Regular lattices in visualization and graphics

在科学中，我们通常研究连续现象。例如，在医学领域，我们对人体进行成像，以便对一个人的健康状况做出准确的诊断。同样，在娱乐行业中，我们模拟流体流动、烟雾、火等的行为，目的是创造特殊效果。通常我们只处理这些连续现象的离散化，从而引入近似。为了保持近似尽可能准确，重要的是找到适当的数据表示，即适当的离散化，并使用适当的工具（插值，有限差分等）来处理这些数据表示。我的工作目标是研究和分析基于不可分格的数据表示，它有望比事实上的标准笛卡尔格更好。

In the sciences we typically study continuous phenomena. For example, in the medical domain we image the human body in order to create an accurate diagnosis about a person's health status. Likewise, in the entertainment industry we simulate the behaviour of fluid flow, smoke, fire, etc. with the goal of creating special effects. Typically we only deal with a discretization of these continuous phenomena and are thereby introducing an approximation. To keep the approximation as accurate as possible, it is important to find proper data representations, i.e. proper discretizations, and to use the proper tools (interpolation, finite differences, etc.) to work with these data representations. The goal of my work is the study and analysis of data representations that are based on non-separable lattices, which promise to be better than Cartesian lattices, which are the de-facto standard.