Mode Surfaces of Symmetric Tensor Fields: Topological Analysis and Seamless Extraction

TL;DR

This paper introduces a topological analysis and seamless extraction method for mode surfaces in 3D symmetric tensor fields, enhancing understanding and visualization of tensor field features.

Contribution

It provides a novel topological framework and a unified parameterization for mode surfaces, enabling seamless extraction and improved analysis of tensor field features.

Findings

Unified parameterization of mode surfaces using 2D asymmetric tensors

Efficient algorithm for seamless mode surface extraction

Application to solid mechanics datasets demonstrates effectiveness

Abstract

Mode surfaces are the generalization of degenerate curves and neutral surfaces, which constitute 3D symmetric tensor field topology. Efficient analysis and visualization of mode surfaces can provide additional insight into not only degenerate curves and neutral surfaces, but also how these features transition into each other. Moreover, the geometry and topology of mode surfaces can help domain scientists better understand the tensor fields in their applications. Existing mode surface extraction methods can miss features in the surfaces. Moreover, the mode surfaces extracted from neighboring cells have gaps, which make their subsequent analysis difficult. In this paper, we provide novel analysis on the topological structures of mode surfaces, including a common parameterization of all mode surfaces of a tensor field using 2D asymmetric tensors. This allows us to not only better understand the structures in mode surfaces and their interactions with degenerate curves and neutral surfaces, but also develop an efficient algorithm to seamlessly extract mode surfaces, including neutral surfaces. The seamless mode surfaces enable efficient analysis of their geometric structures, such as the principal curvature directions. We apply our analysis and visualization to a number of solid mechanics data sets.