Interval analysis and computer graphics algorithms

拟议的研究包括一些活动领域的统一主题下的区间分析，计算机图形学和离散计算。区间分析算法，涉及计算闭集上函数值范围的良好包含的基本问题。这些算法在全局优化算法、计算几何计算、图形学算法和地理信息系统计算中有着广泛的应用。离散计算研究提供了从基于区间的研究到实际算法的连接。计算浮点数和的精确符号的算法用于开发计算几何算法的保证结果的算法。研究在基于物理的计算机图形学领域进行。将特别注意与计划于2007年国际太阳物理年进行的太阳现象研究有关的应用。这些应用包括太阳内部和周围等离子体过程的计算机图形模拟，例如磁结构和耦合太阳行星系统的视觉显示。这是以前对北方光和球状闪电视觉显示研究的延续。

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.Research is conducted in the area of physically based computer graphics. Particular attention will be given to the applications that are of interest to the current investigation of solar phenomena planned for the International Heliophysical Year in 2007. These applications include computer graphics simulations of the plasma processes in and around the Sun such as the visual display of magnetic structures and the coupled solar-planetary system. This is a continuation of previous research on the visual display of the northern lights and ball lightning.