26 Quantitative Dimensions of Paths

  1. Length.
  2. Breadth (transverse width).
  3. Depth (transverse height) (if any).
  4. [Transverse diameter, Transverse radius] (cf. #2, #3).
  5. Transverse circumference (if any).
  6. Transverse area [real or virtual] (if any).
  7. Longitudinal area(s) [two- or three-dimensional] [internal, external, both, averaged, vc] (if any).
  8. Volume (if any).
  9. Length-to-diameter index (elongation vs. compaction).
  10. Curvature indexes [e.g. <average or total> c.; number of inflection points, or changes, over length; <average or total> c. change; quotient of path length to external distance of two ends; c. monotonicity; etc] (as opp. to <rectilinearity or rectangularity> indexes (cf. #13, #15).
  11. Wall width (if any).
  12. Hollowness (vs. solidity) (if any)
  13. Space filling [two-, three-, or n-dimensional] (cf. #10)
  14. Continuity (vs. discontinuity) indexes.
  15. Drift (vs. rectilinearity) index (cf. #10).
  16. Sharpness/definiteness/clarity (vs. vagueness) index.
  17. Branching indexes [e.g. av. inter-branch distance; total branches over length; av. absolute branch length; av. branch length relative to <main path or total 'network'> length; total 'network' length; av. 'sub-branching'; etc].
  18. Anastomosis indexes (e.g. total loops in network; total levels of 'subanastomoses'; etc].
  19. Angularity indexes.
  20. Flux indexes (if any).
  21. Capacity indexes.
  22. Efficiency indexes.
  23. Rate-of-growth indexes.
  24. Uniformity-over-length indexes.
  25. Durational indexes [e.g. age, life-span, half-life, etc].
  26. Symmetry indexes (e.g. resemblance of two ends or halves] (cf. #24).