implement ellipse

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

@@ -1,18 +1,13 @@
-[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="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 )]
-_speed = 1.0
 
-[node name="Railway" parent="." instance=ExtResource( 2 )]
-script = null
+[node name="Orbit System" parent="." instance=ExtResource( 4 )]

scenes/OrbitCamera.tscn

@@ -6,4 +6,5 @@
 script = ExtResource( 1 )
 
 [node name="Camera" type="Camera" parent="."]
-transform = Transform( 0.636065, -0.249781, 0.73009, 0, 0.946159, 0.323703, -0.771636, -0.205896, 0.601818, 8.49012, 5.30069, 6.71091 )
+transform = Transform( 1, 0, 0, 0, 0.964146, 0.265371, 0, -0.265371, 0.964146, 0, 2.21115, 9.48434 )
+fov = 25.0

scenes/OrbitSystem.tscn

@@ -0,0 +1,15 @@
+[gd_scene load_steps=2 format=2]
+
+[ext_resource path="res://scripts/orbits/OrbitSystem.cs" type="Script" id=1]
+
+[node name="Orbit System" type="Spatial"]
+script = ExtResource( 1 )
+_a = NodePath("A")
+_b = NodePath("B")
+_barycenter = NodePath("Barycenter")
+
+[node name="A" type="Spatial" parent="."]
+
+[node name="B" type="Spatial" parent="."]
+
+[node name="Barycenter" type="Spatial" parent="."]

scripts/OrbitCamera.cs

@@ -4,15 +4,44 @@ using System;
 public class OrbitCamera : Spatial
 {
     [Export]
-    private float _speed;
+    private float _sensitivity = 200f;
 
-    public override void _Ready()
+    private Vector2 _rotation;
+    private bool _canRotate = false;
+
+    public override void _Input(InputEvent e)
     {
-
+        if (e is InputEventMouseMotion mouseMotion)
+        {
+            HandleMouseMovement(mouseMotion);
+        }
+        if (e is InputEventMouseButton mouseButton)
+        {
+            HandleMouseButton(mouseButton);
+        }
     }
 
     public override void _Process(float delta)
     {
-        Rotate(Vector3.Up, _speed * delta);
+        Rotation = Vector3.Zero;
+        var sensitivity = -1f / _sensitivity;
+        Rotate(Vector3.Right, _rotation.y * sensitivity);
+        Rotate(Vector3.Up, _rotation.x * sensitivity);
+    }
+
+    // left click to drag
+    private void HandleMouseButton(InputEventMouseButton mouseButton)
+    {
+        if (mouseButton.ButtonIndex != (int)ButtonList.Left) return;
+
+        _canRotate = mouseButton.Pressed;
+    }
+
+    private void HandleMouseMovement(InputEventMouseMotion mouseMotion)
+    {
+        if (!_canRotate) return;
+
+        var delta = mouseMotion.Relative;
+        _rotation += delta;
     }
 }

scripts/orbits/ILocation.cs

@@ -0,0 +1,7 @@
+using Godot;
+using System;
+
+public interface ILocation
+{
+    Vector3 Position { get; }
+}

scripts/orbits/IMassive.cs

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

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

@@ -0,0 +1,109 @@
+using Godot;
+using System;
+
+public class OrbitSystem : Node, IMassive, ILocation
+{
+    [Export] private NodePath _a;
+    [Export] private NodePath _b;
+    [Export] private NodePath _barycenter;
+
+    private readonly PointMass[] _pointMasses = new PointMass[2];
+
+    public Vector3 Position => Barycenter;
+
+    [Export]
+    public Vector3 Barycenter
+    {
+        get
+        {
+            var p0 = _pointMasses[0].Position;
+            var p1 = _pointMasses[1].Position;
+
+            return p0.LinearInterpolate(p1, .5f);
+        }
+        set => _ = value;
+    }
+
+    public float Mass { get; } = 1;
+
+    private Orbit _orbit;
+
+    private ImmediateGeometry _orbitGeometry;
+
+    public override void _Ready()
+    {
+        InitPointMasses();
+        InitGeometry();
+    }
+
+    public override void _Process(float delta)
+    {
+        DrawOrbit();
+    }
+
+    private void InitOrbit()
+    {
+
+    }
+
+    private void DrawOrbit()
+    {
+        int steps = 100;
+
+        _orbitGeometry.Clear();
+        _orbitGeometry.Begin(Mesh.PrimitiveType.LineLoop);
+        _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;
+
+            var v2 = ellipse.Focus0 + ellipse.GetPosition(a);
+
+            _orbitGeometry.AddVertex(new Vector3
+            {
+                x = (float)v2.X,
+                z = (float)v2.Y
+            });
+        }
+        _orbitGeometry.End();
+    }
+
+    private void InitGeometry()
+    {
+        _orbitGeometry = new ImmediateGeometry();
+        var m = new SpatialMaterial();
+        m.VertexColorUseAsAlbedo = true;
+        m.FlagsUnshaded = true;
+        _orbitGeometry.MaterialOverride = m;
+        AddChild(_orbitGeometry);
+    }
+
+    private void InitPointMasses()
+    {
+        var a = GetPointMass(_a);
+        var b = GetPointMass(_b);
+
+        if (a.Mass > b.Mass)
+        {
+            _pointMasses[0] = a;
+            _pointMasses[1] = b;
+        }
+        else
+        {
+            _pointMasses[0] = b;
+            _pointMasses[1] = a;
+        }
+    }
+
+    private PointMass GetPointMass(NodePath path)
+    {
+        var spatial = GetNode<Spatial>(path);
+        //var massive = node.GetChild<IMassive>(0);
+
+        return new PointMass(spatial, 1f);
+    }
+}

scripts/orbits/Planet.cs

@@ -0,0 +1,18 @@
+using Godot;
+using System;
+
+public class Planet : Node, IMassive
+{
+    [Export]
+    public float Mass { get; set; }
+
+    public override void _Ready()
+    {
+
+    }
+
+    //  public override void _Process(float delta)
+    //  {
+    //
+    //  }
+}

scripts/orbits/PointMass.cs

@@ -0,0 +1,25 @@
+using Godot;
+
+public struct PointMass : IMassive, ILocation
+{
+    public float Mass => _massive == null ? _mass : _massive.Mass;
+    public Vector3 Position => _spatial.Translation;
+
+    private IMassive _massive;
+    private Spatial _spatial;
+    private float _mass;
+
+    public PointMass(Spatial spatial, IMassive massive)
+    {
+        _spatial = spatial;
+        _massive = massive;
+        _mass = 0;
+    }
+
+    public PointMass(Spatial spatial, float mass)
+    {
+        _spatial = spatial;
+        _massive = null;
+        _mass = mass;
+    }
+}

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);
+    }
+}