Transformations

Transformations

Mirror

using Compose
set_default_graphic_size(15cm,5cm)

f_points = [(.1, .1), (.9, .1), (.9, .2), (.2, .2), (.2, .4), (.6, .4), (.6, .5),
    (.2, .5), (.2, .9), (.1, .9), (.1, .1)]
f_points = (x->0.4.*x.+0.1).(f_points)
fpoly(ϕ::Float64) = (context(rotation=Rotation(ϕ,0.3,0.46)), polygon(f_points))

imgfa(θ, ϕ=0.0, x=0.5,y=0.5) = compose(context(),
  fill("salmon"), fillopacity(1.0), fpoly(ϕ),
  (context(rotation=Rotation(θ,x,y)), line([(x-0.5,y),(x+0.5,y)]), circle(x,y, 0.02)),
  (context(mirror=Mirror(θ, x, y)), fpoly(ϕ))
)

Fmir = hstack(imgfa(-π/4), imgfa(-π/2.2), imgfa(π/4, 1π))
img = compose(context(), rectangle(), fill(nothing), stroke("black"), Fmir)

Rotation

using Compose
set_default_graphic_size(15cm,5cm)

# This example also illustrates nested contexts
f_points = [(.1, .1), (.9, .1), (.9, .2), (.2, .2), (.2, .4),
    (.6, .4), (.6, .5), (.2, .5), (.2, .9), (.1, .9), (.1, .1)]
rect(c::String) = (context(), rectangle(), stroke(c))
circ(c::String, s::Float64=0.4) =  (context(), circle([x],[y],[0.03,s]), stroke(c))
fpoly(c::String) = (context(), polygon(f_points), fill(c), fillopacity(1.0))
contextC(θ::Float64) = (context(0.5,0.5,1.5,1.5, units=UnitBox(0,0,1,1),
        rotation=Rotation(θ,x,y)), fpoly("steelblue"), circ("orange"))
imgf(θ::Float64) =  compose(context(),
        (context(0.15, 0.15, 0.7, 0.7, units=UnitBox(0,0,2,2)), rect("red"),
        contextC(θ)) # context C in context B in context A
    )

x, y, θ = 0.5, 0.25, π/3
Frot =  hstack(imgf(-θ), imgf(0.), imgf(θ))
img = compose(context(), rectangle(), fill(nothing), stroke("black"), Frot)

Shear

using Compose
set_default_graphic_size(15cm, 5cm)

f_points = [(.1, .1), (.9, .1), (.9, .2), (.2, .2), (.2, .4), (.6, .4),
    (.6, .5), (.2, .5), (.2, .9), (.1, .9), (.1, .1)]
f_points = (x->0.5.*x.+0.3).(f_points)
ctxl(θ, x, y) = (context(rotation=Rotation(θ, x, y)), circle(x,y, 0.01),
    line([(x-0.5,y),(x+0.5,y)]))
fpoly(c::String) = (context(),  polygon(f_points), fill(c) )
ctxf(θ, ϕ, s, x, y,c) = (context(rotation=Rotation(-θ, x, y),
        shear=Shear(s, ϕ, x, y)), fpoly(c))

x, y, θ  = 0.5, 0.5, -π/6
img1 = compose(context(), stroke("black"), ctxl(θ,x,y),  ctxf(0,0,0,x,y, "yellow"),
    (context(), arc(x,y,0.3,π+θ,π-0.15), arrow()) )
img2 = compose(context(), stroke("black"), ctxl(0,x,y),
    ctxf(θ,0,1.8,x,y,"transparent"), ctxf(θ,0,0,x,y,"yellow"),
    text(0.5, 0.1, "x' = x+y*shear", hcenter, vcenter) )
img3 = compose(context(), stroke("black"),
    ctxl(θ, x, y), ctxf(0,θ,1.8,x,y,"yellow") )

hstack(img1, img2, img3)
x' = x+y*shear