Interval analysis and computer graphics algorithms

拟议的研究包括区间分析、计算机图形学和离散计算等统一主题下的若干活动领域。与计算闭集上函数值范围的良好包含这一基本问题有关的区间分析算法。这些算法被应用于全局优化算法、计算几何计算、图形算法和地理信息系统计算。离散计算的研究提供了从基于区间的研究到实用算法的联系。用于计算浮点数和的精确符号的算法被用来开发计算几何算法的计算保证结果的算法。

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.