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Solid body dims
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@@ -11,12 +11,14 @@ struct Properties
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inertia::Matrix{Float64}
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surface_area::Float64
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characteristic_length::Float64
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sb_values::Vector{Float64}
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function Properties(volume, center_of_gravity, inertia, surface_area, characteristic_length)
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function Properties(volume, center_of_gravity, inertia, surface_area, characteristic_length, sb_values)
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@assert size(center_of_gravity) == (3,)
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@assert size(sb_values) == (3,)
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@assert size(inertia) == (3, 3)
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return new(volume, center_of_gravity, inertia, surface_area, characteristic_length)
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return new(volume, center_of_gravity, inertia, surface_area, characteristic_length, sb_values)
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end
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end
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@@ -29,6 +31,7 @@ function get_mass_properties(triangles; scale=1.0)
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x = reduce(hcat, [[v[1] .* scale for v in tri] for tri in triangles])'
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y = reduce(hcat, [[v[2] .* scale for v in tri] for tri in triangles])'
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z = reduce(hcat, [[v[3] .* scale for v in tri] for tri in triangles])'
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points = collect(Set(reduce(vcat, [[Array(Float64.(v)) .* scale for v in tri] for tri in triangles])))
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function subexpression(x)
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w0, w1, w2 = x[:, 1], x[:, 2], x[:, 3]
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@@ -76,16 +79,29 @@ function get_mass_properties(triangles; scale=1.0)
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inertia[1, 2] = inertia[2, 1] = -(intg[8] - volume .* center_of_gravity[1] .* center_of_gravity[2])
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inertia[2, 3] = inertia[3, 2] = -(intg[9] - volume .* center_of_gravity[2] .* center_of_gravity[3])
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inertia[1, 3] = inertia[3, 1] = -(intg[10] - volume .* center_of_gravity[3] .* center_of_gravity[1])
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inertia = inertia / volume
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# https://math.stackexchange.com/questions/128991/how-to-calculate-the-area-of-a-3d-triangle
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surface_area = sum(norm.(eachrow([x0 y0 z0] - [x1 y1 z1]) .× eachrow([x1 y1 z1] - [x2 y2 z2])) / 2)
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characteristic_length = calc_characteristic_length(triangles, inertia, center_of_gravity, scale)
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characteristic_length = calc_characteristic_length(points, inertia, center_of_gravity)
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return Properties(volume, center_of_gravity, inertia ./ volume, surface_area, characteristic_length)
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sb_values = solid_body(points)
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return Properties(volume, center_of_gravity, inertia, surface_area, characteristic_length, sb_values)
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end
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function calc_characteristic_length(triangles, inertia, center_of_gravity, scale; θtol=0.1)
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function solid_body(points)
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pts = reduce(hcat, points)
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Xsb = abs(reduce(-, extrema(@view pts[1, :])))
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Ysb = abs(reduce(-, extrema(@view pts[2, :])))
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Zsb = abs(reduce(-, extrema(@view pts[3, :])))
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return [Xsb, Ysb, Zsb]
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end
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function calc_characteristic_length(points, inertia, center_of_gravity)
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"""
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Calculate the Characteristic Length using eigenvectors.
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@@ -93,27 +109,17 @@ function calc_characteristic_length(triangles, inertia, center_of_gravity, scale
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More information on the geometry used: https://math.stackexchange.com/q/100447
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"""
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eigs = eigvecs(inertia)
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points = collect(Set(reduce(vcat, [[Array(Float64.(v)) .* scale for v in tri] for tri in triangles])))
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function θs_calc(ref, points)
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"""
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Calculates the angle between a reference vector and an array of points.
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"""
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norm_ref = norm(ref)
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return map(
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pt ->
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acos(clamp(dot(ref, pt .- center_of_gravity) / (norm(pt .- center_of_gravity) * norm_ref), -1.0, 1.0)),
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points,
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)
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end
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characteristic_points = []
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# find the characteristic points for each eigenvector
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for eig in eachrow(eigs)
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for eig in eachrow(eigvecs(inertia))
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# Find 3 points for each direction of the eigenvector
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θs = θs_calc(eig, points)
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θs = map(
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point -> acos(
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clamp(dot(eig, point .- center_of_gravity) / (norm(point .- center_of_gravity) * norm(eig)), -1.0, 1.0),
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),
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points,
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)
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sort_index = sortperm(θs)
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min_points = points[sort_index[1:3]]
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max_points = points[sort_index[(end - 2):end]]
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