76 lines
1.8 KiB
Julia
76 lines
1.8 KiB
Julia
include("HittingSet.jl")
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module Engine
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include("Engine.Algebraic.jl")
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include("Engine.Numerical.jl")
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using .Algebraic
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using .Numerical
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export Construction, mprod, codimension, dimension
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end
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# ~~~ sandbox setup ~~~
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using Random
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using Distributions
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using LinearAlgebra
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using AbstractAlgebra
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using HomotopyContinuation
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using GLMakie
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CoeffType = Rational{Int64}
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spheres = [Engine.Sphere{CoeffType}() for _ in 1:3]
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tangencies = [
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Engine.AlignsWithBy{CoeffType}(
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spheres[n],
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spheres[mod1(n+1, length(spheres))],
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CoeffType(1)
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)
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for n in 1:3
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]
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ctx_tan_sph = Engine.Construction{CoeffType}(elements = spheres, relations = tangencies)
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ideal_tan_sph, eqns_tan_sph = Engine.realize(ctx_tan_sph)
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freedom = Engine.dimension(ideal_tan_sph)
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println("Three mutually tangent spheres: $freedom degrees of freedom")
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# --- test rational cut ---
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coordring = base_ring(ideal_tan_sph)
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vbls = Variable.(symbols(coordring))
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# test a random witness set
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system = CompiledSystem(System(eqns_tan_sph, variables = vbls))
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norm2 = vec -> real(dot(conj.(vec), vec))
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rng = MersenneTwister(6071)
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n_planes = 6
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samples = []
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for _ in 1:n_planes
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real_solns = solution.(Engine.Numerical.real_samples(system, freedom, rng = rng))
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for soln in real_solns
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if all(norm2(soln - samp) > 1e-4*length(gens(coordring)) for samp in samples)
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push!(samples, soln)
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end
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end
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end
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println("Found $(length(samples)) sample solutions")
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# show a sample solution
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function show_solution(ctx, vals)
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# evaluate elements
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real_vals = real.(vals)
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disp_points = [Engine.Numerical.evaluate(pt, real_vals) for pt in ctx.points]
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disp_spheres = [Engine.Numerical.evaluate(sph, real_vals) for sph in ctx.spheres]
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# create scene
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scene = Scene()
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cam3d!(scene)
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scatter!(scene, disp_points, color = :green)
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for sph in disp_spheres
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mesh!(scene, sph, color = :gray)
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end
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scene
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end |