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August 1, 2020 13:08
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using GeometryBasics | |
x(a::AbstractVector) = first(a) | |
y(a::AbstractVector) = last(a) | |
x(a::AbstractMatrix) = a[ :, 1 ] | |
y(a::AbstractMatrix) = a[ :, 2 ] | |
function orientation(p::AbstractVector, q::AbstractVector, r::AbstractVector)::Int | |
val = ( y(q) - y(p) ) * ( x(r) - x(q) ) - ( x(q) - x(p) ) * ( y(r) - y(q) ) | |
return (val ≈ 0) ? 0 : ( (val > 0) ? 1 : 2 ) | |
end | |
""" | |
Classic Jarvis/Gift Wrapping Convex Hull | |
""" | |
function convexhull( points::Matrix )::Vector | |
n = size(points, 1) | |
@assert (n > 2) "Convex Hull requires at least 3 points." | |
hull = [] | |
p, q = argmin( x( points ) ), 0 | |
init = p | |
while ( p != init ) || ( length( hull ) == 0 ) | |
push!( hull, p ) | |
q = (( p + 1) % n ) + 1 | |
for i in 1:n | |
if orientation(points[p,:], points[i,:], points[q,:]) == 2 | |
q = i | |
end | |
end | |
p = q; | |
end | |
return hull | |
end | |
function minimum_bounding_rectangle( points, hull_idxs ) | |
n = length(hull_idxs) | |
# calculate edge angles | |
edges = points[ hull_idxs[ 2:end ] ] - points[ hull_idxs[ 1:(end-1) ] ] | |
angles = unique( abs.( atan.( y( edges ), x( edges ) ) .% ( pi/2 ) ) ) | |
# find rotation matrices | |
rot_matrices = zeros( 2, 2, length( angles ) ) | |
rot_matrices[1,1,:] = cos.(angles); rot_matrices[2,1,:] = sin.(angles ) | |
rot_matrices[1,2,:] = -rot_matrices[2,1,:]; rot_matrices[2,2,:] = rot_matrices[1,1,:] | |
const_view = points[ hull_idxs,: ] | |
rot_points = [ rot_matrices[:,:,z] * const_view' for z in 1:size( rot_matrices, 3 ) ] | |
# find the bounding points | |
min_x, max_x, min_y, max_y = Vector{eltype(points)}(undef, length(rot_points)), | |
Vector{eltype(points)}(undef, length(rot_points)), | |
Vector{eltype(points)}(undef, length(rot_points)), | |
Vector{eltype(points)}(undef, length(rot_points)) | |
for (n, rp) in enumerate( rot_points ) | |
min_x[n], max_x[n] = extrema( rp[1,:] ) | |
min_y[n], max_y[n] = extrema( rp[2,:] ) | |
end | |
# find the box with the best area | |
smallest_box = argmin( (max_x .- min_x) .* (max_y .- min_y) ) | |
x1,x2 = min_x[smallest_box], max_x[smallest_box] | |
y1,y2 = min_y[smallest_box], max_y[smallest_box] | |
return ( rot_matrices[:,:,smallest_box]' * [ x1 y1; x1 y2; x2 y2; x2 y1 ]')' | |
end | |
p1 = randn(1000,2) | |
hull_inds = convexhull( p1 ) | |
mbr = minimum_bounding_rectangle( p1, hull_inds ) | |
using Plots | |
scatter( x(p1), y(p1), color = "black", legend = false); | |
scatter!( x(p1[hull_inds,:]), y(p1[hull_inds,:]), color = "purple"); | |
scatter!( x(mbr), y(mbr), color = "pink") |
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