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heart.jl
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heart.jl
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using Random
include("fourier.jl")
ts = LinRange(0, 2 * pi, 500)
# depth = 15 ok
heart_xs = [16 * sin(t)^3 for t in ts]
heart_ys = [12 * cos(t) - 5*cos(2*t) - 2*cos(3*t)-cos(4*t) for t in ts]
scatter(heart_xs, heart_ys, aspect_ratio=:equal)
begin
flip = true
df = CSV.read("input/markus.txt", DataFrame)
# depth = 35 ok
markus_xs = df[!, "x"] / 17 .- 10
markus_ys = -df[!, "y"] / 17 .+ 14 .- (flip ? 4.5 : 0.)
df = CSV.read("input/caroline.csv", DataFrame)
caroline_xs = df[!, "x"] / 17 .- 10
caroline_ys = -df[!, "y"] / 17 .+ 7 .+ (flip ? 5.8 : 0.)
scatter(heart_xs, heart_ys, aspect_ratio=:equal);
scatter!(markus_xs, markus_ys, aspect_ratio=:equal);
scatter!(caroline_xs, caroline_ys, aspect_ratio=:equal)
end
points = markus_xs .+ im .* markus_ys
coeffs = fourier_series(points, 150, 0.01)
markus_coeffs = coeffs
points = caroline_xs .+ im .* caroline_ys
coeffs = fourier_series(points, 150, 0.01)
caroline_coeffs = coeffs
points = heart_xs .+ im .* heart_ys
coeffs = fourier_series(points, 15, 0.01)
heart_coeffs = coeffs
using Statistics
moving_average(vs,n) = [sum(@view vs[i:(i+n-1)])/n for i in 1:(length(vs)-(n-1))]
moving_average2(vs,n) = [mean(@view vs[max(1,i):min(length(vs),(i+n-1))]) for i in 1:length(vs)]
begin
depth = 150 # = number of circles / 2
coeffs = fourier_series(points, depth, 0.01)
F = get_fourier_func(coeffs)
ts = LinRange(0,2π-0.1, 900)
fs = F.(ts)
fs = moving_average2(fs, 10)
plot(fs)
end
function plot_fourier_circles(coeffs::Vector{ComplexF64}, t::Float64=0.; circle_color=1, center_size=2, xlims, ylims, p=nothing, alpha=1)
depth = length(coeffs) ÷ 2
n0 = depth + 1
ts = LinRange(0, 2π, 100)
if isnothing(p)
p = plot(legend=false, size=(600,600), xlims=xlims, ylims=ylims, aspect_ratio=:equal, axis=nothing, border=:none, xlabel="", ylabel="")
end
current = coeffs[n0]
scatter!([coeffs[n0]], mc=2, ms=center_size, alpha=alpha)
for d in 1:depth
n = n0 + d
plot!(current .+ coeffs[n] * exp.(im*d*ts), lc=circle_color, alpha=alpha)
current += coeffs[n] * exp(im*d*t)
if d < 5
scatter!([current], mc=2, ms=center_size, alpha=alpha)
end
n = n0 - d
plot!(current .+ coeffs[n] * exp.(-im*d*ts), lc=circle_color, alpha=alpha)
current += coeffs[n] * exp(-im*d*t)
if d < 5
scatter!([current], mc=2, ms=center_size, alpha=alpha)
end
end
return p
end
function animate_fourier_heart(
markus_coeffs::Vector{ComplexF64}, caroline_coeffs::Vector{ComplexF64}, heart_coeffs::Vector{ComplexF64},
n::Int=100; trace=false,
circle_color=1, center_size=2, lw=3, lc=:black, xlims, ylims)
ts = LinRange(0, 2π, n)
# markus_fs = get_fourier_func(markus_coeffs).(ts)
# caroline_fs = get_fourier_func(caroline_coeffs).(ts)
# heart_fs = get_fourier_func(heart_coeffs).(ts)
#
# markus_trace_range = sum(ts .<= 0.1):sum(ts .< 2π-0.1)
# caroline_trace_range = sum(ts .<= 0.1):sum(ts .< 2π-0.1)
markus_fs = moving_average2(get_fourier_func(markus_coeffs).(ts), 10)
caroline_fs = moving_average2(get_fourier_func(caroline_coeffs).(ts), 10)
heart_fs = get_fourier_func(heart_coeffs).(ts)
#ts = moving_average(ts, 10)
markus_trace_range = sum(ts .<= 0):sum(ts .< 2π-0.1)
caroline_trace_range = sum(ts .<= 0):sum(ts .< 2π-0.1)
moving_average(fs, 10)
anim = Animation()
i = 0
L = length(ts)
@showprogress for (i,t) in enumerate(ts)
a = min(i / 15, 1)
p = plot_fourier_circles(markus_coeffs, -t, circle_color=circle_color, center_size=center_size, xlims=xlims, ylims=ylims, alpha=a)
p = plot_fourier_circles(caroline_coeffs, t, circle_color=circle_color, center_size=center_size, xlims=xlims, ylims=ylims, p=p, alpha=a)
p = plot_fourier_circles(heart_coeffs, t, circle_color=circle_color, center_size=center_size, xlims=xlims, ylims=ylims, p=p, alpha=a)
#plot!(markus_fs[markus_trace_range], lw=lw, lc=:gray)
plot!(markus_fs[intersect(markus_trace_range, (L-i+1):L)], lw=lw, lc=lc)
#plot!(caroline_fs[caroline_trace_range], lw=lw, lc=:gray)
plot!(caroline_fs[intersect(caroline_trace_range, 1:i)], lw=lw, lc=lc)
#plot!(heart_fs, lw=lw, lc=:gray)
plot!(heart_fs[1:i], lw=lw, lc=:red)
xlabel!("")
ylabel!("")
frame(anim, p)
end
@showprogress for i in 1:150
a = max(1 - i / 15, 0)
p = plot_fourier_circles(markus_coeffs, ts[end], circle_color=circle_color, center_size=center_size, xlims=xlims, ylims=ylims, alpha=a)
p = plot_fourier_circles(caroline_coeffs, ts[end], circle_color=circle_color, center_size=center_size, xlims=xlims, ylims=ylims, p=p, alpha=a)
p = plot_fourier_circles(heart_coeffs, ts[end], circle_color=circle_color, center_size=center_size, xlims=xlims, ylims=ylims, p=p, alpha=a)
#plot!(markus_fs[markus_trace_range], lw=lw, lc=:gray)
plot!(markus_fs[markus_trace_range], lw=lw, lc=lc)
#plot!(caroline_fs[caroline_trace_range], lw=lw, lc=:gray)
plot!(caroline_fs[caroline_trace_range], lw=lw, lc=lc)
#plot!(heart_fs, lw=lw, lc=:gray)
plot!(heart_fs, lw=lw, lc=:red)
xlabel!("")
ylabel!("")
frame(anim, p)
end
return anim
end
#n = 450
n = 900
anim = animate_fourier_heart(markus_coeffs, caroline_coeffs, heart_coeffs, n,
lw=4, xlims=(-20, 20), ylims=(-22, 15))
gif(anim, "tmp.gif", fps=30)
mp4(anim, "tmp.mp4", fps=30)