Ellipsoids

In this file, we will visit the basic features provided by Dionysos for manipulating ellipsoids:

• inclusion
• intersection

First, let us import a few packages that are necessary to run this example.

using Dionysos
using StaticArrays
using LinearAlgebra
using Plots

The main package Dionysos provides most important data structures that we will need.

const DI = Dionysos
const UT = DI.Utils

Dionysos.Utils

We define a plotting functions

function plot_config!(fig, El0, El, Elnew)
    if Elnew ∈ El0
        plot!(fig, El0; color = :red, label = "El0")
        plot!(fig, Elnew; color = :green, label = "Elnew")
    else
        plot!(fig, Elnew; color = :green, label = "Elnew")
        plot!(fig, El0; color = :red, label = "El0")
    end
    return plot!(fig, El; color = :blue, label = "El", show = true)
end

function analyze(fig1, fig2, i)
    El0 = E0L[i]
    Elnew = UT.scale_for_inclusion_contact_point(El0, El)
    plot_config!(fig1, El0, El, Elnew)
    println(El0 ∈ El ? "El0 ∈ El" : "El0 ∉ El")

    Elnew = UT.scale_for_noninclusion_contact_point(El0, El)
    plot_config!(fig2, El0, El, Elnew)
    return println(UT.is_intersected(El0, El) ? "El0 ∩ El ≠ ∅" : "El0 ∩ El = ∅")
end

analyze (generic function with 1 method)

We define some ellipsoids

c = [1.5; 1.5]
P = [
    4.0 0.5
    0.5 6.0
]
El = UT.Ellipsoid(P, c)

P0 = [
    0.4 -0.1
    -0.1 0.5
]
vals = [4.1, 3.32, 2.8, 2.4]
E0L = [UT.Ellipsoid(P0, [c0x; c0x - 0.2]) for c0x in vals]

4-element Vector{Dionysos.Utils.Ellipsoid{Float64, Matrix{Float64}, Vector{Float64}}}:
 Dionysos.Utils.Ellipsoid{Float64, Matrix{Float64}, Vector{Float64}}([0.4 -0.1; -0.1 0.5], [4.1, 3.8999999999999995])
 Dionysos.Utils.Ellipsoid{Float64, Matrix{Float64}, Vector{Float64}}([0.4 -0.1; -0.1 0.5], [3.32, 3.1199999999999997])
 Dionysos.Utils.Ellipsoid{Float64, Matrix{Float64}, Vector{Float64}}([0.4 -0.1; -0.1 0.5], [2.8, 2.5999999999999996])
 Dionysos.Utils.Ellipsoid{Float64, Matrix{Float64}, Vector{Float64}}([0.4 -0.1; -0.1 0.5], [2.4, 2.1999999999999997])

Case 1: non intersection

fig1_1 = plot(; aspect_ratio = :equal);
fig1_2 = plot(; aspect_ratio = :equal);
analyze(fig1_1, fig1_2, 1)

El0 ∉ El
El0 ∩ El = ∅

plot!(fig1_1)

plot!(fig1_2)

Case 2: non intersection

fig2_1 = plot(; aspect_ratio = :equal);
fig2_2 = plot(; aspect_ratio = :equal);
analyze(fig2_1, fig2_2, 2)

El0 ∉ El
El0 ∩ El = ∅

plot!(fig2_1)

plot!(fig2_2)

Case 3: intersection, non inclusion

fig3_1 = plot(; aspect_ratio = :equal);
fig3_2 = plot(; aspect_ratio = :equal);
analyze(fig3_1, fig3_2, 3)

El0 ∉ El
El0 ∩ El ≠ ∅

plot!(fig3_1)

plot!(fig3_2)

Case 4: inclusion

fig4_1 = plot(; aspect_ratio = :equal);
fig4_2 = plot(; aspect_ratio = :equal);
analyze(fig4_1, fig4_2, 4)

El0 ∉ El
El0 ∩ El ≠ ∅

plot!(fig4_1)

plot!(fig4_2)

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