cormullion — 2½ D graphics.jl

### A Pluto.jl notebook ###
# v0.12.21

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
        el
    end
end

# ╔═╡ 22644f64-7e9b-11eb-3ba3-0dcdec7e57c6
using Luxor, Thebes, Colors, PlutoUI

# ╔═╡ fc459dbe-7ea0-11eb-04f3-1b7a7ba7f14d
md""" ## 2½ D graphics """

# ╔═╡ 6e73574e-7ea3-11eb-3032-3b9a1352bef7
md""" cormullion, 6th March 2021 """

# ╔═╡ 8646f864-7ea1-11eb-34c3-8d7fc241b6d4
md""" This is a short and very silly Pluto notebook to draw 2½D graphics."""

# ╔═╡ 916a319e-7ea3-11eb-0a55-ad133c6dd750
md""" Here's a list of vertices and the faces they make. I've hidden the contents of the cell because they're pretty boring..."""

# ╔═╡ c3a6d98a-7e9d-11eb-30da-5fbcd64d956b
sphere2 = (Point3D[Point3D(1.0, -0.0, 0.0),
Point3D(0.981, -0.195, 0.0),
Point3D(0.981, -0.0, 0.195),
Point3D(0.924, -0.383, 0.0),
Point3D(0.96, -0.199, 0.199),
Point3D(0.924, -0.0, 0.383),
Point3D(0.707, -0.707, 0.0),
Point3D(0.789, -0.577, 0.211),
Point3D(0.831, -0.556, 0.0),
Point3D(0.816, -0.408, 0.408),
Point3D(0.89, -0.405, 0.209),
Point3D(0.707, -0.0, 0.707),
Point3D(0.831, -0.0, 0.556),
Point3D(0.789, -0.211, 0.577),
Point3D(0.89, -0.209, 0.405),
Point3D(0.0, -1.0, 0.0),
Point3D(0.0, -0.981, 0.195),
Point3D(0.195, -0.981, 0.0),
Point3D(0.0, -0.924, 0.383),
Point3D(0.199, -0.96, 0.199),
Point3D(0.383, -0.924, 0.0),
Point3D(0.0, -0.707, 0.707),
Point3D(0.211, -0.789, 0.577),
Point3D(0.0, -0.831, 0.556),
Point3D(0.408, -0.816, 0.408),
Point3D(0.209, -0.89, 0.405),
Point3D(0.556, -0.831, 0.0),
Point3D(0.577, -0.789, 0.211),
Point3D(0.405, -0.89, 0.209),
Point3D(0.0, -0.0, 1.0),
Point3D(0.195, -0.0, 0.981),
Point3D(0.0, -0.195, 0.981),
Point3D(0.383, -0.0, 0.924),
Point3D(0.199, -0.199, 0.96),
Point3D(0.0, -0.383, 0.924),
Point3D(0.577, -0.211, 0.789),
Point3D(0.556, -0.0, 0.831),
Point3D(0.408, -0.408, 0.816),
Point3D(0.405, -0.209, 0.89),
Point3D(0.0, -0.556, 0.831),
Point3D(0.211, -0.577, 0.789),
Point3D(0.209, -0.405, 0.89),
Point3D(0.64, -0.64, 0.426),
Point3D(0.426, -0.64, 0.64),
Point3D(0.64, -0.426, 0.64),
Point3D(0.981, 0.195, 0.0),
Point3D(0.924, 0.383, 0.0),
Point3D(0.96, 0.199, 0.199),
Point3D(0.707, 0.707, 0.0),
Point3D(0.789, 0.577, 0.211),
Point3D(0.831, 0.556, 0.0),
Point3D(0.816, 0.408, 0.408),
Point3D(0.89, 0.405, 0.209),
Point3D(0.789, 0.211, 0.577),
Point3D(0.89, 0.209, 0.405),
Point3D(0.0, 1.0, 0.0),
Point3D(0.0, 0.981, 0.195),
Point3D(0.195, 0.981, 0.0),
Point3D(0.0, 0.924, 0.383),
Point3D(0.199, 0.96, 0.199),
Point3D(0.383, 0.924, 0.0),
Point3D(0.0, 0.707, 0.707),
Point3D(0.211, 0.789, 0.577),
Point3D(0.0, 0.831, 0.556),
Point3D(0.408, 0.816, 0.408),
Point3D(0.209, 0.89, 0.405),
Point3D(0.556, 0.831, 0.0),
Point3D(0.577, 0.789, 0.211),
Point3D(0.405, 0.89, 0.209),
Point3D(0.0, 0.195, 0.981),
Point3D(0.199, 0.199, 0.96),
Point3D(0.0, 0.383, 0.924),
Point3D(0.577, 0.211, 0.789),
Point3D(0.408, 0.408, 0.816),
Point3D(0.405, 0.209, 0.89),
Point3D(0.0, 0.556, 0.831),
Point3D(0.211, 0.577, 0.789),
Point3D(0.209, 0.405, 0.89),
Point3D(0.64, 0.64, 0.426),
Point3D(0.426, 0.64, 0.64),
Point3D(0.64, 0.426, 0.64),
Point3D(0.981, -0.0, -0.195),
Point3D(0.96, -0.199, -0.199),
Point3D(0.924, -0.0, -0.383),
Point3D(0.789, -0.577, -0.211),
Point3D(0.816, -0.408, -0.408),
Point3D(0.89, -0.405, -0.209),
Point3D(0.707, -0.0, -0.707),
Point3D(0.831, -0.0, -0.556),
Point3D(0.789, -0.211, -0.577),
Point3D(0.89, -0.209, -0.405),
Point3D(0.0, -0.981, -0.195),
Point3D(0.0, -0.924, -0.383),
Point3D(0.199, -0.96, -0.199),
Point3D(0.0, -0.707, -0.707),
Point3D(0.211, -0.789, -0.577),
Point3D(0.0, -0.831, -0.556),
Point3D(0.408, -0.816, -0.408),
Point3D(0.209, -0.89, -0.405),
Point3D(0.577, -0.789, -0.211),
Point3D(0.405, -0.89, -0.209),
Point3D(0.0, -0.0, -1.0),
Point3D(0.195, -0.0, -0.981),
Point3D(0.0, -0.195, -0.981),
Point3D(0.383, -0.0, -0.924),
Point3D(0.199, -0.199, -0.96),
Point3D(0.0, -0.383, -0.924),
Point3D(0.577, -0.211, -0.789),
Point3D(0.556, -0.0, -0.831),
Point3D(0.408, -0.408, -0.816),
Point3D(0.405, -0.209, -0.89),
Point3D(0.0, -0.556, -0.831),
Point3D(0.211, -0.577, -0.789),
Point3D(0.209, -0.405, -0.89),
Point3D(0.64, -0.64, -0.426),
Point3D(0.426, -0.64, -0.64),
Point3D(0.64, -0.426, -0.64),
Point3D(0.96, 0.199, -0.199),
Point3D(0.789, 0.577, -0.211),
Point3D(0.816, 0.408, -0.408),
Point3D(0.89, 0.405, -0.209),
Point3D(0.789, 0.211, -0.577),
Point3D(0.89, 0.209, -0.405),
Point3D(0.0, 0.981, -0.195),
Point3D(0.0, 0.924, -0.383),
Point3D(0.199, 0.96, -0.199),
Point3D(0.0, 0.707, -0.707),
Point3D(0.211, 0.789, -0.577),
Point3D(0.0, 0.831, -0.556),
Point3D(0.408, 0.816, -0.408),
Point3D(0.209, 0.89, -0.405),
Point3D(0.577, 0.789, -0.211),
Point3D(0.405, 0.89, -0.209),
Point3D(0.0, 0.195, -0.981),
Point3D(0.199, 0.199, -0.96),
Point3D(0.0, 0.383, -0.924),
Point3D(0.577, 0.211, -0.789),
Point3D(0.408, 0.408, -0.816),
Point3D(0.405, 0.209, -0.89),
Point3D(0.0, 0.556, -0.831),
Point3D(0.211, 0.577, -0.789),
Point3D(0.209, 0.405, -0.89),
Point3D(0.64, 0.64, -0.426),
Point3D(0.426, 0.64, -0.64),
Point3D(0.64, 0.426, -0.64),
Point3D(-1.0, -0.0, 0.0),
Point3D(-0.981, -0.195, 0.0),
Point3D(-0.981, -0.0, 0.195),
Point3D(-0.924, -0.383, 0.0),
Point3D(-0.96, -0.199, 0.199),
Point3D(-0.924, -0.0, 0.383),
Point3D(-0.707, -0.707, 0.0),
Point3D(-0.789, -0.577, 0.211),
Point3D(-0.831, -0.556, 0.0),
Point3D(-0.816, -0.408, 0.408),
Point3D(-0.89, -0.405, 0.209),
Point3D(-0.707, -0.0, 0.707),
Point3D(-0.831, -0.0, 0.556),
Point3D(-0.789, -0.211, 0.577),
Point3D(-0.89, -0.209, 0.405),
Point3D(-0.195, -0.981, 0.0),
Point3D(-0.199, -0.96, 0.199),
Point3D(-0.383, -0.924, 0.0),
Point3D(-0.211, -0.789, 0.577),
Point3D(-0.408, -0.816, 0.408),
Point3D(-0.209, -0.89, 0.405),
Point3D(-0.556, -0.831, 0.0),
Point3D(-0.577, -0.789, 0.211),
Point3D(-0.405, -0.89, 0.209),
Point3D(-0.195, -0.0, 0.981),
Point3D(-0.383, -0.0, 0.924),
Point3D(-0.199, -0.199, 0.96),
Point3D(-0.577, -0.211, 0.789),
Point3D(-0.556, -0.0, 0.831),
Point3D(-0.408, -0.408, 0.816),
Point3D(-0.405, -0.209, 0.89),
Point3D(-0.211, -0.577, 0.789),
Point3D(-0.209, -0.405, 0.89),
Point3D(-0.64, -0.64, 0.426),
Point3D(-0.426, -0.64, 0.64),
Point3D(-0.64, -0.426, 0.64),
Point3D(-0.981, 0.195, 0.0),
Point3D(-0.924, 0.383, 0.0),
Point3D(-0.96, 0.199, 0.199),
Point3D(-0.707, 0.707, 0.0),
Point3D(-0.789, 0.577, 0.211),
Point3D(-0.831, 0.556, 0.0),
Point3D(-0.816, 0.408, 0.408),
Point3D(-0.89, 0.405, 0.209),
Point3D(-0.789, 0.211, 0.577),
Point3D(-0.89, 0.209, 0.405),
Point3D(-0.195, 0.981, 0.0),
Point3D(-0.199, 0.96, 0.199),
Point3D(-0.383, 0.924, 0.0),
Point3D(-0.211, 0.789, 0.577),
Point3D(-0.408, 0.816, 0.408),
Point3D(-0.209, 0.89, 0.405),
Point3D(-0.556, 0.831, 0.0),
Point3D(-0.577, 0.789, 0.211),
Point3D(-0.405, 0.89, 0.209),
Point3D(-0.199, 0.199, 0.96),
Point3D(-0.577, 0.211, 0.789),
Point3D(-0.408, 0.408, 0.816),
Point3D(-0.405, 0.209, 0.89),
Point3D(-0.211, 0.577, 0.789),
Point3D(-0.209, 0.405, 0.89),
Point3D(-0.64, 0.64, 0.426),
Point3D(-0.426, 0.64, 0.64),
Point3D(-0.64, 0.426, 0.64),
Point3D(-0.981, -0.0, -0.195),
Point3D(-0.96, -0.199, -0.199),
Point3D(-0.924, -0.0, -0.383),
Point3D(-0.789, -0.577, -0.211),
Point3D(-0.816, -0.408, -0.408),
Point3D(-0.89, -0.405, -0.209),
Point3D(-0.707, -0.0, -0.707),
Point3D(-0.831, -0.0, -0.556),
Point3D(-0.789, -0.211, -0.577),
Point3D(-0.89, -0.209, -0.405),
Point3D(-0.199, -0.96, -0.199),
Point3D(-0.211, -0.789, -0.577),
Point3D(-0.408, -0.816, -0.408),
Point3D(-0.209, -0.89, -0.405),
Point3D(-0.577, -0.789, -0.211),
Point3D(-0.405, -0.89, -0.209),
Point3D(-0.195, -0.0, -0.981),
Point3D(-0.383, -0.0, -0.924),
Point3D(-0.199, -0.199, -0.96),
Point3D(-0.577, -0.211, -0.789),
Point3D(-0.556, -0.0, -0.831),
Point3D(-0.408, -0.408, -0.816),
Point3D(-0.405, -0.209, -0.89),
Point3D(-0.211, -0.577, -0.789),
Point3D(-0.209, -0.405, -0.89),
Point3D(-0.64, -0.64, -0.426),
Point3D(-0.426, -0.64, -0.64),
Point3D(-0.64, -0.426, -0.64),
Point3D(-0.96, 0.199, -0.199),
Point3D(-0.789, 0.577, -0.211),
Point3D(-0.816, 0.408, -0.408),
Point3D(-0.89, 0.405, -0.209),
Point3D(-0.789, 0.211, -0.577),
Point3D(-0.89, 0.209, -0.405),
Point3D(-0.199, 0.96, -0.199),
Point3D(-0.211, 0.789, -0.577),
Point3D(-0.408, 0.816, -0.408),
Point3D(-0.209, 0.89, -0.405),
Point3D(-0.577, 0.789, -0.211),
Point3D(-0.405, 0.89, -0.209),
Point3D(-0.199, 0.199, -0.96),
Point3D(-0.577, 0.211, -0.789),
Point3D(-0.408, 0.408, -0.816),
Point3D(-0.405, 0.209, -0.89),
Point3D(-0.211, 0.577, -0.789),
Point3D(-0.209, 0.405, -0.89),
Point3D(-0.64, 0.64, -0.426),
Point3D(-0.426, 0.64, -0.64),
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159, 155], [159, 160, 158], [150, 156, 149], [156, 160, 155], [160, 150, 151], [150, 160, 156], [161, 17, 16], [17, 162, 19], [162, 161, 163], [161, 162, 17], [24, 164, 22], [164, 166, 165], [166, 24, 19], [24, 166, 164], [168, 167, 152], [167, 169, 163], [169, 168, 165], [168, 169, 167], [162, 166, 19], [166, 169, 165], [169, 162, 163], [162, 169, 166], [32, 170, 30], [170, 172, 171], [172, 32, 35], [32, 172, 170], [174, 173, 157], [173, 176, 175], [176, 174, 171], [174, 176, 173], [177, 40, 22], [40, 178, 35], [178, 177, 175], [177, 178, 40], [172, 176, 171], [176, 178, 175], [178, 172, 35], [172, 178, 176], [153, 168, 152], [168, 179, 165], [179, 153, 155], [153, 179, 168], [164, 177, 22], [177, 180, 175], [180, 164, 165], [164, 180, 177], [173, 159, 157], [159, 181, 155], [181, 173, 175], [173, 181, 159], [179, 180, 165], [180, 181, 175], [181, 179, 155], [179, 181, 180], [146, 182, 148], [183, 184, 182], [151, 148, 184], [182, 184, 148], [185, 186, 187], [188, 189, 186], [183, 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210, 211], [147, 211, 210], [152, 213, 154], [214, 215, 213], [149, 154, 215], [213, 215, 154], [216, 217, 218], [212, 219, 217], [214, 218, 219], [217, 219, 218], [149, 215, 211], [214, 219, 215], [212, 211, 219], [215, 219, 211], [16, 92, 161], [93, 220, 92], [163, 161, 220], [92, 220, 161], [95, 221, 97], [222, 223, 221], [93, 97, 223], [221, 223, 97], [152, 167, 224], [163, 225, 167], [222, 224, 225], [167, 225, 224], [93, 223, 220], [222, 225, 223], [163, 220, 225], [223, 225, 220], [102, 226, 104], [227, 228, 226], [107, 104, 228], [226, 228, 104], [216, 229, 230], [231, 232, 229], [227, 230, 232], [229, 232, 230], [95, 112, 233], [107, 234, 112], [231, 233, 234], [112, 234, 233], [227, 232, 228], [231, 234, 232], [107, 228, 234], [232, 234, 228], [152, 224, 213], [222, 235, 224], [214, 213, 235], [224, 235, 213], [95, 233, 221], [231, 236, 233], [222, 221, 236], [233, 236, 221], [216, 218, 229], [214, 237, 218], [231, 229, 237], [218, 237, 229], [222, 236, 235], [231, 237, 236], [214, 235, 237], [236, 237, 235], [210, 182, 146], [182, 238, 183], [238, 210, 212], [210, 238, 182], [187, 239, 185], [239, 241, 240], [241, 187, 183], [187, 241, 239], [242, 217, 216], [217, 243, 212], [243, 242, 240], [242, 243, 217], [238, 241, 183], [241, 243, 240], [243, 238, 212], [238, 243, 241], [192, 124, 56], [124, 244, 125], [244, 192, 194], [192, 244, 124], [129, 245, 127], [245, 247, 246], [247, 129, 125], [129, 247, 245], [248, 198, 185], [198, 249, 194], [249, 248, 246], [248, 249, 198], [244, 247, 125], [247, 249, 246], [249, 244, 194], [244, 249, 247], [134, 226, 102], [226, 250, 227], [250, 134, 136], [134, 250, 226], [230, 251, 216], [251, 253, 252], [253, 230, 227], [230, 253, 251], [254, 140, 127], [140, 255, 136], [255, 254, 252], [254, 255, 140], [250, 253, 227], [253, 255, 252], [255, 250, 136], [250, 255, 253], [239, 248, 185], [248, 256, 246], [256, 239, 240], [239, 256, 248], [245, 254, 127], [254, 257, 252], [257, 245, 246], [245, 257, 254], [251, 242, 216], [242, 258, 240], [258, 251, 252], [251, 258, 242], [256, 257, 246], [257, 258, 252], [258, 256, 240], [256, 258, 257]]);


# ╔═╡ 34c81e7e-7e9b-11eb-0f31-2be4cd8a9f6e
# make a color lighter
function lighten(col::Colorant, f)
    c = convert(RGB, col)
    return RGB(f * c.r, f* c.g, f * c.b)
end

# ╔═╡ 34c77a82-7e9b-11eb-01c6-65fd78885b74
function drawobject(o;
        color=colorant"red")
    setlinejoin("bevel")
    if !isempty(o.faces)
        @layer begin
            for (n, f) in enumerate(o.faces)
                vertices = o.vertices[f]
                sn = surfacenormal(vertices)
                ang = anglebetweenvectors(sn, eyepoint())
                sethue(lighten(color, rescale(ang, 0, π, 0, 1.75)))
                pin(vertices, gfunction = (p3, p2) -> begin
                    poly(p2, :fillstroke)
                    #sethue(edgecolor)
                    #poly(p2, :stroke)
                end)
            end
        end
    end
end

# ╔═╡ 34d23ecc-7e9b-11eb-0781-1f1709f25469
function sphere(size, origin, color;
        upto=1,
        edgecolor=colorant"black")
    s1 = make(sphere2)
    scaleby!(s1, size, size, size)
    moveby!(s1, origin)
    sethue(color)
    setline(.5)
    sortfaces!(s1)
    drawobject(s1, color=color)
end

# ╔═╡ cc118d16-7ea1-11eb-0e95-45e2606042fa
md""" These four sliders adjust the `r, θ, ϕ` parameters (the spherical projection) of your `eyepoint()`, and `P` - the amount of perspective foreshortening.""" 

# ╔═╡ b7dadac2-7e9b-11eb-3f59-0940a80d3b11
@bind r Slider(100:600)

# ╔═╡ c4ccb0fc-7e9b-11eb-0b2b-0f8dfd08b339
@bind θ Slider(0:0.001:2π)

# ╔═╡ dd5252a8-7e9b-11eb-1e46-4f9a4161a1be
@bind ϕ Slider(0.1:0.001:π-0.1)

# ╔═╡ 69e37e9a-7e9c-11eb-2562-7dd5f0c032d0
@bind P Slider(200:800)

# ╔═╡ 3d721dde-7ea2-11eb-2bd2-05e395043188
md""" Now all you have to do is adjust the sliders to make the Julia logo!"""

# ╔═╡ 34dd3386-7e9b-11eb-2979-0f785dc44aa0
begin
    Drawing(800, 800, :svg)
    origin()
    background("black")
    helloworld()
    eyepoint(sphericaltocartesian(r, θ, ϕ))
    perspective(P)
    sphere(90, Point3D(150, 0, 0), RGB(Luxor.julia_red...))
    sphere(90, Point3D(0, 150, 0), RGB(Luxor.julia_purple...))
    sphere(90, Point3D(0, 0, 150), RGB(Luxor.julia_green...))
    axes3D(300)
    sethue("white")
    text("$(eyepoint())", boxtopleft(BoundingBox()) + (0, 20))
    finish()
    preview()
end

# ╔═╡ c4a6daec-7ea2-11eb-2509-e58195371d3a
md""" You'll notice that the three spheres are completely independent of each other; they exist in parallel 3D worlds... Making them aware of each other is a task for the reader!"""

# ╔═╡ 5aa09a66-7ea2-11eb-249e-412766035e22
md""" That's all!"""

# ╔═╡ Cell order:
# ╟─fc459dbe-7ea0-11eb-04f3-1b7a7ba7f14d
# ╟─6e73574e-7ea3-11eb-3032-3b9a1352bef7
# ╟─8646f864-7ea1-11eb-34c3-8d7fc241b6d4
# ╠═22644f64-7e9b-11eb-3ba3-0dcdec7e57c6
# ╟─916a319e-7ea3-11eb-0a55-ad133c6dd750
# ╟─c3a6d98a-7e9d-11eb-30da-5fbcd64d956b
# ╠═34c81e7e-7e9b-11eb-0f31-2be4cd8a9f6e
# ╠═34c77a82-7e9b-11eb-01c6-65fd78885b74
# ╠═34d23ecc-7e9b-11eb-0781-1f1709f25469
# ╟─cc118d16-7ea1-11eb-0e95-45e2606042fa
# ╠═b7dadac2-7e9b-11eb-3f59-0940a80d3b11
# ╠═c4ccb0fc-7e9b-11eb-0b2b-0f8dfd08b339
# ╠═dd5252a8-7e9b-11eb-1e46-4f9a4161a1be
# ╠═69e37e9a-7e9c-11eb-2562-7dd5f0c032d0
# ╟─3d721dde-7ea2-11eb-2bd2-05e395043188
# ╠═34dd3386-7e9b-11eb-2979-0f785dc44aa0
# ╟─c4a6daec-7ea2-11eb-2509-e58195371d3a
# ╟─5aa09a66-7ea2-11eb-249e-412766035e22