Visualization/MASSIVE: Multiresolution, Adaptive, Subdivision Surfaces for Interactive Visualization and Exploration

高级计算科学的一个基本研究挑战是帮助科学家、研究人员、工程师和一般用户更好地理解从计算机模拟或真实世界实验中获得的大规模数据集。因此，它需要更好的建模、分析和可视化工具来揭示原始数据集的洞察力，并促进高级知识的解释。为了实现这一目标，这一多学科项目的技术途径是开发基于可变形建模范式的新算法和计算技术，用于操作、模拟、可视化和处理任何大规模、复杂的数据集，从而更好地理解隐藏在原始数据中的更高层次、更有意义的信息，这些信息隐藏在受不确定性和噪声影响的原始数据中。这项研究的目的是在数学上丰富且广泛适用的可变形模型范式中开发新的理论、算法、计算和软件技术，雄心勃勃的目标是进一步革新可变形模型，并将其推广为有价值的可视化和探索工具。该研究的智能价值在于开发了一套新的可变形模型，并提出了一种集成的方法，用于在大规模、复杂的数据集中对复杂的几何信息和任意未知的拓扑结构进行建模和可视化。我们新的可变形模型的本质是多分辨率、细节层次(LOD)和细分几何，其拓扑结构也是受变分原理(VP)和偏微分方程(PDE)的动态自适应的。通过一系列的研究和教育活动，本研究旨在证明新型可变形模型不仅是用于视觉信息处理的强大的建模、渲染和模拟工具，而且它们潜在地可以作为一种通用计算技术来辅助新的科学探索。同时，我们将把最新开发的理论和算法融入到纽约州立大学石溪分校计算机科学、应用数学和统计学的研究生课程中。这些课程将使研究生接触到基于可变形模型的视觉计算的新视角，这将显著提高他们在跨学科背景下解决问题的技能。

One fundamental research challenge of advanced computational science is to aid scientists, researchers, engineers, and general users to gain a better understanding of large-scale datasets acquired from either computer simulations or real-world experiments. Therefore, it demands better modeling, analysis, and visualization tools that can reveal the insight from raw datasets and facilitate the interpretation of high-level knowledge. Towards this goal, the technical approach in this multi-disciplinary project is to develop novel algorithmic and computational techniques founded upon the principle of the deformable modeling paradigm for manipulating, simulating, visualizing, and processing any large-scale, complex dataset, hence leading to a better understanding of the higher-level, more meaningful information hiddenwithin raw data subject to uncertainty and noise.This research initiative aims to develop new theoretic, algorithmic, computational, and software techniques within the mathematically rich and broadly applicable deformable models paradigm, with an ambitiousgoal to further revolutionize deformable models and promote them as a valuable visualization and exploration tool. The intellectual merit of the proposed research is the unique technical approach of developing asuite of novel deformable models and presenting an integrated methodology for modeling and visualizing both complicated geometric information and arbitrarily, unknown topological structure inlarge-scale, complex datasets. The essence of our novel deformable models is multiresolution, level-of-detail (LOD), and subdivision geometry whose topology is also dynamically adaptive subject to variational principles (VPs) and partial differential equations (PDEs). Through an array of research and education activities, this investigation aims to demonstrate that the novel deformable models are not only a powerful modeling, rendering, and simulation tool for visual information processing, but that they can potentially serve as a general computational technology to aid in new scientific exploration. Meanwhile, we will incorporate the newly-developed theory and algorithms into our graduate curricula in computer science, applied mathematics, and statistics of SUNY at Stony Brook. These curricula will expose graduate students to a novel perspective on visual computing based on deformable models, which will significantly improve their problem-solving skills in an interdisciplinary context.