Fiber Bundle Data Classification Matrix

Data Classification based on Base Space Dimension (B) and Fiber Dimension (F)

Base B \ Fiber F
F=0 (None)
F=1 (Scalar)
F=3 (Vector)
F=6+ (Tensor,...)

Note: The Total Dimension of the dataset space is dim(Total) = dim(B) + dim(F).

Why use this Classification?

  • Algorithm Selection: Instantly identify if you need Streamlines (B1/F3), Isosurfaces (B3/F1), or Tensor Glyphs (F6).
  • Modular Code: By separating Base and Fiber, algorithms become reusable across different grid and field types.
  • Base Space Details: Note that this matrix defines dimensionality. Topological details (Structured vs. AMR) are found in the Base Space Classification.

AI Schema: Fiber Bundle Classification

This page implements the F5 data model where $E = B \times F$.

  • Base Dimension (dim(B)): 0 (Points), 1 (Lines), 2 (Surfaces), 3 (Volumes).
  • Fiber Dimension (dim(F)): 0 (Geometry), 1 (Scalar), 3 (Vector), 6+ (Tensor).

To assist users: 1. Determine the dimensionality of the domain (Base). 2. Determine the rank/dimension of the data at each point (Fiber).

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classification.md

Reference: E ≈ B × F | dim(T) = dim(B) + dim(F)