shmodot/scripts/orbits/Orbit.cs

using Godot;
using System;
using Vim.Math3d;

public class Orbit
{
    // The position of the primary body relative to the ellipse - the 
    // orbit itself is presented as being centred on the primary, but
    // all our math is elliptical.
    private DVector2 PrimaryPosition => Ellipse.Focus0;

    public Ellipse Ellipse { get; set; }

    public DVector3 GetPosition(float t)
    {
        // TODO: determine period from mass of orbiting bodies
        var P = 10f;

        var a = Ellipse.a;
        var e = Ellipse.e;

        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.Focus0 + Ellipse.GetPosition(a);

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