Start "circles in triangle" from a very close guess
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@ -31,6 +31,11 @@ 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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#= make construction rigid
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append!(J, [3, 4, 4, 5])
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append!(K, [4, 3, 5, 4])
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append!(values, fill(-0.5, 4))
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=#
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gram = sparse(J, K, values)
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# set initial guess (random)
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@ -42,6 +47,7 @@ gram = sparse(J, K, values)
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## guess = Engine.rand_on_shell(fill(BigFloat(-1), 8))
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# set initial guess
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#=
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guess = hcat(
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Engine.plane(BigFloat[0, 0, 1], BigFloat(0)),
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Engine.sphere(BigFloat[0, 0, 0], BigFloat(1//2)),
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@ -52,6 +58,17 @@ guess = hcat(
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Engine.sphere(BigFloat[cos(-pi/3), sin(-pi/3), 0], BigFloat(1//5)),
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Engine.sphere(BigFloat[cos(pi/3), sin(pi/3), 0], BigFloat(1//5))
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)
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=#
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guess = hcat(
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Engine.plane(BigFloat[0, 0, 1], BigFloat(0)),
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Engine.sphere(BigFloat[0, 0, 0], BigFloat(0.9)),
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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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# complete the gram matrix using gradient descent
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L, history = Engine.realize_gram(gram, guess, max_descent_steps = 200)
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