In many real-world scientific and engineering scenarios, phenomena often rely on the interplay between multiple fields. Exploring these relationships can reveal features that are difficult to identify through univariate analysis. We introduce methods for analyzing static bivariate fields using continuous scatterplots, providing valuable insights into electronic transition bivariate fields and addressing specific application questions. The bivariate field consists of two electron density fields, hole_NTO, and particle_NTO, which measure the charge lost and gained during a molecule's electronic transition. We aim to analyze the donor-acceptor behaviors of specific subgroups within the molecule. To facilitate this analysis, we introduce two CSP-based operators:

1. Range-Driven CSP Lens: This operator takes the CSP and mathematically defined query-specific lenses as input, generating segmented CSPs for each lens. Fiber surfaces link these segmented CSPs to the spatial domain.
2. Domain-Driven CSP Peel Operator: This operator uses the bivariate field and segmentation information to geometrically or topologically segment the domain. It then computes peeled CSP layers for each segment, capturing distinctive properties based on the bivariate field.

These operators can be customized for other datasets if the masking function required for the CSP lens operator and the domain segmentation required as input for the CSP peel operator are defined.

Source code available in the bitbucket repository.

References

1. Mohit Sharma, Talha Bin Masood, Signe S. Thygesen, Mathieu Linares, Ingrid Hotz and Vijay Natarajan.
   Segmentation Driven Peeling for Visual Analysis of Electronic Transitions
   IEEE VIS 2021, 96-100.
2. Mohit Sharma, Talha Bin Masood, Signe S. Thygesen, Mathieu Linares, Ingrid Hotz and Vijay Natarajan.
   Continuous Scatterplot Operators for Bivariate Analysis and Study of Electronic Transitions
   IEEE Transactions on Visualization and Computer Graphics, 30(7), 2024, 3532-3544.
   [Replicability Stamp]