add area and volume calculations

src/algorithms.jl

@@ -1,3 +1,12 @@
+"""
+The unnormalized normal of three vertices.
+"""
+function orthogonal_vector( v1, v2, v3 )
+        a = v2 - v1
+        b = v3 - v1
+        cross(a, b)
+end
+
 """
 ```
 normals{VT,FD,FT,FO}(vertices::Vector{Point{3, VT}},
@@ -16,9 +25,7 @@ function normals(
     for face in faces
         v = vertices[face]
         # we can get away with two edges since faces are planar.
-        a = v[2] - v[1]
-        b = v[3] - v[1]
-        n = cross(a, b)
+        n = orthogonal_vector(v[1], v[2], v[3])
         for i =1:length(F)
             fi = face[i]
             normals_result[fi] = normals_result[fi] + n
@@ -28,6 +35,48 @@ function normals(
     normals_result
 end
 
+"""
+Calculate the area of one triangle.
+"""
+function area(
+        vertices::AbstractVector{Point{3, VT}},
+        face::Face{3,FT}
+    ) where {VT,FT}
+    v1, v2, v3 = vertices[face]
+    return 0.5norm( orthogonal_vector(v1, v2, v3) )
+end
+
+"""
+Calculate the area of all triangles.
+"""
+function area(
+        vertices::AbstractVector{Point{3, VT}},
+        faces::AbstractVector{Face{3,FT}}
+    ) where {VT,FT}
+    return sum( x->area( vertices, x ), faces )
+end
+
+"""
+Calculate the signed volume of one tetrahedron. Be sure the orientation of your surface is right.
+"""
+function volume(
+        vertices::AbstractVector{Point{3, VT}},
+        face::Face{3,FT}
+    ) where {VT,FT}
+    v1, v2, v3 = vertices[face]
+    sig = sign( orthogonal_vector( v1, v2, v3 ) ⋅ v1 )
+    return sig * abs( v1 ⋅ ( v2 × v3 ) ) / 6
+end
+
+"""
+Calculate the signed volume of all tetrahedra. Be sure the orientation of your surface is right.
+"""
+function volume(
+        vertices::AbstractVector{Point{3, VT}},
+        faces::AbstractVector{Face{3,FT}}
+    ) where {VT,FT}
+    return sum( x->volume( vertices, x), faces )
+end
 
 """
 Slice an AbstractMesh at the specified Z axis value.

test/algorithms.jl

@@ -0,0 +1,16 @@
+using Test, GeometryTypes
+
+@testset "algorithms.jl" begin
+    cube = HyperRectangle(Vec3f0(-0.5), Vec3f0(1))
+    cube_faces = decompose(Face{3,Int}, Face{4, Int}[
+        (1,3,4,2),
+        (2,4,8,6),
+        (4,3,7,8),
+        (1,5,7,3),
+        (1,2,6,5),
+        (5,6,8,7),
+    ])
+    cube_vertices = decompose(Point{3,Float32}, cube) |> Array
+    @test area( cube_vertices, cube_faces ) == 6
+    @test volume( cube_vertices, cube_faces ) ≈ 1
+end

test/runtests.jl

@@ -27,4 +27,5 @@ using Test: @inferred
     include("lines.jl")
     include("polygons.jl")
     include("cylinder.jl")
+    include("algorithms.jl")
 end