drag to rotate camera

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

@@ -10,6 +10,5 @@ transform = Transform( 0.515898, 0.606099, -0.605386, -0.393123, 0.795389, 0.461
 visible = false
 
 [node name="Camera" parent="." instance=ExtResource( 3 )]
-_speed = 0.5
 
 [node name="Orbit System" parent="." instance=ExtResource( 4 )]

scenes/OrbitCamera.tscn

@@ -6,5 +6,5 @@
 script = ExtResource( 1 )
 
 [node name="Camera" type="Camera" parent="."]
-transform = Transform( 1, 0, 0, 0, 0.913325, 0.407231, 0, -0.407231, 0.913325, 0, 24.1191, 58.6188 )
+transform = Transform( 1, 0, 0, 0, 0.964146, 0.265371, 0, -0.265371, 0.964146, 0, 2.21115, 9.48434 )
 fov = 25.0

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/OrbitSystem.cs

@@ -53,15 +53,20 @@ public class OrbitSystem : Node, IMassive, ILocation
         _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 = Mathf.Sin(a),
-                z = Mathf.Cos(a)
+                x = (float)v2.X,
+                z = (float)v2.Y
             });
         }
         _orbitGeometry.End();

scripts/orbits/math/Double2.cs

@@ -1,8 +0,0 @@
-using Godot;
-using System;
-
-public struct Double2
-{
-    public double x;
-    public double y;
-}

scripts/orbits/math/Ellipse.cs

@@ -1,24 +1,53 @@
 using Godot;
 using System;
+using Vim.Math3d;
 
 public struct Ellipse
 {
-    public double a { get => SemiMajorAxis; set => SemiMajorAxis = value; }
-    public double SemiMajorAxis { get; set; }
-
-    public double e { get => Eccentricity; set => Eccentricity = value; }
-    public double Eccentricity { get; set; }
-
-    public double b => SemiMajorAxis;
-    public double SemiMinorAxis => Math.Sqrt(Apisides.max * Apisides.min);
-
-    private Apisides Apisides => new Apisides(a, e);
-
     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