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using EzXML
"""
Get a complex parametric function for a series of cubic bezier curves as described in an .svg file. See README for details on file requirements.
"""
function createCurve(fileName)
doc = readxml(pwd() * "/" * fileName)
svg = root(doc)
layers = []
paths = []
for element in eachelement(svg)
occursin("layer", element["id"]) && push!(layers, element)
end
for element in eachelement(layers[1])
occursin("path", element["id"]) && push!(paths, element)
end
pointPattern = r"(?<=c ).*"
curveString = match(pointPattern, paths[1]["d"]).match
pattern = r"((?:-)?\d*(?:\.\d*)?),((?:-)?\d*(?:\.\d*)?)"
m = collect(eachmatch(pattern, curveString))
b_input = [[0.0,0.0]]
for i in m
k = length(b_input)
Δx = parse(Float64, i[1])
Δy = -parse(Float64, i[2])
new_point = [b_input[k-(k-1)%3][1] + Δx, b_input[k-(k-1)%3][2] + Δy]
push!(b_input, new_point)
end
return t -> parametricBezier(t, b_input)
end
"""
Parametric function for a curve made up of cubic bezier curves described by a vector of complex coordinates `input`.
Format for points taken from svg format.
"""
function parametricBezier(t, input)
t = t%1
n_input = length(input)-1
n_cubics = n_input÷3
cubicIndex = convert(Int, t÷(1//n_cubics)+1)
cubicTime = (t%(1/n_cubics))*n_cubics
currentCubic = input[3(cubicIndex-1)+1:3cubicIndex+1]
b_t = b(cubicTime, currentCubic)
return b_t[1] + b_t[2]*im
end
"""
Get position along bezier curve described by points `p` at time `t` from 0 to 1.
"""
function b(t, p)
s = [0,0]
for i in 1:length(p)
s += B(length(p)-1,i-1,t) * p[i]
end
return s
end
"Bernstein polynomial"
function B(n_p,i,t)
binomial(n_p,i)*t^i*(1-t)^(n_p-i)
end
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