shmodot/scripts/orbits/math/Ellipse.cs

using Godot;
using System;
using Vim.Math3d;

public struct Ellipse : IEllipse
{
    public Ellipse(double a = 1, double e = 0)
    {
        SemiMajorAxis = a;
        Eccentricity = e;

        // TODO: this is an immutable struct, so initialise everything else 
        // in the constructor to avoid recalculating properties whenever
        // they are accessed

        Apisides = new Apisides(a, e);
        b = Math.Sqrt(Apisides.max * Apisides.min);

        var d = Math.Sqrt(a * a - b * b);
        Foci = new DVector2[]
        {
            new DVector2(-d, 0),
            new DVector2(d, 0)
        };
    }

    /// <summary>
    /// Semi-major axis
    /// </summary>
    public double a => SemiMajorAxis;
    public double SemiMajorAxis { get; }

    /// <summary>
    /// Eccentricity
    /// </summary>
    public double e => Eccentricity;
    public double Eccentricity { get; }

    /// <summary>
    /// Semi-minor axis
    /// </summary>
    public double b { get; }

    /// <summary>
    /// Get a position on the auxiliary circle
    /// </summary>
    /// <param name="t">Angle in radians around the circle</param>
    /// <returns>2D position on the circle scaled by the semi-major axis</returns>
    public DVector2 GetAuxiliaryPosition2D(double t = 0) =>
        new DVector2(Math.Cos(t), Math.Sin(t)) * a;

    private Apisides Apisides { get; }

    public DVector2[] Foci { get; }

    private double GetFocusDistance() => Math.Sqrt(a * a - b * b);
}

public struct Apisides
{
    public readonly double min;
    public readonly double max;

    public Apisides(double a, double e)
    {
        min = a * (1 - e);
        max = a * (1 + e);
    }
}