shmodot/scripts/orbits/Orbit.cs

using Godot;
using System;
using Vim.Math3d;

public class Orbit : IOrbit
{
    #region IEllipse
    public double a => Ellipse.a;
    public double b => Ellipse.b;
    public double e => Ellipse.e;
    public DVector2[] Foci => Ellipse.Foci;
    #endregion

    public IEllipse Ellipse { get; set; }
    private double U => Kepler.U(_massive.Mass);

    private readonly IMassive _massive;
    private readonly ILocation _satellite;

    /// <summary>
    /// An orbit is treated as one stationary body at one focus of the orbit's ellipse. 
    /// The satellite is treated as a massless point.
    /// </summary>
    /// <param name="massive">Mass of the object being orbited</param>
    /// <param name="satellite">The orbiting body</param>
    public Orbit(IMassive massive, ILocation satellite)
    {
        // semi-major axis is distance of satellite from origin
        var a = satellite.Position.Magnitude();
        // TODO: determine eccentricity better
        var e = 0.8f;
        this.Ellipse = new Ellipse(a, e);

        _massive = massive;
        _satellite = satellite;
    }

    public DVector3 GetPosition(float t)
    {
        var a = Ellipse.a;
        var e = Ellipse.e;

        Kepler.GetPeriod(a, U);

        // TODO: determine period from mass of orbiting bodies
        var P = 10f;


        var M = Kepler.GetMeanAnomaly(t, P);
        var E = Kepler.GetEccentricAnomaly(e, M) + Math.PI;

        var p = Kepler.GetEccentricPosition2D(e, a, t);
        return new DVector3(p.X, 0, p.Y);
    }

    public void Draw(ImmediateGeometry geo)
    {
        geo.Clear();
        geo.Begin(Mesh.PrimitiveType.LineLoop);
        DrawEllipse(geo);
        geo.End();
    }

    private void DrawEllipse(ImmediateGeometry geo)
    {
        geo.SetColor(new Color(1, 0, 0));

        int steps = 100;

        for (int i = 0; i < steps; i++)
        {
            float t = i / (float)steps;
            float a = t * Mathf.Tau;

            var v2 = Ellipse.Foci[0] + Ellipse.GetPosition(a);

            geo.AddVertex(new Godot.Vector3
            {
                x = (float)v2.X,
                z = (float)v2.Y
            });
        }
    }
}