This book contains the proceedings of the workshop Uncertainty in Geomet- ric Computations that was held in Sheffield, England, July 5-6, 2001. A total of 59 delegates from 5 countries in Europe, North America and Asia attended the workshop. The workshop provided a forum for the discussion of com- putational methods for quantifying, representing and assessing the effects of uncertainty in geometric computations. It was organised around lectures by invited speakers, and presentations in poster form from participants. Computer simulations and modelling are used frequently in science and engi- neering, in applications ranging from the understanding of natural and artificial phenomena, to the design, test and manufacturing stages of production. This widespread use necessarily implies that detailed knowledge of the limitations of computer simulations is required. In particular, the usefulness of a computer simulation is directly dependent on the user's knowledge of the uncertainty in the simulation.
Although an understanding of the phenomena being modelled is an important requirement of a good computer simulation, the model will be plagued by deficiencies if the errors and uncertainties in it are not consid- ered when the results are analysed. The applications of computer modelling are large and diverse, but the workshop focussed on the management of un- certainty in three areas : Geometric modelling, computer vision, and computer graphics.
Contributors and Participants. Preface. 1. Affine Intervals in a CSG Geometric Modeller; A. Bowyer, et al. 2. Fast and Reliable Plotting of Implicit Curves; K. Buehler. 3. Data Assimilation with Sequential Gaussian Processes; L. Csato, et al. 4. Conformal Geometry, Euclidean Space and Geometric Algebra; C. Doran, et al. 5. Towards the Robust Intersection of Implicit Quadrics; L. Dupont, et al. 6. Computational Geometry and Uncertainty; A.R. Forrest. 7. Geometric Uncertainty in Solid Modeling; P.J. Malraison, W.A. Denker. 8. Reliable Geometric Computations with Algebraic Primitives and Predicates; M. Foskey, et al. 9. Feature Localization Error in 3D Computer Vision; D.D. Morris, T. Kanade. 10. Bayesian Analysis of Computer Model Outputs; J. Oakley, A. O'Hagan. 11. b.; T. Poggio, et al. 12. Affine Arithmetic and Bernstein Hull Methods for Algebraic Curve Drawing; H. Shou, et al. 13. Local Polynomial Metrics for kappa Nearest Neighbor Classifiers; R.R. Snapp. 14. Visualisation of Incomplete Data Using Class Information Constraints; Y. Sun, et al. 15. Towards Videorealistic Synthetic Visual Speech; B. Theobald, et al. 16. Properties of the Companion Matrix Resultant for Bernstein Polynomials; J.R. Winkler. 17. Computation with a Number of Neurons; S. Wu, D. Chen. Index.