Centroid of a set of N-dimensional points
In analytic geometry, the centroid of a set of points is a point in the same domain as the set. The centroid point is chosen to show a property which can be calculated for that set.
Centroid of a set of N-dimensional points is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Consider the centroid defined as the arithmetic mean of a set of points of arbitrary dimension.
- Task
Create a function in your chosen programming language to calculate such a centroid using an arbitrary number of points of arbitrary dimension.
- Test your function with the following groups of points
one-dimensional: (1), (2), (3)
two-dimensional: (8, 2), (0, 0)
three-dimensional: the set (5, 5, 0), (10, 10, 0) and the set (1, 3.1, 6.5), (-2, -5, 3.4), (-7, -4, 9), (2, 0, 3)
five-dimensional: (0, 0, 0, 0, 1), (0, 0, 0, 1, 0), (0, 0, 1, 0, 0), (0, 1, 0, 0, 0)
- Stretch task
Show a 3D plot image of the second 3-dimensional set and its centroid.
- See Also
Julia
using Plots
struct Point{T, N}
v::Vector{T}
end
function centroid(points::Vector{Point{T, N}}) where N where T
arr = zeros(T, N)
for p in points, (i, x) in enumerate(p.v)
arr[i] += x
end
return Point{T, N}(arr / length(points))
end
function centroid(arr)
isempty(arr) && return Point{Float64, 0}(arr)
n = length(arr[begin])
t = typeof(arr[begin][begin])
return centroid([Point{t, n}(v) for v in arr])
end
const testvecs = [[[1], [2], [3]],
[(8, 2), (0, 0)],
[[5, 5, 0], [10, 10, 0]],
[[1.0, 3.1, 6.5], [-2, -5, 3.4], [-7, -4, 9.0], [2.0, 0.0, 3.0],],
[[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0],],
]
function test_centroids(tests)
for t in tests
isempty(t) && error("The empty set of points $t has no centroid")
vvec = [Point{Float64, length(t[begin])}(collect(v)) for v in t]
println("$t => $(centroid(vvec))")
end
xyz = [p[1] for p in tests[4]], [p[2] for p in tests[4]], [p[3] for p in tests[4]]
cpoint = centroid(tests[4]).v
for i in eachindex(cpoint)
push!(xyz[i], cpoint[i])
end
scatter(xyz..., color = [:navy, :navy, :navy, :navy, :red], legend = :none)
end
test_centroids(testvecs)
- Output:
[[1], [2], [3]] => Point{Float64, 1}([2.0]) [(8, 2), (0, 0)] => Point{Float64, 2}([4.0, 1.0]) [[5, 5, 0], [10, 10, 0]] => Point{Float64, 3}([7.5, 7.5, 0.0]) [[1.0, 3.1, 6.5], [-2.0, -5.0, 3.4], [-7.0, -4.0, 9.0], [2.0, 0.0, 3.0]] => Point{Float64, 3}([-1.5, -1.475, 5.475]) [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]] => Point{Float64, 5}([0.0, 0.25, 0.25, 0.25, 0.25])
Wren
var centroid = Fn.new { |pts|
var n = pts.count
if (n == 0) Fiber.abort("List must contain at least one point.")
var d = pts[0].count
if (pts.skip(1).any { |p| p.count != d }) {
Fiber.abort("Points must all have the same dimension.")
}
var res = List.filled(d, 0)
for (j in 0...d) {
for (i in 0...n) {
res[j] = res[j] + pts[i][j]
}
res[j] = res[j] / n
}
return res
}
var points = [
[ [1], [2], [3] ],
[ [8, 2], [0, 0] ],
[ [5, 5, 0], [10, 10, 0] ],
[ [1, 3.1, 6.5], [-2, -5, 3.4], [-7, -4, 9], [2, 0, 3] ],
[ [0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0] ]
]
for (pts in points) {
System.print("%(pts) => Centroid: %(centroid.call(pts))")
}
- Output:
[[1], [2], [3]] => Centroid: [2] [[8, 2], [0, 0]] => Centroid: [4, 1] [[5, 5, 0], [10, 10, 0]] => Centroid: [7.5, 7.5, 0] [[1, 3.1, 6.5], [-2, -5, 3.4], [-7, -4, 9], [2, 0, 3]] => Centroid: [-1.5, -1.475, 5.475] [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0]] => Centroid: [0, 0.25, 0.25, 0.25, 0.25]