Area-proportional 3-set circle layout (Wilkinson 2012-style triangulation)

Computes pairwise inter-center distances via bisection on the lens intersection area, then places circle C via barycentric triangulation against AB. Always sets `is_approximate = TRUE` because perfect 3-circle area-proportional fits don't always exist mathematically.

Usage

solve_3set(regions)

Arguments

regions

Named list keyed by `as.character(bitmask)` (1..7) -> exclusive count. Missing keys are treated as 0.

Value

A named list with elements `circles` (length 3), `error` (always NaN in v0.1), `is_approximate` (always TRUE).

Details

Mirrors Python `solve_3set` byte-for-byte (including the `error = NaN` deliberate sentinel - 3-set fit error is not measured in v0.1).

Examples

solve_3set(list("1" = 100L, "2" = 80L, "3" = 30L,
                 "4" = 60L,  "5" = 20L, "6" = 15L, "7" = 5L))
#> $circles
#> $circles[[1]]
#> $circles[[1]]$cx
#> [1] 0
#> 
#> $circles[[1]]$cy
#> [1] 0
#> 
#> $circles[[1]]$r
#> [1] 7.024104
#> 
#> 
#> $circles[[2]]
#> $circles[[2]]$cx
#> [1] 8.589207
#> 
#> $circles[[2]]$cy
#> [1] 0
#> 
#> $circles[[2]]$r
#> [1] 6.432751
#> 
#> 
#> $circles[[3]]
#> $circles[[3]]$cx
#> [1] 4.368278
#> 
#> $circles[[3]]$cy
#> [1] 7.521945
#> 
#> $circles[[3]]$r
#> [1] 5.641896
#> 
#> 
#> 
#> $error
#> [1] NaN
#> 
#> $is_approximate
#> [1] TRUE
#>