Merge branch 'feat/physics2d' into development

TIL, records are not value types and are actually just reference types. So I was pretty much allocating from heap every time I used any of my data types (Like Vector2D). Needless to say, they are all now readonly structs as I originally intended them to be.

.gitignore

@@ -0,0 +1,484 @@
+## Ignore Visual Studio temporary files, build results, and
+## files generated by popular Visual Studio add-ons.
+##
+## Get latest from `dotnet new gitignore`
+
+# dotenv files
+.env
+
+# User-specific files
+*.rsuser
+*.suo
+*.user
+*.userosscache
+*.sln.docstates
+
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+*.userprefs
+
+# Mono auto generated files
+mono_crash.*
+
+# Build results
+[Dd]ebug/
+[Dd]ebugPublic/
+[Rr]elease/
+[Rr]eleases/
+x64/
+x86/
+[Ww][Ii][Nn]32/
+[Aa][Rr][Mm]/
+[Aa][Rr][Mm]64/
+bld/
+[Bb]in/
+[Oo]bj/
+[Ll]og/
+[Ll]ogs/
+
+# Visual Studio 2015/2017 cache/options directory
+.vs/
+# Uncomment if you have tasks that create the project's static files in wwwroot
+#wwwroot/
+
+# Visual Studio 2017 auto generated files
+Generated\ Files/
+
+# MSTest test Results
+[Tt]est[Rr]esult*/
+[Bb]uild[Ll]og.*
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+*.VisualState.xml
+TestResult.xml
+nunit-*.xml
+
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+[Dd]ebugPS/
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+project.fragment.lock.json
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+ScaffoldingReadMe.txt
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+*_i.c
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+*.tmp_proj
+*_wpftmp.csproj
+*.log
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+.builds
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+*.svclog
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+
+# Chutzpah Test files
+_Chutzpah*
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+# Visual C++ cache files
+ipch/
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+
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+.axoCover/*
+!.axoCover/settings.json
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+coverage*.json
+coverage*.xml
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+# Visual Studio code coverage results
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+# NCrunch
+_NCrunch_*
+.*crunch*.local.xml
+nCrunchTemp_*
+
+# MightyMoose
+*.mm.*
+AutoTest.Net/
+
+# Web workbench (sass)
+.sass-cache/
+
+# Installshield output folder
+[Ee]xpress/
+
+# DocProject is a documentation generator add-in
+DocProject/buildhelp/
+DocProject/Help/*.HxT
+DocProject/Help/*.HxC
+DocProject/Help/*.hhc
+DocProject/Help/*.hhk
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+
+# Publish Web Output
+*.[Pp]ublish.xml
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+# Note: Comment the next line if you want to checkin your web deploy settings,
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+*.pubxml
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+# in these scripts will be unencrypted
+PublishScripts/
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+*.snupkg
+# The packages folder can be ignored because of Package Restore
+**/[Pp]ackages/*
+# except build/, which is used as an MSBuild target.
+!**/[Pp]ackages/build/
+# Uncomment if necessary however generally it will be regenerated when needed
+#!**/[Pp]ackages/repositories.config
+# NuGet v3's project.json files produces more ignorable files
+*.nuget.props
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+
+# Microsoft Azure Build Output
+csx/
+*.build.csdef
+
+# Microsoft Azure Emulator
+ecf/
+rcf/
+
+# Windows Store app package directories and files
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+Package.StoreAssociation.xml
+_pkginfo.txt
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+*.appxbundle
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+
+# Visual Studio cache files
+# files ending in .cache can be ignored
+*.[Cc]ache
+# but keep track of directories ending in .cache
+!?*.[Cc]ache/
+
+# Others
+ClientBin/
+~$*
+*~
+*.dbmdl
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+
+# Including strong name files can present a security risk
+# (https://github.com/github/gitignore/pull/2483#issue-259490424)
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+# Since there are multiple workflows, uncomment next line to ignore bower_components
+# (https://github.com/github/gitignore/pull/1529#issuecomment-104372622)
+#bower_components/
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+# RIA/Silverlight projects
+Generated_Code/
+
+# Backup & report files from converting an old project file
+# to a newer Visual Studio version. Backup files are not needed,
+# because we have git ;-)
+_UpgradeReport_Files/
+Backup*/
+UpgradeLog*.XML
+UpgradeLog*.htm
+ServiceFabricBackup/
+*.rptproj.bak
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+# SQL Server files
+*.mdf
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+# Business Intelligence projects
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+*.bim_*.settings
+*.rptproj.rsuser
+*- [Bb]ackup.rdl
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+*- [Bb]ackup ([0-9][0-9]).rdl
+
+# Microsoft Fakes
+FakesAssemblies/
+
+# GhostDoc plugin setting file
+*.GhostDoc.xml
+
+# Node.js Tools for Visual Studio
+.ntvs_analysis.dat
+node_modules/
+
+# Visual Studio 6 build log
+*.plg
+
+# Visual Studio 6 workspace options file
+*.opt
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+# Visual Studio 6 auto-generated workspace file (contains which files were open etc.)
+*.vbw
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+# Visual Studio 6 auto-generated project file (contains which files were open etc.)
+*.vbp
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+**/*.HTMLClient/GeneratedArtifacts
+**/*.DesktopClient/GeneratedArtifacts
+**/*.DesktopClient/ModelManifest.xml
+**/*.Server/GeneratedArtifacts
+**/*.Server/ModelManifest.xml
+_Pvt_Extensions
+
+# Paket dependency manager
+.paket/paket.exe
+paket-files/
+
+# FAKE - F# Make
+.fake/
+
+# CodeRush personal settings
+.cr/personal
+
+# Python Tools for Visual Studio (PTVS)
+__pycache__/
+*.pyc
+
+# Cake - Uncomment if you are using it
+# tools/**
+# !tools/packages.config
+
+# Tabs Studio
+*.tss
+
+# Telerik's JustMock configuration file
+*.jmconfig
+
+# BizTalk build output
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+*.btm.cs
+*.odx.cs
+*.xsd.cs
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+# OpenCover UI analysis results
+OpenCover/
+
+# Azure Stream Analytics local run output
+ASALocalRun/
+
+# MSBuild Binary and Structured Log
+*.binlog
+
+# NVidia Nsight GPU debugger configuration file
+*.nvuser
+
+# MFractors (Xamarin productivity tool) working folder
+.mfractor/
+
+# Local History for Visual Studio
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+# Visual Studio History (VSHistory) files
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+
+# BeatPulse healthcheck temp database
+healthchecksdb
+
+# Backup folder for Package Reference Convert tool in Visual Studio 2017
+MigrationBackup/
+
+# Ionide (cross platform F# VS Code tools) working folder
+.ionide/
+
+# Fody - auto-generated XML schema
+FodyWeavers.xsd
+
+# VS Code files for those working on multiple tools
+.vscode/*
+!.vscode/settings.json
+!.vscode/tasks.json
+!.vscode/launch.json
+!.vscode/extensions.json
+*.code-workspace
+
+# Local History for Visual Studio Code
+.history/
+
+# Windows Installer files from build outputs
+*.cab
+*.msi
+*.msix
+*.msm
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+
+# JetBrains Rider
+*.sln.iml
+.idea
+
+##
+## Visual studio for Mac
+##
+
+
+# globs
+Makefile.in
+*.userprefs
+*.usertasks
+config.make
+config.status
+aclocal.m4
+install-sh
+autom4te.cache/
+*.tar.gz
+tarballs/
+test-results/
+
+# Mac bundle stuff
+*.dmg
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+
+# content below from: https://github.com/github/gitignore/blob/master/Global/macOS.gitignore
+# General
+.DS_Store
+.AppleDouble
+.LSOverride
+
+# Icon must end with two \r
+Icon
+
+
+# Thumbnails
+._*
+
+# Files that might appear in the root of a volume
+.DocumentRevisions-V100
+.fseventsd
+.Spotlight-V100
+.TemporaryItems
+.Trashes
+.VolumeIcon.icns
+.com.apple.timemachine.donotpresent
+
+# Directories potentially created on remote AFP share
+.AppleDB
+.AppleDesktop
+Network Trash Folder
+Temporary Items
+.apdisk
+
+# content below from: https://github.com/github/gitignore/blob/master/Global/Windows.gitignore
+# Windows thumbnail cache files
+Thumbs.db
+ehthumbs.db
+ehthumbs_vista.db
+
+# Dump file
+*.stackdump
+
+# Folder config file
+[Dd]esktop.ini
+
+# Recycle Bin used on file shares
+$RECYCLE.BIN/
+
+# Windows Installer files
+*.cab
+*.msi
+*.msix
+*.msm
+*.msp
+
+# Windows shortcuts
+*.lnk
+
+# Vim temporary swap files
+*.swp

Engine.Core/Abstract/IBehaviour.cs

@@ -16,4 +16,9 @@ public interface IBehaviour : IEntity, IAssignableBehaviourController, IAssignab
     /// Call priority of the <see cref="IBehaviour"/>.
     /// </summary>
     int Priority { get; set; }
+
+    /// <summary>
+    /// If the <see cref="IBehaviour"/> is active.
+    /// </summary>
+    bool IsActive { get; }
 }

Engine.Core/Abstract/ICamera.cs

@@ -1,12 +0,0 @@
-using System;
-
-namespace Syntriax.Engine.Core.Abstract;
-
-public interface ICamera : IAssignableTransform
-{
-    Action<ICamera>? OnZoomChanged { get; set; }
-
-    float Zoom { get; set; }
-
-    void Update();
-}

Engine.Core/Abstract/IGameManager.cs

@@ -0,0 +1,21 @@
+using System;
+using System.Collections.Generic;
+
+namespace Syntriax.Engine.Core.Abstract;
+
+public interface IGameManager : IEntity, IEnumerable<IGameObject>
+{
+    Action<GameManager, IGameObject>? OnGameObjectRegistered { get; set; }
+    Action<GameManager, IGameObject>? OnGameObjectUnRegistered { get; set; }
+
+
+    IReadOnlyList<IGameObject> GameObjects { get; }
+
+
+    void RegisterGameObject(IGameObject gameObject);
+    T InstantiateGameObject<T>(params object?[]? args) where T : class, IGameObject;
+    IGameObject RemoveGameObject(IGameObject gameObject);
+
+    void Update(EngineTime time);
+    void PreDraw();
+}

Engine.Core/Behaviour.cs

@@ -5,6 +5,7 @@ using Syntriax.Engine.Core.Exceptions;
 
 namespace Syntriax.Engine.Core;
 
+[System.Diagnostics.DebuggerDisplay("{GetType().Name, nq}, Priority: {Priority}, Initialized: {Initialized}")]
 public abstract class Behaviour : IBehaviour
 {
     public Action<IAssignable>? OnUnassigned { get; set; } = null;
@@ -25,6 +26,8 @@ public abstract class Behaviour : IBehaviour
     public IStateEnable StateEnable => _stateEnable;
     public IBehaviourController BehaviourController => _behaviourController;
 
+    public bool IsActive => StateEnable.Enabled && BehaviourController.GameObject.StateEnable.Enabled;
+
     public bool Initialized
     {
         get => _initialized;

Engine.Core/BehaviourController.cs

@@ -1,11 +1,13 @@
 using System;
 using System.Collections.Generic;
 using System.Diagnostics.CodeAnalysis;
+using System.Linq;
 
 using Syntriax.Engine.Core.Abstract;
 
 namespace Syntriax.Engine.Core;
 
+[System.Diagnostics.DebuggerDisplay("Behaviour Count: {behaviours.Count}")]
 public class BehaviourController : IBehaviourController
 {
     public Action<IBehaviourController>? OnPreUpdate { get; set; }
@@ -55,17 +57,17 @@ public class BehaviourController : IBehaviourController
 
     public IList<T> GetBehaviours<T>()
     {
-        IList<T> behaviours = new List<T>();
+        List<T>? behaviours = null;
         foreach (var behaviourItem in this.behaviours)
         {
             if (behaviourItem is not T behaviour)
                 continue;
 
-            behaviours ??= new List<T>();
+            behaviours ??= [];
             behaviours.Add(behaviour);
         }
 
-        return behaviours;
+        return behaviours ?? Enumerable.Empty<T>().ToList();
     }
 
     public void RemoveBehaviour<T>(bool removeAll = false) where T : class, IBehaviour

Engine.Core/BehaviourOverride.cs

@@ -39,13 +39,13 @@ public abstract class BehaviourOverride : Behaviour
         OnFinalize();
     }
 
-    protected virtual void OnPreUpdatePreEnabledCheck() { }
+    protected virtual void OnPreUpdatePreActiveCheck() { }
     protected virtual void OnPreUpdate() { }
     private void PreUpdate(IBehaviourController _)
     {
-        OnPreUpdatePreEnabledCheck();
+        OnPreUpdatePreActiveCheck();
 
-        if (!StateEnable.Enabled)
+        if (!IsActive)
             return;
 
         if (isInitializedThisFrame)
@@ -61,23 +61,23 @@ public abstract class BehaviourOverride : Behaviour
         isInitializedThisFrame = false;
     }
 
-    protected virtual void OnUpdatePreEnabledCheck() { }
+    protected virtual void OnUpdatePreActiveCheck() { }
     protected virtual void OnUpdate() { }
     private void Update(IBehaviourController _)
     {
-        OnUpdatePreEnabledCheck();
+        OnUpdatePreActiveCheck();
 
-        if (!StateEnable.Enabled)
+        if (!IsActive)
             return;
 
         OnUpdate();
     }
 
-    protected virtual void OnPreDrawPreEnabledCheck() { }
+    protected virtual void OnPreDrawPreActiveCheck() { }
     protected virtual void OnPreDraw() { }
     private void PreDraw(IBehaviourController _)
     {
-        OnPreDrawPreEnabledCheck();
+        OnPreDrawPreActiveCheck();
 
         if (!StateEnable.Enabled)
             return;

Engine.Core/Engine.Core.sln

@@ -1,25 +0,0 @@
-
-Microsoft Visual Studio Solution File, Format Version 12.00
-# Visual Studio Version 17
-VisualStudioVersion = 17.5.002.0
-MinimumVisualStudioVersion = 10.0.40219.1
-Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "Engine.Core", "Engine.Core.csproj", "{6C1AF4B1-60B0-4225-9A96-F597BC04E9D0}"
-EndProject
-Global
-	GlobalSection(SolutionConfigurationPlatforms) = preSolution
-		Debug|Any CPU = Debug|Any CPU
-		Release|Any CPU = Release|Any CPU
-	EndGlobalSection
-	GlobalSection(ProjectConfigurationPlatforms) = postSolution
-		{6C1AF4B1-60B0-4225-9A96-F597BC04E9D0}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
-		{6C1AF4B1-60B0-4225-9A96-F597BC04E9D0}.Debug|Any CPU.Build.0 = Debug|Any CPU
-		{6C1AF4B1-60B0-4225-9A96-F597BC04E9D0}.Release|Any CPU.ActiveCfg = Release|Any CPU
-		{6C1AF4B1-60B0-4225-9A96-F597BC04E9D0}.Release|Any CPU.Build.0 = Release|Any CPU
-	EndGlobalSection
-	GlobalSection(SolutionProperties) = preSolution
-		HideSolutionNode = FALSE
-	EndGlobalSection
-	GlobalSection(ExtensibilityGlobals) = postSolution
-		SolutionGuid = {CC449885-B99C-4C71-842D-3C19A35E786F}
-	EndGlobalSection
-EndGlobal

Engine.Core/EngineTime.cs

@@ -2,8 +2,8 @@ using System;
 
 namespace Syntriax.Engine.Core;
 
-public record EngineTime
-(
-    TimeSpan Total,
-    TimeSpan Elapsed
-);
+public readonly struct EngineTime(TimeSpan Total, TimeSpan Elapsed)
+{
+    public readonly TimeSpan Total { get; init; } = Total;
+    public readonly TimeSpan Elapsed { get; init; } = Elapsed;
+}

Engine.Core/Extensions/Abstract/TransformExtensions.cs

@@ -0,0 +1,9 @@
+namespace Syntriax.Engine.Core.Abstract;
+
+public static class TransformExtensions
+{
+    public static Vector2D TransformVector2D(this ITransform transform, Vector2D vector)
+        => vector.Scale(transform.Scale)
+                 .Rotate(transform.Rotation * Math.DegreeToRadian)
+                 .Add(transform.Position);
+}

Engine.Core/Extensions/FloatExtensions.cs

@@ -0,0 +1,22 @@
+namespace Syntriax.Engine.Core;
+
+public static class FloatExtensions
+{
+    public static bool ApproximatelyEquals(this float a, float b)
+        => ApproximatelyEquals(a, b, float.Epsilon);
+    public static bool ApproximatelyEquals(this float a, float b, float epsilon)
+    {
+        if (a == b)
+            return true;
+
+        const float floatNormal = (1 << 23) * float.Epsilon;
+        float absA = Math.Abs(a);
+        float absB = Math.Abs(b);
+        float diff = Math.Abs(a - b);
+
+        if (a == 0.0f || b == 0.0f || diff < floatNormal)
+            return diff < (epsilon * floatNormal);
+
+        return diff / Math.Min(absA + absB, float.MaxValue) < epsilon;
+    }
+}

Engine.Core/Extensions/Vector2DExtensions.cs

@@ -4,13 +4,23 @@ public static class Vector2DExtensions
 {
     public static float Length(this Vector2D vector) => Vector2D.Length(vector);
     public static float LengthSquared(this Vector2D vector) => Vector2D.LengthSquared(vector);
+
     public static float Distance(this Vector2D from, Vector2D to) => Vector2D.Distance(from, to);
 
+    public static Vector2D Invert(this Vector2D vector) => Vector2D.Invert(vector);
+    public static Vector2D Add(this Vector2D vector, Vector2D vectorToAdd) => Vector2D.Add(vector, vectorToAdd);
+    public static Vector2D Subtract(this Vector2D vector, Vector2D vectorToSubtract) => Vector2D.Subtract(vector, vectorToSubtract);
+    public static Vector2D Multiply(this Vector2D vector, float value) => Vector2D.Multiply(vector, value);
+    public static Vector2D Subdivide(this Vector2D vector, float value) => Vector2D.Subdivide(vector, value);
+
+    public static Vector2D Abs(this Vector2D vector) => Vector2D.Abs(vector);
     public static Vector2D Reflect(this Vector2D vector, Vector2D normal) => Vector2D.Reflect(vector, normal);
     public static Vector2D Normalize(this Vector2D vector) => Vector2D.Normalize(vector);
     public static Vector2D FromTo(this Vector2D from, Vector2D to) => Vector2D.FromTo(from, to);
     public static Vector2D Scale(this Vector2D vector, Vector2D scale) => Vector2D.Scale(vector, scale);
 
+    public static Vector2D Perpendicular(this Vector2D vector) => Vector2D.Perpendicular(vector);
+    public static Vector2D Rotate(this Vector2D vector, float angleInRadian) => Vector2D.Rotate(vector, angleInRadian);
     public static Vector2D Min(this Vector2D left, Vector2D right) => Vector2D.Min(left, right);
     public static Vector2D Max(this Vector2D left, Vector2D right) => Vector2D.Max(left, right);
     public static Vector2D Clamp(this Vector2D vector, Vector2D min, Vector2D max) => Vector2D.Clamp(vector, min, max);
@@ -19,4 +29,7 @@ public static class Vector2DExtensions
     public static float Cross(this Vector2D left, Vector2D right) => Vector2D.Cross(left, right);
     public static float AngleBetween(this Vector2D left, Vector2D right) => Vector2D.Angle(left, right);
     public static float Dot(this Vector2D left, Vector2D right) => Vector2D.Dot(left, right);
+
+
+    public static bool ApproximatelyEquals(this Vector2D left, Vector2D right, float epsilon = float.Epsilon) => Vector2D.ApproximatelyEquals(left, right, epsilon);
 }

Engine.Core/GameManager.cs

@@ -8,9 +8,9 @@ using Syntriax.Engine.Core.Factory;
 
 namespace Syntriax.Engine.Core;
 
-public class GameManager : IEntity, IEnumerable<IGameObject>
+[System.Diagnostics.DebuggerDisplay("GameObject Count: {_gameObjects.Count}")]
+public class GameManager : IGameManager
 {
-    public Action<GameManager>? OnCameraChanged { get; set; } = null;
     public Action<GameManager, IGameObject>? OnGameObjectRegistered { get; set; } = null;
     public Action<GameManager, IGameObject>? OnGameObjectUnRegistered { get; set; } = null;
 
@@ -20,12 +20,11 @@ public class GameManager : IEntity, IEnumerable<IGameObject>
     public Action<IAssignableStateEnable>? OnStateEnableAssigned { get; set; } = null;
 
 
-    private IList<IGameObject> _gameObjects = new List<IGameObject>(Constants.GAME_OBJECTS_SIZE_INITIAL);
+    private readonly List<IGameObject> _gameObjects = new(Constants.GAME_OBJECTS_SIZE_INITIAL);
 
     private IStateEnable _stateEnable = null!;
     private GameObjectFactory _gameObjectFactory = null!;
     private bool _initialized = false;
-    private ICamera _camera = null!;
 
     private GameObjectFactory GameObjectFactory
     {
@@ -38,7 +37,8 @@ public class GameManager : IEntity, IEnumerable<IGameObject>
     }
 
     public bool Initialized => _initialized;
-    public IList<IGameObject> GameObjects => _gameObjects;
+    public IReadOnlyList<IGameObject> GameObjects => _gameObjects;
+
     public IStateEnable StateEnable
     {
         get
@@ -54,19 +54,6 @@ public class GameManager : IEntity, IEnumerable<IGameObject>
         }
     }
 
-    public ICamera Camera
-    {
-        get => _camera;
-        set
-        {
-            if (_camera == value)
-                return;
-
-            _camera = value;
-            OnCameraChanged?.Invoke(this);
-        }
-    }
-
     public void RegisterGameObject(IGameObject gameObject)
     {
         if (_gameObjects.Contains(gameObject))
@@ -101,6 +88,7 @@ public class GameManager : IEntity, IEnumerable<IGameObject>
         foreach (var gameObject in GameObjects)
             gameObject.Initialize();
 
+        _initialized = true;
         OnInitialized?.Invoke(this);
         return true;
     }
@@ -114,6 +102,7 @@ public class GameManager : IEntity, IEnumerable<IGameObject>
             GameObjects[i].Finalize();
 
         OnFinalized?.Invoke(this);
+        _initialized = false;
         return true;
     }
 

Engine.Core/GameObject.cs

@@ -5,6 +5,7 @@ using Syntriax.Engine.Core.Exceptions;
 
 namespace Syntriax.Engine.Core;
 
+[System.Diagnostics.DebuggerDisplay("Name: {Name}, Initialized: {Initialized}")]
 public class GameObject : IGameObject
 {
     public Action<IAssignableStateEnable>? OnStateEnableAssigned { get; set; } = null;

Engine.Core/Math.cs

@@ -0,0 +1,35 @@
+using System;
+using System.Numerics;
+
+namespace Syntriax.Engine.Core;
+
+public static class Math
+{
+    public const float RadianToDegree = 180f / PI;
+    public const float DegreeToRadian = PI / 180f;
+
+    public const float E = 2.718281828459045f;
+    public const float PI = 3.1415926535897932f;
+    public const float Tau = 2f * PI;
+
+    public static T Abs<T>(T x) where T : INumber<T> => x > T.Zero ? x : -x;
+    public static float Acos(float x) => MathF.Acos(x);
+    public static float Asin(float x) => MathF.Asin(x);
+    public static float Atan2(float y, float x) => MathF.Atan2(y, x);
+    public static float Atanh(float x) => MathF.Atanh(x);
+    public static T Clamp<T>(this T x, T min, T max) where T : INumber<T> => (x < min) ? min : (x > max) ? max : x;
+    public static float Ceiling(float x) => MathF.Ceiling(x);
+    public static float CopySign(float x, float y) => MathF.CopySign(x, y);
+    public static float Floor(float x) => MathF.Floor(x);
+    public static float IEEERemainder(float x, float y) => MathF.IEEERemainder(x, y);
+    public static float Log(float x, float y) => MathF.Log(x, y);
+    public static T Max<T>(T x, T y) where T : INumber<T> => (x > y) ? x : y;
+    public static float MaxMagnitude(float x, float y) => MathF.MaxMagnitude(x, y);
+    public static T Min<T>(T x, T y) where T : INumber<T> => (x < y) ? x : y;
+    public static float MinMagnitude(float x, float y) => MathF.MinMagnitude(x, y);
+    public static float Pow(float x, float y) => MathF.Pow(x, y);
+    public static float Round(float x, int digits, MidpointRounding mode) => MathF.Round(x, digits, mode);
+    public static T Sqr<T>(T x) where T : INumber<T> => x * x;
+    public static float Sqrt(float x) => MathF.Sqrt(x);
+    public static float Truncate(float x) => MathF.Truncate(x);
+}

Engine.Core/Transform.cs

@@ -4,6 +4,7 @@ using Syntriax.Engine.Core.Abstract;
 
 namespace Syntriax.Engine.Core;
 
+[System.Diagnostics.DebuggerDisplay("Position: {Position.ToString(), nq}, Scale: {Scale.ToString(), nq}, Rotation: {Rotation}")]
 public class Transform : ITransform
 {
     public Action<ITransform>? OnPositionChanged { get; set; } = null;

Engine.Core/Vector2D.cs

@@ -2,12 +2,15 @@ using System;
 
 namespace Syntriax.Engine.Core;
 
-[System.Diagnostics.DebuggerDisplay("{ToString(),nq}, Length: {Magnitude}, LengthSquared: {MagnitudeSquared}, Normalized: {Normalized}")]
-public record Vector2D(float X, float Y)
+[System.Diagnostics.DebuggerDisplay("{ToString(),nq}, Length: {Magnitude}, LengthSquared: {MagnitudeSquared}, Normalized: {Normalized.ToString(),nq}")]
+public readonly struct Vector2D(float X, float Y)
 {
-    public float Magnitude => Length(this);
-    public float MagnitudeSquared => LengthSquared(this);
-    public Vector2D Normalized => Normalize(this);
+    public readonly float X { get; init; } = X;
+    public readonly float Y { get; init; } = Y;
+
+    public readonly float Magnitude => Length(this);
+    public readonly float MagnitudeSquared => LengthSquared(this);
+    public readonly Vector2D Normalized => Normalize(this);
 
     public readonly static Vector2D Up = new(0f, 1f);
     public readonly static Vector2D Down = new(0f, -1f);
@@ -22,17 +25,28 @@ public record Vector2D(float X, float Y)
     public static Vector2D operator *(Vector2D vector, float value) => new(vector.X * value, vector.Y * value);
     public static Vector2D operator *(float value, Vector2D vector) => new(vector.X * value, vector.Y * value);
     public static Vector2D operator /(Vector2D vector, float value) => new(vector.X / value, vector.Y / value);
+    public static bool operator ==(Vector2D left, Vector2D right) => left.X == right.X && left.Y == right.Y;
+    public static bool operator !=(Vector2D left, Vector2D right) => left.X != right.X || left.Y != right.Y;
 
     public static float Length(Vector2D vector) => MathF.Sqrt(LengthSquared(vector));
     public static float LengthSquared(Vector2D vector) => vector.X * vector.X + vector.Y * vector.Y;
 
     public static float Distance(Vector2D from, Vector2D to) => Length(FromTo(from, to));
 
+    public static Vector2D Invert(Vector2D vector) => -vector;
+    public static Vector2D Add(Vector2D left, Vector2D right) => left + right;
+    public static Vector2D Subtract(Vector2D left, Vector2D right) => left - right;
+    public static Vector2D Multiply(Vector2D vector, float value) => vector * value;
+    public static Vector2D Subdivide(Vector2D vector, float value) => vector / value;
+
+    public static Vector2D Abs(Vector2D vector) => new(Math.Abs(vector.X), Math.Abs(vector.Y));
     public static Vector2D Normalize(Vector2D vector) => vector / Length(vector);
     public static Vector2D Reflect(Vector2D vector, Vector2D normal) => vector - 2f * Dot(vector, normal) * normal;
     public static Vector2D FromTo(Vector2D from, Vector2D to) => to - from;
     public static Vector2D Scale(Vector2D vector, Vector2D scale) => new(vector.X * scale.X, vector.Y * scale.Y);
 
+    public static Vector2D Perpendicular(Vector2D vector) => new(-vector.Y, vector.X);
+    public static Vector2D Rotate(Vector2D vector, float angleInRadian) => new(MathF.Cos(angleInRadian) * vector.X - MathF.Sin(angleInRadian) * vector.Y, MathF.Sin(angleInRadian) * vector.X + MathF.Cos(angleInRadian) * vector.Y);
     public static Vector2D Min(Vector2D left, Vector2D right) => new((left.X < right.X) ? left.X : right.X, (left.Y < right.Y) ? left.Y : right.Y);
     public static Vector2D Max(Vector2D left, Vector2D right) => new((left.X > right.X) ? left.X : right.X, (left.Y > right.Y) ? left.Y : right.Y);
     public static Vector2D Clamp(Vector2D vector, Vector2D min, Vector2D max) => new(Math.Clamp(vector.X, min.X, max.X), Math.Clamp(vector.Y, min.Y, max.Y));
@@ -42,5 +56,28 @@ public record Vector2D(float X, float Y)
     public static float Angle(Vector2D left, Vector2D right) => MathF.Acos(Dot(left, right) / (Length(left) * Length(right)));
     public static float Dot(Vector2D left, Vector2D right) => left.X * right.X + left.Y * right.Y;
 
-    public override string ToString() => $"{nameof(Vector2D)}({X}, {Y})";
+    /// <summary>
+    /// Finds the Orientation of 3 <see cref="Vector2D"/>s
+    /// </summary>
+    /// <returns>0 -> Collinear, 1 -> Clockwise, 2 -> Counterclockwise</returns>
+    public static int Orientation(Vector2D left, Vector2D middle, Vector2D right)
+    {
+        Vector2D leftToMiddle = left.FromTo(middle);
+        Vector2D middleToRight = middle.FromTo(right);
+
+        float value = leftToMiddle.Y * middleToRight.X -
+                    leftToMiddle.X * middleToRight.Y;
+
+        if (value > 0) return 1;
+        if (value < 0) return 2;
+        return 0;
+    }
+
+    public static bool ApproximatelyEquals(Vector2D left, Vector2D right, float epsilon = float.Epsilon)
+        => left.X.ApproximatelyEquals(right.X, epsilon) && left.Y.ApproximatelyEquals(right.Y, epsilon);
+
+    public override string ToString() => $"{nameof(Vector2D)}({X}, {Y})";
+
+    public override bool Equals(object? obj) => obj is Vector2D objVec && X.Equals(objVec.X) && Y.Equals(objVec.Y);
+    public override int GetHashCode() => HashCode.Combine(X, Y);
 }

Engine.Input/Engine.Input.sln

@@ -1,25 +0,0 @@
-
-Microsoft Visual Studio Solution File, Format Version 12.00
-# Visual Studio Version 17
-VisualStudioVersion = 17.5.002.0
-MinimumVisualStudioVersion = 10.0.40219.1
-Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "Engine.Input", "Engine.Input.csproj", "{637B86E7-3699-4248-9A9F-C5CB09779B53}"
-EndProject
-Global
-	GlobalSection(SolutionConfigurationPlatforms) = preSolution
-		Debug|Any CPU = Debug|Any CPU
-		Release|Any CPU = Release|Any CPU
-	EndGlobalSection
-	GlobalSection(ProjectConfigurationPlatforms) = postSolution
-		{637B86E7-3699-4248-9A9F-C5CB09779B53}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
-		{637B86E7-3699-4248-9A9F-C5CB09779B53}.Debug|Any CPU.Build.0 = Debug|Any CPU
-		{637B86E7-3699-4248-9A9F-C5CB09779B53}.Release|Any CPU.ActiveCfg = Release|Any CPU
-		{637B86E7-3699-4248-9A9F-C5CB09779B53}.Release|Any CPU.Build.0 = Release|Any CPU
-	EndGlobalSection
-	GlobalSection(SolutionProperties) = preSolution
-		HideSolutionNode = FALSE
-	EndGlobalSection
-	GlobalSection(ExtensibilityGlobals) = postSolution
-		SolutionGuid = {FB9A6AA6-FAEF-4DE6-BDE0-C9CC4F02B29A}
-	EndGlobalSection
-EndGlobal

Engine.Physics2D/Abstract/ICircleCollider2D.cs

@@ -0,0 +1,9 @@
+using Syntriax.Engine.Physics2D.Primitives;
+
+namespace Syntriax.Engine.Physics2D.Abstract;
+
+public interface ICircleCollider2D : ICollider2D
+{
+    Circle CircleLocal { get; set; }
+    Circle CircleWorld { get; }
+}

Engine.Physics2D/Abstract/ICollider2D.cs

@@ -0,0 +1,18 @@
+using System;
+
+using Syntriax.Engine.Core.Abstract;
+
+namespace Syntriax.Engine.Physics2D.Abstract;
+
+public interface ICollider2D : IBehaviour, IAssignableTransform
+{
+    Action<ICollider2D, CollisionDetectionInformation>? OnCollisionDetected { get; set; }
+    Action<ICollider2D, CollisionDetectionInformation>? OnCollisionResolved { get; set; }
+
+    Action<ICollider2D, ICollider2D>? OnTriggered { get; set; }
+
+    IRigidBody2D? RigidBody2D { get; }
+    bool IsTrigger { get; set; }
+
+    void Recalculate();
+}

Engine.Physics2D/Abstract/ICollisionDetector2D.cs

@@ -0,0 +1,8 @@
+using Syntriax.Engine.Physics2D.Abstract;
+
+namespace Syntriax.Engine.Physics2D;
+
+public interface ICollisionDetector2D
+{
+    bool TryDetect<T1, T2>(T1 left, T2 right, out CollisionDetectionInformation collisionInformation) where T1 : ICollider2D where T2 : ICollider2D;
+}

Engine.Physics2D/Abstract/ICollisionResolver2D.cs

@@ -0,0 +1,6 @@
+namespace Syntriax.Engine.Physics2D.Abstract;
+
+public interface ICollisionResolver2D
+{
+    void Resolve(CollisionDetectionInformation collisionInformation);
+}

Engine.Physics2D/Abstract/IPhysicsEngine2D.cs

@@ -0,0 +1,11 @@
+namespace Syntriax.Engine.Physics2D.Abstract;
+
+public interface IPhysicsEngine2D
+{
+    int IterationCount { get; set; }
+
+    void AddRigidBody(IRigidBody2D rigidBody);
+    void RemoveRigidBody(IRigidBody2D rigidBody);
+
+    void Step(float deltaTime);
+}

Engine.Physics2D/Abstract/IPhysicsMaterial2D.cs

@@ -0,0 +1,7 @@
+namespace Syntriax.Engine.Physics2D.Abstract;
+
+public interface IPhysicsMaterial2D
+{
+    float Friction { get; }
+    float Restitution { get; }
+}

Engine.Physics2D/Abstract/IRigidBody2D.cs

@@ -0,0 +1,15 @@
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Core.Abstract;
+
+namespace Syntriax.Engine.Physics2D.Abstract;
+
+public interface IRigidBody2D : IBehaviour, IAssignableTransform
+{
+    IPhysicsMaterial2D Material { get; set; }
+
+    Vector2D Velocity { get; set; }
+    float AngularVelocity { get; set; }
+
+    float Mass { get; set; }
+    bool IsStatic { get; set; }
+}

Engine.Physics2D/Abstract/IShapeCollider2D.cs

@@ -0,0 +1,9 @@
+using Syntriax.Engine.Physics2D.Primitives;
+
+namespace Syntriax.Engine.Physics2D.Abstract;
+
+public interface IShapeCollider2D : ICollider2D
+{
+    Shape ShapeLocal { get; set; }
+    Shape ShapeWorld { get; }
+}

Engine.Physics2D/Collider2DBehaviourBase.cs

@@ -0,0 +1,73 @@
+using System;
+
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Core.Abstract;
+using Syntriax.Engine.Physics2D.Abstract;
+
+namespace Syntriax.Engine.Physics2D;
+
+public abstract class Collider2DBehaviourBase : BehaviourOverride, ICollider2D
+{
+    public Action<ICollider2D, CollisionDetectionInformation>? OnCollisionDetected { get; set; } = null;
+    public Action<ICollider2D, CollisionDetectionInformation>? OnCollisionResolved { get; set; } = null;
+    public Action<ICollider2D, ICollider2D>? OnTriggered { get; set; } = null;
+
+
+    protected bool NeedsRecalculation { get; private set; } = true;
+    protected IRigidBody2D? _rigidBody2D = null;
+
+    public IRigidBody2D? RigidBody2D => _rigidBody2D;
+    public bool IsTrigger { get; set; } = false;
+
+    ITransform IAssignableTransform.Transform => Transform;
+    Action<IAssignableTransform>? IAssignableTransform.OnTransformAssigned { get => GameObject.OnTransformAssigned; set => GameObject.OnTransformAssigned = value; }
+
+    bool IAssignableTransform.Assign(ITransform transform) => GameObject.Assign(transform);
+
+    public void Recalculate()
+    {
+        if (!NeedsRecalculation)
+            return;
+
+        CalculateCollider();
+        NeedsRecalculation = false;
+    }
+
+    public abstract void CalculateCollider();
+
+    protected override void OnInitialize()
+    {
+        BehaviourController.TryGetBehaviour(out _rigidBody2D);
+
+        BehaviourController.OnBehaviourAdded += OnBehaviourAddedToController;
+        BehaviourController.OnBehaviourRemoved += OnBehaviourRemovedFromController;
+
+        Transform.OnPositionChanged += SetNeedsRecalculation;
+        Transform.OnRotationChanged += SetNeedsRecalculation;
+        Transform.OnScaleChanged += SetNeedsRecalculation;
+    }
+
+    private void OnBehaviourAddedToController(IBehaviourController _, IBehaviour behaviour)
+    {
+        if (behaviour is IRigidBody2D rigidBody)
+            _rigidBody2D = rigidBody;
+    }
+
+    private void OnBehaviourRemovedFromController(IBehaviourController _, IBehaviour behaviour)
+    {
+        if (behaviour is IRigidBody2D _)
+            _rigidBody2D = null;
+    }
+
+    private void SetNeedsRecalculation(ITransform transform) => NeedsRecalculation = true;
+
+    protected override void OnFinalize()
+    {
+        BehaviourController.OnBehaviourAdded -= OnBehaviourAddedToController;
+        BehaviourController.OnBehaviourRemoved -= OnBehaviourRemovedFromController;
+        Transform.OnScaleChanged -= SetNeedsRecalculation;
+
+        Transform.OnPositionChanged -= SetNeedsRecalculation;
+        Transform.OnRotationChanged -= SetNeedsRecalculation;
+    }
+}

Engine.Physics2D/Collider2DCircleBehaviour.cs

@@ -0,0 +1,17 @@
+using Syntriax.Engine.Physics2D.Abstract;
+using Syntriax.Engine.Physics2D.Primitives;
+
+namespace Syntriax.Engine.Physics2D;
+
+public class Collider2DCircleBehaviour : Collider2DBehaviourBase, ICircleCollider2D
+{
+    public Circle CircleWorld { get; protected set; } = Circle.UnitCircle;
+    public Circle CircleLocal { get; set; } = Circle.UnitCircle;
+
+
+    public override void CalculateCollider() => CircleWorld = Transform.TransformCircle(CircleLocal);
+
+
+    public Collider2DCircleBehaviour() { }
+    public Collider2DCircleBehaviour(Circle circle) => CircleLocal = circle;
+}

Engine.Physics2D/Collider2DShapeBehaviour.cs

@@ -0,0 +1,18 @@
+using Syntriax.Engine.Physics2D.Abstract;
+using Syntriax.Engine.Physics2D.Primitives;
+
+namespace Syntriax.Engine.Physics2D;
+
+public class Collider2DShapeBehaviour : Collider2DBehaviourBase, IShapeCollider2D
+{
+    public Shape ShapeWorld { get => _shapeWorld; protected set => _shapeWorld = value; }
+    public Shape ShapeLocal { get; set; } = Shape.Box;
+
+    private Shape _shapeWorld = Shape.Box.CreateCopy();
+
+    public override void CalculateCollider() => Transform.TransformShape(ShapeLocal, ref _shapeWorld);
+
+
+    public Collider2DShapeBehaviour() { }
+    public Collider2DShapeBehaviour(Shape shape) => ShapeLocal = shape;
+}

Engine.Physics2D/CollisionDetectionInformation.cs

@@ -0,0 +1,19 @@
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Physics2D.Abstract;
+
+namespace Syntriax.Engine.Physics2D;
+
+[System.Diagnostics.DebuggerDisplay("Normal: {Normal.ToString(), nq}, Penetration: {Penetration}")]
+public readonly struct CollisionDetectionInformation
+(
+    ICollider2D Left,
+    ICollider2D Right,
+    Vector2D Normal,
+    float Penetration
+)
+{
+    public ICollider2D Left { get; init; } = Left;
+    public ICollider2D Right { get; init; } = Right;
+    public Vector2D Normal { get; init; } = Normal;
+    public float Penetration { get; init; } = Penetration;
+}

Engine.Physics2D/CollisionDetector2D.cs

@@ -0,0 +1,136 @@
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Physics2D.Abstract;
+using Syntriax.Engine.Physics2D.Primitives;
+
+namespace Syntriax.Engine.Physics2D;
+
+public class CollisionDetector2D : ICollisionDetector2D
+{
+    public bool TryDetect<T1, T2>(T1 left, T2 right, out CollisionDetectionInformation collisionInformation)
+        where T1 : ICollider2D
+        where T2 : ICollider2D
+    {
+        collisionInformation = default;
+        if (left is IShapeCollider2D shapeColliderLeft)
+        {
+            if (right is IShapeCollider2D shapeColliderRight)
+                return DetectShapeShape(shapeColliderLeft, shapeColliderRight, out collisionInformation);
+            else if (right is ICircleCollider2D circleColliderRight)
+                return DetectShapeCircle(shapeColliderLeft, circleColliderRight, out collisionInformation);
+        }
+        else if (left is ICircleCollider2D circleColliderLeft)
+        {
+            if (right is IShapeCollider2D shapeColliderRight)
+                return DetectCircleShape(circleColliderLeft, shapeColliderRight, out collisionInformation);
+            else if (right is ICircleCollider2D circleColliderRight)
+                return DetectCircleCircle(circleColliderLeft, circleColliderRight, out collisionInformation);
+        }
+
+        return false;
+    }
+
+    private static bool DetectCircleShape(ICircleCollider2D circleCollider, IShapeCollider2D shapeCollider, out CollisionDetectionInformation collisionInformation)
+    {
+        return DetectShapeCircle(shapeCollider, circleCollider, out collisionInformation);
+    }
+
+    private static bool DetectShapeShape(IShapeCollider2D left, IShapeCollider2D right, out CollisionDetectionInformation collisionInformation)
+    {
+        collisionInformation = default;
+        return DetectShapeShapeOneWay(left, right, ref collisionInformation) && DetectShapeShapeOneWay(right, left, ref collisionInformation);
+    }
+
+    private static bool DetectShapeShapeOneWay(IShapeCollider2D left, IShapeCollider2D right, ref CollisionDetectionInformation collisionInformation)
+    {
+        var vertices = left.ShapeWorld.Vertices;
+        int count = vertices.Count;
+
+        for (int indexProjection = 0; indexProjection < count; indexProjection++)
+        {
+            Vector2D projectionVector = vertices[indexProjection].FromTo(vertices[(indexProjection + 1) % count]).Perpendicular().Normalized;
+
+            Projection leftProjection = left.ShapeWorld.ToProjection(projectionVector);
+            Projection rightProjection = right.ShapeWorld.ToProjection(projectionVector);
+
+            if (!leftProjection.Overlaps(rightProjection, out float depth))
+                return false;
+
+            if (collisionInformation.Left is null || Math.Abs(collisionInformation.Penetration) > Math.Abs(depth))
+                collisionInformation = new(left, right, projectionVector, depth);
+        }
+
+        return true;
+    }
+
+    private static bool DetectShapeCircle(IShapeCollider2D shapeCollider, ICircleCollider2D circleCollider, out CollisionDetectionInformation collisionInformation)
+    {
+        collisionInformation = default;
+
+        var vertices = shapeCollider.ShapeWorld.Vertices;
+        int count = vertices.Count;
+
+        for (int indexProjection = 0; indexProjection < count; indexProjection++)
+        {
+            Vector2D projectionVector = vertices[indexProjection].FromTo(vertices[(indexProjection + 1) % count]).Perpendicular().Normalized;
+
+            Projection shapeProjection = shapeCollider.ShapeWorld.ToProjection(projectionVector);
+            Projection circleProjection = circleCollider.CircleWorld.ToProjection(projectionVector);
+
+            if (!shapeProjection.Overlaps(circleProjection, out float depth))
+                return false;
+
+            if (collisionInformation.Left is null || Math.Abs(collisionInformation.Penetration) > Math.Abs(depth))
+                collisionInformation = new(shapeCollider, circleCollider, projectionVector, depth);
+        }
+
+        {
+            Vector2D shapeToCircleProjectionVector = shapeCollider.Transform.Position.FromTo(circleCollider.CircleWorld.Center).Normalized;
+
+            Projection shapeProjection = shapeCollider.ShapeWorld.ToProjection(shapeToCircleProjectionVector);
+            Projection circleProjection = circleCollider.CircleWorld.ToProjection(shapeToCircleProjectionVector);
+
+            if (!shapeProjection.Overlaps(circleProjection, out float depth))
+                return false;
+
+            if (collisionInformation.Left is null || Math.Abs(collisionInformation.Penetration) > Math.Abs(depth))
+                collisionInformation = new(shapeCollider, circleCollider, shapeToCircleProjectionVector, depth);
+        }
+
+        return true;
+    }
+
+    private static bool DetectCircleCircle(ICircleCollider2D left, ICircleCollider2D right, out CollisionDetectionInformation collisionInformation)
+    {
+        collisionInformation = default;
+
+        Vector2D leftToRightCenterProjectionVector = left.CircleWorld.Center.FromTo(right.CircleWorld.Center).Normalized;
+
+        Projection leftProjection = left.CircleWorld.ToProjection(leftToRightCenterProjectionVector);
+        Projection rightProjection = right.CircleWorld.ToProjection(leftToRightCenterProjectionVector);
+
+        bool collision = leftProjection.Overlaps(rightProjection, out float depth);
+
+        if (collision)
+            collisionInformation = new(left, right, leftToRightCenterProjectionVector, depth);
+
+        return collision;
+    }
+
+    // private static bool DetectCircleCircle(ICircleCollider2D left, ICircleCollider2D right, out CollisionDetectionInformation collisionInformation)
+    // {
+    //     collisionInformation = default;
+
+    //     Vector2D leftToRightCenter = left.CircleWorld.Center.FromTo(right.CircleWorld.Center);
+    //     float distanceCircleCenter = leftToRightCenter.Magnitude;
+    //     float radiusSum = left.CircleWorld.Radius + right.CircleWorld.Radius;
+
+    //     float circleSurfaceDistance = distanceCircleCenter - radiusSum;
+
+    //     bool collision = circleSurfaceDistance <= 0f;
+
+    //     if (collision)
+    //         collisionInformation = new(left, right, leftToRightCenter.Normalized, -circleSurfaceDistance);
+
+    //     return collision;
+    // }
+}

Engine.Physics2D/CollisionResolver2D.cs

@@ -0,0 +1,44 @@
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Physics2D.Abstract;
+
+namespace Syntriax.Engine.Physics2D;
+
+public class CollisionResolver2D : ICollisionResolver2D
+{
+    public void Resolve(CollisionDetectionInformation collisionInformation)
+    {
+        Vector2D displacementVector = collisionInformation.Normal * collisionInformation.Penetration;
+
+        ICollider2D left = collisionInformation.Left;
+        ICollider2D right = collisionInformation.Right;
+
+        bool isLeftStatic = left.RigidBody2D?.IsStatic ?? true;
+        bool isRightStatic = right.RigidBody2D?.IsStatic ?? true;
+
+        if (isLeftStatic && isRightStatic)
+            return;
+
+        if (isLeftStatic)
+            right.Transform.Position += displacementVector;
+        else if (isRightStatic)
+            left.Transform.Position -= displacementVector;
+        else
+        {
+            float leftMass = left.RigidBody2D?.Mass ?? float.Epsilon;
+            float rightMass = right.RigidBody2D?.Mass ?? float.Epsilon;
+            float sumMass = leftMass + rightMass;
+
+            float leftMomentumPercentage = leftMass / sumMass;
+            float rightMomentumPercentage = rightMass / sumMass;
+
+            right.Transform.Position += leftMomentumPercentage * displacementVector;
+            left.Transform.Position -= rightMomentumPercentage * displacementVector;
+        }
+
+        left.Recalculate();
+        right.Recalculate();
+
+        left.OnCollisionResolved?.Invoke(collisionInformation.Left, collisionInformation);
+        right.OnCollisionResolved?.Invoke(right, collisionInformation);
+    }
+}

Engine.Physics2D/Engine.Physics2D.csproj

@@ -0,0 +1,13 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+  <ItemGroup>
+    <ProjectReference Include="..\Engine.Core\Engine.Core.csproj" />
+  </ItemGroup>
+
+  <PropertyGroup>
+    <TargetFramework>net8.0</TargetFramework>
+    <ImplicitUsings>disable</ImplicitUsings>
+    <Nullable>enable</Nullable>
+  </PropertyGroup>
+
+</Project>

Engine.Physics2D/Physics2D.cs

@@ -0,0 +1,74 @@
+using System;
+
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Physics2D;
+using Syntriax.Engine.Physics2D.Primitives;
+
+namespace Engine.Physics2D;
+
+public static partial class Physics2D
+{
+    public static bool Overlaps(this Circle left, Circle right)
+    {
+        float distanceSquared = left.Center.FromTo(right.Center).LengthSquared();
+        float radiusSumSquared = left.RadiusSquared + right.RadiusSquared;
+
+        return distanceSquared < radiusSumSquared;
+    }
+
+    public static bool Overlaps(this Circle left, Circle right, out Vector2D normal, out float depth)
+    {
+        Vector2D distanceVector = left.Center.FromTo(right.Center);
+        float distanceSquared = distanceVector.LengthSquared();
+        float radiusSumSquared = left.RadiusSquared + right.RadiusSquared;
+        bool isOverlapping = distanceSquared < radiusSumSquared;
+
+        depth = 0f;
+        normal = distanceVector.Normalized;
+
+        if (isOverlapping)
+            depth = MathF.Sqrt(radiusSumSquared - distanceSquared);
+
+        return isOverlapping;
+    }
+
+    public static bool Overlaps(this Circle circle, Vector2D point) => circle.Center.FromTo(point).LengthSquared() <= circle.RadiusSquared;
+    public static bool Overlaps(this Circle circle, Vector2D point, out Vector2D normal, out float depth)
+    {
+        Vector2D distanceVector = circle.Center.FromTo(point);
+        float distanceSquared = distanceVector.LengthSquared();
+        float radiusSquared = circle.RadiusSquared;
+        bool isOverlapping = distanceSquared < radiusSquared;
+
+        depth = 0f;
+        normal = distanceVector.Normalized;
+
+        if (isOverlapping)
+            depth = MathF.Sqrt(radiusSquared - distanceSquared);
+
+        return isOverlapping;
+    }
+
+    public static bool Overlaps(this AABB aabb, Vector2D point)
+        => point.X >= aabb.LowerBoundary.X && point.X <= aabb.UpperBoundary.X &&
+            point.Y >= aabb.LowerBoundary.Y && point.Y <= aabb.UpperBoundary.Y;
+
+    public static bool Overlaps(this AABB left, AABB right)
+        => left.LowerBoundary.X <= right.UpperBoundary.X && left.UpperBoundary.X >= right.LowerBoundary.X &&
+            left.LowerBoundary.Y <= right.UpperBoundary.Y && left.UpperBoundary.Y >= right.LowerBoundary.Y;
+
+    public static bool Overlaps(Triangle triangle, Vector2D point)
+    {
+        float originalTriangleArea = triangle.Area;
+
+        float pointTriangleArea1 = new Triangle(point, triangle.B, triangle.C).Area;
+        float pointTriangleArea2 = new Triangle(triangle.A, point, triangle.C).Area;
+        float pointTriangleArea3 = new Triangle(triangle.A, triangle.B, point).Area;
+
+        float pointTriangleAreasSum = pointTriangleArea1 + pointTriangleArea2 + pointTriangleArea3;
+
+        return originalTriangleArea.ApproximatelyEquals(pointTriangleAreasSum, float.Epsilon * 3f);
+    }
+
+    public static bool LaysOn(this Vector2D point, Line line) => Line.Intersects(line, point);
+}

Engine.Physics2D/PhysicsEngine2D.cs

@@ -0,0 +1,125 @@
+using System.Collections.Generic;
+
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Core.Abstract;
+using Syntriax.Engine.Physics2D.Abstract;
+
+namespace Syntriax.Engine.Physics2D;
+
+public class PhysicsEngine2D : IPhysicsEngine2D
+{
+    private readonly List<IRigidBody2D> rigidBodies = new(32);
+    private readonly List<ICollider2D> colliders = new(64);
+
+    private int _iterationCount = 1;
+    private ICollisionDetector2D collisionDetector = new CollisionDetector2D();
+    private ICollisionResolver2D collisionResolver = new CollisionResolver2D();
+
+    public int IterationCount { get => _iterationCount; set => _iterationCount = value < 1 ? 1 : value; }
+
+    public void AddRigidBody(IRigidBody2D rigidBody)
+    {
+        if (rigidBodies.Contains(rigidBody))
+            return;
+
+        rigidBodies.Add(rigidBody);
+
+        foreach (var collider2D in rigidBody.BehaviourController.GetBehaviours<ICollider2D>())
+            colliders.Add(collider2D);
+
+        rigidBody.BehaviourController.OnBehaviourAdded += OnBehaviourAdded;
+        rigidBody.BehaviourController.OnBehaviourRemoved += OnBehaviourRemoved;
+    }
+
+    public void RemoveRigidBody(IRigidBody2D rigidBody)
+    {
+        rigidBodies.Remove(rigidBody);
+    }
+
+    public void Step(float deltaTime)
+    {
+        float intervalDeltaTime = deltaTime / IterationCount;
+
+        for (int iterationIndex = 0; iterationIndex < IterationCount; iterationIndex++)
+        {
+            // Can Parallel
+            for (int i = 0; i < rigidBodies.Count; i++)
+                StepRigidBody(rigidBodies[i], intervalDeltaTime);
+
+            // Can Parallel
+            foreach (var collider in colliders)
+                collider.Recalculate();
+
+            // Can Parallel
+            for (int x = 0; x < colliders.Count; x++)
+            {
+                ICollider2D? colliderX = colliders[x];
+                if (!colliderX.IsActive)
+                    return;
+
+                for (int y = x + 1; y < colliders.Count; y++)
+                {
+                    ICollider2D? colliderY = colliders[y];
+
+                    if (!colliderY.IsActive)
+                        return;
+
+                    if (colliderX.RigidBody2D == colliderY.RigidBody2D)
+                        continue;
+
+                    bool bothCollidersAreTriggers = colliderX.IsTrigger && colliderX.IsTrigger == colliderY.IsTrigger;
+                    if (bothCollidersAreTriggers)
+                        continue;
+
+                    bool bothCollidersAreStatic = colliderX.RigidBody2D?.IsStatic ?? true && colliderX.RigidBody2D?.IsStatic == colliderY.RigidBody2D?.IsStatic;
+                    if (bothCollidersAreStatic)
+                        continue;
+
+                    if (collisionDetector.TryDetect(colliderX, colliderY, out CollisionDetectionInformation information))
+                    {
+                        if (colliderX.IsTrigger)
+                        {
+                            colliderX.OnTriggered?.Invoke(colliderX, colliderY);
+                            continue;
+                        }
+                        else if (colliderY.IsTrigger)
+                        {
+                            colliderY.OnTriggered?.Invoke(colliderY, colliderY);
+                            continue;
+                        }
+
+                        colliderX.OnCollisionDetected?.Invoke(colliderX, information);
+                        colliderY.OnCollisionDetected?.Invoke(colliderY, information);
+
+                        collisionResolver?.Resolve(information);
+                    }
+                }
+            }
+        }
+    }
+
+    private static void StepRigidBody(IRigidBody2D rigidBody, float intervalDeltaTime)
+    {
+        if (rigidBody.IsStatic)
+            return;
+
+        rigidBody.Transform.Position += rigidBody.Velocity * intervalDeltaTime;
+        rigidBody.Transform.Rotation += rigidBody.AngularVelocity * intervalDeltaTime;
+    }
+
+    private void OnBehaviourAdded(IBehaviourController controller, IBehaviour behaviour)
+    {
+        if (behaviour is not ICollider2D collider2D)
+            return;
+
+        colliders.Add(collider2D);
+    }
+
+    private void OnBehaviourRemoved(IBehaviourController controller, IBehaviour behaviour)
+    {
+        if (behaviour is not ICollider2D collider2D)
+            return;
+
+        colliders.Remove(collider2D);
+    }
+}

Engine.Physics2D/PhysicsMaterial2D.cs

@@ -0,0 +1,9 @@
+using Syntriax.Engine.Physics2D.Abstract;
+
+namespace Syntriax.Engine.Physics2D;
+
+public readonly struct PhysicsMaterial2D(float Friction, float Restitution) : IPhysicsMaterial2D
+{
+    public readonly float Friction { get; init; } = Friction;
+    public readonly float Restitution { get; init; } = Restitution;
+}

Engine.Physics2D/PhysicsMaterial2DDefault.cs

@@ -0,0 +1,10 @@
+using Syntriax.Engine.Physics2D.Abstract;
+
+namespace Syntriax.Engine.Physics2D;
+
+public readonly struct PhysicsMaterial2DDefault : IPhysicsMaterial2D
+{
+    public readonly float Friction => .1f;
+
+    public readonly float Restitution => .1f;
+}

Engine.Physics2D/Primitives/AABB.cs

@@ -0,0 +1,46 @@
+using System.Collections.Generic;
+
+using Syntriax.Engine.Core;
+
+namespace Syntriax.Engine.Physics2D.Primitives;
+
+[System.Diagnostics.DebuggerDisplay("LowerBoundary: {LowerBoundary.ToString(), nq}, UpperBoundary: {UpperBoundary.ToString(), nq}")]
+public readonly struct AABB(Vector2D LowerBoundary, Vector2D UpperBoundary)
+{
+    public readonly Vector2D LowerBoundary { get; init; } = LowerBoundary;
+    public readonly Vector2D UpperBoundary { get; init; } = UpperBoundary;
+
+    public readonly Vector2D Center => (LowerBoundary + UpperBoundary) * .5f;
+    public readonly Vector2D Size => LowerBoundary.FromTo(UpperBoundary).Abs();
+    public readonly Vector2D SizeHalf => Size * .5f;
+
+    public static AABB FromVectors(IEnumerable<Vector2D> vectors)
+    {
+        int counter = 0;
+
+        Vector2D lowerBoundary = new(float.MaxValue, float.MaxValue);
+        Vector2D upperBoundary = new(float.MinValue, float.MinValue);
+
+        foreach (Vector2D vector in vectors)
+        {
+            lowerBoundary = Vector2D.Min(lowerBoundary, vector);
+            upperBoundary = Vector2D.Max(upperBoundary, vector);
+            counter++;
+        }
+
+        if (counter < 2)
+            throw new System.ArgumentException($"Parameter {nameof(vectors)} must have at least 2 items.");
+
+        return new(lowerBoundary, upperBoundary);
+    }
+
+    public static bool ApproximatelyEquals(AABB left, AABB right)
+        => left.LowerBoundary.ApproximatelyEquals(right.LowerBoundary) && left.UpperBoundary.ApproximatelyEquals(right.UpperBoundary);
+}
+
+public static class AABBExtensions
+{
+    public static AABB ToAABB(this IEnumerable<Vector2D> vectors) => AABB.FromVectors(vectors);
+
+    public static bool ApproximatelyEquals(this AABB left, AABB right) => AABB.ApproximatelyEquals(left, right);
+}

Engine.Physics2D/Primitives/Circle.cs

@@ -0,0 +1,47 @@
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Core.Abstract;
+
+namespace Syntriax.Engine.Physics2D.Primitives;
+
+[System.Diagnostics.DebuggerDisplay("Center: {Center.ToString(), nq}, Radius: {Radius}")]
+public readonly struct Circle(Vector2D Center, float Radius)
+{
+    public static readonly Circle UnitCircle = new(Vector2D.Zero, 1f);
+
+    public readonly Vector2D Center { get; init; } = Center;
+    public readonly float Radius { get; init; } = Radius;
+
+    public readonly float RadiusSquared => Radius * Radius;
+    public readonly float Diameter => 2f * Radius;
+
+    public static Circle SetCenter(Circle circle, Vector2D center) => new(center, circle.Radius);
+    public static Circle SetRadius(Circle circle, float radius) => new(circle.Center, radius);
+
+    public static Circle Displace(Circle circle, Vector2D displaceVector) => new(circle.Center + displaceVector, circle.Radius);
+
+    public static Projection Project(Circle circle, Vector2D projectionVector)
+    {
+        float projectedCenter = circle.Center.Dot(projectionVector);
+        return new(projectedCenter - circle.Radius, projectedCenter + circle.Radius);
+    }
+
+    public static Circle TransformCircle(ITransform transform, Circle circle)
+        => new(transform.TransformVector2D(circle.Center), circle.Radius * transform.Scale.Magnitude);
+
+    public static bool ApproximatelyEquals(Circle left, Circle right)
+        => left.Center.ApproximatelyEquals(right.Center) && left.Radius.ApproximatelyEquals(right.Radius);
+}
+
+public static class CircleExtensions
+{
+    public static Circle SetCenter(this Circle circle, Vector2D center) => Circle.SetCenter(circle, center);
+    public static Circle SetRadius(this Circle circle, float radius) => Circle.SetRadius(circle, radius);
+
+    public static Circle Displace(this Circle circle, Vector2D displaceVector) => Circle.Displace(circle, displaceVector);
+
+    public static Projection ToProjection(this Circle circle, Vector2D projectionVector) => Circle.Project(circle, projectionVector);
+
+    public static Circle TransformCircle(this ITransform transform, Circle circle) => Circle.TransformCircle(transform, circle);
+
+    public static bool ApproximatelyEquals(this Circle left, Circle right) => Circle.ApproximatelyEquals(left, right);
+}

Engine.Physics2D/Primitives/Line.cs

@@ -0,0 +1,158 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics.CodeAnalysis;
+
+using Syntriax.Engine.Core;
+
+namespace Syntriax.Engine.Physics2D.Primitives;
+
+[System.Diagnostics.DebuggerDisplay("From: {From.ToString(), nq}, To: {To.ToString(), nq}, Direction: {Direction.ToString(), nq}, Length: {Length}")]
+public readonly struct Line(Vector2D From, Vector2D To)
+{
+    public readonly Vector2D From { get; init; } = From;
+    public readonly Vector2D To { get; init; } = To;
+
+    public readonly Line Reversed => new(To, From);
+    public readonly Vector2D Direction => From.FromTo(To).Normalize();
+    public readonly float Length => From.FromTo(To).Length();
+    public readonly float LengthSquared => From.FromTo(To).LengthSquared();
+
+    public static LineEquation GetLineEquation(Line line)
+    {
+        Vector2D slopeVector = line.From.FromTo(line.To);
+        float slope = slopeVector.Y / slopeVector.X;
+
+        float yOffset = line.From.Y - (slope * line.From.X);
+
+        return new LineEquation(slope, yOffset);
+    }
+
+    public static bool Intersects(Line line, Vector2D point)
+        => LineEquation.Resolve(GetLineEquation(line), point.X).ApproximatelyEquals(point.Y);
+
+    public static float GetT(Line line, Vector2D point)
+    {
+        float fromX = MathF.Abs(line.From.X);
+        float toX = MathF.Abs(line.To.X);
+        float pointX = MathF.Abs(point.X);
+
+        float min = MathF.Min(fromX, toX);
+        float max = MathF.Max(fromX, toX) - min;
+
+        pointX -= min;
+
+        float t = pointX / max;
+
+        // FIXME
+        // I don't even know, apparently whatever I wrote up there doesn't take into account of the direction of the line
+        // Which... I can see how, but I am also not sure how I can make it take into account. Or actually I'm for some reason
+        // too unmotivated to find a solution. Future me, find a better way if possible, please.
+        if (!Lerp(line, t).ApproximatelyEquals(point))
+            return 1f - t;
+        return t;
+    }
+
+    public static bool Exist(Line line, List<Vector2D> vertices)
+    {
+        for (int i = 0; i < vertices.Count - 1; i++)
+        {
+            Vector2D vertexCurrent = vertices[i];
+            Vector2D vertexNext = vertices[i];
+            if (line.From == vertexCurrent && line.To == vertexNext) return true;
+            if (line.From == vertexNext && line.To == vertexCurrent) return true;
+        }
+
+        Vector2D vertexFirst = vertices[0];
+        Vector2D vertexLast = vertices[^1];
+        if (line.From == vertexFirst && line.To == vertexLast) return true;
+        if (line.From == vertexLast && line.To == vertexFirst) return true;
+        return false;
+    }
+
+    public static float IntersectionParameterT(Line left, Line right)
+    {
+        float numerator = (left.From.X - right.From.X) * (right.From.Y - right.To.Y) - (left.From.Y - right.From.Y) * (right.From.X - right.To.X);
+        float denominator = (left.From.X - left.To.X) * (right.From.Y - right.To.Y) - (left.From.Y - left.To.Y) * (right.From.X - right.To.X);
+
+        // Lines are parallel
+        if (denominator == 0)
+            return float.NaN;
+
+        return numerator / denominator;
+    }
+
+    public static Vector2D Lerp(Line line, float t)
+        => new Vector2D(
+            line.From.X + (line.To.X - line.From.X) * t,
+            line.From.Y + (line.To.Y - line.From.Y) * t
+        );
+
+    public static Vector2D ClosestPointTo(Line line, Vector2D point)
+    {
+        // Convert edge points to vectors
+        var edgeVector = new Vector2D(line.To.X - line.From.X, line.To.Y - line.From.Y);
+        var pointVector = new Vector2D(point.X - line.From.X, point.Y - line.From.Y);
+
+        // Calculate the projection of pointVector onto edgeVector
+        float t = (pointVector.X * edgeVector.X + pointVector.Y * edgeVector.Y) / (edgeVector.X * edgeVector.X + edgeVector.Y * edgeVector.Y);
+
+        // Clamp t to the range [0, 1] to ensure the closest point is on the edge
+        t = MathF.Max(0, MathF.Min(1, t));
+
+        // Calculate the closest point on the edge
+        float closestX = line.From.X + t * edgeVector.X;
+        float closestY = line.From.Y + t * edgeVector.Y;
+
+        return new Vector2D((float)closestX, (float)closestY);
+    }
+
+    public static Vector2D IntersectionPoint(Line left, Line right)
+        => Vector2D.Lerp(left.From, left.To, IntersectionParameterT(left, right));
+
+    public static bool Intersects(Line left, Line right)
+    {
+        int o1 = Vector2D.Orientation(left.From, left.To, right.From);
+        int o2 = Vector2D.Orientation(left.From, left.To, right.To);
+        int o3 = Vector2D.Orientation(right.From, right.To, left.From);
+        int o4 = Vector2D.Orientation(right.From, right.To, left.To);
+
+        if (o1 != o2 && o3 != o4)
+            return true;
+
+        if (o1 == 0 && OnSegment(left, right.From)) return true;
+        if (o2 == 0 && OnSegment(left, right.To)) return true;
+        if (o3 == 0 && OnSegment(right, left.From)) return true;
+        if (o4 == 0 && OnSegment(right, left.To)) return true;
+
+        return false;
+    }
+
+    public static bool OnSegment(Line line, Vector2D point)
+    {
+        if (point.X <= MathF.Max(line.From.X, line.To.X) && point.X >= MathF.Min(line.From.X, line.To.X) &&
+            point.Y <= MathF.Max(line.From.Y, line.To.Y) && point.Y >= MathF.Min(line.From.Y, line.To.Y))
+            return true;
+
+        return false;
+    }
+
+    public static bool Intersects(Line left, Line right, [NotNullWhen(returnValue: true)] out Vector2D? point)
+    {
+        point = null;
+
+        bool result = Intersects(left, right);
+
+        if (result)
+            point = IntersectionPoint(left, right);
+
+        return result;
+    }
+
+    public static bool ApproximatelyEquals(Line left, Line right)
+        => left.From.ApproximatelyEquals(right.From) && left.To.ApproximatelyEquals(right.To);
+}
+
+public static class LineExtensions
+{
+    public static bool ApproximatelyEquals(this Line left, Line right) => Line.ApproximatelyEquals(left, right);
+}

Engine.Physics2D/Primitives/LineEquation.cs

@@ -0,0 +1,21 @@
+using Syntriax.Engine.Core;
+
+namespace Syntriax.Engine.Physics2D.Primitives;
+
+[System.Diagnostics.DebuggerDisplay("y = {Slope}x + {OffsetY}")]
+public readonly struct LineEquation(float Slope, float OffsetY)
+{
+    public readonly float Slope { get; init; } = Slope;
+    public readonly float OffsetY { get; init; } = OffsetY;
+
+    public static float Resolve(LineEquation lineEquation, float x) => lineEquation.Slope * x + lineEquation.OffsetY; // y = mx + b
+
+    public static bool ApproximatelyEquals(LineEquation left, LineEquation right)
+        => left.Slope.ApproximatelyEquals(right.Slope) && left.OffsetY.ApproximatelyEquals(right.OffsetY);
+}
+
+public static class LineEquationExtensions
+{
+    public static float Resolve(this LineEquation lineEquation, float x) => LineEquation.Resolve(lineEquation, x);
+    public static bool ApproximatelyEquals(this LineEquation left, LineEquation right) => LineEquation.ApproximatelyEquals(left, right);
+}

Engine.Physics2D/Primitives/Projection.cs

@@ -0,0 +1,49 @@
+namespace Syntriax.Engine.Physics2D.Primitives;
+
+[System.Diagnostics.DebuggerDisplay("Min: {Min}, Max: {Max}")]
+public readonly struct Projection(float Min, float Max)
+{
+    public readonly float Min { get; init; } = Min;
+    public readonly float Max { get; init; } = Max;
+
+    public static bool Overlaps(Projection left, Projection right) => Overlaps(left, right, out var _);
+    public static bool Overlaps(Projection left, Projection right, out float depth)
+    {
+        // TODO Try to improve this
+        bool rightMinInLeft = right.Min > left.Min && right.Min < left.Max;
+        if (rightMinInLeft)
+        {
+            depth = left.Max - right.Min;
+            return true;
+        }
+
+        bool rightMaxInLeft = right.Max < left.Max && right.Max > left.Min;
+        if (rightMaxInLeft)
+        {
+            depth = left.Min - right.Max;
+            return true;
+        }
+
+        bool leftMinInRight = left.Min > right.Min && left.Min < right.Max;
+        if (leftMinInRight)
+        {
+            depth = right.Max - left.Min;
+            return true;
+        }
+
+        bool leftMaxInRight = left.Max < right.Max && left.Max > right.Min;
+        if (leftMaxInRight)
+        {
+            depth = right.Min - left.Max;
+            return true;
+        }
+
+        depth = 0f;
+        return false;
+    }
+}
+public static class ProjectionExtensions
+{
+    public static bool Overlaps(this Projection left, Projection right) => Projection.Overlaps(left, right);
+    public static bool Overlaps(this Projection left, Projection right, out float depth) => Projection.Overlaps(left, right, out depth);
+}

Engine.Physics2D/Primitives/Shape.cs

@@ -0,0 +1,155 @@
+using System.Collections;
+using System.Collections.Generic;
+
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Core.Abstract;
+
+namespace Syntriax.Engine.Physics2D.Primitives;
+
+[System.Diagnostics.DebuggerDisplay("Vertices Count: {Vertices.Count}")]
+public readonly struct Shape(IList<Vector2D> Vertices) : IEnumerable<Vector2D>
+{
+    public static readonly Shape Triangle = CreateNgon(3, Vector2D.Up);
+    public static readonly Shape Box = CreateNgon(4, Vector2D.One);
+    public static readonly Shape Pentagon = CreateNgon(5, Vector2D.Up);
+    public static readonly Shape Hexagon = CreateNgon(6, Vector2D.Right);
+
+    public readonly IList<Vector2D> Vertices { get; init; } = Vertices;
+
+
+    public Vector2D this[System.Index index] => Vertices[index];
+
+    public static Shape CreateCopy(Shape shape) => new(new List<Vector2D>(shape.Vertices));
+
+    public static Shape CreateNgon(int vertexCount) => CreateNgon(vertexCount, Vector2D.Up);
+    public static Shape CreateNgon(int vertexCount, Vector2D positionToRotate)
+    {
+        if (vertexCount < 3)
+            throw new System.ArgumentException($"{nameof(vertexCount)} must have a value of more than 2.");
+
+        List<Vector2D> vertices = new(vertexCount);
+
+        float radiansPerVertex = 360f / vertexCount * Math.DegreeToRadian;
+
+        for (int i = 0; i < vertexCount; i++)
+            vertices.Add(positionToRotate.Rotate(i * radiansPerVertex));
+
+        return new(vertices);
+    }
+
+    public static Triangle GetSuperTriangle(Shape shape)
+    {
+        float minX = float.MaxValue, minY = float.MaxValue;
+        float maxX = float.MinValue, maxY = float.MinValue;
+
+        foreach (Vector2D point in shape.Vertices)
+        {
+            minX = Math.Min(minX, point.X);
+            minY = Math.Min(minY, point.Y);
+            maxX = Math.Max(maxX, point.X);
+            maxY = Math.Max(maxY, point.Y);
+        }
+
+        float dx = maxX - minX;
+        float dy = maxY - minY;
+        float deltaMax = Math.Max(dx, dy);
+        float midX = (minX + maxX) / 2;
+        float midY = (minY + maxY) / 2;
+
+        Vector2D p1 = new((float)midX - 20f * (float)deltaMax, (float)midY - (float)deltaMax);
+        Vector2D p2 = new((float)midX, (float)midY + 20 * (float)deltaMax);
+        Vector2D p3 = new((float)midX + 20 * (float)deltaMax, (float)midY - (float)deltaMax);
+
+        return new Triangle(p1, p2, p3);
+    }
+
+    public static void GetLines(Shape shape, IList<Line> lines)
+    {
+        lines.Clear();
+        for (int i = 0; i < shape.Vertices.Count - 1; i++)
+            lines.Add(new(shape.Vertices[i], shape.Vertices[i + 1]));
+        lines.Add(new(shape.Vertices[^1], shape.Vertices[0]));
+    }
+
+    public static List<Line> GetLines(Shape shape)
+    {
+        List<Line> lines = new(shape.Vertices.Count - 1);
+        GetLines(shape, lines);
+        return lines;
+    }
+
+    public static void Project(Shape shape, Vector2D projectionVector, IList<float> list)
+    {
+        list.Clear();
+
+        int count = shape.Vertices.Count;
+        for (int i = 0; i < count; i++)
+            list.Add(projectionVector.Dot(shape[i]));
+    }
+
+    public static Projection Project(Shape shape, Vector2D projectionVector)
+    {
+        float min = float.MaxValue;
+        float max = float.MinValue;
+
+        for (int i = 0; i < shape.Vertices.Count; i++)
+        {
+            float projectedLength = projectionVector.Dot(shape.Vertices[i]);
+            min = Math.Min(projectedLength, min);
+            max = Math.Max(projectedLength, max);
+        }
+
+        return new(min, max);
+    }
+
+    public static Shape TransformShape(Shape shape, ITransform transform)
+    {
+        List<Vector2D> vertices = new(shape.Vertices.Count);
+
+        int count = shape.Vertices.Count;
+        for (int i = 0; i < count; i++)
+            vertices.Add(transform.TransformVector2D(shape[i]));
+
+        return new Shape(vertices);
+    }
+
+    public static void TransformShape(Shape from, ITransform transform, ref Shape to)
+    {
+        to.Vertices.Clear();
+
+        int count = from.Vertices.Count;
+        for (int i = 0; i < count; i++)
+            to.Vertices.Add(transform.TransformVector2D(from[i]));
+    }
+
+    public static bool ApproximatelyEquals(Shape left, Shape right)
+    {
+        if (left.Vertices.Count != right.Vertices.Count)
+            return false;
+
+        for (int i = 0; i < left.Vertices.Count; i++)
+            if (!left.Vertices[i].ApproximatelyEquals(right.Vertices[i]))
+                return false;
+
+        return true;
+    }
+
+    public IEnumerator<Vector2D> GetEnumerator() => Vertices.GetEnumerator();
+    IEnumerator IEnumerable.GetEnumerator() => Vertices.GetEnumerator();
+}
+
+public static class ShapeExtensions
+{
+    public static Shape CreateCopy(this Shape shape) => Shape.CreateCopy(shape);
+    public static Triangle ToSuperTriangle(this Shape shape) => Shape.GetSuperTriangle(shape);
+    public static void ToLines(this Shape shape, IList<Line> lines) => Shape.GetLines(shape, lines);
+    public static List<Line> ToLines(this Shape shape) => Shape.GetLines(shape);
+
+    public static void ToProjection(this Shape shape, Vector2D projectionVector, IList<float> list) => Shape.Project(shape, projectionVector, list);
+    public static Projection ToProjection(this Shape shape, Vector2D projectionVector) => Shape.Project(shape, projectionVector);
+
+    public static Shape TransformShape(this ITransform transform, Shape shape) => Shape.TransformShape(shape, transform);
+    public static void TransformShape(this ITransform transform, Shape from, ref Shape to) => Shape.TransformShape(from, transform, ref to);
+
+    public static bool ApproximatelyEquals(this Shape left, Shape right) => Shape.ApproximatelyEquals(left, right);
+}

Engine.Physics2D/Primitives/Triangle.cs

@@ -0,0 +1,49 @@
+using System;
+
+using Syntriax.Engine.Core;
+
+namespace Syntriax.Engine.Physics2D.Primitives;
+
+[System.Diagnostics.DebuggerDisplay("A: {A.ToString(), nq}, B: {B.ToString(), nq}, B: {C.ToString(), nq}")]
+public readonly struct Triangle(Vector2D A, Vector2D B, Vector2D C)
+{
+    public readonly Vector2D A { get; init; } = A;
+    public readonly Vector2D B { get; init; } = B;
+    public readonly Vector2D C { get; init; } = C;
+
+    public readonly float Area
+        => .5f * MathF.Abs(
+                A.X * (B.Y - C.Y) +
+                B.X * (C.Y - A.Y) +
+                C.X * (A.Y - B.Y)
+            );
+
+    public static Circle GetCircumCircle(Triangle triangle)
+    {
+        Vector2D midAB = (triangle.A + triangle.B) / 2f;
+        Vector2D midBC = (triangle.B + triangle.C) / 2f;
+
+        float slopeAB = (triangle.B.Y - triangle.A.Y) / (triangle.B.X - triangle.A.X);
+        float slopeBC = (triangle.C.Y - triangle.B.Y) / (triangle.C.X - triangle.B.X);
+
+        Vector2D center;
+        if (MathF.Abs(slopeAB - slopeBC) > float.Epsilon)
+        {
+            float x = (slopeAB * slopeBC * (triangle.A.Y - triangle.C.Y) + slopeBC * (triangle.A.X + triangle.B.X) - slopeAB * (triangle.B.X + triangle.C.X)) / (2f * (slopeBC - slopeAB));
+            float y = -(x - (triangle.A.X + triangle.B.X) / 2f) / slopeAB + (triangle.A.Y + triangle.B.Y) / 2f;
+            center = new Vector2D(x, y);
+        }
+        else
+            center = (midAB + midBC) * .5f;
+
+        return new(center, Vector2D.Distance(center, triangle.A));
+    }
+
+    public static bool ApproximatelyEquals(Triangle left, Triangle right)
+        => left.A.ApproximatelyEquals(right.A) && left.B.ApproximatelyEquals(right.B) && left.C.ApproximatelyEquals(right.C);
+}
+
+public static class TriangleExtensions
+{
+    public static bool ApproximatelyEquals(this Triangle left, Triangle right) => Triangle.ApproximatelyEquals(left, right);
+}

Engine.Physics2D/RigidBody2D.cs

@@ -0,0 +1,29 @@
+using System;
+
+using Syntriax.Engine.Core;
+using Syntriax.Engine.Core.Abstract;
+using Syntriax.Engine.Physics2D.Abstract;
+
+namespace Syntriax.Engine.Physics2D;
+
+public class RigidBody2D : BehaviourOverride, IRigidBody2D
+{
+    public Action<IAssignableTransform>? OnTransformAssigned { get => GameObject.OnTransformAssigned; set => GameObject.OnTransformAssigned = value; }
+
+    private const float LOWEST_ALLOWED_MASS = 0.00001f;
+    private float _mass = 1f;
+
+
+    public IPhysicsMaterial2D Material { get; set; } = new PhysicsMaterial2DDefault();
+
+    public Vector2D Velocity { get; set; } = Vector2D.Zero;
+    public float AngularVelocity { get; set; } = 0f;
+    public bool IsStatic { get; set; } = false;
+
+    public float Mass { get => _mass; set => _mass = Core.Math.Max(value, LOWEST_ALLOWED_MASS); }
+
+    ITransform IAssignableTransform.Transform => Transform;
+
+
+    public bool Assign(ITransform transform) => GameObject.Assign(transform);
+}

Engine.sln

@@ -7,6 +7,8 @@ Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Engine.Core", "Engine.Core\
 EndProject
 Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Engine.Input", "Engine.Input\Engine.Input.csproj", "{12149E55-1EE8-45B4-A82E-15BA981B0C6A}"
 EndProject
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "Engine.Physics2D", "Engine.Physics2D\Engine.Physics2D.csproj", "{3B3C3332-07E3-4A00-9898-0A5410BCB08C}"
+EndProject
 Global
 	GlobalSection(SolutionConfigurationPlatforms) = preSolution
 		Debug|Any CPU = Debug|Any CPU
@@ -24,5 +26,9 @@ Global
 		{12149E55-1EE8-45B4-A82E-15BA981B0C6A}.Debug|Any CPU.Build.0 = Debug|Any CPU
 		{12149E55-1EE8-45B4-A82E-15BA981B0C6A}.Release|Any CPU.ActiveCfg = Release|Any CPU
 		{12149E55-1EE8-45B4-A82E-15BA981B0C6A}.Release|Any CPU.Build.0 = Release|Any CPU
+		{3B3C3332-07E3-4A00-9898-0A5410BCB08C}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{3B3C3332-07E3-4A00-9898-0A5410BCB08C}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{3B3C3332-07E3-4A00-9898-0A5410BCB08C}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{3B3C3332-07E3-4A00-9898-0A5410BCB08C}.Release|Any CPU.Build.0 = Release|Any CPU
 	EndGlobalSection
 EndGlobal