L. Guibas. Modeling Motion. In Handbook of Discrete and Computational Geometry, J. Goodman and J. O'Rourke, Eds, 2nd Ed., Chapman and Hall/CRC, 2004, pp. 1117-1134.
Motion is ubiquitous in the physical world, yet its study is much less developed than that of another common physical modality, namely shape. While we have several standardized mathematical shape descriptions, and even entire disciplines devoted to that area---such as Computer-Aided Geometric Design (CAGD)---the state of formal motion descriptions is still in flux. This in part because motion descriptions span many levels of detail; they also tend to be intimately coupled to an underlying physical process generating the motion (dynamics). Thus, until recently, proper abstractions were lacking and there was only limited work on algorithmic descriptions of motion and their associated complexity measures. This chapter aims to show how an algorithmic study of motion is
intimately tied to discrete and computational geometry. After a quick
survey of earlier work, we devote the bulk of this chapter to discussing the framework of Kinetic Data Structures. We also briefly discuss methods for querying moving objects.
author = "L. Guibas",
title = "Modeling Motion",
booktitle = "Handbook of Discrete and Computational Geometry",
editor = "J. Goodman and J. O'Rourke",
edition = "2nd",
year = "2004",
pages = "1117--1134",
publisher = "Chapman and Hall/CRC)