Calculate Characteristic Length

src/stlProcess.jl

@@ -10,16 +10,17 @@ struct Properties
     center_of_gravity::Vector{Float64}
     inertia::Matrix{Float64}
     surface_area::Float64
+    characteristic_length::Float64
 
-    function Properties(volume, center_of_gravity, inertia, surface_area)
+    function Properties(volume, center_of_gravity, inertia, surface_area, characteristic_length)
         @assert size(center_of_gravity) == (3,)
         @assert size(inertia) == (3, 3)
 
-        return new(volume, center_of_gravity, inertia, surface_area)
+        return new(volume, center_of_gravity, inertia, surface_area, characteristic_length)
     end
 end
 
-function get_mass_properties(triangles; scale=1)
+function get_mass_properties(triangles; scale=1.0)
     """
     Reference:
     	https://github.com/WoLpH/numpy-stl/blob/42b6c67324e13b8712af6730f77e5e9544ef63b0/stl/base.py#L362
@@ -79,7 +80,70 @@ function get_mass_properties(triangles; scale=1)
     # https://math.stackexchange.com/questions/128991/how-to-calculate-the-area-of-a-3d-triangle
     surface_area = sum(norm.(eachrow([x0 y0 z0] - [x1 y1 z1]) .× eachrow([x1 y1 z1] - [x2 y2 z2])) / 2)
 
-    return Properties(volume, center_of_gravity, inertia ./ volume, surface_area)
+    characteristic_length = calc_characteristic_length(triangles, inertia, center_of_gravity, scale)
+
+    return Properties(volume, center_of_gravity, inertia ./ volume, surface_area, characteristic_length)
+end
+
+function calc_characteristic_length(triangles, inertia, center_of_gravity, scale; θtol=0.1)
+    """
+    Calculate the Characteristic Length using eigenvectors.
+
+    More information on characteristic length: https://ntrs.nasa.gov/api/citations/20090019123/downloads/20090019123.pdf
+    More information on the geometry used: https://math.stackexchange.com/q/100447
+    """
+
+    eigs = eigvecs(inertia)
+    points = collect(Set(reduce(vcat, [[Array(Float64.(v)) .* scale for v in tri] for tri in triangles])))
+
+    function θs_calc(ref, points)
+        """
+        Calculates the angle between a reference vector and an array of points. 
+        """
+        norm_ref = norm(ref)
+        return map(
+            pt ->
+                acos(clamp(dot(ref, pt .- center_of_gravity) / (norm(pt .- center_of_gravity) * norm_ref), -1.0, 1.0)),
+            points,
+        )
+    end
+
+    characteristic_points = []
+    # find the characteristic points for each eigenvector
+    for eig in eachrow(eigs)
+
+        # Find 3 points for each direction of the eigenvector
+        θs = θs_calc(eig, points)
+        sort_index = sortperm(θs)
+        min_points = points[sort_index[1:3]]
+        max_points = points[sort_index[(end - 2):end]]
+
+        # Create a parameterized function using the eigenvector and center_of_gravity
+        line_func(t) = center_of_gravity .+ eig .* t
+
+        # create a plane using 3 points, then find where the parameterized function intercepts it
+        max_normal = (max_points[1] - max_points[2]) × (max_points[2] - max_points[3])
+        max_t = find_zero(t -> let
+            l = line_func(t)
+            sum(max_normal .* (l .- max_points[1]))
+        end, norm(eig))
+
+        max_point = line_func(max_t)
+
+        # Build a plane in the opposite direction, and find the intercept again
+        min_normal = (min_points[1] - min_points[2]) × (min_points[2] - min_points[3])
+        min_t = find_zero(t -> let
+            l = line_func(t)
+            sum(min_normal .* (l .- min_points[1]))
+        end, -norm(eig))
+
+        min_point = line_func(min_t)
+
+        push!(characteristic_points, (min_point, max_point))
+    end
+
+    # Calculate the characteristic length. 
+    return sum([sqrt(sum((max - min) .^ 2)) for (min, max) in characteristic_points]) / 3.0
 end
 
 function fast_volume(triangles; scale=1)