June 2018 Update

Task/Problem-of-Apollonius/Julia/problem-of-apollonius-1.julia

@@ -0,0 +1,51 @@
+module ApolloniusProblems
+
+using Polynomials
+export Circle
+
+struct Point{T<:Real}
+    x::T
+    y::T
+end
+
+xcoord(p::Point) = p.x
+ycoord(p::Point) = p.y
+
+struct Circle{T<:Real}
+    c::Point{T}
+    r::T
+end
+Circle(x::T, y::T, r::T) where T<:Real = Circle(Point(x, y), r)
+
+radius(c::Circle) = c.r
+center(c::Circle) = c.c
+xcenter(c::Circle) = xcoord(center(c))
+ycenter(c::Circle) = ycoord(center(c))
+
+Base.show(io::IO, c::Circle) =
+    @printf(io, "centered at (%0.4f, %0.4f) with radius %0.4f",
+        xcenter(c), ycenter(c), radius(c))
+
+function solve(ap::Vector{Circle{T}}, enc=()) where T<:Real
+    length(ap) == 3 || error("This Apollonius problem needs 3 circles.")
+    x = @. xcenter(ap)
+    y = @. ycenter(ap)
+    r = map(u -> ifelse(u ∈ enc, -1, 1), 1:3) .* radius.(ap)
+    @views begin
+        a = 2x[1] .- 2x[2:3]
+        b = 2y[1] .- 2y[2:3]
+        c = 2r[1] .- 2r[2:3]
+        d = (x[1] ^ 2 + y[1] ^ 2 - r[1] ^ 2) .- (x[2:3] .^ 2 .+ y[2:3] .^ 2 .- r[2:3] .^ 2)
+    end
+    u = Poly([-det([b d]), det([b c])] ./ det([a b]))
+    v = Poly([det([a d]), -det([a c])] ./ det([a b]))
+    w = Poly([r[1], 1.0]) ^ 2
+    s = (u - x[1]) ^ 2 + (v - y[1]) ^ 2 - w
+    r = filter(x -> iszero(imag(x)) && x > zero(x), roots(s))
+    length(r) <  2 || error("The solution is not unique.")
+    length(r) == 1 || error("There is no solution.")
+    r = r[1]
+    return Circle(polyval(u, r), polyval(v, r), r)
+end
+
+end  # module ApolloniusProblem

Task/Problem-of-Apollonius/Julia/problem-of-apollonius-2.julia

@@ -0,0 +1,8 @@
+include("module.jl")
+using ApolloniusProblems
+
+let test = [Circle(0.0, 0.0, 1.0), Circle(4.0, 0.0, 1.0), Circle(2.0, 4.0, 2.0)]
+    println("The defining circles are: \n - ", join(test, "\n - "))
+    println("The internal circle is:\n\t", ApolloniusProblems.solve(test))
+    println("The external circle is:\n\t", ApolloniusProblems.solve(test, 1:3))
+end

Task/Problem-of-Apollonius/Julia/problem-of-apollonius.julia

@@ -1,55 +0,0 @@
-using Polynomials
-
-immutable Point{T<:Real}
-    x::T
-    y::T
-end
-
-immutable Circle{T<:Real}
-    c::Point{T}
-    r::T
-end
-Circle{T<:Real}(x::T, y::T, r::T) = Circle(Point(x,y), r)
-
-function apollonius{T<:Real}(ap::Array{Circle{T},1},
-                             enc::Array{Int,1}=Int[])
-    length(ap) == 3 || error("This Apollonius problem needs 3 circles.")
-    x = map(u->u.c.x, ap)
-    y = map(u->u.c.y, ap)
-    r = map(u->u in enc ? -1 : 1, 1:3) .* map(u->u.r, ap)
-    a = 2x[1] - 2x[2:3]
-    b = 2y[1] - 2y[2:3]
-    c = 2r[1] - 2r[2:3]
-    d = (x[1]^2 + y[1]^2 - r[1]^2)
-    d -= (map(u->u^2, x) + map(u->u^2, y) - map(u->u^2, r))[2:3]
-    u = Poly([-det(hcat(b,d)), det(hcat(b,c))]/det(hcat(a,b)))
-    v = Poly([det(hcat(a,d)), -det(hcat(a,c))]/det(hcat(a,b)))
-    w = Poly([r[1], 1.0])^2
-    s = (u - x[1])^2 + (v - y[1])^2 - w
-    r = filter(x->imag(x)==0 && 0<x, roots(s))
-    length(r) < 2 || error("The solution is not unique.")
-    length(r) == 1 || error("There is no solution.")
-    r = r[1]
-    Circle(polyval(u,r), polyval(v,r), r)
-end
-
-function detail(c::Circle)
-    x = @sprintf "%.4f" c.c.x
-    y = @sprintf "%.4f" c.c.y
-    r = @sprintf "%.4f" c.r
-    @sprintf "centered at (%s, %s) with radius %s" x y r
-end
-
-
-test = [Circle(0.,0.,1.),
-        Circle(4.,0.,1.),
-        Circle(2.,4.,2.)]
-
-println("The defining circles are:")
-for c in test
-    println("    ", detail(c))
-end
-println("The internal circle is:")
-println("    ", detail(apollonius(test)))
-println("The external circle is:")
-println("    ", detail(apollonius(test, [1:3])))