implement ellipse

scenes/Main.tscn

@@ -1,19 +1,14 @@
-[gd_scene load_steps=4 format=2]
+[gd_scene load_steps=3 format=2]
 
-[ext_resource path="res://scenes/Train.tscn" type="PackedScene" id=1]
-[ext_resource path="res://scenes/Railway.tscn" type="PackedScene" id=2]
 [ext_resource path="res://scenes/OrbitCamera.tscn" type="PackedScene" id=3]
+[ext_resource path="res://scenes/OrbitSystem.tscn" type="PackedScene" id=4]
 
 [node name="Main" type="Node2D"]
 
 [node name="DirectionalLight" type="DirectionalLight" parent="."]
 transform = Transform( 0.515898, 0.606099, -0.605386, -0.393123, 0.795389, 0.461314, 0.76112, -2.26831e-08, 0.648611, 0, 0, 0 )
+visible = false
 
-[node name="OrbitCamera" parent="." instance=ExtResource( 3 )]
+[node name="Camera" parent="." instance=ExtResource( 3 )]
-_speed = 0.5
 
-[node name="Railway" parent="." instance=ExtResource( 2 )]
+[node name="Orbit System" parent="." instance=ExtResource( 4 )]
-
-[node name="Train" parent="." instance=ExtResource( 1 )]
-_speed = 5.0
-_railwayPath = NodePath("../Railway")

scripts/orbits/Orbit.cs

@@ -0,0 +1,12 @@
+using Godot;
+using System;
+
+public class Orbit
+{
+    public Orbit(PointMass a, PointMass b)
+    {
+
+    }
+
+    // ellipse
+}

scripts/orbits/OrbitSystem.cs

@@ -26,7 +26,9 @@ public class OrbitSystem : Node, IMassive, ILocation
 
     public float Mass { get; } = 1;
 
-    private ImmediateGeometry _orbit;
+    private Orbit _orbit;
+
+    private ImmediateGeometry _orbitGeometry;
 
     public override void _Ready()
     {
@@ -39,35 +41,45 @@ public class OrbitSystem : Node, IMassive, ILocation
         DrawOrbit();
     }
 
+    private void InitOrbit()
+    {
+
+    }
+
     private void DrawOrbit()
     {
         int steps = 100;
 
-        _orbit.Clear();
+        _orbitGeometry.Clear();
-        _orbit.Begin(Mesh.PrimitiveType.LineLoop);
+        _orbitGeometry.Begin(Mesh.PrimitiveType.LineLoop);
-        _orbit.SetColor(new Color(1, 0, 0));
+        _orbitGeometry.SetColor(new Color(1, 0, 0));
+
+        var ellipse = new Ellipse(1, .5);
+
         for (int i = 0; i < steps; i++)
         {
             float t = i / (float)steps;
             float a = t * Mathf.Tau;
 
-            _orbit.AddVertex(new Vector3
+            var v2 = ellipse.Focus0 + ellipse.GetPosition(a);
+
+            _orbitGeometry.AddVertex(new Vector3
             {
-                x = Mathf.Sin(a),
+                x = (float)v2.X,
-                z = Mathf.Cos(a)
+                z = (float)v2.Y
             });
         }
-        _orbit.End();
+        _orbitGeometry.End();
     }
 
     private void InitGeometry()
     {
-        _orbit = new ImmediateGeometry();
+        _orbitGeometry = new ImmediateGeometry();
         var m = new SpatialMaterial();
         m.VertexColorUseAsAlbedo = true;
         m.FlagsUnshaded = true;
-        _orbit.MaterialOverride = m;
+        _orbitGeometry.MaterialOverride = m;
-        AddChild(_orbit);
+        AddChild(_orbitGeometry);
     }
 
     private void InitPointMasses()

scripts/orbits/Planet.cs

@@ -1,7 +1,7 @@
 using Godot;
 using System;
 
-public class Planet : Node
+public class Planet : Node, IMassive
 {
     [Export]
     public float Mass { get; set; }

scripts/orbits/PointMass.cs

@@ -1,6 +1,6 @@
 using Godot;
 
-struct PointMass : IMassive, ILocation
+public struct PointMass : IMassive, ILocation
 {
     public float Mass => _massive == null ? _mass : _massive.Mass;
     public Vector3 Position => _spatial.Translation;

scripts/orbits/math/Ellipse.cs

@@ -0,0 +1,63 @@
+using Godot;
+using System;
+using Vim.Math3d;
+
+public struct Ellipse
+{
+    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
+    }
+
+    /// <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 => SemiMinorAxis;
+    public double SemiMinorAxis => Math.Sqrt(Apisides.max * Apisides.min);
+
+    /// <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 => new Apisides(a, e);
+
+    public DVector2 GetPosition(double t) =>
+        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);
+}
+
+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);
+    }
+}