added function to find volume

src/stlProcess.jl

@@ -16,15 +16,52 @@ struct Properties
     end
 end
 
-function get_mass_properties(triangles)
+function get_volume(triangles; scale=1)
+    """
+    Reference:
+        https://people.eecs.berkeley.edu/~wkahan/VtetLang.pdf
+    """
+
+    volume = 0.0
+    for tri in triangles
+        a, b, c = tri .* scale
+
+        W = sqrt(sum((a .- b) .^ 2))
+        V = sqrt(sum((b .- c) .^ 2))
+        U = sqrt(sum((c .- a) .^ 2))
+
+        v = sqrt(sum(a .^ 2))
+        u = sqrt(sum(b .^ 2))
+        w = sqrt(sum(c .^ 2))
+
+        X = (w - U + v) * (U + v + w)
+        Y = (u - V + w) * (V + w + u)
+        Z = (v - W + u) * (W + u + v)
+
+        x = (U - v + w) * (v - w + U)
+        y = (V - w + u) * (w - u + V)
+        z = (W - u + v) * (u - v + W)
+
+        ξ = sqrt(x * Y * Z)
+        η = sqrt(y * Z * X)
+        ζ = sqrt(z * X * Y)
+        λ = sqrt(x * y * z)
+
+        volume += sqrt((ξ + η + ζ - λ) * (λ + ξ + η - ζ) * (η + ζ + λ - ξ) * (ζ + λ + ξ - η)) / (192 * u * v * w)
+    end
+
+    return volume
+end
+
+function get_mass_properties(triangles; scale=1)
     """
     Reference:
     	https://github.com/WoLpH/numpy-stl/blob/42b6c67324e13b8712af6730f77e5e9544ef63b0/stl/base.py#L362
     	https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf
     """
-    x = reduce(hcat, [[v[1] for v in tri] for tri in triangles])'
-    y = reduce(hcat, [[v[2] for v in tri] for tri in triangles])'
-    z = reduce(hcat, [[v[3] for v in tri] for tri in triangles])'
+    x = reduce(hcat, [[v[1] .* scale for v in tri] for tri in triangles])'
+    y = reduce(hcat, [[v[2] .* scale for v in tri] for tri in triangles])'
+    z = reduce(hcat, [[v[3] .* scale for v in tri] for tri in triangles])'
 
     function subexpression(x)
         w0, w1, w2 = x[:, 1], x[:, 2], x[:, 3]
@@ -76,6 +113,6 @@ function get_mass_properties(triangles)
     return Properties(volume, center_of_gravity, inertia)
 end
 
-export get_mass_properties
+export get_mass_properties, get_volume
 
 end # module

test/runtests.jl

@@ -8,12 +8,25 @@ using MeshIO
 using LinearAlgebra
 
 @testset "simple cube stl" begin
-    # https://hepweb.ucsd.edu/ph110b/110b_notes/node26.html
-    stl = load(raw"test\test_assets\cubeblender.stl")
+    """
+    inertia math:
+        https://hepweb.ucsd.edu/ph110b/110b_notes/node26.html
 
-    props = get_mass_properties(stl)
+    Cube is a standard cube with a length of 2 for each side.
+    """
+    cube_path = raw"test_assets\cubeblender.stl"
+    stl = load(cube_path)
 
-    @test props.volume == 8.0
-    @test all(props.center_of_gravity .== 0.0)
-    @test all(eigvals(props.inertia) .≈ (5.0 + 1 / 3))
+    @testset "get_mass_properties" begin
+        props = get_mass_properties(stl)
+
+        @test props.volume == 8.0
+        @test all(props.center_of_gravity .== 0.0)
+        @test all(eigvals(props.inertia) .≈ (5.0 + 1 / 3))
+
+        @testset "get_volume" begin
+            @test get_volume(stl; scale=1) ≈ props.volume rtol = 0.01
+            @test get_volume(stl; scale=4) ≈ (4 * 2)^3 rtol = 0.01
+        end
+    end
 end