Abstract
Moving objects are currently represented in databases by means of an explicit representation of their trajectory. However from a physical point of view, or more specifically according to Newton’s second law of motion, a moving object is fully described by its equation of motion. We introduce a new data model for moving objects in which a trajectory is represented by a differential equation. A similar approach is taken in computer animation where this is known as physically based modeling. We give a query language for our data model and use techniques from physically based modeling to evaluate queries in this language.
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Agarwal, P.K., Guibas, L.J., Edelsbrunner, H., Erickson, J., Isard, M., Har-Peled, S., Hershberger, J., Jensen, C., Kavraki, L., Koehl, P., Lin, M., Manocha, D., Metaxas, D., Mirtich, B., Mount, D., Muthukrishnan, S., Pai, D., Sacks, E., Snoeyink, J., Suri, S., Wolefson, O.: Algorithmic issues in modeling motion. ACM Comput. Surv. 34(4), 550–572 (2002)
Arnold, V.I., Weinstein, A., Vogtmann, K.: Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics, vol. 60. Springer, Heidelberg (1997)
Baraff, D.: Curved surfaces and coherence for non-penetrating rigid body simulation. Computer Graphics 24(4), 19–28 (1990)
Baraff, D., Witkin, A.: Physically Based Modelling. Pixar Animation studios 2001. SIGGRAPH 2001, Course Notes (2001)
Basch, J., Guibas, L.J., Hershberger, J.: Data structures for mobile data. Journal of Algorithms 31(3), 1–28 (1999)
Chomicki, J., Revesz, P.: Constraint-based interoperability of spatiotemporal databases. Geoinformatica 3(3), 211–2423 (1999)
Erwig, M., Güting, R.H., Schneider, M., Vazirgiannis, M.: Spatio-temporal data types: An approach to modeling and querying moving objects in databases. Geoinformatica 3(3), 269–296 (1999)
Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics. Addison-Wesley, Reading (1989)
Güting, R.H., Böhlen, M.H., Erwig, M., Jensen, C.S., Lorentzos, N.A., Schneider, M., Vazirgiannis, M.: A foundation for representing and querying moving objects. ACM Trans. Database Syst. 25(1), 1–42 (2000)
Iserles, A. (ed.): A First Course in the Numerical Analysis of Differential Equations. Cambridge University Press, Cambridge (1996)
Kanellakis, P.C., Kuper, G.M., Revesz, P.Z.: Constraint query languages. Journal of Computing and Systems Sciences 51(1), 26–52 (1995)
Kuper, G.M., Paredaens, J., Libkin, L. (eds.): Constraint Databases. Springer, Heidelberg (2000)
Lin, M., Gottschalk, S.: Collision detection between geometric models. In: Proceedings of the IMA Conference on Mathematics of Surfaces (1998)
Mirtich, B.: Timewarp rigid body simulation. In: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pp. 193–200 (2000)
Mokthar, H., Su, J., Ibarra, O.: On moving object queries. In: Proceedings of the Twenty-first ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 188–198. ACM Press, New York (2002)
Nedialkov, N.S.: Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation. PhD thesis, Computer Science Dept., University of Toronto (1999)
Newton, I.: Philosophiae Naturalis Principia Mathematica (1687)
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge (1992)
Revesz, P.: Introduction to Constraint Databases. Springer, Heidelberg (2001)
Shampine, L.F.: Numerical Solution of Ordinary Differential Equations. Chapman & Hall, Boca Raton (1994)
Su, J., Xu, H., Ibarra, O.H.: Moving objects: Logical relationships and queries. In: Jensen, C.S., Schneider, M., Seeger, B., Tsotras, V.J. (eds.) SSTD 2001. LNCS, vol. 2121, pp. 3–19. Springer, Heidelberg (2001)
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Geerts, F. (2004). Moving Objects and Their Equations of Motion. In: Kuijpers, B., Revesz, P. (eds) Constraint Databases. CDB 2004. Lecture Notes in Computer Science, vol 3074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25954-1_3
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DOI: https://doi.org/10.1007/978-3-540-25954-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22126-5
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