99 lines
2.7 KiB
Julia
99 lines
2.7 KiB
Julia
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include("Engine.jl")
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using LinearAlgebra
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using SparseArrays
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function sphere_in_tetrahedron_shape()
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# initialize the partial gram matrix for a sphere inscribed in a regular
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# tetrahedron
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J = Int64[]
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K = Int64[]
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values = BigFloat[]
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for j in 1:5
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for k in 1:5
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push!(J, j)
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push!(K, k)
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if j == k
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push!(values, 1)
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elseif (j <= 4 && k <= 4)
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push!(values, -1/BigFloat(3))
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else
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push!(values, -1)
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end
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end
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end
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gram = sparse(J, K, values)
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# plot loss along a slice
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loss_lin = []
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loss_sq = []
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mesh = range(0.9, 1.1, 101)
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for t in mesh
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L = hcat(
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Engine.plane(normalize(BigFloat[ 1, 1, 1]), BigFloat(1)),
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Engine.plane(normalize(BigFloat[ 1, -1, -1]), BigFloat(1)),
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Engine.plane(normalize(BigFloat[-1, 1, -1]), BigFloat(1)),
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Engine.plane(normalize(BigFloat[-1, -1, 1]), BigFloat(1)),
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Engine.sphere(BigFloat[0, 0, 0], BigFloat(t))
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)
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Δ_proj = Engine.proj_diff(gram, L'*Engine.Q*L)
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push!(loss_lin, norm(Δ_proj))
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push!(loss_sq, dot(Δ_proj, Δ_proj))
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end
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mesh, loss_lin, loss_sq
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end
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function circles_in_triangle_shape()
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# initialize the partial gram matrix for a sphere inscribed in a regular
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# tetrahedron
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J = Int64[]
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K = Int64[]
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values = BigFloat[]
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for j in 1:8
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for k in 1:8
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filled = false
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if j == k
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push!(values, 1)
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filled = true
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elseif (j == 1 || k == 1)
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push!(values, 0)
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filled = true
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elseif (j == 2 || k == 2)
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push!(values, -1)
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filled = true
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end
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#=elseif (j <= 5 && j != 2 && k == 9 || k == 9 && k <= 5 && k != 2)
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push!(values, 0)
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filled = true
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end=#
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if filled
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push!(J, j)
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push!(K, k)
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end
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end
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end
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append!(J, [6, 4, 6, 5, 7, 5, 7, 3, 8, 3, 8, 4])
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append!(K, [4, 6, 5, 6, 5, 7, 3, 7, 3, 8, 4, 8])
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append!(values, fill(-1, 12))
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# plot loss along a slice
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loss_lin = []
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loss_sq = []
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mesh = range(0.99, 1.01, 101)
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for t in mesh
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L = hcat(
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Engine.plane(BigFloat[0, 0, 1], BigFloat(0)),
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Engine.sphere(BigFloat[0, 0, 0], BigFloat(t)),
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Engine.plane(BigFloat[1, 0, 0], BigFloat(1)),
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Engine.plane(BigFloat[cos(2pi/3), sin(2pi/3), 0], BigFloat(1)),
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Engine.plane(BigFloat[cos(-2pi/3), sin(-2pi/3), 0], BigFloat(1)),
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Engine.sphere(4//3*BigFloat[-1, 0, 0], BigFloat(1//3)),
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Engine.sphere(4//3*BigFloat[cos(-pi/3), sin(-pi/3), 0], BigFloat(1//3)),
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Engine.sphere(4//3*BigFloat[cos(pi/3), sin(pi/3), 0], BigFloat(1//3))
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)
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Δ_proj = Engine.proj_diff(gram, L'*Engine.Q*L)
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push!(loss_lin, norm(Δ_proj))
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push!(loss_sq, dot(Δ_proj, Δ_proj))
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end
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mesh, loss_lin, loss_sq
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end
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