete orientation polytope (k-DOP), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies (BV-trees) of bounding k-DOPs. Further, we propose algorithms for maintaining an effective BV-tree of k-DOPs for moving objects, as they rotate, and for performing fast collision detection using BV-trees of the moving objects and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods.

Nanocubes for Real-Time Exploration of Spatiotemporal Datasets

Consider real-time exploration of large multidimensional spatiotemporal datasets with billions of entries, each defined by a location, a time, and other attributes. Are certain attributes correlated spatially or temporally? Are there trends or outliers in the data? Answering these questions requires aggregation over arbitrary regions of the domain and attributes of the data. Many relational databases implement the well-known data cube aggregation operation, which in a sense precomputes every possible aggregate query over the database. Data cubes are sometimes assumed to take a prohibitively large amount of space, and to consequently require disk storage. In contrast, we show how to construct a data cube that fits in a modern laptops main memory, even for billions of entries; we call this data structure a nanocube. We present algorithms to compute and query a nanocube, and show how it can be used to generate well-known visual encodings such as heatmaps, histograms, and parallel coordinate plots. When compared to exact visualizations created by scanning an entire dataset, nanocube plots have bounded screen error across a variety of scales, thanks to a hierarchical structure in space and time. We demonstrate the effectiveness of our technique on a variety of real-world datasets, and present memory, timing, and network bandwidth measurements. We find that the timings for the queries in our examples are dominated by network and user-interaction latencies.

Geometric algorithms for conflict detection/resolution in air traffic management

We consider the problems of conflict detection and resolution in air traffic management (ATM) from the perspective of computational geometry and give algorithms for solving these problems efficiently. For conflict resolution, we propose a simple method that can route multiple aircraft, conflict-free, through a cluttered airspace, using a prioritized routing scheme in space-time. Our algorithms have been implemented into a simulation system that tracks a large set of flights, having multiple conflicts, and proposes modified routes to resolve them. We report on the preliminary results from an extensive set of experiments that are under may to determine the effectiveness of our methods.

Collision detection for fly-throughs in virtual environments

Real-time collision detection is of criticaJ importance in physical simulations and in interactive use of virtual environments. For example, the goal of one application in the aircraft industry is to let mechanics verify the serviceability of an aircraft in a VR environment (CAD model of the aircraft), rather than on a full-scale physical mock-up. Wearing a sensor-laden suit, they should be able to test and train routine maintenance tasks such as the inspection and replacement of parts. High-speed collision detection within the virtual environment is essential in order to provide interactive feedback about the feasibility of the mechanics’ actions, Haptic force-feedback can require about 1000 simulation updates per second. We have been investigating various approaches to collision detection in a polyhedral environment 2 (whose boundary representation is given), in which one or more polyhedral “flying objects” move. The assumption is that the environment t may be huge (millions of facets), but that it is largely static and can be preprocessed to support efficient intersection queries with the flying objects, which are assumed to be relatively small in number and moderate in complexity (thousands of facets).

Corrections to "the prioritized-layered projection algorithm for visible set estimation"

Fig. 11. 5CBEM results. (a) The top curve, labeled Exact, is the number of visible triangles for each given frame. The next four curves are the number of the visible triangles PLP finds with a given budget. From top to bottom, budgets of 10 percent, 5 percent, 2 percent, and 1 percent are reported. The bottom curve is the number of visible triangles that the centroid sorting algorithm finds. (b) Rendering times in seconds for each curve shown in (a), with the exception of the centroid sorting algorithm, which required 6-7 seconds per frame. (c) Image of all the visible triangles. (d) Image of the 10 percent PLP visible set.