Area-proportional 2-set circle layout — solve

Solves for two circles whose areas equal `a_only + ab` and `b_only + ab` and whose intersection area equals `ab`, by analytical bisection on the inter-center distance. Always exact (returns `is_approximate = FALSE`).

Usage

solve_2set(a_only, b_only, ab)

Arguments

a_only: Items in A only (integer >= 0).
b_only: Items in B only (integer >= 0).
ab: Items in A intersection B (integer >= 0).

Value

A named list with elements:

circles: Length-2 list of `list(cx, cy, r)` named lists.
error: Relative error of the achieved area fit (typically < 1e-4).
is_approximate: Always `FALSE` for 2-set.

Details

Mirrors Python `solve_2set` byte-for-byte.

Examples

solve_2set(a_only = 30L, b_only = 30L, ab = 10L)
#> $circles
#> $circles[[1]]
#> $circles[[1]]$cx
#> [1] -2.264784
#> 
#> $circles[[1]]$cy
#> [1] 0
#> 
#> $circles[[1]]$r
#> [1] 3.568248
#> 
#> 
#> $circles[[2]]
#> $circles[[2]]$cx
#> [1] 2.264784
#> 
#> $circles[[2]]$cy
#> [1] 0
#> 
#> $circles[[2]]$r
#> [1] 3.568248
#> 
#> 
#> 
#> $error
#> [1] 1.185185e-12
#> 
#> $is_approximate
#> [1] FALSE
#>