Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …

Learn How to Design Effective Visualization SystemsVisualization Analysis and Design
provides a systematic, comprehensive framework for thinking about visualization in terms of …

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to
understand and design deep learning models. This paper posits that TDL may complement …

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 …

A survey of the development of the marching cubes algorithm [W. Lorensen, H. Cline,
Marching cubes: a high resolution 3D surface construction algorithm. Computer Graphics …

Reeb graphs are compact shape descriptors which convey topological information related to
the level sets of a function defined on the shape. Their definition dates back to 1946, and …

Reeb graphs are a fundamental data structure for understanding and representing the
topology of shapes. They are used in computer graphics, solid modeling, and visualization …

The Morse-Smale (MS) complex has proven to be a useful tool in extracting and visualizing
features from scalar-valued data. However, efficient computation of the MS complex for large …

Large-scale simulations are increasingly being used to study complex scientific and
engineering phenomena. As a result, advanced visualization and data analysis are also …

When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface
create a characteristic structure of rising bubbles and falling spikes known as Rayleigh …