Generate a Chain of Interlocked Circles in High-Dimensional Space

This function generates \(k\) interlocked circular clusters in a \(p\)-dimensional space. Unlike make_klink_circles(), the circles are arranged in a **chain-like structure**, where each circle interlocks only with its immediate neighbor, resembling links in a chain.

Usage

make_chain_circles(n = c(200, 100), p = 4, k = 2, offset = 0.5, angle = 90)

Arguments

n

An integer vector of length \(k\) giving the number of points in each circle. Default is c(200, 100).

p

Integer, the dimensionality of the embedding space. Must be at least 3. Default is 4.

k

Integer, the number of circles to generate. Default is 2.

offset

Numeric, the positional shift applied to each circle along its linking axis to ensure interlocking instead of overlap. Default is 0.5.

angle

Numeric, the rotation angle (in degrees) used when placing each subsequent circle into its respective plane. Default is 90.

Value

A data frame (or tibble, depending on gen_multicluster()) containing the generated points and cluster assignments.

Examples

# Generate two chain-linked circles in 4-D
twochain_circles <- make_chain_circles()
#> ✔ Data generation completed successfully!!!
#> ✔ Data generation completed successfully!!!
#> ✔ Multiple clusters generation completed successfully!!!