Visualzing digits

vis_digits.jl

using Luxor, ColorSchemes
using UnicodeFun
using Primes

struct PNGScene
    opts::Dict{Symbol, Any}
end

function get_coord(val, radius)
    θ = 2π*0.1*val
    return Point(
        radius*sin(θ),
        -radius*cos(θ),
    )
end

function draw_background(scene, framenumber)
    background("black")

    radius = scene.opts[:radius]
    show_dots = scene.opts[:show_dots]
    show_dots && (radius += 20)
    show_bars = scene.opts[:show_bars]
    show_bars && (radius += 5)

    colors = scene.opts[:colors]
    center_text = scene.opts[:center_text]

    setline(10)
    fontsize(20)
    for i in 0:9
        from = get_coord(i, radius)
        to = get_coord(i+1, radius)
        sethue(colors[i+1])

        θ = 2π*0.1*i+0.1*π
        mid = Point(
            radius*sin(θ),
            -radius*cos(θ),
        )
        if show_bars
            label(string(i), -π/2+θ, mid; offset=35)
        else
            label(string(i), -π/2+θ, mid; offset=15)
        end
        move(from)
        arc2r(O, from, to, :stroke)
    end

    sethue("white")
    fontsize(60)
    text(center_text, Point(-2, 0), valign=:middle, halign=:center)
end

function draw_bars(scene, framenumber)
    next_digit_mat = scene.opts[:next_digit_mat]
    next_digit_mat .= 0

    digits = scene.opts[:digits]
    colors = scene.opts[:colors]
    max_digits = scene.opts[:max_digits]
    
    radius = scene.opts[:radius]
    show_dots = scene.opts[:show_dots]
    show_dots && (radius += 20)
    show_bars = scene.opts[:show_bars]
    show_bars && (radius += 8)

    last_i = min(framenumber, max_digits-1)
    multiplier = 1000
    for i=1:last_i
        from_val = digits[i]
        to_val = digits[i+1]

        next_digit_mat[from_val+1, to_val+1] += 1
        ndm = next_digit_mat[from_val+1, to_val+1]
        sethue(colors[to_val+1])
        θ = 2π*0.1*(from_val+to_val/10)
        height = ndm/max_digits*multiplier
        bl = Point((radius+5)*sin(θ), -(radius+5)*cos(θ))
        tl = Point((radius+5+height)*sin(θ), -(radius+5+height)*cos(θ))

        θ = 2π*0.1*(from_val+(to_val+1)/10)
        tr = Point((radius+5+height)*sin(θ), -(radius+5+height)*cos(θ))
        br = Point((radius+5)*sin(θ), -(radius+5)*cos(θ))
       
        poly([bl,tl,tr,br,bl], :fill)
    end
end


function dig_line(scene, framenumber)
    radius = scene.opts[:radius]
    colors = scene.opts[:colors]
    center_text = scene.opts[:center_text]
    bezier_radius = scene.opts[:bezier_radius]
    max_digits = scene.opts[:max_digits]
    digits = scene.opts[:digits]

    setline(0.1)

    for i in 1:min(framenumber, max_digits-1)
        from_val = digits[i]
        to_val = digits[i+1]

        f = from_val+(i-1)/max_digits
        t = to_val+i/max_digits

        from = get_coord(f, radius)
        to = get_coord(t, radius)
    
        # get the correct mid point for example for 0-9 it should be 9.5 and not 4.5
        mid_val = (f+t)/2
        mid_control = get_coord(mid_val, bezier_radius)
        if abs(f-t) >= 5
            mid_control = get_coord(mid_val+5, bezier_radius)
        end

        pts = Point[from, mid_control, mid_control, to]
        bezpath = BezierPathSegment(pts...)
        # reverse the color to see where it is going
        setblend(blend(from, to, colors[to_val+1], colors[from_val+1]))
        drawbezierpath(bezpath, :stroke, close=false)
    end
end

function draw_dots(scene, framenumber)
    radius = scene.opts[:radius]
    colors = scene.opts[:colors]
    center_text = scene.opts[:center_text]
    bezier_radius = scene.opts[:bezier_radius]
    max_digits = scene.opts[:max_digits]
    digits = scene.opts[:digits]

    current_len = 1
    for i in 1:min(framenumber, max_digits-1)
        from_val = digits[i]
        to_val = digits[i+1]
        if from_val == to_val 
            current_len += 1
            continue
        end
        current_len == 1 && continue
        
        f = from_val+(i-1)/max_digits
        
        from = get_coord(f, radius + 10)

        sethue(colors[to_val+1])
        circle(from, current_len, :fill)

        current_len = 1
    end
end

function viz(;radius=250, bezier_radius=50, colors=ColorSchemes.rainbow[7:end],
        max_digits=1000, show_dots=false, show_bars=false, number=:pi, anim=true, width=500, height=500,
        fname="testing", show_lines=true
    )

    center_text = ""
    if number isa Symbol
        
        if number == :primes
            println("You have chosen to visualize the last digit of primes.")
            println("Be aware that max_digits now means the largest number.")
            digits_arr = [digits(x)[1] for x in primes(max_digits)]
            max_digits = length(digits_arr)
        else
            center_text = to_latex("\\$number")
            digits_arr = setprecision(BigFloat, Int(ceil(log2(10) * max_digits+10))) do
                if number == :pi
                    return parse.(Int, collect(string(BigFloat(pi))[3:max_digits+2]))
                elseif number == :tau
                    return parse.(Int, collect(string(2*BigFloat(pi))[3:max_digits+2]))
                end
            end
        end
    elseif number isa Integer
        digits_arr = reverse(digits(number))
    elseif eltype(number) <: Integer
        digits_arr = number
    else
        throw(DomainError(number, "$number should be either :pi, :tau, :primes or an integer"))
    end

    args = Dict(:radius => radius,
        :bezier_radius => bezier_radius,
        :colors => colors, :max_digits => max_digits,
        :digits => digits_arr, :center_text => center_text,
        :show_dots => show_dots, 
        :show_bars => show_bars, :next_digit_mat => zeros(Int, (10,10))
    )
    

    if anim
        movie = Movie(width, height, "test")
        scenes =  [
            Scene(movie, draw_background, 0:max_digits+50, optarg=args),
        ]
        if show_lines
            push!(scenes, Scene(movie, dig_line, 0:max_digits+50, optarg=args))
        end
        if show_dots
            push!(scenes, Scene(movie, draw_dots, 0:max_digits+50, optarg=args))
        end
        if show_bars
            push!(scenes, Scene(movie, draw_bars, 0:max_digits+50, optarg=args))
        end
        animate(movie, scenes,
            creategif = true,
            pathname = "./$fname.gif"
        )
    else
        scene = PNGScene(args)
        @png begin
            draw_background(scene, max_digits)
            if show_lines
                dig_line(scene, max_digits)
            end
            if show_dots
                draw_dots(scene, max_digits+50)
            end
            if show_bars
                draw_bars(scene, max_digits+50)
            end
        end 700 700 "./$fname.png"
    end
end