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No commits in common. "orbital-elements" and "main" have entirely different histories.
orbital-el
...
main
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@ -2,7 +2,4 @@
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<PropertyGroup>
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<TargetFramework>net472</TargetFramework>
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</PropertyGroup>
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<ItemGroup>
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<PackageReference Include="vim.math3d" Version="1.6.0" />
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</ItemGroup>
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</Project>
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@ -1,18 +1,17 @@
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[gd_scene load_steps=3 format=2]
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[gd_scene load_steps=4 format=2]
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[ext_resource path="res://scenes/Train.tscn" type="PackedScene" id=1]
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[ext_resource path="res://scenes/Railway.tscn" type="PackedScene" id=2]
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[ext_resource path="res://scenes/OrbitCamera.tscn" type="PackedScene" id=3]
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[ext_resource path="res://scenes/orbits/OrbitSystem.tscn" type="PackedScene" id=4]
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[node name="Main" type="Node2D"]
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[node name="Train" parent="." instance=ExtResource( 1 )]
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[node name="DirectionalLight" type="DirectionalLight" parent="."]
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transform = Transform( 0.515898, 0.606099, -0.605386, -0.393123, 0.795389, 0.461314, 0.76112, -2.26831e-08, 0.648611, 0, 0, 0 )
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[node name="OrbitCamera" parent="." instance=ExtResource( 3 )]
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[node name="Orbit System" parent="." instance=ExtResource( 4 )]
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transform = Transform( 0.856869, 0.3292, -0.396741, 0.0949996, 0.655565, 0.749139, 0.506706, -0.679604, 0.53046, -0.599122, 0, 0 )
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SemiMajorAxis = 6.166
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Eccentricity = 0.239
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Period = 1.0
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_speed = 0.877
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[node name="Railway" parent="." instance=ExtResource( 2 )]
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script = null
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@ -1,22 +0,0 @@
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[gd_scene load_steps=3 format=2]
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[ext_resource path="res://scripts/orbits/OrbitSystem.cs" type="Script" id=1]
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[ext_resource path="res://scenes/orbits/Planet.tscn" type="PackedScene" id=2]
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[node name="Orbit System" type="Spatial"]
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script = ExtResource( 1 )
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SemiMajorAxis = 6.881
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Eccentricity = 0.399
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Period = 10.0
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_a = NodePath("Planet A")
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_b = NodePath("Planet B")
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_barycenter = NodePath("Barycenter")
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[node name="Barycenter" type="Spatial" parent="."]
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[node name="Planet A" parent="." instance=ExtResource( 2 )]
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transform = Transform( 0.999977, 0.00603502, 0.00319089, -0.00604282, 0.999979, 0.0024369, -0.00317609, -0.00245615, 0.999992, 0, 0, 0 )
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[node name="Planet B" parent="." instance=ExtResource( 2 )]
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transform = Transform( 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0.5, -8.44634, 0, -3.53339 )
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Mass = 0.125
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@ -1,11 +0,0 @@
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[gd_scene load_steps=2 format=2]
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[ext_resource path="res://scripts/orbits/Planet.cs" type="Script" id=1]
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[node name="Planet" type="Spatial"]
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script = ExtResource( 1 )
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Mass = 1.0
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[node name="CSGSphere" type="CSGSphere" parent="."]
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radial_segments = 20
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rings = 20
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@ -5,10 +5,9 @@ public class OrbitCamera : Spatial
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{
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[Export]
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private float _lookSensitivity = 200f;
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[Export]
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private float _zoomSensitivity = 10f;
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[Export]
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private Vector2 _fovRange = new Vector2(10, 60);
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[Export]
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private NodePath _cameraPath;
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@ -66,18 +65,9 @@ public class OrbitCamera : Spatial
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}
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}
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private void Zoom(int dir)
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private void Zoom(float amount)
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{
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if (dir != 1 && dir != -1)
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throw new ArgumentException();
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var fov = Camera.Fov;
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var zoom = _zoomSensitivity / Camera.Fov;
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fov += (float)dir * zoom;
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fov = Mathf.Clamp(fov, _fovRange.x, _fovRange.y);
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Camera.Fov = fov;
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Camera.Fov += amount * _zoomSensitivity / Camera.Fov;
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}
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private void HandleMouseMovement(InputEventMouseMotion mouseMotion)
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@ -1,6 +0,0 @@
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using Vim.Math3d;
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public interface ILocation
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{
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DVector3 Position { get; set; }
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}
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@ -1,7 +0,0 @@
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using Godot;
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using System;
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public interface IMassive
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{
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float Mass { get; }
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}
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@ -1,7 +0,0 @@
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using Vim.Math3d;
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public interface IOrbit
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{
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DVector3 GetPosition(double t);
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IEllipse Ellipse { get; set; }
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}
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@ -1,29 +0,0 @@
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using Godot;
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public static class IOrbitExtensions
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{
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public static void Draw(this IOrbit orbit, ImmediateGeometry geo)
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{
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geo.Clear();
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geo.Begin(Mesh.PrimitiveType.LineLoop);
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geo.SetColor(new Color(1, 0, 0));
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int steps = 100;
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var ellipse = orbit.Ellipse;
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for (int i = 0; i < steps; i++)
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{
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float t = i / (float)steps;
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float a = t * Mathf.Tau;
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var v2 = ellipse.Foci[0] + ellipse.GetPosition(a);
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geo.AddVertex(new Godot.Vector3
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{
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x = (float)v2.X,
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z = (float)v2.Y
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});
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}
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geo.End();
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}
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}
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@ -1,13 +0,0 @@
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using Vim.Math3d;
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using static System.Math;
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public static class IOrbitalElementsExtensions
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{
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/// <summary>
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/// Get the Cartesian position on the orbit for a given mean anomaly.
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/// </summary>
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/// <param name="M">Mean anomaly</param>
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/// <returns>Position</returns>
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public static DVector2 GetEccentricPosition2D(this OrbitalElements elements, double M) =>
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Kepler.GetEccentricPosition2D(elements.e, elements.a, M);
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}
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@ -1,3 +0,0 @@
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public interface IPointMass : IMassive, ILocation
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{
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}
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@ -1,57 +0,0 @@
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using Godot;
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using System;
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using Vim.Math3d;
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public class Orbit
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{
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// The position of the primary body relative to the ellipse - the
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// orbit itself is presented as being centred on the primary, but
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// all our math is elliptical.
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private DVector2 PrimaryPosition => Ellipse.Focus0;
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public Ellipse Ellipse { get; set; }
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public DVector3 GetPosition(float t)
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{
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// TODO: determine period from mass of orbiting bodies
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var P = 10f;
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var a = Ellipse.a;
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var e = Ellipse.e;
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var M = Kepler.GetMeanAnomaly(t, P);
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var E = Kepler.GetEccentricAnomaly(e, M) + Math.PI;
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var p = Kepler.GetEccentricPosition2D(e, a, t);
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return new DVector3(p.X, 0, p.Y);
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}
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public void Draw(ImmediateGeometry geo)
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{
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geo.Clear();
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geo.Begin(Mesh.PrimitiveType.LineLoop);
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DrawEllipse(geo);
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geo.End();
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}
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private void DrawEllipse(ImmediateGeometry geo)
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{
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geo.SetColor(new Color(1, 0, 0));
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int steps = 100;
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for (int i = 0; i < steps; i++)
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{
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float t = i / (float)steps;
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float a = t * Mathf.Tau;
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var v2 = Ellipse.Focus0 + Ellipse.GetPosition(a);
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geo.AddVertex(new Godot.Vector3
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{
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x = (float)v2.X,
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z = (float)v2.Y
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});
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}
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}
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}
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@ -1,153 +0,0 @@
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using Godot;
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using System;
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using Vim.Math3d;
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[Tool]
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public class OrbitSystem : Node, IMassive, ILocation
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{
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[Export] private NodePath _a;
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[Export] private NodePath _b;
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[Export] private NodePath _barycenter;
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private double _semiMajorAxis;
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[Export]
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private double SemiMajorAxis
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{
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get => _semiMajorAxis;
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set
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{
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_semiMajorAxis = value;
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if (!Engine.EditorHint) return;
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InvalidateGeometry();
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}
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}
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private double _eccentricity;
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[Export(PropertyHint.Range, "0,1")]
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private double Eccentricity
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{
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get => _eccentricity;
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set
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{
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_eccentricity = value;
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if (!Engine.EditorHint) return;
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InvalidateGeometry();
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}
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}
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#region Point Masses
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private IPointMass Primary
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{
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get
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{
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if (_pointMasses[0] == null)
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{
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InitPointMasses();
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}
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return _pointMasses[0];
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}
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}
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private IPointMass Secondary
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{
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get
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{
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if (_pointMasses[1] == null)
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{
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InitPointMasses();
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}
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return _pointMasses[1];
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}
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}
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private readonly IPointMass[] _pointMasses = new IPointMass[2];
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private void InitPointMasses()
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{
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var a = GetNode<IPointMass>(_a);
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var b = GetNode<IPointMass>(_b);
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if (a.Mass > b.Mass)
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{
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_pointMasses[0] = a;
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_pointMasses[1] = b;
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}
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else
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{
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_pointMasses[0] = b;
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_pointMasses[1] = a;
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}
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}
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#endregion
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public float Mass => Primary.Mass + Secondary.Mass;
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public DVector3 Position
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{
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get => Barycenter;
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set => Barycenter = value;
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}
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public DVector3 Barycenter
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{
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get
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{
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var p0 = Primary.Position;
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var p1 = Secondary.Position;
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return p0.Lerp(p1, .5f);
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}
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// TODO - make setting the berycenter do something sensible?
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set => _ = value;
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}
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private Orbit _orbit = null;
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private Orbit Orbit
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{
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get
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{
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if (_orbit == null)
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{
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_orbit = new Orbit();
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}
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return _orbit;
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}
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}
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private ImmediateGeometry _orbitGeometry = null;
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public ImmediateGeometry OrbitGeometry
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{
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get
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{
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if (_orbitGeometry == null)
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{
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_orbitGeometry = new ImmediateGeometry();
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var m = new SpatialMaterial();
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m.VertexColorUseAsAlbedo = true;
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m.FlagsUnshaded = true;
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_orbitGeometry.MaterialOverride = m;
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AddChild(_orbitGeometry);
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}
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return _orbitGeometry;
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}
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}
|
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private float _time = 0;
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|
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[Export]
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private float _speed = 3f;
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||||
|
||||
public override void _Process(float delta)
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{
|
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_time += delta * _speed;
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InvalidateGeometry();
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}
|
||||
|
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private void InvalidateGeometry()
|
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{
|
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Orbit.Ellipse = new Ellipse(SemiMajorAxis, Eccentricity);
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Orbit.Draw(OrbitGeometry);
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Secondary.Position = Orbit.GetPosition(_time);
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}
|
||||
}
|
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|
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@ -1,46 +0,0 @@
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public struct OrbitalElements
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{
|
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private Ellipse _ellipse;
|
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/// <summary>
|
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/// Semi-major axis in AU
|
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/// </summary>
|
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public double a => _ellipse.a;
|
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/// <summary>
|
||||
/// Eccentricity
|
||||
/// </summary>
|
||||
public double e => _ellipse.e;
|
||||
/// <summary>
|
||||
/// Inclination in degrees
|
||||
/// </summary>
|
||||
public double i { get; private set; }
|
||||
/// <summary>
|
||||
/// Argument of ascending node in degrees
|
||||
/// </summary>
|
||||
public double W { get; private set; }
|
||||
/// <summary>
|
||||
/// Argument of periapsis in degrees
|
||||
/// </summary>
|
||||
public double p { get; private set; }
|
||||
/// <summary>
|
||||
/// Mean anomaly at epoch
|
||||
/// </summary>
|
||||
public double M0 { get; private set; }
|
||||
|
||||
/// <summary>
|
||||
///
|
||||
/// </summary>
|
||||
/// <param name="a">Semi-major axis in AU</param>
|
||||
/// <param name="e">eccentricity</param>
|
||||
/// <param name="i">Inclination in degrees</param>
|
||||
/// <param name="W">Argument of ascending node in degrees</param>
|
||||
/// <param name="p">Argument of periapsis in degrees</param>
|
||||
/// <param name="M0">Mean anomaly at epoch</param>
|
||||
public OrbitalElements(double a, double e, double i, double W, double p, double M0)
|
||||
{
|
||||
_ellipse = new Ellipse(a, e);
|
||||
this.i = i;
|
||||
this.W = W;
|
||||
this.p = p;
|
||||
this.M0 = M0;
|
||||
}
|
||||
}
|
||||
|
|
@ -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
|
||||
};
|
||||
}
|
||||
}
|
||||
}
|
||||
|
|
@ -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);
|
||||
}
|
||||
}
|
||||
|
|
@ -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; }
|
||||
}
|
||||
|
|
@ -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);
|
||||
}
|
||||
|
|
@ -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);
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue