Swirl effect using warp operation
In this example, we illustrate how to construct a custom warping map and pass it to warp. This swirl example comes from the Princeton Computer Graphics course for Image Warping (Fall 2000) and scikit-image swirl example.
using ImageTransformations
using OffsetArrays, StaticArrays
using ImageShow, TestImages
using LinearAlgebra
img = imresize(testimage("cameraman"), (256, 256));As we've illustrated in image warping, a warp operation consists of two operations: backward coordinate map ϕ and intensity estimator. To implement swirl operation, we need to customize the coordinate map ϕ. A valid coordinate map q = ϕ(p) follows the following interface:
# SVector comes from StaticArrays
ϕ(::SVector{N})::SVector{N} where NA cartesian position (x, y) can be transfered to/from polar coordinate (ρ, θ) using formula:
# Cartesian to Polar
ρ = norm(y-y0, x-x0)
θ = atan(y/x)
# Polar to Cartesian
y = y0 + ρ*sin(θ)
x = x0 + ρ*cos(θ)For given input index p, a swirl operation enforces more rotations in its polar coordinate using θ̃ = θ + ϕ + s*exp(-ρ/r), and returns the cartesian index (x̃, ỹ) from the warped polor coordinate (ρ, θ̃). (Here we use the formula from scikit-image swirl example to build our version.)
function swirl(rotation, strength, radius)
x0 = OffsetArrays.center(img)
r = log(2)*radius/5
function swirl_map(x::SVector{N}) where N
xd = x .- x0
ρ = norm(xd)
θ = atan(reverse(xd)...)
# Note that `x == x0 .+ ρ .* reverse(sincos(θ))`
# swirl adds more rotations to θ based on the distance to center point
θ̃ = θ + rotation + strength * exp(-ρ/r)
SVector{N}(x0 .+ ρ .* reverse(sincos(θ̃)))
end
warp(img, swirl_map, axes(img))
endswirl (generic function with 1 method)Now let's see how radius argument affects the result
preview = ImageShow.gif([swirl(0, 10, radius) for radius in 10:10:150]; fps=5)256×256×15 ImageShow.AnimatedGIF{Gray{N0f8}, StackViews.StackView{Gray{N0f8}, 3, 3, Vector{Matrix{Gray{N0f8}}}}}:
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0.51 0.51 0.533 0.533 0.522 0.502 0.49 0.49 0.498 0.533 0.557 0.545 0.537 0.588 0.604 0.604 0.612 0.62 0.624 0.639 0.639 0.639 0.635 0.643 0.647 0.643 0.655 0.655 0.643 0.651 0.639 0.647 0.651 0.659 0.663 0.663 0.678 0.702 0.659 0.325 0.031 0.035 0.043 0.047 0.047 0.051 0.047 0.047 0.043 0.047 0.047 0.047 0.055 0.059 0.067 0.063 0.063 0.055 0.051 0.055 0.055 0.055 0.047 0.047 0.051 0.055 0.051 0.047 0.039 0.039 0.047 0.051 0.047 0.047 0.055 0.059 0.059 0.055 0.051 0.047 0.047 0.059 0.063 0.063 0.063 0.055 0.059 0.059 0.055 0.055 0.055 0.047 0.055 0.055 0.055 0.059 0.059 0.059 0.055 0.063 0.059 0.059 0.055 0.047 0.047 0.051 0.039 0.208 0.659 0.647 0.631 0.643 0.647 0.631 0.631 0.651 0.659 0.71 0.576 0.075 0.035 0.02 0.173 0.471 0.145 0.125 0.482 0.678 0.678 0.498 0.118 0.357 0.529 0.812 0.906 0.808 0.51 0.455 0.647 0.624 0.631 0.631 0.631 0.565 0.361 0.267 0.271 0.306 0.353 0.388 0.424 0.467 0.392 0.082 0.031 0.039 0.106 0.173 0.137 0.467 0.647 0.655 0.655 0.659 0.675 0.675 0.663 0.659 0.678 0.706 0.722 0.729 0.741 0.741 0.757 0.773 0.784 0.788 0.784 0.773 0.745 0.671 0.58 0.561 0.569 0.565 0.584 0.616 0.62 0.612 0.588 0.537 0.62 0.69 0.682 0.69 0.69 0.706 0.706 0.71 0.714 0.722 0.737 0.698 0.627 0.612 0.612 0.612 0.612 0.612 0.612 0.62 0.604 0.608 0.612 0.612 0.612 0.62 0.616 0.596 0.588 0.588 0.58 0.588 0.58 0.569 0.576 0.584 0.588 0.588 0.62 0.604 0.596 0.592 0.596 0.588 0.592 0.596 0.592 0.584 0.588 0.588 0.573 0.576 0.584 0.576 0.576 0.576 0.58 0.565 0.573 0.58 0.573 0.565 0.573 0.569
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0.443 0.431 0.439 0.439 0.424 0.447 0.455 0.463 0.459 0.447 0.451 0.439 0.447 0.455 0.49 0.525 0.557 0.596 0.624 0.635 0.639 0.643 0.651 0.639 0.639 0.651 0.647 0.647 0.655 0.655 0.655 0.663 0.659 0.659 0.667 0.678 0.718 0.6 0.118 0.035 0.039 0.039 0.039 0.035 0.031 0.035 0.031 0.031 0.035 0.039 0.043 0.047 0.047 0.055 0.059 0.059 0.055 0.059 0.063 0.063 0.059 0.055 0.059 0.055 0.059 0.055 0.051 0.055 0.055 0.055 0.063 0.063 0.055 0.047 0.051 0.055 0.071 0.063 0.047 0.047 0.051 0.063 0.059 0.059 0.055 0.055 0.063 0.063 0.055 0.055 0.055 0.055 0.051 0.059 0.063 0.063 0.063 0.059 0.055 0.055 0.055 0.063 0.055 0.051 0.051 0.063 0.282 0.682 0.643 0.639 0.69 0.71 0.729 0.741 0.737 0.733 0.757 0.686 0.29 0.027 0.035 0.039 0.231 0.463 0.047 0.259 0.698 0.659 0.667 0.498 0.133 0.373 0.541 0.8 0.898 0.796 0.494 0.443 0.612 0.557 0.51 0.565 0.655 0.604 0.439 0.322 0.376 0.459 0.522 0.557 0.553 0.533 0.576 0.541 0.2 0.031 0.031 0.106 0.204 0.102 0.404 0.784 0.725 0.557 0.424 0.471 0.529 0.58 0.62 0.651 0.686 0.702 0.722 0.737 0.725 0.722 0.725 0.729 0.737 0.741 0.749 0.741 0.745 0.718 0.651 0.569 0.569 0.604 0.608 0.604 0.58 0.533 0.639 0.733 0.729 0.722 0.71 0.686 0.671 0.694 0.718 0.725 0.749 0.725 0.639 0.612 0.612 0.608 0.612 0.612 0.608 0.608 0.612 0.612 0.616 0.604 0.604 0.616 0.627 0.596 0.565 0.58 0.584 0.58 0.584 0.569 0.573 0.573 0.576 0.576 0.62 0.6 0.588 0.592 0.588 0.588 0.588 0.588 0.588 0.588 0.588 0.58 0.588 0.58 0.576 0.584 0.584 0.58 0.596 0.584 0.58 0.58 0.576 0.576 0.573 0.58
0.427 0.416 0.416 0.427 0.416 0.424 0.435 0.455 0.447 0.435 0.435 0.42 0.42 0.435 0.471 0.478 0.482 0.537 0.6 0.639 0.627 0.631 0.639 0.643 0.635 0.643 0.651 0.659 0.659 0.655 0.647 0.655 0.659 0.663 0.671 0.69 0.675 0.416 0.035 0.039 0.039 0.039 0.043 0.047 0.047 0.039 0.039 0.035 0.035 0.039 0.035 0.039 0.039 0.039 0.047 0.051 0.055 0.063 0.063 0.063 0.063 0.059 0.059 0.055 0.059 0.055 0.051 0.055 0.055 0.055 0.059 0.063 0.051 0.055 0.059 0.094 0.137 0.075 0.051 0.055 0.055 0.071 0.063 0.063 0.059 0.059 0.063 0.063 0.055 0.055 0.055 0.055 0.059 0.063 0.059 0.055 0.055 0.063 0.055 0.059 0.055 0.055 0.055 0.051 0.043 0.122 0.459 0.671 0.588 0.549 0.557 0.561 0.569 0.576 0.573 0.584 0.627 0.541 0.137 0.035 0.031 0.086 0.302 0.314 0.071 0.337 0.69 0.671 0.686 0.51 0.129 0.376 0.557 0.816 0.906 0.792 0.502 0.443 0.584 0.529 0.518 0.573 0.639 0.604 0.443 0.314 0.376 0.455 0.51 0.545 0.537 0.51 0.541 0.588 0.392 0.035 0.035 0.063 0.149 0.118 0.235 0.702 0.71 0.584 0.549 0.608 0.643 0.639 0.659 0.675 0.702 0.714 0.71 0.71 0.69 0.682 0.682 0.69 0.698 0.714 0.733 0.722 0.718 0.737 0.729 0.655 0.588 0.596 0.612 0.608 0.584 0.529 0.631 0.722 0.706 0.706 0.698 0.686 0.678 0.698 0.714 0.722 0.737 0.722 0.635 0.616 0.624 0.612 0.612 0.612 0.604 0.612 0.616 0.616 0.62 0.62 0.612 0.624 0.627 0.6 0.557 0.573 0.576 0.584 0.588 0.573 0.576 0.592 0.588 0.573 0.604 0.588 0.588 0.596 0.588 0.584 0.596 0.588 0.588 0.592 0.596 0.584 0.588 0.588 0.596 0.588 0.584 0.592 0.592 0.58 0.576 0.58 0.58 0.576 0.573 0.576
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0.427 0.478 0.553 0.533 0.569 0.557 0.537 0.494 0.545 0.537 0.58 0.514 0.518 0.518 0.557 0.58 0.573 0.525 0.51 0.541 0.545 0.576 0.525 0.553 0.545 0.596 0.592 0.627 0.62 0.573 0.239 0.055 0.063 0.063 0.051 0.039 0.047 0.055 0.047 0.043 0.047 0.051 0.047 0.047 0.055 0.047 0.051 0.055 0.055 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.055 0.051 0.051 0.051 0.051 0.051 0.055 0.051 0.051 0.047 0.047 0.047 0.051 0.055 0.059 0.055 0.051 0.047 0.051 0.047 0.043 0.035 0.035 0.051 0.055 0.055 0.047 0.051 0.051 0.051 0.055 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.051 0.047 0.047 0.047 0.043 0.137 0.467 0.588 0.573 0.584 0.592 0.604 0.584 0.557 0.549 0.541 0.478 0.49 0.616 0.522 0.102 0.035 0.031 0.016 0.278 0.69 0.051 0.196 0.616 0.553 0.549 0.408 0.314 0.298 0.235 0.478 0.714 0.318 0.122 0.173 0.224 0.259 0.314 0.384 0.655 0.769 0.612 0.729 0.718 0.416 0.357 0.427 0.506 0.541 0.557 0.471 0.376 0.337 0.31 0.282 0.259 0.271 0.29 0.392 0.447 0.337 0.447 0.541 0.337 0.039 0.031 0.039 0.102 0.133 0.078 0.259 0.541 0.549 0.247 0.196 0.271 0.349 0.314 0.259 0.243 0.286 0.4 0.412 0.404 0.345 0.196 0.231 0.251 0.169 0.129 0.129 0.133 0.157 0.169 0.157 0.149 0.145 0.145 0.149 0.204 0.275 0.188 0.161 0.157 0.141 0.129 0.133 0.122 0.125 0.129 0.122 0.106 0.165 0.322 0.533 0.667 0.69 0.698 0.675 0.588 0.416 0.282 0.243 0.243 0.286 0.29 0.243 0.188 0.149 0.224 0.392 0.412 0.408 0.4 0.4 0.384 0.38 0.388 0.349 0.192 0.114 0.122 0.125 0.129 0.161 0.208 0.173 0.176 0.208 0.161 0.137 0.165 0.118 0.137 0.204 0.173 0.118
0.412 0.451 0.525 0.518 0.588 0.612 0.545 0.471 0.522 0.525 0.557 0.502 0.494 0.475 0.514 0.557 0.553 0.51 0.51 0.529 0.514 0.514 0.443 0.475 0.447 0.486 0.49 0.514 0.506 0.431 0.098 0.059 0.059 0.063 0.055 0.039 0.047 0.055 0.043 0.039 0.039 0.047 0.047 0.051 0.047 0.047 0.055 0.055 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.051 0.047 0.047 0.051 0.055 0.047 0.047 0.051 0.047 0.051 0.051 0.047 0.047 0.047 0.051 0.059 0.059 0.055 0.055 0.051 0.047 0.043 0.035 0.035 0.051 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.051 0.047 0.043 0.039 0.2 0.58 0.506 0.51 0.537 0.549 0.545 0.537 0.529 0.545 0.549 0.455 0.459 0.596 0.471 0.051 0.035 0.039 0.039 0.302 0.608 0.043 0.2 0.565 0.494 0.494 0.396 0.306 0.251 0.267 0.639 0.58 0.188 0.176 0.263 0.216 0.196 0.259 0.4 0.557 0.596 0.447 0.424 0.776 0.729 0.451 0.478 0.565 0.565 0.525 0.467 0.431 0.431 0.412 0.361 0.314 0.322 0.31 0.345 0.349 0.275 0.416 0.522 0.408 0.118 0.031 0.027 0.071 0.145 0.082 0.216 0.545 0.561 0.247 0.157 0.235 0.373 0.329 0.235 0.216 0.263 0.42 0.439 0.341 0.29 0.196 0.251 0.243 0.173 0.165 0.141 0.125 0.133 0.145 0.149 0.149 0.149 0.153 0.149 0.165 0.176 0.161 0.157 0.161 0.145 0.129 0.141 0.133 0.133 0.141 0.133 0.118 0.102 0.125 0.235 0.42 0.588 0.631 0.537 0.424 0.314 0.263 0.263 0.286 0.322 0.31 0.247 0.216 0.18 0.22 0.361 0.396 0.384 0.361 0.376 0.392 0.388 0.392 0.306 0.137 0.086 0.098 0.094 0.106 0.118 0.137 0.125 0.145 0.169 0.129 0.118 0.141 0.106 0.122 0.157 0.125 0.094
0.353 0.4 0.482 0.482 0.525 0.549 0.502 0.439 0.486 0.49 0.537 0.486 0.486 0.447 0.482 0.533 0.522 0.478 0.478 0.51 0.494 0.502 0.42 0.427 0.392 0.427 0.447 0.502 0.463 0.329 0.051 0.063 0.055 0.055 0.047 0.031 0.039 0.047 0.047 0.047 0.043 0.043 0.043 0.047 0.055 0.051 0.047 0.055 0.059 0.059 0.055 0.055 0.055 0.055 0.051 0.055 0.051 0.047 0.051 0.051 0.047 0.047 0.051 0.047 0.051 0.055 0.051 0.051 0.047 0.055 0.059 0.063 0.063 0.059 0.055 0.055 0.047 0.039 0.039 0.055 0.051 0.055 0.055 0.055 0.059 0.055 0.059 0.055 0.055 0.055 0.051 0.055 0.059 0.055 0.059 0.055 0.055 0.047 0.078 0.365 0.714 0.667 0.675 0.675 0.682 0.706 0.702 0.698 0.729 0.741 0.71 0.714 0.745 0.475 0.031 0.031 0.027 0.102 0.412 0.435 0.078 0.282 0.447 0.376 0.353 0.267 0.227 0.192 0.392 0.729 0.384 0.184 0.302 0.447 0.376 0.463 0.396 0.376 0.329 0.31 0.322 0.271 0.416 0.8 0.71 0.345 0.275 0.278 0.271 0.322 0.392 0.369 0.361 0.424 0.451 0.486 0.431 0.31 0.2 0.196 0.384 0.486 0.431 0.259 0.031 0.035 0.043 0.094 0.102 0.145 0.498 0.576 0.259 0.161 0.286 0.463 0.404 0.302 0.294 0.408 0.573 0.584 0.431 0.329 0.208 0.212 0.188 0.157 0.165 0.133 0.106 0.114 0.141 0.22 0.286 0.212 0.145 0.141 0.137 0.153 0.165 0.153 0.149 0.137 0.125 0.129 0.125 0.137 0.157 0.149 0.141 0.165 0.157 0.149 0.192 0.314 0.424 0.353 0.322 0.357 0.329 0.286 0.302 0.337 0.325 0.263 0.243 0.235 0.263 0.361 0.392 0.4 0.38 0.373 0.384 0.384 0.361 0.239 0.086 0.067 0.078 0.071 0.082 0.078 0.086 0.098 0.133 0.145 0.106 0.102 0.122 0.11 0.11 0.125 0.114 0.098
0.0 0.431 0.522 0.502 0.529 0.545 0.51 0.451 0.502 0.533 0.584 0.537 0.525 0.494 0.529 0.549 0.553 0.51 0.51 0.533 0.525 0.545 0.494 0.502 0.451 0.463 0.494 0.557 0.478 0.216 0.051 0.055 0.055 0.055 0.043 0.035 0.031 0.039 0.043 0.039 0.047 0.047 0.047 0.043 0.047 0.051 0.055 0.055 0.059 0.063 0.055 0.055 0.055 0.055 0.047 0.051 0.051 0.051 0.055 0.051 0.047 0.055 0.055 0.055 0.051 0.047 0.047 0.055 0.055 0.055 0.055 0.059 0.059 0.063 0.055 0.051 0.047 0.039 0.043 0.055 0.055 0.055 0.055 0.059 0.059 0.059 0.059 0.055 0.051 0.051 0.055 0.055 0.055 0.055 0.055 0.055 0.051 0.035 0.176 0.682 0.894 0.886 0.882 0.882 0.886 0.898 0.89 0.894 0.918 0.914 0.918 0.918 0.839 0.416 0.031 0.039 0.02 0.188 0.561 0.239 0.169 0.576 0.533 0.322 0.247 0.196 0.173 0.208 0.6 0.706 0.22 0.204 0.341 0.51 0.51 0.608 0.518 0.357 0.192 0.18 0.204 0.204 0.2 0.443 0.796 0.643 0.329 0.294 0.212 0.22 0.275 0.263 0.294 0.4 0.502 0.576 0.545 0.369 0.251 0.271 0.447 0.498 0.467 0.384 0.094 0.031 0.031 0.071 0.125 0.098 0.298 0.408 0.227 0.235 0.376 0.502 0.541 0.518 0.522 0.604 0.647 0.62 0.525 0.408 0.267 0.235 0.227 0.231 0.239 0.224 0.235 0.204 0.235 0.369 0.459 0.373 0.282 0.271 0.235 0.247 0.275 0.243 0.196 0.176 0.176 0.208 0.2 0.204 0.267 0.278 0.271 0.341 0.376 0.322 0.275 0.314 0.4 0.329 0.345 0.455 0.447 0.357 0.337 0.341 0.333 0.322 0.322 0.341 0.38 0.408 0.392 0.447 0.471 0.408 0.384 0.369 0.314 0.176 0.059 0.055 0.059 0.063 0.071 0.059 0.067 0.086 0.118 0.122 0.09 0.094 0.102 0.094 0.102 0.106 0.094 0.098
0.0 0.486 0.565 0.541 0.549 0.557 0.537 0.502 0.537 0.557 0.576 0.522 0.529 0.486 0.525 0.533 0.549 0.506 0.51 0.573 0.58 0.584 0.576 0.569 0.541 0.557 0.58 0.576 0.439 0.102 0.051 0.055 0.063 0.059 0.039 0.039 0.039 0.043 0.043 0.039 0.043 0.047 0.047 0.047 0.043 0.043 0.043 0.047 0.051 0.051 0.051 0.055 0.055 0.047 0.051 0.051 0.047 0.055 0.059 0.051 0.051 0.055 0.055 0.063 0.055 0.055 0.051 0.055 0.055 0.055 0.059 0.063 0.055 0.059 0.055 0.047 0.043 0.039 0.043 0.055 0.055 0.051 0.051 0.055 0.055 0.055 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.051 0.055 0.051 0.047 0.031 0.259 0.878 0.953 0.949 0.941 0.945 0.953 0.953 0.941 0.949 0.953 0.949 0.953 0.973 0.808 0.263 0.027 0.039 0.02 0.255 0.682 0.098 0.224 0.765 0.624 0.333 0.227 0.192 0.165 0.306 0.729 0.557 0.129 0.216 0.365 0.518 0.569 0.678 0.573 0.357 0.157 0.165 0.157 0.176 0.212 0.247 0.447 0.792 0.714 0.502 0.376 0.29 0.235 0.224 0.294 0.373 0.471 0.494 0.478 0.424 0.427 0.416 0.478 0.478 0.447 0.478 0.29 0.031 0.031 0.055 0.114 0.102 0.169 0.4 0.361 0.365 0.42 0.447 0.486 0.471 0.435 0.435 0.427 0.443 0.42 0.361 0.318 0.314 0.306 0.314 0.337 0.369 0.376 0.298 0.314 0.404 0.502 0.533 0.478 0.384 0.322 0.322 0.353 0.357 0.314 0.251 0.239 0.294 0.314 0.306 0.341 0.361 0.361 0.4 0.447 0.42 0.38 0.416 0.478 0.376 0.353 0.482 0.506 0.416 0.392 0.353 0.369 0.435 0.369 0.4 0.431 0.416 0.38 0.424 0.467 0.408 0.369 0.341 0.259 0.133 0.051 0.047 0.047 0.063 0.067 0.059 0.071 0.086 0.118 0.114 0.086 0.094 0.086 0.086 0.106 0.098 0.078 0.086
0.4 0.431 0.455 0.439 0.478 0.6 0.624 0.624 0.635 0.573 0.471 0.416 0.435 0.4 0.42 0.431 0.443 0.416 0.435 0.561 0.624 0.616 0.627 0.627 0.635 0.639 0.647 0.604 0.373 0.055 0.051 0.055 0.055 0.055 0.039 0.039 0.043 0.047 0.047 0.043 0.047 0.047 0.039 0.043 0.047 0.043 0.047 0.043 0.039 0.039 0.043 0.047 0.047 0.047 0.051 0.055 0.055 0.059 0.059 0.055 0.055 0.055 0.059 0.059 0.055 0.055 0.055 0.055 0.055 0.059 0.063 0.063 0.055 0.055 0.055 0.051 0.043 0.031 0.043 0.059 0.055 0.051 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.051 0.055 0.051 0.043 0.059 0.353 0.91 0.918 0.91 0.89 0.886 0.878 0.882 0.875 0.863 0.867 0.859 0.867 0.89 0.671 0.11 0.031 0.035 0.024 0.294 0.714 0.051 0.251 0.792 0.584 0.325 0.255 0.204 0.165 0.514 0.733 0.345 0.11 0.227 0.404 0.573 0.718 0.769 0.58 0.361 0.153 0.157 0.145 0.165 0.251 0.365 0.337 0.463 0.816 0.729 0.463 0.443 0.353 0.282 0.329 0.365 0.4 0.408 0.439 0.408 0.408 0.365 0.365 0.369 0.38 0.482 0.42 0.086 0.031 0.031 0.086 0.145 0.122 0.373 0.463 0.427 0.439 0.42 0.4 0.369 0.349 0.325 0.329 0.373 0.353 0.325 0.345 0.373 0.345 0.322 0.345 0.392 0.416 0.337 0.345 0.38 0.451 0.475 0.463 0.396 0.349 0.353 0.373 0.396 0.384 0.337 0.333 0.376 0.384 0.38 0.404 0.404 0.396 0.412 0.42 0.431 0.431 0.431 0.451 0.404 0.388 0.431 0.447 0.416 0.408 0.353 0.341 0.369 0.353 0.376 0.392 0.388 0.369 0.376 0.4 0.4 0.353 0.302 0.251 0.192 0.161 0.176 0.184 0.192 0.196 0.188 0.216 0.235 0.255 0.255 0.251 0.243 0.231 0.216 0.227 0.224 0.22 0.227
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0.51 0.51 0.533 0.533 0.522 0.502 0.49 0.49 0.498 0.533 0.557 0.545 0.537 0.588 0.604 0.604 0.612 0.62 0.624 0.639 0.639 0.639 0.635 0.643 0.647 0.643 0.655 0.655 0.643 0.651 0.639 0.647 0.651 0.659 0.663 0.663 0.678 0.702 0.659 0.325 0.031 0.035 0.043 0.047 0.047 0.051 0.047 0.047 0.043 0.047 0.047 0.047 0.055 0.059 0.067 0.063 0.063 0.055 0.051 0.055 0.055 0.055 0.047 0.047 0.051 0.055 0.051 0.047 0.039 0.039 0.047 0.051 0.047 0.047 0.055 0.059 0.059 0.055 0.051 0.047 0.047 0.059 0.063 0.063 0.063 0.055 0.059 0.059 0.055 0.055 0.055 0.047 0.055 0.055 0.055 0.059 0.059 0.059 0.055 0.063 0.059 0.059 0.055 0.047 0.047 0.051 0.039 0.212 0.659 0.647 0.631 0.643 0.647 0.631 0.635 0.655 0.667 0.702 0.525 0.067 0.035 0.043 0.224 0.416 0.141 0.196 0.522 0.678 0.643 0.424 0.161 0.388 0.576 0.827 0.894 0.773 0.506 0.471 0.647 0.624 0.631 0.631 0.631 0.561 0.361 0.267 0.271 0.306 0.353 0.388 0.424 0.467 0.392 0.082 0.031 0.039 0.106 0.173 0.137 0.467 0.647 0.655 0.655 0.659 0.675 0.675 0.663 0.659 0.678 0.706 0.722 0.729 0.741 0.741 0.757 0.773 0.784 0.788 0.784 0.773 0.745 0.671 0.58 0.561 0.569 0.565 0.584 0.616 0.62 0.612 0.588 0.537 0.62 0.69 0.682 0.69 0.69 0.706 0.706 0.71 0.714 0.722 0.737 0.698 0.627 0.612 0.612 0.612 0.612 0.612 0.612 0.62 0.604 0.608 0.612 0.612 0.612 0.62 0.616 0.596 0.588 0.588 0.58 0.588 0.58 0.569 0.576 0.584 0.588 0.588 0.62 0.604 0.596 0.592 0.596 0.588 0.592 0.596 0.592 0.584 0.588 0.588 0.573 0.576 0.584 0.576 0.576 0.576 0.58 0.565 0.573 0.58 0.573 0.565 0.573 0.569
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0.412 0.451 0.525 0.518 0.588 0.612 0.545 0.471 0.522 0.525 0.557 0.502 0.494 0.475 0.514 0.557 0.553 0.51 0.51 0.529 0.514 0.514 0.443 0.475 0.447 0.486 0.49 0.514 0.506 0.431 0.098 0.059 0.059 0.063 0.055 0.039 0.047 0.055 0.043 0.039 0.039 0.047 0.047 0.051 0.047 0.047 0.055 0.055 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.051 0.047 0.047 0.051 0.055 0.047 0.047 0.051 0.047 0.051 0.051 0.047 0.047 0.047 0.051 0.059 0.059 0.055 0.055 0.051 0.047 0.043 0.035 0.035 0.051 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.051 0.047 0.043 0.039 0.2 0.58 0.506 0.51 0.537 0.549 0.545 0.537 0.529 0.545 0.549 0.455 0.459 0.596 0.471 0.051 0.035 0.039 0.039 0.302 0.608 0.043 0.2 0.565 0.494 0.494 0.396 0.306 0.251 0.267 0.639 0.58 0.188 0.176 0.263 0.216 0.196 0.259 0.4 0.557 0.596 0.447 0.424 0.776 0.729 0.451 0.478 0.565 0.565 0.525 0.467 0.431 0.431 0.412 0.361 0.314 0.322 0.31 0.345 0.349 0.275 0.416 0.522 0.408 0.118 0.031 0.027 0.071 0.145 0.082 0.216 0.545 0.561 0.247 0.157 0.235 0.373 0.329 0.235 0.216 0.263 0.42 0.439 0.341 0.29 0.196 0.251 0.243 0.173 0.165 0.141 0.125 0.133 0.145 0.149 0.149 0.149 0.153 0.149 0.165 0.176 0.161 0.157 0.161 0.145 0.129 0.141 0.133 0.133 0.141 0.133 0.118 0.102 0.125 0.235 0.42 0.588 0.631 0.537 0.424 0.314 0.263 0.263 0.286 0.322 0.31 0.247 0.216 0.18 0.22 0.361 0.396 0.384 0.361 0.376 0.392 0.388 0.392 0.306 0.137 0.086 0.098 0.094 0.106 0.118 0.137 0.125 0.145 0.169 0.129 0.118 0.141 0.106 0.122 0.157 0.125 0.094
0.353 0.4 0.482 0.482 0.525 0.549 0.502 0.439 0.486 0.49 0.537 0.486 0.486 0.447 0.482 0.533 0.522 0.478 0.478 0.51 0.494 0.502 0.42 0.427 0.392 0.427 0.447 0.502 0.463 0.329 0.051 0.063 0.055 0.055 0.047 0.031 0.039 0.047 0.047 0.047 0.043 0.043 0.043 0.047 0.055 0.051 0.047 0.055 0.059 0.059 0.055 0.055 0.055 0.055 0.051 0.055 0.051 0.047 0.051 0.051 0.047 0.047 0.051 0.047 0.051 0.055 0.051 0.051 0.047 0.055 0.059 0.063 0.063 0.059 0.055 0.055 0.047 0.039 0.039 0.055 0.051 0.055 0.055 0.055 0.059 0.055 0.059 0.055 0.055 0.055 0.051 0.055 0.059 0.055 0.059 0.055 0.055 0.047 0.078 0.365 0.714 0.667 0.675 0.675 0.682 0.706 0.702 0.698 0.729 0.741 0.71 0.714 0.745 0.475 0.031 0.031 0.027 0.102 0.412 0.435 0.078 0.282 0.447 0.376 0.353 0.267 0.227 0.192 0.392 0.729 0.384 0.184 0.302 0.447 0.376 0.463 0.396 0.376 0.329 0.31 0.322 0.271 0.416 0.8 0.71 0.345 0.275 0.278 0.271 0.322 0.392 0.369 0.361 0.424 0.451 0.486 0.431 0.31 0.2 0.196 0.384 0.486 0.431 0.259 0.031 0.035 0.043 0.094 0.102 0.145 0.498 0.576 0.259 0.161 0.286 0.463 0.404 0.302 0.294 0.408 0.573 0.584 0.431 0.329 0.208 0.212 0.188 0.157 0.165 0.133 0.106 0.114 0.141 0.22 0.286 0.212 0.145 0.141 0.137 0.153 0.165 0.153 0.149 0.137 0.125 0.129 0.125 0.137 0.157 0.149 0.141 0.165 0.157 0.149 0.192 0.314 0.424 0.353 0.322 0.357 0.329 0.286 0.302 0.337 0.325 0.263 0.243 0.235 0.263 0.361 0.392 0.4 0.38 0.373 0.384 0.384 0.361 0.239 0.086 0.067 0.078 0.071 0.082 0.078 0.086 0.098 0.133 0.145 0.106 0.102 0.122 0.11 0.11 0.125 0.114 0.098
0.0 0.431 0.522 0.502 0.529 0.545 0.51 0.451 0.502 0.533 0.584 0.537 0.525 0.494 0.529 0.549 0.553 0.51 0.51 0.533 0.525 0.545 0.494 0.502 0.451 0.463 0.494 0.557 0.478 0.216 0.051 0.055 0.055 0.055 0.043 0.035 0.031 0.039 0.043 0.039 0.047 0.047 0.047 0.043 0.047 0.051 0.055 0.055 0.059 0.063 0.055 0.055 0.055 0.055 0.047 0.051 0.051 0.051 0.055 0.051 0.047 0.055 0.055 0.055 0.051 0.047 0.047 0.055 0.055 0.055 0.055 0.059 0.059 0.063 0.055 0.051 0.047 0.039 0.043 0.055 0.055 0.055 0.055 0.059 0.059 0.059 0.059 0.055 0.051 0.051 0.055 0.055 0.055 0.055 0.055 0.055 0.051 0.035 0.176 0.682 0.894 0.886 0.882 0.882 0.886 0.898 0.89 0.894 0.918 0.914 0.918 0.918 0.839 0.416 0.031 0.039 0.02 0.188 0.561 0.239 0.169 0.576 0.533 0.322 0.247 0.196 0.173 0.208 0.6 0.706 0.22 0.204 0.341 0.51 0.51 0.608 0.518 0.357 0.192 0.18 0.204 0.204 0.2 0.443 0.796 0.643 0.329 0.294 0.212 0.22 0.275 0.263 0.294 0.4 0.502 0.576 0.545 0.369 0.251 0.271 0.447 0.498 0.467 0.384 0.094 0.031 0.031 0.071 0.125 0.098 0.298 0.408 0.227 0.235 0.376 0.502 0.541 0.518 0.522 0.604 0.647 0.62 0.525 0.408 0.267 0.235 0.227 0.231 0.239 0.224 0.235 0.204 0.235 0.369 0.459 0.373 0.282 0.271 0.235 0.247 0.275 0.243 0.196 0.176 0.176 0.208 0.2 0.204 0.267 0.278 0.271 0.341 0.376 0.322 0.275 0.314 0.4 0.329 0.345 0.455 0.447 0.357 0.337 0.341 0.333 0.322 0.322 0.341 0.38 0.408 0.392 0.447 0.471 0.408 0.384 0.369 0.314 0.176 0.059 0.055 0.059 0.063 0.071 0.059 0.067 0.086 0.118 0.122 0.09 0.094 0.102 0.094 0.102 0.106 0.094 0.098
0.0 0.486 0.565 0.541 0.549 0.557 0.537 0.502 0.537 0.557 0.576 0.522 0.529 0.486 0.525 0.533 0.549 0.506 0.51 0.573 0.58 0.584 0.576 0.569 0.541 0.557 0.58 0.576 0.439 0.102 0.051 0.055 0.063 0.059 0.039 0.039 0.039 0.043 0.043 0.039 0.043 0.047 0.047 0.047 0.043 0.043 0.043 0.047 0.051 0.051 0.051 0.055 0.055 0.047 0.051 0.051 0.047 0.055 0.059 0.051 0.051 0.055 0.055 0.063 0.055 0.055 0.051 0.055 0.055 0.055 0.059 0.063 0.055 0.059 0.055 0.047 0.043 0.039 0.043 0.055 0.055 0.051 0.051 0.055 0.055 0.055 0.055 0.055 0.051 0.055 0.055 0.055 0.055 0.051 0.055 0.051 0.047 0.031 0.259 0.878 0.953 0.949 0.941 0.945 0.953 0.953 0.941 0.949 0.953 0.949 0.953 0.973 0.808 0.263 0.027 0.039 0.02 0.255 0.682 0.098 0.224 0.765 0.624 0.333 0.227 0.192 0.165 0.306 0.729 0.557 0.129 0.216 0.365 0.518 0.569 0.678 0.573 0.357 0.157 0.165 0.157 0.176 0.212 0.247 0.447 0.792 0.714 0.502 0.376 0.29 0.235 0.224 0.294 0.373 0.471 0.494 0.478 0.424 0.427 0.416 0.478 0.478 0.447 0.478 0.29 0.031 0.031 0.055 0.114 0.102 0.169 0.4 0.361 0.365 0.42 0.447 0.486 0.471 0.435 0.435 0.427 0.443 0.42 0.361 0.318 0.314 0.306 0.314 0.337 0.369 0.376 0.298 0.314 0.404 0.502 0.533 0.478 0.384 0.322 0.322 0.353 0.357 0.314 0.251 0.239 0.294 0.314 0.306 0.341 0.361 0.361 0.4 0.447 0.42 0.38 0.416 0.478 0.376 0.353 0.482 0.506 0.416 0.392 0.353 0.369 0.435 0.369 0.4 0.431 0.416 0.38 0.424 0.467 0.408 0.369 0.341 0.259 0.133 0.051 0.047 0.047 0.063 0.067 0.059 0.071 0.086 0.118 0.114 0.086 0.094 0.086 0.086 0.106 0.098 0.078 0.086
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