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scripts/orbits/IOrbit.cs

@@ -0,0 +1,7 @@
+using Vim.Math3d;
+
+public interface IOrbit
+{
+    DVector3 GetPosition(double t);
+    IEllipse Ellipse { get; set; }
+}

scripts/orbits/IOrbitExtensions.cs

@@ -0,0 +1,29 @@
+using Godot;
+
+public static class IOrbitExtensions
+{
+    public static void Draw(this IOrbit orbit, ImmediateGeometry geo)
+    {
+        geo.Clear();
+        geo.Begin(Mesh.PrimitiveType.LineLoop);
+        geo.SetColor(new Color(1, 0, 0));
+
+        int steps = 100;
+        var ellipse = orbit.Ellipse;
+
+        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
+            });
+        }
+        geo.End();
+    }
+}

scripts/orbits/IOrbitalElementsExtensions.cs

@@ -0,0 +1,13 @@
+using Vim.Math3d;
+using static System.Math;
+
+public static class IOrbitalElementsExtensions
+{
+    /// <summary>
+    /// Get the Cartesian position on the orbit for a given mean anomaly.
+    /// </summary>
+    /// <param name="M">Mean anomaly</param>
+    /// <returns>Position</returns>
+    public static DVector2 GetEccentricPosition2D(this OrbitalElements elements, double M) =>
+        Kepler.GetEccentricPosition2D(elements.e, elements.a, M);
+}

scripts/orbits/OrbitalElements.cs

@@ -0,0 +1,46 @@
+public struct OrbitalElements
+{
+    private Ellipse _ellipse;
+    /// <summary>
+    /// Semi-major axis in AU
+    /// </summary>
+    public double a => _ellipse.a;
+    /// <summary>
+    /// Eccentricity
+    /// </summary>
+    public double e => _ellipse.e;
+    /// <summary>
+    /// Inclination in degrees
+    /// </summary>
+    public double i { get; private set; }
+    /// <summary>
+    /// Argument of ascending node in degrees
+    /// </summary>
+    public double W { get; private set; }
+    /// <summary>
+    /// Argument of periapsis in degrees
+    /// </summary>
+    public double p { get; private set; }
+    /// <summary>
+    /// Mean anomaly at epoch
+    /// </summary>
+    public double M0 { get; private set; }
+
+    /// <summary>
+    ///
+    /// </summary>
+    /// <param name="a">Semi-major axis in AU</param>
+    /// <param name="e">eccentricity</param>
+    /// <param name="i">Inclination in degrees</param>
+    /// <param name="W">Argument of ascending node in degrees</param>
+    /// <param name="p">Argument of periapsis in degrees</param>
+    /// <param name="M0">Mean anomaly at epoch</param>
+    public OrbitalElements(double a, double e, double i, double W, double p, double M0)
+    {
+        _ellipse = new Ellipse(a, e);
+        this.i = i;
+        this.W = W;
+        this.p = p;
+        this.M0 = M0;
+    }
+}

scripts/orbits/math/Ellipse.cs

@@ -2,7 +2,7 @@ using Godot;
 using System;
 using Vim.Math3d;
 
-public struct Ellipse
+public struct Ellipse : IEllipse
 {
     public Ellipse(double a = 1, double e = 0)
     {
@@ -12,6 +12,16 @@ public struct Ellipse
         // 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>
@@ -29,8 +39,7 @@ public struct Ellipse
     /// <summary>
     /// Semi-minor axis
     /// </summary>
-    public double b => SemiMinorAxis;
+    public double b { get; }
-    public double SemiMinorAxis => Math.Sqrt(Apisides.max * Apisides.min);
 
     /// <summary>
     /// Get a position on the auxiliary circle
@@ -40,13 +49,10 @@ public struct Ellipse
     public DVector2 GetAuxiliaryPosition2D(double t = 0) =>
         new DVector2(Math.Cos(t), Math.Sin(t)) * a;
 
-    private Apisides Apisides => new Apisides(a, e);
+    private Apisides Apisides { get; }
 
-    public DVector2 GetPosition(double t) =>
+    public DVector2[] Foci { get; }
-        new DVector2(Math.Cos(t) * a, Math.Sin(t) * b);
 
-    public DVector2 Focus0 => new DVector2(-GetFocusDistance(), 0);
-    public DVector2 Focus1 => new DVector2(GetFocusDistance(), 0);
     private double GetFocusDistance() => Math.Sqrt(a * a - b * b);
 }
 

scripts/orbits/math/IEllipse.cs

@@ -0,0 +1,20 @@
+using Godot;
+using System;
+using Vim.Math3d;
+
+public interface IEllipse
+{
+    /// <summary>
+    /// Semi-major axis
+    /// </summary>
+    double a { get; }
+    double b { get; }
+    /// <summary>
+    /// Eccentricity
+    /// </summary>
+    double e { get; }
+    /// <summary>
+    /// Positions of the two foci of the ellipse
+    /// </summary>
+    DVector2[] Foci { get; }
+}

scripts/orbits/math/IEllipseExtensions.cs

@@ -0,0 +1,8 @@
+using Vim.Math3d;
+using System;
+
+public static class IEllipseExtensions
+{
+    public static DVector2 GetPosition(this IEllipse e, double t) =>
+        new DVector2(Math.Cos(t) * e.a, Math.Sin(t) * e.b);
+}