S.K. Lodha, N.M. Faaland, P.K. Varshney, and K.G. Mehrotra (USA)

: uncertainty, visualization, probability.

This paper addresses the computation and visualization of the uncertainty associated with the positions of moving particles, using temporal projections based on uncertain knowledge of previous particle position and velocity. First, we present an algorithm for computing the probability distribution describing the position of a particle moving in 2D or 3D space, given the probability distributions that separately characterize the initial position, speed, and direction of the particle. The initial distributions are ar bitrary, but the special case of Gaussian distributions is considered in greater detail. We also discuss the algo rithmic complexity of the algorithm, and ways to improve its performance. Three visualization techniques (galaxy, transparency, and pseudo-color) are developed to represent the resulting probability distribution associated with the particle at a later time. An appropriate time-dependent sampling approach is adopted to make the visualizations more comprehensible to the human viewer. Experiments with different distributions indicate that the resulting visu alizations often take the form of recognizable real-world shapes, assisting the user in understanding the nature of a particleâ€™s movement.

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