Julia package for sampling and generating points on the boundary of an ellipse with methods for random, equally spaced and clustered points
Home Page: https://joeltrent.github.io/EllipseSampling.jl/
License: MIT License
Minimum working example (for version 0.1.1):
using EllipseSampling
import Distributions
using Plots
gr()
N=8
a, b = 2.0, 1.0
α = 0.25*π
Cx, Cy= 2.0, 2.0
points=generate_N_equally_spaced_points(N, a, b, α, Cx, Cy, start_point_shift=0.0)
plt=scatter(points[1,:], points[2,:], label=nothing, mw=0, ms=8, aspect_ratio=:equal)
Hw11 = (cos(α)^2 / a^2 + sin(α)^2 / b^2)
Hw22 = (sin(α)^2 / a^2 + cos(α)^2 / b^2)
Hw12 = cos(α)*sin(α)*(1/a^2 - 1/b^2)
Hw_norm = [Hw11 Hw12; Hw12 Hw22]
confidence_level=0.95
Hw = Hw_norm ./ (0.5 ./ (Distributions.quantile(Distributions.Chisq(2), confidence_level)*0.5))
Γ = inv(Hw)
points2 = generate_N_equally_spaced_points(N, Γ, [Cx, Cy], 1, 2, confidence_level=confidence_level, start_point_shift=0.0)
scatter!(points2[1, :], points2[2, :], label=nothing, markeralpha=0.5, mw=0, ms=4)
display(plt)
If we modify the rotation slightly away from 0.25pi the problem goes away:
a, b = 2.0, 1.0
α = 0.251*π
Cx, Cy= 2.0, 2.0
points=generate_N_equally_spaced_points(N, a, b, α, Cx, Cy, start_point_shift=0.0)
plt=scatter(points[1,:], points[2,:], label=nothing, mw=0, ms=8, aspect_ratio=:equal)
Hw11 = (cos(α)^2 / a^2 + sin(α)^2 / b^2)
Hw22 = (sin(α)^2 / a^2 + cos(α)^2 / b^2)
Hw12 = cos(α)*sin(α)*(1/a^2 - 1/b^2)
Hw_norm = [Hw11 Hw12; Hw12 Hw22]
confidence_level=0.95
Hw = Hw_norm ./ (0.5 ./ (Distributions.quantile(Distributions.Chisq(2), confidence_level)*0.5))
Γ = inv(Hw)
points2 = generate_N_equally_spaced_points(N, Γ, [Cx, Cy], 1, 2, confidence_level=confidence_level, start_point_shift=0.0)
scatter!(points2[1, :], points2[2, :], label=nothing, markeralpha=0.5, mw=0, ms=4)
display(plt)
We can confirm this issue by inspecting the ellipse values returned by calculate_ellipse_parameters:
# for α = 0.25*π
a_calc, b_calc, _, _, α_calc = EllipseSampling.calculate_ellipse_parameters(Γ, 1, 2, confidence_level)
println("a=", a_calc); println("b=", b_calc); println("α/pi=", α_calc/pi)a=1.7994708216848752
b=1.0307764064044151
α=0.24999999999999992
@JuliaRegistrator register branch=main
Release notes:
This patch contains minor performance improvements, documentation updates and fixes, Tagbot update and logo addition in the documentation page. No changes to api or results.
The images folder in docs has been renamed to assets per standard practice. The installation guide has been updated now the package is registered. StaticArrays has been added as a dependency and is used in function E_inverse to pass in parameter values to the function to find the zero of (ellipse_zero), instead of the previous anonymous function.
@JuliaRegistrator register branch=main
@JuliaRegistrator register branch=main
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@JuliaRegistrator register branch=main
Release notes:
Added integer dof argument to calculate_ellipse_parameters and generate_N_clustered_points (when calculated from a covariance matrix). By default it is set to 2, which gives the same behaviour as before this release. Setting it to below 2 will return an error. The ability to set higher values is useful when e.g. calculating ellipses for multiple sets of pairwise indexes simultaneously.
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