Multi-Scale Topological Analysis of Asymmetric Tensor Fields on Surfaces

Area of Science:

• Scientific visualization
• Computational science
• Applied mathematics

Background:

• Asymmetric tensor fields are crucial in science and engineering, particularly fluid dynamics.
• Current 2D analysis methods often rely on pointwise examination and visualization metaphors like color and glyphs.
• A need exists for advanced topological analysis of tensor fields on surfaces.

Purpose of the Study:

• To develop a novel multi-scale topological analysis framework for asymmetric tensor fields on surfaces.
• To enhance the clarity and focus of tensor field visualization through multi-scale simplification.
• To provide a robust framework applicable to various data sizes and complexities.

Main Methods:

• The framework utilizes eigenvalue and eigenvector graphs for topological analysis.
• Atomic operations for graph modification and a scale definition for simplification are core components.
• Efficient algorithms are developed for realizing these operations and graph simplification.

Main Results:

• A multi-scale topological analysis framework for asymmetric tensor fields on surfaces has been established.
• The framework enables a systematic simplification of topological structures at different scales.
• Physical interpretations of the eigenvalue and eigenvector graphs are provided.

Conclusions:

• The proposed multi-scale framework offers a novel approach to analyzing asymmetric tensor fields on surfaces.
• The method provides enhanced clarity and focus for visualization, aiding scientific discovery.
• The framework's utility is demonstrated through applications in computational fluid dynamics.