IEEE Trans Vis Comput Graph. 2018 Jan;24(1):832-842. doi: 10.1109/TVCG.2017.2743938. Epub 2017 Aug 29.
This system paper presents the Topology ToolKit (TTK), a software platform designed for the topological analysis of scalar data in scientific visualization. While topological data analysis has gained in popularity over the last two decades, it has not yet been widely adopted as a standard data analysis tool for end users or developers. TTK aims at addressing this problem by providing a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependency-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions. TTK is open source (BSD license) and its code, online documentation and video tutorials are available on TTK's website [108].
本系统论文介绍了拓扑工具包（TTK），这是一个专为科学可视化中标量数据的拓扑分析而设计的软件平台。尽管拓扑数据分析在过去二十年中越来越受欢迎，但它尚未被广泛采用为终端用户或开发者的标准数据分析工具。TTK 旨在通过提供标量数据拓扑分析的关键算法的统一、通用、高效和稳健的实现来解决这个问题，包括：临界点、积分线、持久图、持久曲线、合并树、轮廓树、Morse-Smale 复形、纤维曲面、连续散点图、Jacobi 集、Reeb 空间等等。由于与 ParaView 的紧密集成，TTK 易于终端用户使用。通过各种绑定（Python、VTK/C++），它也易于开发者快速原型设计，或者通过直接、无依赖的 C++，轻松集成到现有的复杂系统中。在开发 TTK 时，我们遇到了几个算法和软件工程方面的挑战，我们在本文中记录了这些挑战。特别是，我们提出了一种在分段线性设置中提取临界点的离散梯度构造算法。该算法保证了 TTK 所支持的拓扑抽象之间的组合一致性，并且重要的是，它实现了拓扑数据简化的统一，以支持多尺度探索和分析。我们还提出了一种缓存三角剖分数据结构，它支持高效的通用遍历，根据输入单纯形网格的需求自适应调整其内存使用，并隐式模拟具有零内存开销的规则网格的三角剖分。最后，我们描述了一种原始的软件架构，它保证了对 TTK 功能的高效内存访问，同时仍然允许研究人员进行强大而易于绑定和扩展。TTK 是开源的（BSD 许可证），其代码、在线文档和视频教程可在 TTK 的网站上获得[108]。
