Interval analysis and computer graphics algorithms

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The proposed research encompasses a number of areas of activity under the unifying themes of interval analysis, computer graphics and discrete computations. Interval analysis algorithms relating to the fundamental question of computing good inclusions for the range of values of a function over a closed set. These algorithms are applied in global optimization algorithms, computational geometry computations, graphics algorithms and geographic information systems computations. The discrete computations research provides the connection from interval based research to practical algorithms. Algorithms for computing the exact sign of a sum of floating point numbers are used to develop algorithms that compute guaranteed results for computational geometry algorithms.