add plate shape

src/MultipleScattering.jl

@@ -3,7 +3,7 @@ __precompile__()
 module MultipleScattering
 
 ## Shapes
-export Shape, Circle, Rectangle, Box, EmptyShape, Halfspace, TimeOfFlight, TimeOfFlightFromPoint
+export Shape, Circle, Rectangle, Box, EmptyShape, Halfspace, Plate, TimeOfFlight, TimeOfFlightFromPoint
 
 export outer_radius, volume, name, iscongruent, (≅), congruent, in, issubset, origin, shape, Sphere, (==), isequal, show
 export boundary_functions, boundary_points, boundary_data, bounding_box, box_corners

src/physics/special_functions.jl

@@ -190,7 +190,7 @@ cartesian_to_radial_coordinates(x::Vector) = cartesian_to_radial_coordinates(SVe
 radial_to_cartesian_coordinates(θ::Vector) = radial_to_cartesian_coordinates(SVector(θ...))
 
 function cartesian_to_radial_coordinates(x::SVector{3,CT}) where CT
-    r = sqrt(sum(x .^2)) # note this should be complex if x is complex
+    r = sqrt(sum(x .^2)) # note this is, and should be, a complex number when x is a complex vector
     θ = atan(sqrt(x[1]^2+x[2]^2),x[3])
     φ = atan(x[2], x[1])
     return [r,θ,φ]

src/shapes/halfspace.jl

@@ -1,7 +1,7 @@
 """
     Halfspace(normal::AbstractVector{T} [, origin::AbstractVector{T}=zeros()])
 
-N-dimensional [`Shape`](@ref) defined by all points x = origin - λ * normal, for any λ > 0.
+A halfspace defined by all the points ``\\mathbf x`` that satify ``(\\mathbf x - \\mathbf o) \\cdot \\mathbf n < 0`` where ``\\mathbf n`` is the unit normal and ``\\mathbf o`` is the origin.
 """
 struct Halfspace{T,Dim} <: Shape{T,Dim}
     normal::SVector{Dim,T} # outward pointing normal vector

src/shapes/plate.jl

@@ -0,0 +1,69 @@
+"""
+    Plate(normal::AbstractVector{T}, width::T, [, origin::AbstractVector{T}=zeros()])
+
+A plate defined by all the points ``\\mathbf x`` that satify ``|(\\mathbf x - \\mathbf o) \\cdot \\mathbf n| < w /2`` where ``\\mathbf n`` is the unit normal, ``\\mathbf o`` is the origin, and ``w`` is the width.
+"""
+struct Plate{T,Dim} <: Shape{T,Dim}
+    normal::SVector{Dim,T} # outward pointing normal vector
+    width::T # the width
+    origin::SVector{Dim,T}
+end
+
+# Constructors
+Plate(normal::AbstractVector{T}, width::T, origin::AbstractVector{T} = zeros(T,length(normal))) where {T} = Plate{T,length(normal)}(normal ./ norm(normal), width, origin)
+
+Plate(normal::NTuple{Dim,T}, width::T, origin::AbstractVector{T} = zeros(T,Dim)) where {T,Dim} = Plate{T,Dim}(normal ./ norm(normal), width, origin)
+
+name(shape::Plate) = "Plate"
+
+volume(shape::Plate) = Inf
+outer_radius(hs::Plate{T}) where T = T(Inf)
+
+# import Base.issubset
+# function issubset(inner_rect::Plate{T}, outer_rect::Plate{T}) where T
+#     all(topright(inner_rect) .<= topright(outer_rect)) &&
+#     all(bottomleft(inner_rect) .>= bottomleft(outer_rect))
+# end
+
+import Base.in
+function in(x::AbstractVector{T}, p::Plate)::Bool where T
+    abs(dot(x - p.origin, p.normal)) < p.width / T(2)
+end
+
+import Base.(==)
+function ==(h1::Plate{T}, h2::Plate{T}) where T
+    h1.origin == h2.origin &&
+    h1.width == h2.width &&
+    h1.normal == h2.normal
+end
+
+import Base.isequal
+function isequal(h1::Plate{T}, h2::Plate{T}) where T
+    isequal(h1.origin, h2.origin) &&
+    isequal(h1.width, h2.width) &&
+    isequal(h1.normal, h2.normal)
+end
+
+function iscongruent(h1::Plate{T}, h2::Plate{T}) where T
+    (h1.normal  == h2.normal) && (h1.width  == h2.width)
+end
+
+function congruent(h::Plate{T}, x) where T
+    Plate(h.normal, h.width, x)
+end
+
+# function boundary_functions(h::Plate{T,2}, scale::T = 10.0) where T
+#     surface_vec = [-h.normal[2], h.normal[1]]
+#
+#     function x(t)
+#         check_boundary_coord_range(t)
+#         h.origin[1] + surface_vec[1] * width/2 + t * scale * surface_vec[1]
+#     end
+#
+#     function y(t)
+#         check_boundary_coord_range(t)
+#         h.origin[2] + t * scale * surface_vec[2]
+#     end
+#
+#     return x, y
+# end

src/shapes/shapes.jl

@@ -41,9 +41,11 @@ end
 include("box.jl")
 include("sphere.jl")
 include("halfspace.jl")
+include("plate.jl")
 include("time_of_flight.jl")
 include("time_of_flight_from_point.jl")
 include("empty_shape.jl")
+
 """
     points_in_shape(Shape; res = 20, xres = res, yres = res,
              exclude_region = EmptyShape(region), kws...)

test/shapetests.jl

@@ -142,4 +142,20 @@
 
         @test true
     end
+
+    @testset "Infinite volume shapes" begin
+        normal = rand(3);
+        origin = rand(3);
+        width = 1.0 + rand();
+        p = Plate(normal, width, origin)
+        h = Halfspace(normal, origin)
+
+        shapes = [p,h];
+
+        @test isempty(findall( (volume.(shapes) .== Inf) .== 0))
+
+        xs = [rand(3) for i = 1:10];
+        [[x ∈ s for x in xs] for s in shapes]
+
+    end
 end