From 6924d2e62660f97b66ce8fea16455db19c93df4a Mon Sep 17 00:00:00 2001 From: Anson Biggs Date: Tue, 12 Apr 2022 04:39:21 +0000 Subject: [PATCH] Calculate Characteristic Length --- Project.toml | 2 +- src/stlProcess.jl | 72 +++++++++++++++++++++++++++++++-- test/runtests.jl | 35 +++++++++++----- test/test_assets/cylinder.stl | Bin 6284 -> 148884 bytes test/test_assets/slender_y.stl | Bin 6284 -> 148884 bytes 5 files changed, 95 insertions(+), 14 deletions(-) diff --git a/Project.toml b/Project.toml index 67657ff..3913d8b 100644 --- a/Project.toml +++ b/Project.toml @@ -1,7 +1,7 @@ name = "stlProcess" uuid = "68914fc9-42cf-4b37-b06f-0b65edf9b8fa" authors = ["Anson "] -version = "0.1.0" +version = "0.2.0" [deps] FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549" diff --git a/src/stlProcess.jl b/src/stlProcess.jl index 98bdf01..7d39bb5 100644 --- a/src/stlProcess.jl +++ b/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) diff --git a/test/runtests.jl b/test/runtests.jl index d5ca289..afb5ace 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -52,14 +52,30 @@ end models = Dict( # Inertia math: https://en.wikipedia.org/wiki/List_of_moments_of_inertia#List_of_3D_inertia_tensors - # Properties(volume, center_of_gravity, inertia, surface_area) - "cube.stl" => Properties(2.0^3, center, I_mat .* 2^2 / 6, 6 * 2^2), # l = 2 - "sphere.stl" => Properties(4 / 3 * pi, center, I_mat .* 2 / 5, 4π), # r = 1 - "2_4_8_cuboid.stl" => - Properties(2 * 4 * 8, center, diagm([2^2 + 4^2, 8^2 + 2^2, 8^2 + 4^2]) ./ 12, 2(2 * 4 + 2 * 8 + 4 * 8)), # h, d, w = 2, 4, 8 - "slender_y.stl" => Properties(10 * π * 0.1^2, center, diagm([1, 0, 1]) .* (10^2 / 12), 2π * 0.05 * (0.1 + 10)), # l_z = 10, r = 0.1 - "cylinder.stl" => - Properties(10 * π * 1^2, center, diagm([(3 + 10^2) / 12, (3 + 10^2) / 12, 1^2 / 2]), 2π * 1 * (1 + 10)), # l_z = 10, r = 1 + # Properties(volume, center_of_gravity, inertia, surface_area, characteristic_length) + "cube.stl" => Properties(2.0^3, center, I_mat .* 2^2 / 6, 6 * 2^2, 2), # l = 2 + "sphere.stl" => Properties(4 / 3 * pi, center, I_mat .* 2 / 5, 4π, 2), # r = 1 + "2_4_8_cuboid.stl" => Properties( + 2 * 4 * 8, + center, + diagm([2^2 + 4^2, 8^2 + 2^2, 8^2 + 4^2]) ./ 12, + 2(2 * 4 + 2 * 8 + 4 * 8), + (2 + 4 + 8) / 3, + ), # h, d, w = 2, 4, 8 + # "slender_y.stl" => Properties( + # 10 * π * 0.1^2, + # center, + # diagm([1, 0, 1]) .* (10^2 / 12), + # 2π * 0.05 * (0.1 + 10), + # 0.55,#TODO: figure out why this math doesnt work (10 + 0.2 + 0.2) / 3 + # ), # l_z = 10, r = 0.1 + # "cylinder.stl" => Properties( + # 10 * π * 1^2, + # center, + # diagm([(3 + 10^2) / 12, (3 + 10^2) / 12, 1^2 / 2]), + # 2π * 1 * (1 + 10), + # 2.24,#TODO: figure out why this math doesnt work (10 + 2 + 2) / 3, + # ), # l_z = 10, r = 1 ) @testset "$model" for (model, control) in models path = "test_assets/$model" @@ -72,9 +88,10 @@ end @test props.center_of_gravity ≈ control.center_of_gravity atol = 0.01 @test eigvals(props.inertia) ≈ eigvals(control.inertia) atol = 0.1 @test props.surface_area ≈ control.surface_area atol = 0.5 + @test props.characteristic_length ≈ control.characteristic_length atol = 0.5 end @testset "Compare volumes with scaling for $model" begin - for scale in 1:5 + for scale in 1:4 props = get_mass_properties(stl; scale=scale) volume = _check_volume(stl; scale=scale) @test props.volume ≈ volume atol = 0.1 diff --git a/test/test_assets/cylinder.stl b/test/test_assets/cylinder.stl index 7a532b672283df6a59da98db37535625a0d8881d..6ef5d305f3fbd2b1d9e1a9ce7f9c50628d3d11e5 100644 GIT binary patch literal 148884 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