learnin.csproj

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

scenes/Main.tscn

@@ -1,18 +1,17 @@
-[gd_scene load_steps=3 format=2]
+[gd_scene load_steps=4 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="Orbit System" parent="." instance=ExtResource( 4 )]
+[node name="Railway" parent="." instance=ExtResource( 2 )]
-transform = Transform( 0.856869, 0.3292, -0.396741, 0.0949996, 0.655565, 0.749139, 0.506706, -0.679604, 0.53046, -0.599122, 0, 0 )
+script = null
-SemiMajorAxis = 6.166
-Eccentricity = 0.239
-Period = 1.0
-_speed = 0.877

scenes/orbits/OrbitSystem.tscn

@@ -1,22 +0,0 @@
-[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

@@ -1,11 +0,0 @@
-[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

@@ -5,10 +5,9 @@ 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;
@@ -66,18 +65,9 @@ public class OrbitCamera : Spatial
         }
     }
 
-    private void Zoom(int dir)
+    private void Zoom(float amount)
     {
-        if (dir != 1 && dir != -1)
+        Camera.Fov += amount * _zoomSensitivity / Camera.Fov;
-            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

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

scripts/orbits/IMassive.cs

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

scripts/orbits/IOrbit.cs

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

scripts/orbits/IOrbitExtensions.cs

@@ -1,29 +0,0 @@
-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

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

scripts/orbits/Orbit.cs

@@ -1,57 +0,0 @@
-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

@@ -1,153 +0,0 @@
-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

@@ -1,32 +0,0 @@
-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

@@ -1,69 +0,0 @@
-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

@@ -1,20 +0,0 @@
-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

@@ -1,8 +0,0 @@
-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

@@ -1,127 +0,0 @@
-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);
-    }
-}