extract IOrbit and IOrbitExtensions

move planet around ellipse

adjust orbit speed

learnin.csproj

@@ -2,4 +2,7 @@
   <PropertyGroup>
     <TargetFramework>net472</TargetFramework>
   </PropertyGroup>
+  <ItemGroup>
+    <PackageReference Include="vim.math3d" Version="1.6.0" />
+  </ItemGroup>
 </Project>

scenes/Main.tscn

@@ -1,17 +1,18 @@
-[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/orbits/OrbitSystem.tscn" type="PackedScene" id=4]
 
 [node name="Main" type="Node2D"]
 
-[node name="Train" parent="." instance=ExtResource( 1 )]
-
 [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 )
 
 [node name="OrbitCamera" parent="." instance=ExtResource( 3 )]
 
-[node name="Railway" parent="." instance=ExtResource( 2 )]
+[node name="Orbit System" parent="." instance=ExtResource( 4 )]
-script = null
+transform = Transform( 0.856869, 0.3292, -0.396741, 0.0949996, 0.655565, 0.749139, 0.506706, -0.679604, 0.53046, -0.599122, 0, 0 )
+SemiMajorAxis = 6.166
+Eccentricity = 0.239
+Period = 1.0
+_speed = 0.877

scenes/orbits/OrbitSystem.tscn

@@ -0,0 +1,22 @@
+[gd_scene load_steps=3 format=2]
+
+[ext_resource path="res://scripts/orbits/OrbitSystem.cs" type="Script" id=1]
+[ext_resource path="res://scenes/orbits/Planet.tscn" type="PackedScene" id=2]
+
+[node name="Orbit System" type="Spatial"]
+script = ExtResource( 1 )
+SemiMajorAxis = 6.881
+Eccentricity = 0.399
+Period = 10.0
+_a = NodePath("Planet A")
+_b = NodePath("Planet B")
+_barycenter = NodePath("Barycenter")
+
+[node name="Barycenter" type="Spatial" parent="."]
+
+[node name="Planet A" parent="." instance=ExtResource( 2 )]
+transform = Transform( 0.999977, 0.00603502, 0.00319089, -0.00604282, 0.999979, 0.0024369, -0.00317609, -0.00245615, 0.999992, 0, 0, 0 )
+
+[node name="Planet B" parent="." instance=ExtResource( 2 )]
+transform = Transform( 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0.5, -8.44634, 0, -3.53339 )
+Mass = 0.125

scenes/orbits/Planet.tscn

@@ -0,0 +1,11 @@
+[gd_scene load_steps=2 format=2]
+
+[ext_resource path="res://scripts/orbits/Planet.cs" type="Script" id=1]
+
+[node name="Planet" type="Spatial"]
+script = ExtResource( 1 )
+Mass = 1.0
+
+[node name="CSGSphere" type="CSGSphere" parent="."]
+radial_segments = 20
+rings = 20

scripts/OrbitCamera.cs

@@ -5,9 +5,10 @@ public class OrbitCamera : Spatial
 {
     [Export]
     private float _lookSensitivity = 200f;
-
     [Export]
     private float _zoomSensitivity = 10f;
+    [Export]
+    private Vector2 _fovRange = new Vector2(10, 60);
 
     [Export]
     private NodePath _cameraPath;
@@ -65,9 +66,18 @@ public class OrbitCamera : Spatial
         }
     }
 
-    private void Zoom(float amount)
+    private void Zoom(int dir)
     {
-        Camera.Fov += amount * _zoomSensitivity / Camera.Fov;
+        if (dir != 1 && dir != -1)
+            throw new ArgumentException();
+
+        var fov = Camera.Fov;
+        var zoom = _zoomSensitivity / Camera.Fov;
+
+        fov += (float)dir * zoom;
+        fov = Mathf.Clamp(fov, _fovRange.x, _fovRange.y);
+
+        Camera.Fov = fov;
     }
 
     private void HandleMouseMovement(InputEventMouseMotion mouseMotion)

scripts/orbits/ILocation.cs

@@ -0,0 +1,6 @@
+using Vim.Math3d;
+
+public interface ILocation
+{
+    DVector3 Position { get; set; }
+}

scripts/orbits/IMassive.cs

@@ -0,0 +1,7 @@
+using Godot;
+using System;
+
+public interface IMassive
+{
+    float Mass { get; }
+}

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/IPointMass.cs

@@ -0,0 +1,3 @@
+public interface IPointMass : IMassive, ILocation
+{
+}

scripts/orbits/Orbit.cs

@@ -0,0 +1,57 @@
+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
+            });
+        }
+    }
+}

scripts/orbits/OrbitSystem.cs

@@ -0,0 +1,153 @@
+using Godot;
+using System;
+using Vim.Math3d;
+
+[Tool]
+public class OrbitSystem : Node, IMassive, ILocation
+{
+    [Export] private NodePath _a;
+    [Export] private NodePath _b;
+    [Export] private NodePath _barycenter;
+
+    private double _semiMajorAxis;
+    [Export]
+    private double SemiMajorAxis
+    {
+        get => _semiMajorAxis;
+        set
+        {
+            _semiMajorAxis = value;
+
+            if (!Engine.EditorHint) return;
+
+            InvalidateGeometry();
+        }
+    }
+
+
+    private double _eccentricity;
+    [Export(PropertyHint.Range, "0,1")]
+    private double Eccentricity
+    {
+        get => _eccentricity;
+        set
+        {
+            _eccentricity = value;
+
+            if (!Engine.EditorHint) return;
+
+            InvalidateGeometry();
+        }
+    }
+
+    #region Point Masses
+    private IPointMass Primary
+    {
+        get
+        {
+            if (_pointMasses[0] == null)
+            {
+                InitPointMasses();
+            }
+            return _pointMasses[0];
+        }
+    }
+    private IPointMass Secondary
+    {
+        get
+        {
+            if (_pointMasses[1] == null)
+            {
+                InitPointMasses();
+            }
+            return _pointMasses[1];
+        }
+    }
+    private readonly IPointMass[] _pointMasses = new IPointMass[2];
+    private void InitPointMasses()
+    {
+        var a = GetNode<IPointMass>(_a);
+        var b = GetNode<IPointMass>(_b);
+
+        if (a.Mass > b.Mass)
+        {
+            _pointMasses[0] = a;
+            _pointMasses[1] = b;
+        }
+        else
+        {
+            _pointMasses[0] = b;
+            _pointMasses[1] = a;
+        }
+    }
+    #endregion
+
+    public float Mass => Primary.Mass + Secondary.Mass;
+    public DVector3 Position
+    {
+        get => Barycenter;
+        set => Barycenter = value;
+    }
+
+    public DVector3 Barycenter
+    {
+        get
+        {
+            var p0 = Primary.Position;
+            var p1 = Secondary.Position;
+            return p0.Lerp(p1, .5f);
+        }
+        // TODO - make setting the berycenter do something sensible?
+        set => _ = value;
+    }
+
+    private Orbit _orbit = null;
+    private Orbit Orbit
+    {
+        get
+        {
+            if (_orbit == null)
+            {
+                _orbit = new Orbit();
+            }
+            return _orbit;
+        }
+    }
+
+    private ImmediateGeometry _orbitGeometry = null;
+    public ImmediateGeometry OrbitGeometry
+    {
+        get
+        {
+            if (_orbitGeometry == null)
+            {
+                _orbitGeometry = new ImmediateGeometry();
+                var m = new SpatialMaterial();
+                m.VertexColorUseAsAlbedo = true;
+                m.FlagsUnshaded = true;
+                _orbitGeometry.MaterialOverride = m;
+                AddChild(_orbitGeometry);
+            }
+            return _orbitGeometry;
+        }
+    }
+
+    private float _time = 0;
+
+    [Export]
+    private float _speed = 3f;
+
+    public override void _Process(float delta)
+    {
+        _time += delta * _speed;
+        InvalidateGeometry();
+    }
+
+    private void InvalidateGeometry()
+    {
+        Orbit.Ellipse = new Ellipse(SemiMajorAxis, Eccentricity);
+        Orbit.Draw(OrbitGeometry);
+
+        Secondary.Position = Orbit.GetPosition(_time);
+    }
+}

scripts/orbits/Planet.cs

@@ -0,0 +1,32 @@
+using Godot;
+using System;
+using Vim.Math3d;
+
+[Tool]
+public class Planet : Spatial, IPointMass
+{
+    [Export]
+    public float Mass { get; set; }
+
+    private DVector3? _position;
+    public DVector3 Position
+    {
+        get
+        {
+            if (_position.HasValue) return _position.Value;
+
+            var t = Translation;
+            return new DVector3(t.x, t.y, t.z);
+        }
+        set
+        {
+            _position = value;
+            Translation = new Godot.Vector3
+            {
+                x = (float)value.X,
+                y = (float)value.Y,
+                z = (float)value.Z
+            };
+        }
+    }
+}

scripts/orbits/math/Ellipse.cs

@@ -0,0 +1,69 @@
+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);
+    }
+}

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);
+}

scripts/orbits/math/Kepler.cs

@@ -0,0 +1,127 @@
+using static System.Math;
+using Vim.Math3d;
+
+public static class Kepler
+{
+    /// <summary>
+    /// 2 * PI
+    /// </summary>
+    private static double TAU => PI * 2.0;
+    /// <summary>
+    /// Universal gravitational constant
+    /// </summary>
+    private static double G => 6.677e-11;
+
+    /// <summary>
+    /// Get the mean anomaly of an orbit given at a given time, given
+    /// the period of the orbit.
+    /// </summary>
+    /// <param name="time">Time of mean anomaly</param>
+    /// <param name="P">Orbital period</param>
+    /// <returns></returns>
+    public static double GetMeanAnomaly(double time, double P)
+    {
+        var M = ((time % P / P) * TAU) % TAU;
+        return M % TAU;
+    }
+
+    /// <summary>
+    /// 
+    /// </summary>
+    /// <param name="P">Orbital period</param>
+    /// <returns></returns>
+    public static double GetMeanAngularVelocity(double P) => TAU / P;
+
+    /// <summary>
+    /// 
+    /// </summary>
+    /// <param name="a">Semimajor axis in AU</param>
+    /// <param name="U">Standard gravitational parameter</param>
+    /// <returns></returns>
+    public static double GetPeriod(double a, double U)
+    {
+        var a3 = a * a * a;
+        var T = TAU * Sqrt(a3 / U);
+
+        return T;
+    }
+
+    /// <summary>
+    /// Get the standard gravitational parameter of a mass
+    /// </summary>
+    /// <param name="M">Mass in kilograms</param>
+    /// <returns>Standard gravitational parameter</returns>
+    public static double U(double M) => M * G;
+    /// <summary>
+    /// Get the standard gravitational parameter of a mass
+    /// </summary>
+    /// <param name="M">Mass in kilograms</param>
+    /// <returns>Standard gravitational parameter</returns>
+    public static double GetStandardGravitationalParameter(double M) => M * G;
+
+    /// <summary>
+    /// Get the eccentric anomaly for a given mean anomaly.
+    /// </summary>
+    /// <param name="e">Eccentricity</param>
+    /// <param name="M">Mean anomaly</param>
+    /// <returns>Eccentric anomaly</returns>
+    public static double GetEccentricAnomaly(double e, double M) =>
+        GetEccentricAnomalyBS(e, M);
+
+    /// <summary>
+    /// Get the eccentric anomaly for a given mean anomaly 
+    /// using a binary search.
+    /// </summary>
+    /// <param name="e">Eccentricity</param>
+    /// <param name="M">Mean anomaly</param>
+    /// <returns>Eccentric anomaly</returns>
+    private static double GetEccentricAnomalyBS(double e, double M)
+    {
+        // from Astronomical Algorithms, p. 206
+        const int iterations = 33;
+        double E0, D;
+
+        double F = Sign(M);
+        M = Abs(M) / TAU;
+        M = (M - (int)M) * TAU * F;
+        if (M < 0)
+        {
+            M = M + TAU;
+        }
+        F = 1.0;
+        if (M > PI)
+        {
+            F = -1.0;
+            M = TAU - M;
+        }
+        E0 = PI / 2;
+        D = PI / 4;
+        for (int J = 0; J < iterations; J++)
+        {
+            double M1 = E0 - e * Sin(E0);
+            E0 = E0 + D * Sign(M - M1);
+            D *= 0.5;
+        }
+        E0 *= F;
+
+        return E0;
+    }
+
+    /// <summary>
+    /// Get the Cartesian position on an orbit given its eccentricity, 
+    /// its semi-major axis and a given mean anomaly.
+    /// </summary>
+    /// <param name="e">Eccentricity</param>
+    /// <param name="a">Semi-major axis</param>
+    /// <param name="M">Mean anomaly</param>
+    /// <returns>Position on the orbit</returns>
+    public static DVector2 GetEccentricPosition2D(double e, double a, double M)
+    {
+        var E = Kepler.GetEccentricAnomaly(e, M);
+
+        var P = a * (Cos(E) - e);
+        var Q = a * Sin(E) * Sqrt(1.0 - Pow(e, 2));
+
+        return new DVector2(P, Q);
+    }
+}