another convex hull / GrahamScan function added

[ig-or]

faster convex hull function added. I tested it an it works fast and reliable for my case in 10 millions hulls.
what is not perfect:

• not using existing Meshes.jl data structures like Point etc.
• Probably not work correctly with corner cases (like making a hull from just two points)

[juliohm]

@ig-or appreciate the attempt to add a faster implementation here. Can you please consider improving our existing Graham scan implementation instead?

The low level function you implemented could be refactored and then used behind a more high-level interface with Vector{Point} etc.

[DanielVandH]

This implementation seems to fail for this (contrived) example:

n = 4
p1 = [27.643564356435643, -21.881188118811881]
p2 = [83.366336633663366, 15.544554455445542]
p3 = [4.0, 4.0]
p4 = [73.415841584158414, 8.8613861386138595]
p = hcat(p1, p2, p3, p4)

h = zeros(Int32, n)
v = zeros(Float64, n)
s = zero(h)
u = hull_simple(p, h, s, v)
s = s[1:u]
push!(s, s[begin])

fig = Figure()
ax = Axis(fig[1, 1])
scatter!(ax, p[1, :], p[2, :], color=:red)
lines!(ax, p[1, s], p[2, s])

fig

Meshes.jl's existing implementation works, though.

_p = PointSet(p)
viz(hull(_p, GrahamScan()))

[juliohm]

Thank you for constructing the example @DanielVandH .

@ig-or I will close the PR because it is not fitting our interface, and because it has the bug mentioned above. I am happy to review future PRs with improvements to our hull implementation.

[ig-or]

Thanks for looking at my code. I fixed this issue with several points on one line on my side. But as I said make this fitting your interface might be more challenging (but possible). The main idea of the increase of speed is to remove all the memory allocations from the code.

I realized my use case is not common. I'm creating millions of convex hulls from just a few points. Usually people have millions of points and need make one convex hull out of it.

[DanielVandH]

FYI @ig-or, you might be interested to test on some of the cases discussed in this paper https://doi.org/10.1016/j.comgeo.2007.06.003 (it's where my example from above comes from) for convex hulls. They are all for convex hulls of very small point sets.

[ig-or]

Thanks Daniel!