引入最短舵角行驶的CommonUsage并更新项目引用

Co-authored-by: Cursor <cursoragent@cursor.com>
2026-07-28 18:38:12 +08:00
parent 8e8af847db
commit 583a7d00ca
78 changed files with 5585 additions and 12 deletions
@@ -21,9 +21,6 @@
 </ItemGroup>

  <ItemGroup>
-    <Reference Include="CommonUsage">
-      <HintPath>ref\CommonUsage.dll</HintPath>
-    </Reference>
    <Reference Include="LessokajiWeaverUtilities">
      <HintPath>ref\LessokajiWeaverUtilities.dll</HintPath>
    </Reference>
@@ -39,6 +36,9 @@
    <Reference Include="FundamentalLib">
      <HintPath>ref\RefFundamentalLib.dll</HintPath>
    </Reference>
+    <Reference Include="CommonUsage">
+      <HintPath>..\ref\CommonUsage.dll</HintPath>
+    </Reference>
  </ItemGroup>

 </Project>
@@ -13,7 +13,7 @@ using System.Reflection;
 [assembly: System.Reflection.AssemblyCompanyAttribute("ClumsyPilot")]
 [assembly: System.Reflection.AssemblyConfigurationAttribute("Debug")]
 [assembly: System.Reflection.AssemblyFileVersionAttribute("1.0.0.0")]
-[assembly: System.Reflection.AssemblyInformationalVersionAttribute("1.0.0+e6b99c45b352f24ff58092f7855d0eadd8828d42")]
+[assembly: System.Reflection.AssemblyInformationalVersionAttribute("1.0.0")]
 [assembly: System.Reflection.AssemblyProductAttribute("ClumsyPilot")]
 [assembly: System.Reflection.AssemblyTitleAttribute("ClumsyPilot")]
 [assembly: System.Reflection.AssemblyVersionAttribute("1.0.0.0")]
@@ -1 +1 @@
-3e5507bf56e38facdc245d5ff407e181c060d8094f38b94ad743b8c3305523f2
+5d77794fa0720c6591db5b06ac60427413c18989a6f7b64420ccb07d122d85bc
@@ -1,6 +1,6 @@
 is_global = true
 build_property.RootNamespace = MultiWheelC
-build_property.ProjectDir = d:\MyParking\ClumsyPilot\
+build_property.ProjectDir = D:\Users\Desktop\入职培训\停车机器人\MyParking\ClumsyPilot\
 build_property.EnableComHosting = 
 build_property.EnableGeneratedComInterfaceComImportInterop = 
 build_property.CsWinRTUseWindowsUIXamlProjections = false
@@ -1 +1 @@
-e5afef3021b83202643b31f468b83ac62f224cd367fe52dc0a1cbb98570c91e1
+e972a413d047c4137a8ce86cbff54a8d2e2558806d9d974d3d6312467ee8ba4d
@@ -0,0 +1,2 @@
+*.cs text eol=crlf
+.gitattributes text eol=lf
@@ -0,0 +1,362 @@
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+# (https://github.com/github/gitignore/pull/1529#issuecomment-104372622)
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+# to a newer Visual Studio version. Backup files are not needed,
+# because we have git ;-)
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+Backup*/
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+FakesAssemblies/
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+# Visual Studio LightSwitch build output
+**/*.HTMLClient/GeneratedArtifacts
+**/*.DesktopClient/GeneratedArtifacts
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+_Pvt_Extensions
+
+# Paket dependency manager
+.paket/paket.exe
+paket-files/
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+.fake/
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+.cr/personal
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+__pycache__/
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+MigrationBackup/
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+.ionide/
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+# Fody - auto-generated XML schema
+FodyWeavers.xsd
@@ -0,0 +1,126 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using System.IO;
+using System.Numerics;
+using System.Security.Cryptography.X509Certificates;
+using System.Text;
+using FundamentalLib;
+using Newtonsoft.Json;
+
+namespace CommonUsage.Chassis
+{
+    public abstract class AbstractChassis
+    {
+	    protected AbstractChassis()
+	    {
+		    Valid = false;
+	    }
+
+	    public abstract void Initialize();
+
+        public abstract void Visualize();
+
+	    public abstract void AfterDirectionChanged();
+
+        /// <summary>
+        /// 当前行进方向。
+        /// </summary>
+        [Obsolete]
+        public float DirectionAngle
+        {
+	        get => _originBiasTh;
+	        set
+	        {
+                _originBiasTh = value;
+				if (_originBiasTh != _lastDirectionAngle) AfterDirectionChanged();
+                _lastDirectionAngle = _originBiasTh;
+	        }
+        }
+
+        protected float _originBiasX = 0f, _originBiasY = 0f, _originBiasTh;
+
+        public Vector3 GetOriginBias()
+        {
+            return new Vector3(_originBiasX, _originBiasY, _originBiasTh);
+        }
+
+        public class CarSpeed
+        {
+            public float Vx,Vy,Vw;
+        }
+
+        public abstract CarSpeed GetCarSpeed(bool isActual = false);
+        public List<GeometricControlPoint> GetGeometricControlPoints()
+        {
+	        return GeometricControlPoints;
+        }
+
+        public void ComputeWheelsGeometrically(float speed)
+        {
+            // 打印调用位置信息
+            var stackTrace = new StackTrace(true);
+            var callerFrame = stackTrace.GetFrame(1); // 获取调用者的帧
+            if (callerFrame != null)
+            {
+                var fileName = callerFrame.GetFileName();
+                var lineNumber = callerFrame.GetFileLineNumber();
+                DLog.Log($"s:{speed:0.000} from {fileName} ln.{lineNumber}", $"WheelComputeCaller");
+            }
+
+            DefineGeometricWheelComputation(speed);
+        }
+
+        protected abstract void DefineGeometricWheelComputation(float speed);
+
+        public void DriveStop()
+        {
+            PredefinedDriveStop();
+            CustomDriveStop?.Invoke();
+        }
+
+        public abstract void PredefinedDriveStop();
+
+        public Action CustomDriveStop;
+
+        public abstract bool ComputeRotateWheels(float rotSpeed);
+
+        public abstract float CalculateTurningSpeedDecayFac(float turn);
+
+        public enum ChassisState
+        {
+	        Standby,
+            Running,
+            AbnormalFeedback,
+            ExceedMotionAbility,
+        }
+
+        protected ChassisState State;
+
+        protected string StateDescription;
+
+        public (ChassisState State, string Description) GetChassisState()
+        {
+	        return (State, StateDescription);
+        }
+
+        public bool Debug = false;
+        public float AccPerSecond = 0.2f;
+        public float DeAccPerSecond = 0.2f;
+        public float MaxSpeed = 1; // m/s
+        public float MinTurnSpeedFac = 0.5f;
+        public float MaxTurnThreshold = 90f;
+
+        public float GcpThetaPerSecond = 10f;
+
+        public DateTime LastMoveTime = DateTime.MinValue;
+
+		protected bool Valid = false;
+		protected List<GeometricControlPoint> GeometricControlPoints = new();
+		protected bool RotatingActive = false;
+		protected bool GoingActive = false;
+		protected bool GoingWheelAligned = false;
+
+		private float _lastDirectionAngle = 0;
+    }
+}
@@ -0,0 +1,47 @@
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Text;
+
+namespace CommonUsage.Chassis
+{
+    public class DiffSteerWheel:SteerWheel
+    {
+        public DiffSteerWheel(float wheelDistance,Vector2 position, float angleLowerLimit, float angleUpperLimit, Action<float> speedWriter,
+            Func<float> speedReader, Action<float> angleWriter, Func<float> angleReader, Action<float> leftSpeedWriter, Action<float> rightSpeedWriter,
+            float angleLimitMarginDeg = 15f) : base(position,
+            angleLowerLimit, angleUpperLimit, speedWriter, speedReader, angleWriter, angleReader, angleLimitMarginDeg)
+        {
+            _leftSpeedWriter = leftSpeedWriter;
+            _rightSpeedWriter = rightSpeedWriter;
+            WheelDistance = wheelDistance;
+        }
+
+        public float GetLeftSendSpeed()
+        {
+            return _leftSendSpeed;
+        }
+
+        public float GetRightSendSpeed()
+        {
+            return _rightSendSpeed;
+        }
+
+        public void WriteLeftSpeed(float speed)
+        {
+            _leftSpeedWriter(_leftSendSpeed = speed);
+        }
+
+        public void WriteRightSpeed(float speed)
+        {
+            _rightSpeedWriter(_rightSendSpeed = speed);
+        }
+
+        public float WheelDistance;
+        private readonly Action<float> _leftSpeedWriter;
+        private readonly Action<float> _rightSpeedWriter;
+
+        private float _leftSendSpeed;
+        private float _rightSendSpeed;
+    }
+}
@@ -0,0 +1,170 @@
+using FundamentalLib;
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Text;
+using System.Diagnostics;
+
+namespace CommonUsage.Chassis
+{
+	public class DifferentialChassis : AbstractChassis
+	{
+		public void SetLeftRightWheels(Wheel wheelL, Wheel wheelR)
+		{
+			_leftWheel = wheelL;
+			_rightWheel = wheelR;
+			_halfWheelTrack = Math.Abs(_leftWheel.Position.Y);
+		}
+
+        public override void Visualize()
+        {
+            
+        }
+
+        public override CarSpeed GetCarSpeed(bool isActual = false)
+        {
+            if (!isActual)
+            {
+                return new CarSpeed()
+                {
+                    Vx = (_speedL + _speedR) / 2f,
+                    Vw = (_speedR - _speedL) / Math.Abs(_leftWheel.Position.Y - _rightWheel.Position.Y) /
+                        (float)Math.PI * 180f * 1000f,
+                    Vy = 0
+                };
+            }
+            else
+            {
+                return new CarSpeed()
+                {
+                    Vx = GetLinearSpeed(),
+                    Vw = (_rightWheel.ReadSpeed() - _leftWheel.ReadSpeed()) /
+                        Math.Abs(_leftWheel.Position.Y - _rightWheel.Position.Y) /
+                        (float)Math.PI * 180f * 1000f,
+                    Vy = 0
+                };
+            }
+            
+        }
+
+        public (Wheel,Wheel) GetWheels()
+        {
+            return (_leftWheel, _rightWheel);
+        }
+
+		public float GetLinearSpeed()
+		{
+			return (_leftWheel.ReadSpeed() + _rightWheel.ReadSpeed()) / 2f;
+		}
+
+		public override void Initialize()
+		{
+			GeometricControlPoints.Add(new GeometricControlPoint(new Vector2(0, 0)));
+			Valid = true;
+		}
+
+		public override void AfterDirectionChanged()
+		{
+
+		}
+
+		public override void PredefinedDriveStop()
+		{
+			if (!Valid) return;
+			_sendSpeedL = _sendSpeedR = 0;
+            _speedL = _speedR = 0;
+			_leftWheel.WriteSpeed(_sendSpeedL);
+			_rightWheel.WriteSpeed(_sendSpeedR);
+			GoingActive = false;
+			RotatingActive = false;
+		}
+
+        protected override void DefineGeometricWheelComputation(float speed)
+        {
+            var now = DateTime.Now;
+            if (!GoingActive) LastMoveTime = now;
+
+            SendSpeed(speed, GeometricControlPoints[0].Theta, now - LastMoveTime);
+
+            GoingActive = true;
+            RotatingActive = false;
+        }
+
+		public override bool ComputeRotateWheels(float rotSpeed)
+		{
+			if (!RotatingActive) LastMoveTime = DateTime.Now;
+
+			SendSpeed(0, rotSpeed);
+
+			GoingActive = false;
+			RotatingActive = true;
+			return true;
+		}
+
+		public override float CalculateTurningSpeedDecayFac(float turn)
+		{
+			return 1 - Math.Min(turn, MaxTurnThreshold) / MaxTurnThreshold * MinTurnSpeedFac;
+		}
+
+		public void SendSpeed(float linearSpeed, float angularSpeed, TimeSpan? deltaTime = null)
+		{
+			var edgeLinearSpeed = (float)(angularSpeed / 180f * Math.PI * _halfWheelTrack / 1000);
+			var vl = linearSpeed - edgeLinearSpeed;
+			var vr = linearSpeed + edgeLinearSpeed;
+            _speedL = vl;
+			_speedR = vr;
+			AccumulateSpeed(vl, vr, deltaTime);
+            LastMoveTime = DateTime.Now;
+        }
+
+		private void AccumulateSpeed(float vl, float vr, TimeSpan? deltaTime = null)
+		{
+            // var dTime = (float)(deltaTime ?? DateTime.Now - LastMoveTime).TotalSeconds;
+            //
+            // var speedSignL = Math.Sign(vl - _sendSpeedL);
+            // var accL = Math.Abs(vl) > Math.Abs(_sendSpeedL) ? AccPerSecond : DeAccPerSecond;
+            // _sendSpeedL += speedSignL * Math.Min(Math.Abs(vl - _sendSpeedL), accL * dTime);
+            // _leftWheel.WriteSpeed(_sendSpeedL);
+            //
+            // var speedSignR = Math.Sign(vr - _sendSpeedR);
+            // var accR = Math.Abs(vr) > Math.Abs(_sendSpeedR) ? AccPerSecond : DeAccPerSecond;
+            // _sendSpeedR += speedSignR * Math.Min(Math.Abs(vr - _sendSpeedR), accR * dTime);
+            // _rightWheel.WriteSpeed(_sendSpeedR);
+
+            // if (Debug)
+            // 	Console.WriteLine($"DiffChassis, target:{v:0.00},send:{_sendSpeed:0.0}");
+            // var dTime = (float)(deltaTime ?? DateTime.Now - LastMoveTime).TotalSeconds;
+            var dTime = (float)(deltaTime ?? DateTime.Now - LastMoveTime).TotalSeconds;
+            float diffL = vl - _sendSpeedL;
+            float diffR = vr - _sendSpeedR;
+
+            float accL = Math.Abs(vl) > Math.Abs(_sendSpeedL) ? AccPerSecond : DeAccPerSecond;
+            float accR = Math.Abs(vr) > Math.Abs(_sendSpeedR) ? AccPerSecond : DeAccPerSecond;
+
+            float maxDeltaL = accL * dTime;
+            float maxDeltaR = accR * dTime;
+
+            float factorL = Math.Abs(diffL) > maxDeltaL ? maxDeltaL / Math.Abs(diffL) : 1.0f;
+            float factorR = Math.Abs(diffR) > maxDeltaR ? maxDeltaR / Math.Abs(diffR) : 1.0f;
+
+            float factor = Math.Min(factorL, factorR);
+
+            _sendSpeedL += diffL * factor;
+            _sendSpeedR += diffR * factor;
+
+            _leftWheel.WriteSpeed(_sendSpeedL);
+            _rightWheel.WriteSpeed(_sendSpeedR);
+            // Console.WriteLine($"DiffChassis, target:{vl:0.00},send:{_sendSpeedL:0.00} dTime：{dTime} diffL:{diffL} factor:{factor}" );
+        }
+
+        private Wheel _leftWheel;
+		private Wheel _rightWheel;
+		private float _halfWheelTrack; // millimeter
+
+		private float _sendSpeedL;
+		private float _sendSpeedR;
+		private int _direction = 1; // 1 forward, -1 backward
+        private float _speedL;
+        private float _speedR;
+    }
+}
@@ -0,0 +1,172 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Numerics;
+using System.Text;
+using System.Diagnostics;
+using CommonUsage.Mathematics;
+using FundamentalLib;
+
+namespace CommonUsage.Chassis
+{
+	public class SingleSteerChassis : AbstractChassis
+	{
+		public void SetSteerWheel(SteerWheel wheel)
+		{
+			_steerWheel = wheel;
+		}
+
+		public SteerWheel GetSteerWheel()
+		{
+			return _steerWheel;
+		}
+
+        public override void Visualize()
+        {
+            
+        }
+
+        public override CarSpeed GetCarSpeed(bool isActual = false)
+        {
+            if (!isActual)
+            {
+                var sendAngle = _steerWheel.GetSendAngle();
+                var sendAngleRad = _steerWheel.GetSendAngle() / 180f * Math.PI;
+                // VSteer* Cos = v;
+                var vsteer = _sendSpeed / ((Math.Cos(Math.Abs(sendAngleRad)) + 0.000001));
+                var vsteerY = vsteer * Math.Sin(sendAngleRad);
+				// Console.WriteLine($"{vsteer} {vsteerY} {sendAngleRad} {_sendSpeed}");
+                return new CarSpeed()
+                {
+                    Vx = (float)(_sendSpeed * Math.Cos(Math.Abs(sendAngle) / 180f * Math.PI)),
+                    Vy = 0,
+                    Vw = (float)(_sendSpeed * Math.Sin(Math.Abs(sendAngle) / 180f * Math.PI) /
+                        Math.Abs(_steerWheel.Position.X / 1000f) / Math.PI * 180f)
+					//阿克曼
+                    // Vx = (float)(_sendSpeed),
+                    // Vy = 0,
+                    // Vw = (float)(vsteerY / Math.Abs(_steerWheel.Position.X / 1000f) / Math.PI * 180f)
+                };
+            }
+            else
+            {
+                return new CarSpeed()
+                {
+                    Vx = (float)(_steerWheel.ReadSpeed() *
+                                 Math.Cos(Math.Abs(_steerWheel.ReadAngle()) / 180f * Math.PI)),
+                    Vy = 0,
+                    Vw = (float)(_steerWheel.ReadSpeed() *
+                        Math.Sin(Math.Abs(_steerWheel.ReadAngle()) / 180f * Math.PI) /
+                        Math.Abs(_steerWheel.Position.X / 1000f) / Math.PI * 180f)
+                };
+            }
+            
+        }
+
+        public override void Initialize()
+		{
+			GeometricControlPoints = new List<GeometricControlPoint>()
+			{
+				new (_steerWheel.Position),
+				new (Vector2.Zero)
+			};
+			Valid = true;
+		}
+
+		public override void AfterDirectionChanged()
+		{
+			if (Math.Abs(CommonMath.ThDiff(0, _originBiasTh)) > 90)
+			{
+				GeometricControlPoints = new List<GeometricControlPoint>()
+				{
+					new (-_steerWheel.Position),
+				};
+				_direction = -1;
+			}
+			else
+			{
+				GeometricControlPoints = new List<GeometricControlPoint>()
+				{
+					new (_steerWheel.Position),
+				};
+				_direction = 1;
+			}
+		}
+
+		public override void PredefinedDriveStop()
+		{
+			if (!Valid) return;
+			_sendSpeed = 0;
+			_steerWheel.WriteSpeed(_sendSpeed);
+			GoingActive = false;
+			RotatingActive = false;
+		}
+
+        protected override void DefineGeometricWheelComputation(float speed)
+        {
+            var now = DateTime.Now;
+
+            if (!GoingActive)
+            {
+                LastMoveTime = now;
+                GoingWheelAligned = false;
+            }
+
+            SendSteerMotion(speed * _direction, GeometricControlPoints[0].Theta, now - LastMoveTime);
+
+            GoingActive = true;
+            RotatingActive = false;
+        }
+
+		public override bool ComputeRotateWheels(float rotSpeed)
+		{
+			if (!RotatingActive)
+            {
+                LastMoveTime = DateTime.Now;
+                GoingWheelAligned = false;
+            }
+
+			SendSteerMotion(rotSpeed, 90);
+
+			GoingActive = false;
+			RotatingActive = true;
+			return true;
+		}
+
+		public void SendSteerMotion(float speed, float theta, TimeSpan? deltaTime = null)
+		{
+			_steerWheel.WriteAngle(theta);
+
+            if (!GoingWheelAligned && Math.Abs(CommonMath.ThDiff(_steerWheel.ReadAngle(), theta)) < 1)
+                GoingWheelAligned = true;
+			if (!GoingWheelAligned) speed = 0;
+
+			var turnThresholdSpeed = CalculateTurningSpeedDecayFac(Math.Abs(theta)) * MaxSpeed;
+			AccumulateSpeed(Math.Min(turnThresholdSpeed, Math.Abs(speed)) * Math.Sign(speed), deltaTime);
+
+            LastMoveTime = DateTime.Now;
+        }
+
+		public override float CalculateTurningSpeedDecayFac(float turn)
+		{
+			return 1 - Math.Min(turn, MaxTurnThreshold) / MaxTurnThreshold * MinTurnSpeedFac;
+		}
+
+		private void AccumulateSpeed(float v, TimeSpan? deltaTime = null)
+		{
+			// _targetSpeed = v;
+			var speedSign = Math.Sign(v - _sendSpeed);
+			var acc = Math.Abs(v) > Math.Abs(_sendSpeed) ? AccPerSecond : DeAccPerSecond;
+			_sendSpeed += speedSign * Math.Min(Math.Abs(v - _sendSpeed),
+				acc * (float)(deltaTime ?? DateTime.Now - LastMoveTime).TotalSeconds);
+			_steerWheel.WriteSpeed(_sendSpeed);
+
+			if (Debug)
+				Console.WriteLine($"SingleSteer, target:{v:0.00},send:{_sendSpeed:0.0}");
+		}
+
+		private SteerWheel _steerWheel;
+		private float _sendSpeed;
+		private int _direction = 1; // 1 forward, -1 backward
+	}
+}
@@ -0,0 +1,100 @@
+using Newtonsoft.Json;
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Text;
+using CommonUsage.Mathematics;
+
+namespace CommonUsage.Chassis
+{
+	public class SteerWheel : Wheel
+	{
+		public SteerWheel(Vector2 position, float angleLowerLimit, float angleUpperLimit, Action<float> speedWriter,
+			Func<float> speedReader, Action<float> angleWriter, Func<float> angleReader, float angleLimitMarginDeg = 15f) : base(position, speedWriter,
+			speedReader)
+		{
+			_angleLowerLimit = angleLowerLimit;
+			_angleUpperLimit = angleUpperLimit;
+			_angleWriter = angleWriter;
+			_angleReader = angleReader;
+			_centerDistance = position.Length();
+            AngleLimitMarginDeg = angleLimitMarginDeg;
+		}
+
+        public float AngleLimitMarginDeg = 15f;
+
+		public bool TrySetDirection(bool allowReverse, ref float desireDirection, ref int dir)
+		{
+            if (TryNormalizeAngleInLimit(desireDirection, out var normalized))
+			{
+				dir = 1;
+                desireDirection = normalized;
+				return true;
+			}
+
+			if (!allowReverse) return false;
+
+			var oppositeTh = (float)CommonMath.RoundTh(desireDirection + 180);
+			if (TryNormalizeAngleInLimit(oppositeTh, out normalized))
+			{
+				dir = -1;
+				desireDirection = normalized;
+				return true;
+			}
+
+			dir = 0;
+			return false;
+		}
+
+        private bool TryNormalizeAngleInLimit(float angle, out float normalized)
+        {
+            var lower = CommonMath.RoundTh(_angleLowerLimit);
+            var upper = CommonMath.RoundTh(_angleUpperLimit);
+            while (upper < lower) upper += 360;
+
+            normalized = (float)CommonMath.RoundTh(angle);
+            while (normalized < lower) normalized += 360;
+            while (normalized > upper && normalized - 360 >= lower) normalized -= 360;
+
+            var margin = Math.Min(normalized - lower, upper - normalized);
+            return normalized >= lower && normalized <= upper && margin >= Math.Max(0, AngleLimitMarginDeg);
+        }
+
+		public float ReadAngle()
+		{
+			return _angleReader();
+		}
+
+		public void WriteAngle(float angle)
+        {
+            _angleWriter.Invoke(_sendAngle = Math.Max(_angleLowerLimit, Math.Min(angle, _angleUpperLimit)));
+        }
+
+        public float GetSendAngle()
+        {
+            return _sendAngle;
+        }
+
+        public float GetAngleRelativeToChassis()
+        {
+            return ZeroDirection + _sendAngle;
+        }
+
+		public float CenterDistance()
+		{
+			return _centerDistance;
+		}
+
+        public float AngleLowerLimit => _angleLowerLimit;
+
+		public float AngleUpperLimit => _angleUpperLimit;
+
+		[JsonIgnore] private readonly Action<float> _angleWriter;
+		[JsonIgnore] private readonly Func<float> _angleReader;
+
+		private float _angleLowerLimit = -90, _angleUpperLimit = 90;
+		private float _centerDistance;
+
+        public float _sendAngle = 0f;
+    }
+}
@@ -0,0 +1,56 @@
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Text;
+using Newtonsoft.Json;
+
+namespace CommonUsage.Chassis
+{
+    public class Wheel
+    {
+	    public Wheel(Vector2 position, Action<float> speedWriter, Func<float> speedReader)
+	    {
+		    PhysicalPosition = Position = position;
+			SpeedWriter = speedWriter;
+			SpeedReader = speedReader;
+	    }
+
+	    public void WriteSpeed(float speed)
+	    {
+		    SpeedWriter.Invoke(_sendSpeed = speed);
+        }
+
+        public float GetSendSpeed()
+        {
+            return _sendSpeed;
+        }
+
+	    public float ReadSpeed()
+	    {
+		    return SpeedReader();
+	    }
+
+        // PhysicalPosition ===(chassis transform)===> Position
+		// useful in dual agv coordination
+        public readonly Vector2 PhysicalPosition;
+        public Vector2 Position;
+
+        public float ZeroDirection = 0;
+
+        [JsonIgnore] public readonly Action<float> SpeedWriter;
+        [JsonIgnore] public readonly Func<float> SpeedReader;
+
+        public float _sendSpeed;
+    }
+
+    public class GeometricControlPoint
+    {
+	    public GeometricControlPoint(Vector2 position)
+	    {
+			Position = position;
+	    }
+
+	    public Vector2 Position;
+	    public float Theta;
+    }
+}
@@ -0,0 +1,48 @@
+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <TargetFramework>netstandard2.0</TargetFramework>
+  </PropertyGroup>
+
+  <PropertyGroup>
+   <LangVersion>latest</LangVersion>
+   <AllowUnsafeBlocks>True</AllowUnsafeBlocks>
+  </PropertyGroup>
+
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|AnyCPU'">
+    <DebugType>embedded</DebugType>
+  </PropertyGroup>
+
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|AnyCPU'">
+    <DebugType>embedded</DebugType>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <Compile Remove="Hedingben.cs" />
+    <Compile Remove="IPCConcurrentDictionary.cs" />
+  </ItemGroup>
+
+  <ItemGroup>
+    <PackageReference Include="MQTTnet" Version="4.3.7.1207" />
+    <PackageReference Include="MQTTnet.Extensions.ManagedClient" Version="4.3.7.1207" />
+    <PackageReference Include="Newtonsoft.Json" Version="13.0.3" />
+    <PackageReference Include="System.Buffers" Version="4.5.1" />
+    <PackageReference Include="System.Numerics.Vectors" Version="4.5.0" />
+  </ItemGroup>
+
+  <ItemGroup>
+    <Reference Include="FundamentalLib">
+      <HintPath>..\..\MedullaAdapter\ref\RefFundamentalLib.dll</HintPath>
+    </Reference>
+    <Reference Include="ClumsyCore">
+      <HintPath>..\..\ClumsyPilot\ref\RefClumsyCore.dll</HintPath>
+    </Reference>
+  </ItemGroup>
+
+  <Target Name="CopyCommonUsageToMyParkingRef" AfterTargets="Build">
+    <MakeDir Directories="..\..\ref" />
+    <Copy SourceFiles="$(TargetPath)"
+          DestinationFolder="..\..\ref" />
+  </Target>
+
+</Project>
@@ -0,0 +1,25 @@
+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 17
+VisualStudioVersion = 17.5.33424.131
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "CommonUsage", "CommonUsage.csproj", "{E1C5DEA8-3785-40A9-9965-E51E65BF5947}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Any CPU = Debug|Any CPU
+		Release|Any CPU = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{E1C5DEA8-3785-40A9-9965-E51E65BF5947}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{E1C5DEA8-3785-40A9-9965-E51E65BF5947}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{E1C5DEA8-3785-40A9-9965-E51E65BF5947}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{E1C5DEA8-3785-40A9-9965-E51E65BF5947}.Release|Any CPU.Build.0 = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+	GlobalSection(ExtensibilityGlobals) = postSolution
+		SolutionGuid = {709F9C19-45DB-46AD-B70A-0E1E3C6CFB0C}
+	EndGlobalSection
+EndGlobal
@@ -0,0 +1,93 @@
+using System;
+using System.Collections.Generic;
+using System.Drawing;
+using System.Numerics;
+using System.Text;
+using static CommonUsage.Geometries.CircularArc;
+
+namespace CommonUsage.Geometries
+{
+	/// <summary>
+	/// 便于直接创建几何形状并求几何形状的切点、切线等。
+	/// </summary>
+	public abstract class AbstractGeometry
+	{
+		protected AbstractGeometry()
+		{
+			PaddingType = Padding.StartExtendEndExtend;
+			VisualizeOption = new VisualizeOption(Color.Red, Color.Gray);
+		}
+
+		public Padding PaddingType;
+
+		public abstract (Vector2 Pt, float Angle, float Bias, float Position) QueryTangentPoint(Vector2 point);
+
+		public abstract void Visualize(Action<VisDot> processDot, Action<VisLine> processLine,
+			bool visExtendedPart = false);
+
+		public VisualizeOption VisualizeOption;
+
+		/// <summary>
+		/// 查询指定位置的曲率。
+		/// </summary>
+		/// <param name="position">从起点到查询位置的距离。</param>
+		/// <returns></returns>
+		public abstract float QueryCurvature(float position);
+
+		public abstract float Length();
+	}
+
+	public class VisualizeOption
+	{
+		public VisualizeOption(Color mainColor, Color auxiliaryColor)
+		{
+			MainColor = mainColor;
+			AuxiliaryColor = auxiliaryColor;
+		}
+
+		public Color MainColor;
+		public Color AuxiliaryColor;
+		public bool DrawAuxiliary = true;
+		public bool VisualizeDirection = true;
+	}
+
+	public enum Padding
+	{
+		StartLineEndLine = 0b_0001_0001,
+		StartLineEndExtend = 0b_0001_0010,
+		StartExtendEndLine = 0b_0010_0001,
+		StartExtendEndExtend = 0b_0010_0010,
+	}
+
+	public class VisDot
+	{
+		public VisDot(Vector2 point, Color color)
+		{
+			Point = point;
+			Color = color;
+		}
+
+		public Vector2 Point;
+		public Color Color;
+	}
+
+	public class VisLine
+	{
+		public VisLine(Vector2 start, Vector2 end, bool startArrow, bool endArrow, Color color, float width = 1)
+		{
+			Start = start;
+			End = end;
+			StartArrow = startArrow;
+			EndArrow = endArrow;
+			Color = color;
+			Width = width;
+		}
+
+		public Vector2 Start;
+		public Vector2 End;
+		public bool StartArrow = false;
+		public bool EndArrow = false;
+		public Color Color;
+		public float Width;
+	}
+}
@@ -0,0 +1,334 @@
+using System;
+using System.Collections.Generic;
+using System.Diagnostics;
+using System.Linq;
+using System.Numerics;
+using System.Reflection;
+using CommonUsage.Mathematics;
+
+namespace CommonUsage.Geometries
+{
+    public class BezierCurve : AbstractGeometry
+    {
+
+        public BezierCurve(List<Vector2> controlPoints, int resolution = 100)
+        {
+            // Console.WriteLine($"BezierCurve1");
+            // Console.WriteLine(string.Join("  ",controlPoints.Select(p=>$"{p.X:f2},{p.Y:f2}")));
+            _controlPoints = controlPoints;
+            _resolution = resolution;
+            InitializeBezier();
+        }
+
+        public override void Visualize(Action<VisDot> processDot, Action<VisLine> processLine, bool visExtendedPart = false)
+        {
+            if (VisualizeOption.DrawAuxiliary)
+                for (var i = 0; i < _controlPoints.Count - 1; ++i)
+                {
+                    processLine(new VisLine(_controlPoints[i], _controlPoints[i + 1],
+                        false, false, VisualizeOption.AuxiliaryColor));
+                    if (i == 0) continue;
+                    processDot(new VisDot(_controlPoints[i], VisualizeOption.AuxiliaryColor));
+                }
+
+            for (var i = 0; i < _bezierPoints.Count - 1; ++i)
+            {
+                if (Direction == -1)
+                {
+                    processLine(new VisLine(_bezierPoints[i + 1], _bezierPoints[i],
+                        false, i == (int)(_bezierPoints.Count / 2), VisualizeOption.MainColor, 2));
+                }
+                else
+                {
+                    processLine(new VisLine(_bezierPoints[i], _bezierPoints[i + 1],
+                        false, i == (int)(_bezierPoints.Count / 2), VisualizeOption.MainColor, 2));
+                }
+
+
+            }
+        }
+
+        public (Vector2 Point, int Id) QueryPoint(Vector2 point)
+        {
+            var p = new Vector2();
+            var id = -1;
+            var bestDistance = float.MaxValue;
+
+            var hashes = _bias.Select(bb => CalculateHash(point, 100, bb.X, bb.Y)).ToList();
+
+            void TryQuery(Dictionary<uint, List<(Vector2 Point, int Id)>> dict, List<uint> hashList)
+            {
+                foreach (var hash in hashList)
+                {
+                    if (!dict.TryGetValue(hash, out var ll)) continue;
+                    foreach (var (q, qId) in ll)
+                    {
+                        var d = Vector2.Distance(q, point);
+                        if (d < bestDistance)
+                        {
+                            p = q;
+                            id = qId;
+                            bestDistance = d;
+                        }
+                    }
+                }
+            }
+            //map目前有bug,取消cpu占用也不严重，必要时候在优化
+            // TryQuery(_pointsMappingSmall, hashes);
+            //
+            // if (id == -1)
+            // {
+            // 	hashes = _bias.Select(bb => CalculateHash(point, 1000, bb.X, bb.Y)).ToList();
+            // 	TryQuery(_pointsMappingBig, hashes);
+            // }
+
+            if (id == -1)
+            {
+                // todo: improve the way to find closest point if mappings fail
+                (p, id) = _bezierPoints.Select((p, i) => (p, i))
+                    .OrderBy(pair => CommonMath.dist(pair.p.X, pair.p.Y, point.X, point.Y)).First();
+            }
+
+            return (p, id);
+        }
+
+        public override (Vector2 Pt, float Angle, float Bias, float Position) QueryTangentPoint(Vector2 point)
+        {
+            var (p, id) = QueryPoint(point);
+            var tangent = _tangents[id];
+            var (bias, lp, fd) = CommonMath.Project2DLine(point, p, tangent);
+            var next = fd > 0 ? id + 1 : id - 1;
+            if (id == 0) next = 1;
+            // Console.WriteLine($"id:{id} next:{next} tangent:{tangent} _tangents.Count:{_tangents.Count}");
+            if (next > 0 && next < _tangents.Count)//线性插值
+            {
+                var (_, _, t) = CommonMath.Project2DLine(point, _bezierPoints[id], _bezierPoints[next]);
+                var partial = t / Vector2.Distance(_bezierPoints[id], _bezierPoints[next]);
+                if (partial >= 0 && partial <= 1)
+                {
+                    tangent = CommonMath.RoundTh(_tangents[id] +
+                                                 partial * CommonMath.RoundTh(_tangents[next] - _tangents[id]));
+                    if (CommonMath.RoundTh(_tangents[next] - _tangents[id]) > 5)
+                        Console.WriteLine($"bezier tangents bug, tanget: {id}:{_tangents[id]} {next}:{_tangents[next]}");
+                }
+                // else Console.WriteLine("bezier tangents bug");
+            }
+            return (lp, tangent, bias, fd + _sumDistances[id]);
+        }
+
+        public override float Length()
+        {
+            return _length;
+        }
+
+        public override float QueryCurvature(float position)
+        {
+            int id = _sumDistances.Count - 1;
+            if (position <= 0) id = 0;
+            else
+            {
+                for (int i = 1; i < _sumDistances.Count; i++)
+                {
+                    if (position > _sumDistances[i - 1] && position <= _sumDistances[i])
+                    {
+                        id = i;
+                        break;
+                    }
+                }
+            }
+
+            var result = _curvatures[id];
+            if (id > 0 && id < _sumDistances.Count - 1)//插值
+            {
+                var partial = (position - _sumDistances[id - 1]) / (_sumDistances[id] - _sumDistances[id - 1]);
+                if (partial >= 0 && partial <= 1) result = (1 - partial) * _curvatures[id - 1] + partial * _curvatures[id];
+                else Console.WriteLine("bezier curvature bug");
+            }
+
+            return result;
+        }
+
+        public Vector3 QueryBezierPointsById(int id)
+        {
+            if (id < 0 || id > Resolution)
+            {
+                Console.WriteLine($"QueryBezierPointsById out of range, Resolution:{Resolution},id:{id}.");
+                return new Vector3(0, 0, 0);
+            }
+
+            return new Vector3(_bezierPoints[id].X, _bezierPoints[id].Y, _tangents[id]);
+        }
+
+        public List<Vector2> ControlPoints => _controlPoints;
+
+        public int Resolution => _resolution;
+        /// <summary>
+        /// 仅用于simple显示路径方向
+        /// </summary>
+        public int Direction = 1;
+        public int Order => _order;
+
+        // public List<float> Tangents => _tangents;
+
+        public void UpdateControlPoint(int id, Vector2 point)
+        {
+            _controlPoints[id] = point;
+            InitializeBezier();
+        }
+
+        public void AddControlPoint(int id, Vector2 point)
+        {
+            _controlPoints.Insert(id, point);
+            InitializeBezier();
+        }
+
+        public void RemoveControlPoint(int id)
+        {
+            _controlPoints.RemoveAt(id);
+            InitializeBezier();
+        }
+
+        public Vector2 GetMidPoint()
+        {
+            return _bezierPoints[(int)Math.Ceiling(_resolution / 2d)];
+        }
+
+        private void InitializeBezier()
+        {
+            _order = _controlPoints.Count - 1;
+            // _bezierPoints = new List<Vector2>();
+            var delta = 1.0f / _resolution;
+            // for (int t = 0; t <= _resolution; t += 1)//下面循环算了，没必要先递归算一遍
+            // 	_bezierPoints.Add(new Vector2(DeCasteljauX(_order, 0, t*delta), DeCasteljauY(_order, 0, t*delta)));
+            var allPoints = new List<List<List<Vector2>>>();
+            for (var i = 0; i < _order; i++)
+            {
+                var size = allPoints.Count;
+                var morePoints = new List<List<Vector2>>();
+                for (var j = 0; j < _order - i; j++)
+                {
+                    var points = new List<Vector2>();
+                    for (int t = 0; t <= _resolution; t += 1)
+                    {
+                        float p0x;
+                        float p1x;
+                        float p0y;
+                        float p1y;
+                        var z = t;
+                        if (size > 0)
+                        {
+                            p0x = allPoints[i - 1][j][z].X;
+                            p1x = allPoints[i - 1][j + 1][z].X;
+                            p0y = allPoints[i - 1][j][z].Y;
+                            p1y = allPoints[i - 1][j + 1][z].Y;
+                        }
+                        else
+                        {
+                            p0x = _controlPoints[j].X;
+                            p1x = _controlPoints[j + 1].X;
+                            p0y = _controlPoints[j].Y;
+                            p1y = _controlPoints[j + 1].Y;
+                        }
+
+                        var part = t * delta;
+                        points.Add(new Vector2((1 - part) * p0x + part * p1x, (1 - part) * p0y + part * p1y));
+                    }
+                    morePoints.Add(points);
+                }
+                allPoints.Add(morePoints);
+            }
+
+            _bezierPoints = allPoints.Last().Last();
+            _tangentInfo = allPoints;
+            _tangents = Enumerable.Repeat(0f, _bezierPoints.Count).ToList();
+            _curvatures = Enumerable.Repeat(0f, _bezierPoints.Count).ToList();
+            var p2 = allPoints[Order - 2];
+            for (var id = 0; id < _bezierPoints.Count; ++id)
+            {
+                _tangents[id] =
+                    (float)(Math.Atan2(p2[1][id].Y - p2[0][id].Y, p2[1][id].X - p2[0][id].X) / Math.PI * 180);
+                if (id != 0) _curvatures[id] = (float)((CommonMath.ThDiff(_tangents[id], _tangents[id - 1]) / 180 * Math.PI)
+                    / (Vector2.Distance(_bezierPoints[id], _bezierPoints[id - 1]) / 1000));
+            }
+            // Console.WriteLine($"{string.Join("\n", _tangents.Select((val, i) => $"{i}: {val}"))}");
+            _tangents[0] = _tangents[1]; // todo: here is temporary fix
+            _curvatures[0] = _curvatures[1];
+            for (var id = 1; id < _bezierPoints.Count - 1; ++id)//前移0.5
+                _curvatures[id] = (_curvatures[id] + _curvatures[id + 1]) / 2;
+
+            _remainDistances = Enumerable.Repeat(0f, _bezierPoints.Count).ToList();
+            _sumDistances = Enumerable.Repeat(0f, _bezierPoints.Count).ToList();
+            for (var i = _bezierPoints.Count - 2; i >= 0; --i)
+            {
+                _remainDistances[i] =
+                    _remainDistances[i + 1] + Vector2.Distance(_bezierPoints[i], _bezierPoints[i + 1]);
+            }
+            for (var i = 1; i < _bezierPoints.Count; ++i)
+            {
+                _sumDistances[i] =
+                    _sumDistances[i - 1] + Vector2.Distance(_bezierPoints[i], _bezierPoints[i - 1]);
+            }
+            _length = _sumDistances.Last();
+
+            _minX = _bezierPoints.Min(pp => pp.X);
+            _minY = _bezierPoints.Min(pp => pp.Y);
+
+            var tmpList = _bezierPoints.Select((point, index) => (point, index)).ToList();
+            return;
+            void GenerateGridMapping(ref Dictionary<uint, List<(Vector2 Point, int Id)>> dict, float gSize)
+            {
+                dict = new Dictionary<uint, List<(Vector2 Point, int Id)>>();
+                foreach (var (point, index) in tmpList)
+                {
+                    var hash = CalculateHash(point, gSize);
+                    if (dict.TryGetValue(hash, out var ll))
+                        ll.Add((point, index));
+                    else dict[hash] = new List<(Vector2 Point, int Id)>() { (point, index) };
+                }
+            }
+
+            GenerateGridMapping(ref _pointsMappingSmall, 100);
+            GenerateGridMapping(ref _pointsMappingBig, 1000);
+        }
+
+        private uint CalculateHash(Vector2 point, float gridSize, int xBias = 0, int yBias = 0)
+        {
+            return (uint)(((int)((point.X - _minX) / gridSize) + xBias) << 16 + (((int)((point.Y - _minY) / gridSize) + yBias) & 0xffff));
+        }
+
+        private readonly List<(int X, int Y)> _bias = new()
+        {
+            new(-1, -1), new(-1, 0), new(-1, 1),
+            new(0, -1), new(0, 0), new(0, 1),
+            new(1, -1), new(1, 0), new(1, 1),
+        };
+
+        private float DeCasteljauX(int i, int j, float t)
+        {
+            if (i == 1)
+                return (1 - t) * _controlPoints[j].X + t * _controlPoints[j + 1].X;
+            return (1 - t) * DeCasteljauX(i - 1, j, t) + t * DeCasteljauX(i - 1, j + 1, t);
+        }
+
+        private float DeCasteljauY(int i, int j, float t)
+        {
+            if (i == 1)
+                return (1 - t) * _controlPoints[j].Y + t * _controlPoints[j + 1].Y;
+            return (1 - t) * DeCasteljauY(i - 1, j, t) + t * DeCasteljauY(i - 1, j + 1, t);
+        }
+
+        private int _order;
+        private int _resolution;
+        private List<Vector2> _controlPoints;
+        private List<Vector2> _bezierPoints;
+        private List<List<List<Vector2>>> _tangentInfo;
+        private List<float> _tangents;
+        private List<float> _remainDistances;
+        private List<float> _sumDistances;
+        private List<float> _curvatures;
+        private Dictionary<uint, List<(Vector2 Point, int Id)>> _pointsMappingSmall;
+        private Dictionary<uint, List<(Vector2 Point, int Id)>> _pointsMappingBig;
+        private float _minX, _minY;
+        private float _length;
+    }
+}
@@ -0,0 +1,256 @@
+using System;
+using System.Collections.Generic;
+using System.Drawing;
+using System.Numerics;
+using System.Reflection;
+using System.Security.Cryptography;
+using System.Text;
+using CommonUsage.Mathematics;
+
+namespace CommonUsage.Geometries
+{
+	public class CircularArc : AbstractGeometry
+	{
+		/// <summary>
+		/// 以center为圆心、radius为半径，从angleStart逆时针转到angleEnd所构成的圆弧。direction表示圆弧走向。
+		/// </summary>
+		/// <param name="center"></param>
+		/// <param name="radius"></param>
+		/// <param name="angleStart"></param>
+		/// <param name="angleEnd"></param>
+		/// <param name="direction">表示圆弧走向，1为angleStart到angleEnd，-1为angleEnd到angleStart</param>
+		public CircularArc(Vector2 center, float radius, float angleStart, float angleEnd, int direction, Padding paddingType)
+		{
+			_center = center;
+			_radius = radius;
+			_angleStart = angleStart;
+			_angleEnd = angleEnd;
+			_direction = direction;
+			PaddingType = paddingType;
+
+			ChangeShape();
+			CalculateVisPoints();
+		}
+
+		public override void Visualize(Action<VisDot> processDot, Action<VisLine> processLine,
+			bool visExtendedPart = false)
+		{
+			lock (_visPoints)
+			{
+				if (visExtendedPart)
+				{
+
+				}
+
+				for (var i = 0; i < _visPoints.Length - 1; ++i)
+				{
+					if ((i == 0 || i == _visPoints.Length - 2) && !visExtendedPart) continue;
+					var color = Color.Red;
+					if (i == 0 || i == _visPoints.Length - 2) color = Color.Gray;
+					processLine(new VisLine(_visPoints[i], _visPoints[i + 1], 
+						false, i == (_visPoints.Length - 1) / 2, color));
+				}
+
+				if (visExtendedPart)
+				{
+
+				}
+			}
+		}
+
+		public void SwitchSide()
+		{
+			(_angleStart, _angleEnd) = (_angleEnd, _angleStart);
+			ChangeShape();
+			CalculateVisPoints();
+		}
+
+		public float VisAngleResolution = 1;
+
+		public Vector2 Center
+		{
+			get => _center;
+			set
+			{
+				_center = value;
+				ChangeShape();
+				CalculateVisPoints();
+			}
+		}
+
+		public float Radius
+		{
+			get => _radius;
+			set
+			{
+				_radius = value;
+				ChangeShape();
+				CalculateVisPoints();
+			}
+		}
+
+		public float AngleStart
+		{
+			get => _angleStart;
+			set
+			{
+				_angleStart = value;
+				ChangeShape();
+				CalculateVisPoints();
+			}
+		}
+
+		public float AngleEnd
+		{
+			get => _angleEnd;
+			set
+			{
+				_angleEnd = value;
+				ChangeShape();
+				CalculateVisPoints();
+			}
+		}
+
+		public int Direction
+		{
+			get => _direction;
+			set
+			{
+				_direction = value;
+				ChangeShape();
+				CalculateVisPoints();
+			}
+		}
+
+        public float AngleRange => _totalTh;
+
+		public Vector2 PointStart => _center + new Vector2(_radius * (float)Math.Cos(_angleStart / 180 * Math.PI),
+			_radius * (float)Math.Sin(_angleStart / 180 * Math.PI));
+
+		public Vector2 PointEnd => _center + new Vector2(_radius * (float)Math.Cos(_angleEnd / 180 * Math.PI),
+			_radius * (float)Math.Sin(_angleEnd / 180 * Math.PI));
+
+		public Vector2 Src => _src;
+
+		public Vector2 Dst => _dst;
+
+		public float TangentSrc => _tangentSrc;
+
+		public float TangentDst => _tangentDst;
+
+		public override (Vector2 Pt, float Angle, float Bias, float Position) QueryTangentPoint(Vector2 point)
+		{
+			var queryTh = (float)(Math.Atan2(point.Y - _center.Y, point.X - _center.X) / Math.PI * 180);
+
+			var p = new Vector2();
+			var tangent = 0f;
+			var pd = 0f;
+			var bestBias = float.MaxValue;
+
+			if ((((int)PaddingType >> 4) & 0x1) == 1)
+			{
+				var (bias1, hPnt1, fd1) = CommonMath.Project2DLine(point, _beforeStartSrc, _src);
+                if (fd1 <= 1000)
+				{
+					p = hPnt1;
+					tangent = (_direction >= 0 ? _angleStart : _angleEnd) + 90 * _direction;
+					pd = fd1;
+					bestBias = bias1;
+				}
+			}
+
+			if (((int)PaddingType & 0x1) == 1)
+			{
+				var (bias2, hPnt2, fd2) = CommonMath.Project2DLine(point, _dst, _afterEndDst);
+				if (fd2 >= 0 && Math.Abs(bias2) < Math.Abs(bestBias))
+				{
+					p = hPnt2;
+					tangent = (_direction >= 0 ? _angleEnd : _angleStart) + 90 * _direction;
+					pd = _totalLen + fd2;
+					bestBias = bias2;
+				}
+			}
+
+			var th1 = _direction == 1 ? CommonMath.ThDiff(queryTh, _angleStart) : CommonMath.ThDiff(_angleEnd, queryTh);
+			// todo: urgent bug! should use better strategy to prevent sign problem
+            if (th1 < -55) th1 += 360;
+			var arcBias = (_radius - Vector2.Distance(point, _center)) * _direction;
+			if (Math.Abs(arcBias) < Math.Abs(bestBias))
+			{
+				p = _center + _radius * new Vector2((float)Math.Cos(queryTh / 180 * Math.PI),
+					(float)Math.Sin(queryTh / 180 * Math.PI));
+				tangent = queryTh + 90 * _direction;
+				pd = _radius * th1 / 180 * (float)Math.PI;
+				bestBias = arcBias;
+			}
+
+			return (p, tangent, bestBias, pd);
+		}
+
+		public override float QueryCurvature(float position)
+		{
+			// var theta = (float)(_angleEnd - position / _radius / Math.PI * 180f + Math.PI);
+			// return Vectoriel.FromAngleLen(theta, 1f / _radius);
+            return 1000f / _radius * _direction;
+        }
+
+		public override float Length()
+		{
+			return _totalLen;
+		}
+
+		private void CalculateVisPoints()
+		{
+			lock (_visPoints)
+			{
+				// todo: overlapping start and end is problematic
+				var ptCnt = (int)Math.Ceiling((_angleEnd + 360 - _angleStart) % 360 / VisAngleResolution);
+				_visPoints = new Vector2[ptCnt + 2];
+
+				var starting = _angleStart;
+				if (_direction == -1) starting = _angleEnd;
+				_visPoints[0] = _beforeStartSrc;
+
+				for (var j = 0; j < ptCnt; ++j)
+				{
+					var th = starting + j * VisAngleResolution * _direction;
+					var radAngle = (float)(th / 180f * Math.PI);
+					_visPoints[j + 1] = Center + new Vector2((float)Math.Cos(radAngle), (float)Math.Sin(radAngle)) * Radius;
+				}
+				
+				_visPoints[ptCnt + 1] = _afterEndDst;
+			}
+		}
+
+		private void ChangeShape()
+		{
+			_totalTh = CommonMath.ThDiff(_angleEnd, _angleStart);
+			if (_totalTh < 0) _totalTh += 360;
+			_totalLen = _radius * _totalTh / 180 * (float)Math.PI;
+
+			var radAngleStart = _angleStart / 180 * Math.PI;
+			var radAngleEnd = _angleEnd / 180 * Math.PI;
+			double srcAngle = radAngleStart, dstAngle = radAngleEnd;
+			if (_direction == -1) (srcAngle, dstAngle) = (dstAngle, srcAngle);
+			_src = _center + new Vector2((float)Math.Cos(srcAngle), (float)Math.Sin(srcAngle)) * _radius;
+			_dst = _center + new Vector2((float)Math.Cos(dstAngle), (float)Math.Sin(dstAngle)) * _radius;
+			_beforeStartSrc = CommonMath.Transform2D(_src,
+				(_direction >= 0 ? _angleStart : _angleEnd) + 90 * _direction, new Vector2(-1000, 0));
+			_afterEndDst = CommonMath.Transform2D(_dst, (_direction >= 0 ? _angleEnd : _angleStart) + 90 * _direction,
+				new Vector2(1000, 0));
+			_tangentSrc = QueryTangentPoint(_src).Angle;
+			_tangentDst = QueryTangentPoint(_dst).Angle;
+		}
+
+		private Vector2 _center;
+		private float _radius, _angleStart, _angleEnd;
+		private int _direction;
+
+		private float _totalTh, _totalLen;
+		private Vector2 _src, _dst;
+		private float _tangentSrc, _tangentDst;
+		private Vector2 _beforeStartSrc, _afterEndDst;
+
+		private Vector2[] _visPoints = Array.Empty<Vector2>();
+	}
+}
@@ -0,0 +1,349 @@
+using CommonUsage.Mathematics;
+using System.Collections.Generic;
+using System.Numerics;
+using System;
+using System.Linq;
+
+namespace CommonUsage.Geometries
+{
+    public class NurbsCurve : AbstractGeometry
+    {
+
+        public NurbsCurve(List<Vector2> controlPoints, List<float> weights, List<float> knotVector, int frame = 100)
+        {
+            _controlPoints = controlPoints;
+            _weights = weights;
+            _knotVector = knotVector;
+            _frame = frame;
+            InitializeNurbs();
+        }
+
+        public override void Visualize(Action<VisDot> processDot, Action<VisLine> processLine, bool visExtendedPart = false)
+        {
+            if (VisualizeOption.DrawAuxiliary)
+                for (var i = 0; i < _controlPoints.Count - 1; ++i)
+                {
+                    processLine(new VisLine(_controlPoints[i], _controlPoints[i + 1],
+                        false, false, VisualizeOption.AuxiliaryColor));
+                    if (i == 0) continue;
+                    processDot(new VisDot(_controlPoints[i], VisualizeOption.AuxiliaryColor));
+                }
+
+            for (var i = 0; i < _nurbsPoints.Count - 1; ++i)
+            {
+                if (Direction == -1)
+                {
+                    processLine(new VisLine(_nurbsPoints[i + 1], _nurbsPoints[i],
+                        false, i == (int)(_nurbsPoints.Count / 2), VisualizeOption.MainColor, 2));
+                }
+                else
+                {
+                    processLine(new VisLine(_nurbsPoints[i], _nurbsPoints[i + 1],
+                        false, i == (int)(_nurbsPoints.Count / 2), VisualizeOption.MainColor, 2));
+                }
+            }
+        }
+        public (Vector2 Point, int Id) QueryPoint(Vector2 point)
+        {
+            var p = new Vector2();
+            var id = -1;
+            var bestDistance = float.MaxValue;
+
+            var hashes = _bias.Select(bb => CalculateHash(point, 100, bb.X, bb.Y)).ToList();
+
+            void TryQuery(Dictionary<uint, List<(Vector2 Point, int Id)>> dict, List<uint> hashList)
+            {
+                foreach (var hash in hashList)
+                {
+                    if (!dict.TryGetValue(hash, out var ll)) continue;
+                    foreach (var (q, qId) in ll)
+                    {
+                        var d = Vector2.Distance(q, point);
+                        if (d < bestDistance)
+                        {
+                            p = q;
+                            id = qId;
+                            bestDistance = d;
+                        }
+                    }
+                }
+            }
+
+            if (id == -1)
+            {
+                // todo: improve the way to find closest point if mappings fail
+                (p, id) = _nurbsPoints.Select((p, i) => (p, i))
+                    .OrderBy(pair => CommonMath.dist(pair.p.X, pair.p.Y, point.X, point.Y)).First();
+            }
+
+            return (p, id);
+        }
+
+        private uint CalculateHash(Vector2 point, float gridSize, int xBias = 0, int yBias = 0)
+        {
+            return (uint)(((int)((point.X - _minX) / gridSize) + xBias) << 16 + (((int)((point.Y - _minY) / gridSize) + yBias) & 0xffff));
+        }
+
+        private readonly List<(int X, int Y)> _bias = new()
+        {
+            new(-1, -1), new(-1, 0), new(-1, 1),
+            new(0, -1), new(0, 0), new(0, 1),
+            new(1, -1), new(1, 0), new(1, 1),
+        };
+
+        public override (Vector2 Pt, float Angle, float Bias, float Position) QueryTangentPoint(Vector2 point)
+        {
+            var (p, id) = QueryPoint(point);
+            var tangent = _tangents[id];
+            var (bias, lp, fd) = CommonMath.Project2DLine(point, p, tangent);
+            var next = fd > 0 ? id + 1 : id - 1;
+            if (next > 0 && next < _tangents.Count)//线性插值
+            {
+                var (_, _, t) = CommonMath.Project2DLine(point, _nurbsPoints[id], _nurbsPoints[next]);
+                var partial = t / Vector2.Distance(_nurbsPoints[id], _nurbsPoints[next]);
+                if (partial >= 0 && partial <= 1)
+                {
+                    tangent = CommonMath.RoundTh(_tangents[id] +
+                                                 partial * CommonMath.RoundTh(_tangents[next] - _tangents[id]));
+                    if (CommonMath.RoundTh(_tangents[next] - _tangents[id]) > 5)
+                        Console.WriteLine($"Nurbs tangents bug, tanget: {id}:{_tangents[id]} {next}:{_tangents[next]}");
+                }
+                else Console.WriteLine("Nurbs tangents bug");
+            }
+            return (lp, tangent, bias, fd + _sumDistances[id]);
+        }
+
+        public override float QueryCurvature(float position)
+        {
+            int id = _sumDistances.Count - 1;
+            if (position <= 0) id = 0;
+            else
+            {
+                for (int i = 1; i < _sumDistances.Count; i++)
+                {
+                    if (position > _sumDistances[i - 1] && position <= _sumDistances[i])
+                    {
+                        id = i;
+                        break;
+                    }
+                }
+            }
+
+            var result = _curvatures[id];
+            if (id > 0 && id < _sumDistances.Count - 1)//插值
+            {
+                var partial = (position - _sumDistances[id - 1]) / (_sumDistances[id] - _sumDistances[id - 1]);
+                if (partial >= 0 && partial <= 1) result = (1 - partial) * _curvatures[id - 1] + partial * _curvatures[id];
+                else Console.WriteLine("Nurbs curvature bug");
+            }
+
+            return result;
+        }
+
+        public Vector3 QueryNurbsPointsById(int id)
+        {
+            if (id < 0 || id > Frame)
+            {
+                Console.WriteLine($"QueryBezierPointsById out of range, Resolution:{Frame},id:{id}.");
+                return new Vector3(0, 0, 0);
+            }
+
+            return new Vector3(_nurbsPoints[id].X, _nurbsPoints[id].Y, _tangents[id]);
+        }
+        public override float Length()
+        {
+            return _length;
+        }
+
+        public int Order => _order;
+        public List<Vector2> ControlPoints => _controlPoints;
+        public List<float> Weights => _weights;
+        public List<float> KnotVector => _knotVector;
+        public int Frame => _frame;
+
+        public int Direction = 1;
+
+
+        public void UpdateControlPoint(int id, Vector2 point)
+        {
+            _controlPoints[id] = point;
+            InitializeNurbs();
+        }
+        public void UpdateNurbsWeihgts(int id, float weight)
+        {
+            _weights[id] = weight;
+            InitializeNurbs();
+
+        }
+        public void AddControlPoint(int id, Vector2 point)
+        {
+            _controlPoints.Insert(id, point);
+            InitializeNurbs();
+        }
+
+        public void RemoveControlPoint(int id)
+        {
+            _controlPoints.RemoveAt(id);
+            InitializeNurbs();
+        }
+
+        public Vector2 GetMidPoint()
+        {
+            return _nurbsPoints[(int)Math.Ceiling(_frame / 2d)];
+        }
+
+        private void InitializeNurbs()
+        {
+            _order = _controlPoints.Count - 1;
+            List<List<Vector2>> allpoints = new List<List<Vector2>>();
+            List<Vector2> nurbsCurvePoints = new List<Vector2>();
+            float delta = 1.0f / Frame;
+
+            for (float t = 0; t <= 1; t += delta)
+            {
+                var (point, tangent) = DeBoorAlgorithm(t);
+                var points = new List<Vector2>
+                {
+                    point,
+                    point + tangent // Tangent endpoint
+                };
+                allpoints.Add(points);
+                nurbsCurvePoints.Add(point); // Store the curve point separately
+            }
+
+            _nurbsPoints = nurbsCurvePoints;
+            _tangents = Enumerable.Repeat(0f, _nurbsPoints.Count).ToList();
+            _curvatures = Enumerable.Repeat(0f, _nurbsPoints.Count).ToList();
+
+            for (var id = 0; id < _nurbsPoints.Count - 1; ++id)
+            {
+                Vector2 p1 = _nurbsPoints[id];
+                Vector2 p2 = _nurbsPoints[id + 1];
+
+                float tangentAngle = (float)Math.Atan2(p2.Y - p1.Y, p2.X - p1.X) * 180 / (float)Math.PI;
+                _tangents[id] = tangentAngle;
+
+                // Calculate curvature using finite differences of tangent (second derivative approximation)
+                if (id > 0)
+                {
+                    float previousTangent = _tangents[id - 1];
+                    float curvature = (float)(CommonMath.ThDiff(tangentAngle, previousTangent) * Math.PI / 180) /
+                                      (Vector2.Distance(p1, p2) / 1000);
+                    _curvatures[id] = curvature;
+                }
+            }
+
+            _curvatures.Insert(0, _curvatures[0]);
+            for (var id = 1; id < _curvatures.Count - 1; ++id)
+            {
+                _curvatures[id] = (_curvatures[id] + _curvatures[id + 1]) / 2;
+            }
+
+            _remainDistances = Enumerable.Repeat(0f, _nurbsPoints.Count).ToList();
+            _sumDistances = Enumerable.Repeat(0f, _nurbsPoints.Count).ToList();
+            _remainDistances[_nurbsPoints.Count - 1] = 0;
+
+            for (var i = _nurbsPoints.Count - 2; i >= 0; --i)
+            {
+                _remainDistances[i] = _remainDistances[i + 1] + Vector2.Distance(_nurbsPoints[i], _nurbsPoints[i + 1]);
+            }
+
+            _sumDistances[0] = 0;
+            for (var i = 1; i < _nurbsPoints.Count; ++i)
+            {
+                _sumDistances[i] = _sumDistances[i - 1] + Vector2.Distance(_nurbsPoints[i], _nurbsPoints[i - 1]);
+            }
+
+            _length = _sumDistances.Last();
+
+            _minX = _nurbsPoints.Min(pp => pp.X);
+            _minY = _nurbsPoints.Min(pp => pp.Y);
+
+            var tmpList = _nurbsPoints.Select((point, index) => (point, index)).ToList();
+            // GenerateGridMapping(ref _pointsMappingSmall, 100, tmpList);
+            // GenerateGridMapping(ref _pointsMappingBig, 1000, tmpList);
+        }
+
+
+       
+
+        private float CalculateLength()
+        {
+            return _nurbsPoints.Zip(_nurbsPoints.Skip(1), Vector2.Distance).Sum();
+        }
+
+        private (Vector2, Vector2) DeBoorAlgorithm(float t)
+        {
+            Vector2 numerator = Vector2.Zero;
+            Vector2 tangentNumerator = Vector2.Zero;
+            float denominator = 0f;
+
+            // Calculate the point on the curve
+            for (int i = 0; i < ControlPoints.Count; ++i)
+            {
+                float basis = BasisFunction(i, _order, t) * Weights[i];
+                numerator += basis * ControlPoints[i];
+                denominator += basis;
+            }
+
+            Vector2 point = numerator / denominator;
+
+            // Calculate the tangent vector using the analytical derivative
+            for (int i = 0; i < ControlPoints.Count; ++i)
+            {
+                float basisDerivative = BasisFunctionDerivative(i, _order, t) * Weights[i];
+                tangentNumerator += basisDerivative * ControlPoints[i];
+            }
+            Vector2 tangent = tangentNumerator / denominator;
+
+            return (point, tangent);
+        }
+
+        private float BasisFunction(int i, int p, float t)
+        {
+            if (p == 0)
+                return (KnotVector[i] <= t && t < KnotVector[i + 1]) ? 1.0f : 0.0f;
+
+            float denom1 = KnotVector[i + p] - KnotVector[i];
+            float term1 = denom1 == 0 ? 0 : ((t - KnotVector[i]) / denom1) * BasisFunction(i, p - 1, t);
+
+            float denom2 = KnotVector[i + p + 1] - KnotVector[i + 1];
+            float term2 = denom2 == 0 ? 0 : ((KnotVector[i + p + 1] - t) / denom2) * BasisFunction(i + 1, p - 1, t);
+
+            return term1 + term2;
+        }
+
+        private float BasisFunctionDerivative(int i, int k, float t)
+        {
+            if (k == 0) return 0;
+
+            float denom1 = KnotVector[i + k] - KnotVector[i];
+            float denom2 = KnotVector[i + k + 1] - KnotVector[i + 1];
+
+            float term1 = denom1 != 0 ? BasisFunction(i, k - 1, t) / denom1 : 0;
+            float term2 = denom1 != 0 ? (t - KnotVector[i]) * BasisFunctionDerivative(i, k - 1, t) / denom1 : 0;
+
+            float term3 = denom2 != 0 ? -BasisFunction(i + 1, k - 1, t) / denom2 : 0;
+            float term4 = denom2 != 0 ? (KnotVector[i + k + 1] - t) * BasisFunctionDerivative(i + 1, k - 1, t) / denom2 : 0;
+
+            return term1 + term2 + term3 + term4;
+        }
+       
+        private int _order;
+        private List<Vector2> _controlPoints;
+        private List<float> _weights;
+        private List<float> _knotVector;
+        private int _frame;
+        private List<Vector2> _nurbsPoints;
+        private List<List<List<Vector2>>> _tangentPoints;
+        private List<float> _curvatures;
+        private List<float> _sumDistances;
+        private List<float> _remainDistances;
+        private float _minX, _minY;
+        private float _length;
+        private Dictionary<uint, List<(Vector2 Point, int Id)>> _pointsMappingSmall;
+        private Dictionary<uint, List<(Vector2 Point, int Id)>> _pointsMappingBig;
+        private List<float> _tangents;
+
+    }
+}
@@ -0,0 +1,71 @@
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Text;
+
+namespace CommonUsage.Geometries
+{
+	/// <summary>
+	/// MDCS数学类：向量。
+	/// </summary>
+	public class Vectoriel
+	{
+        public Vectoriel()
+        {
+            _vec2 = Vector2.Zero;
+            _dir2 = Vector2.Normalize(_vec2);
+            _len = _vec2.Length();
+            _angle = (float)(Math.Atan2(_vec2.Y, _vec2.X) / Math.PI * 180f);
+        }
+
+		public Vectoriel(Vector2 vec)
+		{
+			_vec2 = vec;
+			_dir2 = Vector2.Normalize(_vec2);
+			_len = _vec2.Length();
+			_angle = (float)(Math.Atan2(_vec2.Y, _vec2.X) / Math.PI * 180f);
+		}
+
+		/// <summary>
+		/// 通过笛卡尔坐标系X和Y值构建向量。
+		/// </summary>
+		/// <param name="x"></param>
+		/// <param name="y"></param>
+		/// <returns></returns>
+		public static Vectoriel FromXY(float x, float y)
+		{
+			return new Vectoriel(new Vector2(x, y));
+		}
+
+		/// <summary>
+		/// 通过极坐标系的角度和距离值构建向量。
+		/// </summary>
+		/// <param name="angle"></param>
+		/// <param name="len"></param>
+		/// <returns></returns>
+		public static Vectoriel FromAngleLen(float angle, float len)
+		{
+			var rad = angle / 180f * Math.PI;
+			return new Vectoriel(new Vector2((float)Math.Cos(rad), (float)Math.Sin(rad)) * len);
+		}
+
+		public static implicit operator Vector2(Vectoriel vec)
+		{
+			return vec._vec2;
+		}
+
+		public static explicit operator Vectoriel(Vector2 vec)
+		{
+			return FromXY(vec.X, vec.Y);
+		}
+
+		public Vector2 Direction => _dir2;
+
+		public float Length => _len;
+
+		public float Angle => _angle;
+
+		private Vector2 _vec2, _dir2;
+		private float _len, _angle;
+	}
+}
@@ -0,0 +1,774 @@
+using System;
+using System.Collections.Generic;
+using System.Drawing;
+using System.Linq;
+using System.Numerics;
+using System.Reflection;
+using System.Runtime.CompilerServices;
+using System.Runtime.InteropServices;
+
+namespace CommonUsage.Mathematics
+{
+
+    using T3 = Tuple<float, float, float>;
+    using D3 = Tuple<double, double, double>;
+
+    public class CommonMath
+    {
+	    public class PrimeEnumerator<T>
+	    {
+		    public PrimeEnumerator(List<T> items, Func<T, bool> process)
+		    {
+                _n = items.Count;
+                _items = items;
+                _process = process;
+
+                foreach (var pNum in _primes)
+                {
+	                if (_n % pNum != 0)
+	                {
+		                _a = pNum;
+		                _b = 11;
+		                break;
+	                }
+                }
+			}
+
+		    public void Enumerate()
+		    {
+			    using (var enumerator = Get().GetEnumerator())
+			    {
+                    while (enumerator.MoveNext()) { }
+			    }
+		    }
+
+		    private readonly int _n, _a, _b;
+		    private readonly int[] _primes = new[] { 29, 23, 19, 17, 13 };
+		    private List<T> _items;
+            private readonly Func<T, bool> _process;
+
+		    private IEnumerable<bool> Get()
+		    {
+			    for (var i = 0; i < _n; ++i)
+			    {
+				    var id = (i * _a + _b) % _n;
+				    yield return _process(_items[id]);
+			    }
+			}
+	    }
+
+        private static IEnumerable<IEnumerable<T>> GetPermutationsInternal<T>(IEnumerable<T> list, int length)
+        {
+            if (length == 1) return list.Select(t => new T[] { t });
+
+            return GetPermutationsInternal(list, length - 1)
+                .SelectMany(t => list.Where(e => !t.Contains(e)),
+                    (t1, t2) => t1.Concat(new T[] { t2 }));
+        }
+
+        /// <summary>
+        /// 得到一组数据的所有排列。
+        /// </summary>
+        /// <typeparam name="T">元素数据类型</typeparam>
+        /// <param name="list">所有待选元素</param>
+        /// <param name="selectNum">所选出的元素数量</param>
+        /// <returns></returns>
+        public static List<List<T>> GetPermutations<T>(List<T> list, int selectNum)
+        {
+            return GetPermutationsInternal(list, selectNum).Select(ll => ll.ToList()).ToList();
+        }
+
+        public static (float bias, Vector2 hPnt, float d) Project2DLine(Vector2 pnt, Vector2 segSt,
+            Vector2 segEnd)
+        {
+            var dir = Vector2.Normalize(segEnd - segSt);
+            var fd = Vector2.Dot(pnt - segSt, dir);
+            var hPnt = segSt + fd * dir;
+            var bias = dir.X * (pnt.Y-segSt.Y) - (pnt.X-segSt.X) * dir.Y;
+            return (bias, hPnt, fd);
+        }
+
+        public static (float bias, Vector2 hPnt, float fd) Project2DLine(Vector2 pnt, Vector2 segSt, float tangent)
+        {
+	        var dir = new Vector2((float)System.Math.Cos(tangent / 180 * System.Math.PI), (float)System.Math.Sin(tangent / 180 * System.Math.PI));
+	        var fd = Vector2.Dot(pnt - segSt, dir);
+	        var hPnt = segSt + fd * dir;
+	        var bias = dir.X * (pnt.Y - segSt.Y) - (pnt.X - segSt.X) * dir.Y;
+	        return (bias, hPnt, fd);
+		}
+
+        public class LineEqu
+        {
+            public double A, B, C, ln, dAB;
+            public double px1, px2, py1, py2;
+            public float midX;
+            public float midY;
+        }
+        // Fit line with PCA.
+        public LineEqu CalcLine(IEnumerable<Vector2> tls)
+        {
+            var lidarPoint2Ds = tls as Vector2[] ?? tls.ToArray();
+            float fx = lidarPoint2Ds.Average(f => f.X);
+            float fy = lidarPoint2Ds.Average(f => f.Y);
+            float fxx = lidarPoint2Ds.Average(f => f.X * f.X);
+            float fxy = lidarPoint2Ds.Average(f => f.X * f.Y);
+            float fyy = lidarPoint2Ds.Average(f => f.Y * f.Y);
+            float a = fxx - fx * fx, b = fxy - fx * fy, c = fyy - fy * fy;
+            double sqt = System.Math.Sqrt((a - c) * (a - c) + 4 * b * b);
+            double l1 = a + c + sqt;
+            double l2 = a + c - sqt;
+            double dx, dy;
+            if (System.Math.Abs(a - l1 / 2) > System.Math.Abs(c - l1 / 2))
+            {
+                dy = l1 / 2 - a; dx = b;
+            }
+            else
+            {
+                dx = l1 / 2 - c; dy = b;
+            }
+            double norm = System.Math.Sqrt(dx * dx + dy * dy);
+            dx /= norm; dy /= norm;
+            double A = dy, B = -dx, C = dx * fy - dy * fx;
+            double dAB = System.Math.Sqrt(A * A + B * B);
+
+            return new CommonMath.LineEqu
+            {
+                A = A,
+                B = B,
+                C = C,
+                ln = lidarPoint2Ds.Average(p => System.Math.Abs(p.X * A + p.Y * B + C) / dAB),
+                midX = fx,
+                midY = fy
+            };
+        }
+
+        public static double QuadInterp3(double[] confsF)
+        {
+            if (confsF[0] > confsF[1] && confsF[0] > confsF[2])
+            {
+                //printf("left overflow...\n");
+                return -1;
+            }
+
+            if (confsF[1] > confsF[0] && confsF[1] > confsF[2])
+            {
+                return (-(confsF[2] - confsF[0]) / 2.0f / (confsF[0] + confsF[2] - 2.0f * confsF[1] + 0.0001f));
+            }
+            if (confsF[2] > confsF[0] && confsF[2] > confsF[1])
+            {
+                //printf("right overflow...\n");
+                return 1;
+            }
+            return 0;
+        }
+
+        public static double cross(PointF O, PointF A, PointF B)
+        {
+            return (A.X - O.X) * (B.Y - O.Y) - (A.Y - O.Y) * (B.X - O.X);
+        }
+
+        public static List<PointF> GetConvexHull(List<PointF> points)
+        {
+            if (points == null)
+                return null;
+
+            if (points.Count() <= 1)
+                return points;
+
+            int n = points.Count(), k = 0;
+            List<PointF> H = new List<PointF>(new PointF[2 * n]);
+
+            points.Sort((a, b) =>
+                a.X == b.X ? a.Y.CompareTo(b.Y) : a.X.CompareTo(b.X));
+
+            // Build lower hull
+            for (int i = 0; i < n; ++i)
+            {
+                while (k >= 2 && cross(H[k - 2], H[k - 1], points[i]) <= 0)
+                    k--;
+                H[k++] = points[i];
+            }
+
+            // Build upper hull
+            for (int i = n - 2, t = k + 1; i >= 0; i--)
+            {
+                while (k >= t && cross(H[k - 2], H[k - 1], points[i]) <= 0)
+                    k--;
+                H[k++] = points[i];
+            }
+
+            return H.Take(k - 1).ToList();
+        }
+
+        public static bool IsPointInPolygon4(PointF[] polygon, PointF testPoint)
+        {
+            // ray casting odd even test.
+            bool result = false;
+            int j = polygon.Count() - 1;
+            for (int i = 0; i < polygon.Count(); i++)
+            {
+                if (polygon[i].Y < testPoint.Y && polygon[j].Y >= testPoint.Y ||
+                    polygon[j].Y < testPoint.Y && polygon[i].Y >= testPoint.Y)
+                {
+                    if (polygon[i].X + (testPoint.Y - polygon[i].Y) / (polygon[j].Y - polygon[i].Y) *
+                        (polygon[j].X - polygon[i].X) < testPoint.X)
+                    {
+                        result = !result;
+                    }
+                }
+
+                j = i;
+            }
+
+            return result;
+        }
+
+        public static double Exp(double val)
+        {
+            if (val < -20) return 0.0000001;
+            if (val > 20) return 99999999999999;
+            long tmp = (long)(1512775 * val + 1072632447);
+            return BitConverter.Int64BitsToDouble(tmp << 32);
+        }
+        public static double gaussmf(double x, double sig, double c)
+        {
+            return Exp(-(x - c) * (x - c) / (2 * sig * sig));
+        }
+
+        public static float Exp(float x)
+        {
+            if (x < -10) return 0;
+            if (x > 10) return 99999999999999;
+            x = 1.0f + x / 64f;
+            x *= x;
+            x *= x;
+            x *= x;
+            x *= x;
+            x *= x;
+            x *= x;
+            return x;
+        }
+        public static float gaussmf(float x, float sig, float c)
+        {
+            return Exp(-(x - c) * (x - c) / (2 * sig * sig));
+        }
+
+        public static D3 Transform2D(D3 src, D3 t)
+        {
+            var rth = src.Item3 / 180.0 * System.Math.PI;
+            var p1dtx = (src.Item1 + System.Math.Cos(rth) * t.Item1 -
+                                System.Math.Sin(rth) * t.Item2);
+            var p1dty = (src.Item2 + System.Math.Sin(rth) * t.Item1 +
+                                System.Math.Cos(rth) * t.Item2);
+            var p1dtth = src.Item3 + t.Item3;
+            return Tuple.Create(p1dtx, p1dty, p1dtth);
+        }
+
+        public struct LngLatToXY
+        {
+            public double scale;
+            public double rad;
+            public double biasX, biasY;
+        }
+
+        public static LngLatToXY GetTransformLngLatToXY(Vector2 lnglat1, Vector2 xy1, Vector2 lnglat2, Vector2 xy2)
+        {
+            var scale = (xy1 - xy2).Length() / (lnglat1 - lnglat2).Length();
+            var dxy = (xy1 - xy2);
+            var dlnglat = lnglat1 - lnglat2;
+            var rad = System.Math.Atan2(dxy.X, dxy.Y) - System.Math.Atan2(dlnglat.X, dlnglat.Y);
+            var intm = lnglat1 * scale;
+            var biasX = xy1.X - (intm.X * System.Math.Cos(rad) - intm.Y * System.Math.Sin(rad));
+            var biasY = xy1.Y - (intm.X * System.Math.Sin(rad) + intm.Y * System.Math.Cos(rad));
+            return new LngLatToXY {rad = rad, biasX = biasX, biasY = biasY, scale = scale};
+        }
+
+        public Vector2 TransformLngLatToXY(Vector2 lnglat, LngLatToXY t)
+        {
+            var intm = lnglat * (float) t.scale;
+            return new Vector2((float) (intm.X * System.Math.Cos(t.rad) - intm.Y * System.Math.Sin(t.rad) + t.biasX),
+                (float) (intm.X * System.Math.Sin(t.rad) + intm.Y * System.Math.Cos(t.rad) + t.biasY));
+        }
+
+        public static D3 ReverseTransform(D3 dest, D3 t)
+        {
+            var rth = (dest.Item3 - t.Item3) / 180.0 * System.Math.PI;
+            var nxT = (dest.Item1 - System.Math.Cos(rth) * t.Item1 +
+                              System.Math.Sin(rth) * t.Item2);
+            var nyT = (dest.Item2 - System.Math.Sin(rth) * t.Item1 -
+                              System.Math.Cos(rth) * t.Item2);
+            var pth = dest.Item3 - t.Item3;
+            return Tuple.Create(nxT, nyT, pth);
+        }
+
+        public static D3 SolveTransform2D(D3 src, D3 dest)
+        {
+            var th = dest.Item3 - src.Item3;
+            th = (th - System.Math.Round((th) / 360.0f) * 360);
+            var rth = src.Item3 / 180.0 * System.Math.PI;
+            var x = ((dest.Item1 - src.Item1) * System.Math.Cos(rth) +
+                            (dest.Item2 - src.Item2) * System.Math.Sin(rth));
+            var y = (-(dest.Item1 - src.Item1) * System.Math.Sin(rth) +
+                            (dest.Item2 - src.Item2) * System.Math.Cos(rth));
+            return Tuple.Create(x, y, th);
+        }
+
+        public static T3 Transform2D(T3 src, T3 t)
+        {
+            var rth = src.Item3 / 180.0 * System.Math.PI;
+            var p1dtx = (float)(src.Item1 + System.Math.Cos(rth) * t.Item1 -
+                                System.Math.Sin(rth) * t.Item2);
+            var p1dty = (float)(src.Item2 + System.Math.Sin(rth) * t.Item1 +
+                                System.Math.Cos(rth) * t.Item2);
+            var p1dtth = src.Item3 + t.Item3;
+            return Tuple.Create(p1dtx, p1dty, p1dtth);
+        }
+
+        public static Vector2 Transform2D(Vector3 src, Vector3 t)
+        {
+	        var tup = Transform2D(Tuple.Create(src.X, src.Y, src.Z), Tuple.Create(t.X, t.Y, t.Z));
+	        return new Vector2(tup.Item1, tup.Item2);
+        }
+
+        public static Vector2 Transform2D(Vector2 srcPos, float srcTh, Vector2 dt, float dth = 0)
+        {
+	        var tup = Transform2D(Tuple.Create(srcPos.X, srcPos.Y, srcTh), Tuple.Create(dt.X, dt.Y, dth));
+	        return new Vector2(tup.Item1, tup.Item2);
+		}
+
+		public static T3 ReverseTransform(T3 dest, T3 t)
+        {
+            var rth = (dest.Item3 - t.Item3) / 180.0 * System.Math.PI;
+            var nxT = (float)(dest.Item1 - System.Math.Cos(rth) * t.Item1 +
+                              System.Math.Sin(rth) * t.Item2);
+            var nyT = (float)(dest.Item2 - System.Math.Sin(rth) * t.Item1 -
+                              System.Math.Cos(rth) * t.Item2);
+            var pth = dest.Item3 - t.Item3;
+            return Tuple.Create(nxT, nyT, pth);
+        }
+
+        public static T3 SolveTransform2D(T3 src, T3 dest)
+        {
+            var th = dest.Item3 - src.Item3;
+            th = (float)(th - System.Math.Round((th) / 360.0f) * 360);
+            var rth = src.Item3 / 180.0 * System.Math.PI;
+            var x = (float)((dest.Item1 - src.Item1) * System.Math.Cos(rth) +
+                            (dest.Item2 - src.Item2) * System.Math.Sin(rth));
+            var y = (float)(-(dest.Item1 - src.Item1) * System.Math.Sin(rth) +
+                            (dest.Item2 - src.Item2) * System.Math.Cos(rth));
+            return Tuple.Create(x, y, th);
+        }
+
+		public static Vector2 SolveTransform2D(Vector2 srcPos, float srcTh, Vector2 dt, float dth = 0)
+		{
+			var tup = SolveTransform2D(Tuple.Create(srcPos.X, srcPos.Y, srcTh), Tuple.Create(dt.X, dt.Y, dth));
+			return new Vector2(tup.Item1, tup.Item2);
+		}
+
+		public static double dist(double x1, double y1, double x2, double y2)
+        {
+            return System.Math.Sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
+        }
+
+        [StructLayout(LayoutKind.Explicit)]
+        private struct FloatIntUnion
+        {
+            [FieldOffset(0)] public float f;
+
+            [FieldOffset(0)] public int tmp;
+        }
+
+        public static float Sqrt(float z)
+        {
+            FloatIntUnion u;
+            u.tmp = 0;
+            u.f = z;
+            u.tmp -= 1 << 23; /* Subtract 2^m. */
+            u.tmp >>= 1; /* Divide by 2. */
+            u.tmp += 1 << 29; /* Add ((b + 1) / 2) * 2^m. */
+            return u.f;
+        }
+
+        public static float dist2(float x1, float y1, float x2, float y2)
+        {
+            return ((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
+        }
+
+
+        public static float d2(float x1, float y1, float x2, float y2)
+        {
+            return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);
+        }
+
+        public static float ThAverage(List<float> angles)
+        {
+	        var anchor = angles[0];
+	        var diff = 0f;
+	        foreach (var angle in angles)
+		        diff += ThDiff(angle, anchor);
+	        return RoundTh(anchor + diff / angles.Count);
+        }
+
+        public static float ThDiff(float th1, float th2)
+        {
+            return (float)(th1 - th2 -
+                           System.Math.Round((th1 - th2) / 360.0f) * 360);
+        }
+
+        public static double ThDiff(double th1, double th2)
+        {
+            return th1 - th2 -
+                           System.Math.Round((th1 - th2) / 360.0f) * 360;
+        }
+
+        public static double refine(double x)
+        {
+            if (x < 1 && x > -1) return x;
+            if (x > 1)
+                return (2 / (1 + System.Math.Exp(-((x - 1) * 2))));
+            return (2 / (1 + System.Math.Exp(-((x + 1) * 2)))) - 2;
+        }
+
+        /// <summary>
+        /// 求点p到两点式直线p1p2的距离
+        /// </summary>
+        /// <param name="x">点p的x坐标</param>
+        /// <param name="y">点p的y坐标</param>
+        /// <param name="x1">直线点p1的x坐标</param>
+        /// <param name="y1">直线点p1的y坐标</param>
+        /// <param name="x2">直线点p2的x坐标</param>
+        /// <param name="y2">直线点p2的y坐标</param>
+        /// <returns></returns>
+        public static double Point2LineDist(double x, double y, double x1, double y1, double x2, double y2)
+        {
+            double a1 = -(y1 - y2) / 10;
+            double b1 = (x1 - x2) / 10;
+            double c1 = (x1 * (y1 - y2) - y1 * (x1 - x2)) / 10;
+            return System.Math.Abs(a1 * x + b1 * y + c1) / System.Math.Sqrt(a1 * a1 + b1 * b1);
+        }
+
+        public static double Point2LineDist(Vector2 p, LineSegment ll)
+        {
+            double a1 = -(ll.Src.Y - ll.Dst.Y) / 10;
+            double b1 = (ll.Src.X - ll.Dst.X) / 10;
+            double c1 = (ll.Src.X * (ll.Src.Y - ll.Dst.Y) - ll.Src.Y * (ll.Src.X - ll.Dst.X)) / 10;
+            return System.Math.Abs(a1 * p.X + b1 * p.Y + c1) / System.Math.Sqrt(a1 * a1 + b1 * b1);
+        }
+
+        /// <summary>
+        /// 两条两点式直线间的夹角
+        /// </summary>
+        /// <param name="x1"></param>
+        /// <param name="y1"></param>
+        /// <param name="x2"></param>
+        /// <param name="y2"></param>
+        /// <param name="x3"></param>
+        /// <param name="y3"></param>
+        /// <param name="x4"></param>
+        /// <param name="y4"></param>
+        /// <returns>角度制</returns>
+        public static double AngleBetweenLines(double x1, double y1, double x2, double y2, double x3, double y3,
+            double x4, double y4)
+        {
+            var vec1 = new Vector2((float)(x2 - x1), (float)(y2 - y1));
+            var vec2 = new Vector2((float)(x4 - x3), (float)(y4 - y3));
+            return System.Math.Acos(System.Math.Abs(Vector2.Dot(vec1, vec2) / vec1.Length() / vec2.Length())) / System.Math.PI * 180;
+        }
+
+        public static double AngleBetweenLines(LineSegment ls1, LineSegment ls2)
+        {
+	        return AngleBetweenLines(ls1.Src.X, ls1.Src.Y, ls1.Dst.X, ls1.Dst.Y, ls2.Src.X, ls2.Src.Y, ls2.Dst.X,
+		        ls2.Dst.Y);
+        }
+
+		/// <summary>
+		/// 两向量间夹角
+		/// </summary>
+		/// <param name="x1"></param>
+		/// <param name="y1"></param>
+		/// <param name="x2"></param>
+		/// <param name="y2"></param>
+		/// <param name="x3"></param>
+		/// <param name="y3"></param>
+		/// <param name="x4"></param>
+		/// <param name="y4"></param>
+		/// <returns>角度制</returns>
+		public static double AngleBetweenVectors(double x1, double y1, double x2, double y2, double x3, double y3,
+            double x4, double y4)
+        {
+            var vec1 = new Vector2((float)(x2 - x1), (float)(y2 - y1));
+            var vec2 = new Vector2((float)(x4 - x3), (float)(y4 - y3));
+            return System.Math.Acos(Vector2.Dot(vec1, vec2) / vec1.Length() / vec2.Length()) / System.Math.PI * 180;
+        }
+
+        /// <summary>
+        /// 两向量间夹角.
+        /// </summary>
+        /// <param name="vec1"></param>
+        /// <param name="vec2"></param>
+        /// <returns>角度制</returns>
+        public static double AngleBetweenVectors(Vector2 vec1, Vector2 vec2)
+        {
+            return System.Math.Acos(Vector2.Dot(vec1, vec2) / vec1.Length() / vec2.Length()) / System.Math.PI * 180;
+        }
+
+        public static double AngleBetweenVectors(Vector3 vector1, Vector3 vector2)
+        {
+	        float dotProduct = Vector3.Dot(vector1, vector2);
+	        float magnitude1 = vector1.Length();
+	        float magnitude2 = vector2.Length();
+	        float cosine = dotProduct / (magnitude1 * magnitude2);
+
+	        return System.Math.Acos(cosine) / System.Math.PI * 180;
+        }
+
+		/// <summary>
+		/// 求点到直线的垂足
+		/// </summary>
+		/// <param name="x"></param>
+		/// <param name="y"></param>
+		/// <param name="x1"></param>
+		/// <param name="y1"></param>
+		/// <param name="x2"></param>
+		/// <param name="y2"></param>
+		/// <returns></returns>
+		public static (double, double) PerpendicularPoint(double x, double y, double x1, double y1, double x2, double y2)
+        {
+            double lx = x2 - x1, ly = y2 - y1, dAB = lx * lx + ly * ly;
+            var u = ((x - x1) * lx + (y - y1) * ly) / dAB;
+            return new(x1 + u * lx, y1 + u * ly);
+        }
+
+        public static Vector2 PerpendicularPoint(Vector2 p, LineSegment ls)
+        {
+            double lx = ls.Dst.X - ls.Src.X, ly = ls.Dst.Y - ls.Src.Y, dAB = lx * lx + ly * ly;
+            var u = ((p.X - ls.Src.X) * lx + (p.Y - ls.Src.Y) * ly) / dAB;
+            return new Vector2((float)(ls.Src.X + u * lx), (float)(ls.Src.Y + u * ly));
+        }
+
+        public static double PerpendicularPosition(double x, double y, double x1, double y1, double x2, double y2)
+        {
+            double lx = x2 - x1, ly = y2 - y1;
+            var dAB = CommonMath.Sqrt((float)(lx * lx + ly * ly));
+            lx /= dAB;
+            ly /= dAB;
+            return (x - x1) * lx + (y - y1) * ly;
+        }
+
+
+        /// <summary>
+        /// 最小二乘法拟合直线，得到两点式。
+        /// </summary>
+        /// <param name="pts">待拟合的点集，应至少有2个点。</param>
+        /// <param name="maxDist2Line">检查是否所有点距直线的距离均小于maxDist2Line，若为-1则不检查。</param>
+        /// <returns>返回两点式的两个端点坐标。若坐标为全0，则拟合失败。</returns>
+        public static (bool, Vector2, Vector2) FitLineSegment(List<Vector2> pts, double maxDist2Line = -1)
+        {
+            if (pts.Count < 2)
+            {
+                Console.WriteLine($"Points too Few! {pts.Count}! Cannot perform line fitting!",
+                    MethodBase.GetCurrentMethod()?.Name ?? "FitLine");
+                return (false, Vector2.Zero, Vector2.Zero);
+            };
+
+            // y = kx + b
+            double A = 0, B = 0, C = 0, D = 0;
+            foreach (var p in pts)
+            {
+                A += p.X * p.X;
+                B += p.X;
+                C += p.X * p.Y;
+                D += p.Y;
+            }
+
+            var tmp = A * pts.Count - B * B;
+            var k = (C * pts.Count - B * D) / tmp;
+            var b = (A * D - C * B) / tmp;
+
+            double x1 = 0,
+                y1 = k * x1 + b,
+                x2 = 1000,
+                y2 = k * x2 + b;
+
+            double CalcDist(ref bool fail, ref Vector2 endP, ref Vector2 endQ)
+            {
+                double distSum = 0;
+                double lx = x2 - x1, ly = y2 - y1, dAB = lx * lx + ly * ly;
+                double minU = double.MaxValue, maxU = double.MinValue;
+
+                foreach (var p in pts)
+                {
+                    var u = ((p.X - x1) * lx + (p.Y - y1) * ly) / dAB;
+                    var perp = new Vector2((float)(x1 + u * lx), (float)(y1 + u * ly));
+                    if (u < minU)
+                    {
+                        endP = perp;
+                        minU = u;
+                    }
+                    if (u > maxU)
+                    {
+                        endQ = perp;
+                        maxU = u;
+                    }
+
+                    var curDist = dist(perp.X, perp.Y, p.X, p.Y);
+                    if (maxDist2Line > -1 && curDist > maxDist2Line) fail = true;
+                    distSum += curDist;
+                }
+
+                return distSum;
+            }
+
+            var kbFail = false;
+            Vector2 endP1 = new Vector2(), endQ1 = new Vector2();
+            double kbDist = CalcDist(ref kbFail, ref endP1, ref endQ1);
+            
+            // x = my + n
+            A = 0;
+            B = 0;
+            C = 0;
+            D = 0;
+            foreach (var p in pts)
+            {
+                A += p.X * p.Y;
+                B += p.Y * p.Y;
+                C += p.Y;
+                D += p.X;
+            }
+
+            tmp = C * C - B * pts.Count;
+            var m = (C * D - A * pts.Count) / tmp;
+            var n = (A * C - B * D) / tmp;
+            y1 = 0;
+            x1 = m * y1 + n;
+            y2 = 1000;
+            x2 = m * y2 + n;
+
+            var mnFail = false;
+            Vector2 endP2 = new Vector2(), endQ2 = new Vector2();
+            double mnDist = CalcDist(ref mnFail, ref endP2, ref endQ2);
+
+            Vector2 endP = endP1, endQ = endQ1;
+            if (mnDist < kbDist)
+            {
+                if (mnFail) return (false, new Vector2(), new Vector2());
+                endP = endP2;
+                endQ = endQ2;
+            }
+            else if (kbFail) return (false, new Vector2(), new Vector2());
+
+            return (true, endP, endQ);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static int toId(int x, int y, int z)
+        {
+            return (x * 1140671485 + 12820163) ^ (y * 134775813 + 1) ^ (z * 1103515245 + 12345);
+        }
+
+        public class Clustering<T>
+        {
+	        public int numIteration = 3;
+	        public int itemNumThreshold = 10;
+
+	        public Func<T, T, bool> inRange;
+	        public Func<List<T>, T> average;
+	        private readonly List<T> _inputData;
+	        private Dictionary<T, List<T>> _clusters = new Dictionary<T, List<T>>();
+
+	        public Clustering(List<T> data, Func<T, T, bool> inRange, Func<List<T>, T> average)
+	        {
+		        _inputData = data;
+		        this.inRange = inRange;
+		        this.average = average;
+	        }
+
+	        public Dictionary<T, List<T>> GetClusters()
+	        {
+		        var tmp = new List<(T center, List<T> items)>();
+
+		        for (var iter = 0; iter < numIteration; iter++)
+		        {
+			        tmp = tmp.Where(cluster => cluster.items.Count > itemNumThreshold)
+				        .Select(cluster => (average(cluster.items), new List<T>())).ToList();
+
+			        foreach (var data in _inputData)
+			        {
+				        var added = false;
+				        foreach (var cluster in tmp)
+				        {
+					        if (inRange(cluster.center, data))
+					        {
+						        cluster.items.Add(data);
+						        added = true;
+						        break;
+					        }
+				        }
+
+				        if (!added)
+					        tmp.Add((data, new List<T>() { data }));
+			        }
+		        }
+
+		        _clusters = tmp.Where(cluster => cluster.items.Count > itemNumThreshold)
+			        .ToDictionary(cluster => cluster.center, cluster => cluster.items);
+		        return _clusters;
+	        }
+        }
+
+        public static (bool, Vector2) TwoLinesIntersection(Vector2 A, Vector2 B, Vector2 C, Vector2 D)
+        {
+	        // Line AB represented as a1x + b1y = c1
+	        double a1 = B.Y - A.Y;
+	        double b1 = A.X - B.X;
+	        double c1 = a1 * (A.X) + b1 * (A.Y);
+
+	        // Line CD represented as a2x + b2y = c2
+	        double a2 = D.Y - C.Y;
+	        double b2 = C.X - D.X;
+	        double c2 = a2 * (C.X) + b2 * (C.Y);
+
+	        double determinant = a1 * b2 - a2 * b1;
+
+	        if (determinant == 0)
+	        {
+		        // The lines are parallel. This is simplified
+		        // by returning a pair of FLT_MAX
+		        return new(false, new Vector2());
+	        }
+	        else
+	        {
+		        double x = (b2 * c1 - b1 * c2) / determinant;
+		        double y = (a1 * c2 - a2 * c1) / determinant;
+		        return (true, new Vector2((float)x, (float)y));
+	        }
+        }
+
+        public static bool IsAtLeft(Vector2 anchor, Vector2 dest, Vector2 p)
+        {
+	        var v1 = new Vector3(anchor - p, 0);
+	        var v2 = new Vector3(dest - p, 0);
+	        return Vector3.Cross(v1, v2).Z > 0;
+        }
+
+        /// <summary>
+        /// 将角度转化至-180到180度的范围内。
+        /// </summary>
+        /// <param name="th"></param>
+        /// <returns></returns>
+        public static double RoundTh(double th)
+        {
+	        return th - System.Math.Round(th / 360) * 360;
+        }
+
+        /// <summary>
+        /// 将角度转化至-180到180度的范围内。
+        /// </summary>
+        /// <param name="th"></param>
+        /// <returns></returns>
+        public static float RoundTh(float th)
+        {
+	        return th - (float)System.Math.Round(th / 360f) * 360f;
+        }
+	}
+}
@@ -0,0 +1,161 @@
+using System;
+using System.Numerics;
+
+namespace CommonUsage.Mathematics
+{
+	/// <summary>
+	/// 表示一条线段。
+	/// </summary>
+	public class LineSegment
+	{
+		/// <summary>
+		/// 默认构造函数。所有坐标初始化为0。
+		/// </summary>
+		public LineSegment()
+		{
+
+		}
+
+		/// <summary>
+		/// 使用两个端点初始化一段2D线段。
+		/// </summary>
+		/// <param name="src">线段起点。</param>
+		/// <param name="dst">线段终点。</param>
+		public LineSegment(Vector2 src, Vector2 dst)
+		{
+			Src = src;
+			Dst = dst;
+		}
+
+		/// <summary>
+		/// 使用两个端点初始化一段3D线段。
+		/// </summary>
+		/// <param name="src">线段起点。</param>
+		/// <param name="dst">线段终点。</param>
+		public LineSegment(Vector3 src, Vector3 dst)
+		{
+			Src3D = src;
+			Dst3D = dst;
+		}
+
+		/// <summary>
+		/// 使用两个端点初始化一条线段，2D。
+		/// </summary>
+		/// <param name="x1">线段起点x坐标。</param>
+		/// <param name="y1">线段起点y坐标。</param>
+		/// <param name="x2">线段终点x坐标。</param>
+		/// <param name="y2">线段终点y坐标。</param>
+		public LineSegment(double x1, double y1, double x2, double y2)
+		{
+			Src = new Vector2((float)x1, (float)y1);
+			Dst = new Vector2((float)x2, (float)y2);
+		}
+
+		/// <summary>
+		/// 使用两个端点初始化一条线段，2D。
+		/// </summary>
+		/// <param name="x1">线段起点x坐标。</param>
+		/// <param name="y1">线段起点y坐标。</param>
+		/// <param name="z1">线段起点y坐标。</param>
+		/// <param name="x2">线段终点x坐标。</param>
+		/// <param name="y2">线段终点y坐标。</param>
+		/// <param name="z2">线段终点y坐标。</param>
+		public LineSegment(double x1, double y1, double z1, double x2, double y2, double z2)
+		{
+			Src3D = new Vector3((float)x1, (float)y1, (float)z1);
+			Dst3D = new Vector3((float)x2, (float)y2, (float)z2);
+		}
+
+		/// <summary>
+		/// 返回线段长度，2D。
+		/// </summary>
+		/// <returns></returns>
+		public double Length()
+		{
+			return Vector2.Distance(Src, Dst);
+		}
+
+		/// <summary>
+		/// 返回线段长度，3D。
+		/// </summary>
+		/// <returns></returns>
+		public double Length3D()
+		{
+			return Vector3.Distance(Src3D, Dst3D);
+		}
+
+		/// <summary>
+		/// 返回线段与x轴正方向夹角度数，角度制。
+		/// </summary>
+		/// <returns></returns>
+		public double Angle()
+		{
+			return Math.Atan2(Dst.Y - Src.Y, Dst.X - Src.X) / Math.PI * 180;
+		}
+
+		/// <summary>
+		/// 返回一段方向相反的线段。
+		/// </summary>
+		/// <returns></returns>
+		public LineSegment Reverse()
+		{
+			return new LineSegment(Dst3D, Src3D);
+		}
+
+		/// <summary>
+		/// 线段2D起点。
+		/// </summary>
+		public Vector2 Src
+		{
+			get => new(_srcX, _srcY);
+			set
+			{
+				_srcX = value.X;
+				_srcY = value.Y;
+			}
+		}
+
+		/// <summary>
+		/// 线段2D终点。
+		/// </summary>
+		public Vector2 Dst
+		{
+			get => new(_dstX, _dstY);
+			set
+			{
+				_dstX = value.X;
+				_dstY = value.Y;
+			}
+		}
+
+		/// <summary>
+		/// 线段3D起点。
+		/// </summary>
+		public Vector3 Src3D
+		{
+			get => new(_srcX, _srcY, _srcZ);
+			set
+			{
+				_srcX = value.X;
+				_srcY = value.Y;
+				_srcZ = value.Z;
+			}
+		}
+
+		/// <summary>
+		/// 线段3D终点。
+		/// </summary>
+		public Vector3 Dst3D
+		{
+			get => new(_dstX, _dstY, _dstZ);
+			set
+			{
+				_dstX = value.X;
+				_dstY = value.Y;
+				_dstZ = value.Z;
+			}
+		}
+
+		private float _srcX, _srcY, _srcZ, _dstX, _dstY, _dstZ;
+	}
+}
@@ -0,0 +1,12 @@
+{
+  "profiles": {
+    "CommonUsage": {
+      "commandName": "Project"
+    },
+    "配置文件 1": {
+      "commandName": "Executable",
+      "executablePath": "D:\\Code\\Core\\Medulla\\build\\Medulla.exe",
+      "workingDirectory": "D:\\Code\\Core\\Medulla\\build\\"
+    }
+  }
+}
@@ -0,0 +1,19 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050
+{
+    public class CommunicationProtocolFactory
+    {
+        public static IVDACommunicationProtocol CreateProtocol(string protocolType, string host, int port)
+        {
+            return protocolType.ToLower() switch
+            {
+                "http" => new HTTPCommunication(host, port),
+                "mqtt" => new MQTTCommunication(host, port),
+                _ => throw new NotSupportedException($"Protocol {protocolType} is not supported")
+            };
+        }
+    }
+}
@@ -0,0 +1,94 @@
+using System;
+using System.Collections.Generic;
+using System.Net.Http;
+using System.Text;
+using System.Threading.Tasks;
+using CommonUsage.Protocols.VDA5050.Messages;
+using FundamentalLib;
+using Newtonsoft.Json;
+
+namespace CommonUsage.Protocols.VDA5050
+{
+    public class HTTPCommunication : IVDACommunicationProtocol
+    {
+        private readonly string _host;
+        private readonly int _port;
+
+        public HTTPCommunication(string host, int port)
+        {
+            _host = host;
+            _port = port;
+        }
+
+        public async Task PublishConnectionStatus(string status)
+        {
+            var message = new connectionMessage()
+            {
+                serialNumber = "test-01",
+                headerId = 1,
+                timestamp = DateTime.Now,
+                connectionState = status
+            };
+
+            await SendMessageAsync(message, "vda5050/connection");
+        }
+
+        public void SetupOrderListener(Action<orderMessage> orderReceived)
+        {
+            PicoHttpServer.AddPostTextHandler("/order", new { }, (_, str) =>
+            {
+                var order = JsonConvert.DeserializeObject<orderMessage>(str);
+                orderReceived(order);
+                return "";
+            });
+        }
+
+        public void SetUpInstanActionListener(Action<instanceAction> onInstanceActionReceived)
+        {
+            PicoHttpServer.AddPostTextHandler("/instanceAction", new { }, (_, str) =>
+            {
+                var instanceAction = JsonConvert.DeserializeObject<instanceAction>(str);
+                onInstanceActionReceived(instanceAction);
+                return "";
+            });
+        }
+
+        public void SetUpImmediateCommandListener(Action<string> onChangeCarFieldsReceived)
+        {
+            throw new NotImplementedException();
+        }
+
+        public async Task SendMessageAsync<T>(T message, string topic)
+        {
+            try
+            {
+                var url = $"http://{_host}:{_port}/{topic}";
+                using var client = new HttpClient();
+                var response = await client.PostAsync(url, new StringContent(JsonConvert.SerializeObject(message), Encoding.UTF8, "application/json"));
+
+                if (!response.IsSuccessStatusCode)
+                {
+                    Console.WriteLine($" >> Sending Message: Failed to send message. Status Code: {response.StatusCode}");
+                }
+            }
+            catch (Exception ex)
+            {
+                Console.WriteLine($"Error in sending message: {ex.Message}");
+            }
+        }
+
+        public async Task SendVisualizationMessageAsync<T>(T msg, string topic)
+        {
+            throw new NotImplementedException();
+        }
+
+        public void SetupTestListener(Action<string> testMsg)
+        {
+            throw new NotImplementedException();
+        }
+        public async Task PublishFactSheet(factsheetMessage message)
+        {
+            throw new NotImplementedException();
+        }
+    }
+}
@@ -0,0 +1,19 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+using System.Threading.Tasks;
+using CommonUsage.Protocols.VDA5050.Messages;
+
+namespace CommonUsage.Protocols.VDA5050
+{
+    public interface IVDACommunicationProtocol
+    {
+        Task PublishConnectionStatus(string status);
+        Task PublishFactSheet(factsheetMessage msg);
+        void SetupOrderListener(Action<orderMessage> orderReceived);
+        void SetUpInstanActionListener(Action<instanceAction> onInstanceActionReceived);
+        void SetUpImmediateCommandListener(Action<string> onChangeCarFieldsReceived);
+        Task SendMessageAsync<T>(T message, string topic);
+        Task SendVisualizationMessageAsync<T>(T message, string topic);
+    }
+}
@@ -0,0 +1,319 @@
+using System.IO;
+using System;
+using System.Collections.Generic;
+using System.Text;
+using System.Threading;
+using System.Threading.Tasks;
+using CommonUsage.Protocols.VDA5050.Messages;
+using MQTTnet;
+using MQTTnet.Client;
+using MQTTnet.Extensions.ManagedClient;
+using MQTTnet.Packets;
+using MQTTnet.Protocol;
+using MQTTnet.Server;
+using Newtonsoft.Json;
+using FundamentalLib;
+using CommonUsage.Protocols.VDA5050.Objects;
+using FundamentalLib.MiscHelpers;
+
+namespace CommonUsage.Protocols.VDA5050
+{
+    public class MQTTCommunication : IVDACommunicationProtocol
+    {
+        private readonly string _host;
+        private readonly int _port;
+        private readonly string _orderTopic = "vda5050/frldAGV/order";
+        private readonly string _connectionTopic = "vda5050/frldAGV/connection";
+        private readonly string _instanceAction = "vda5050/frldAGV/instantActions";
+        private readonly string _factsheet = "vda5050/frldAGV/factsheet";
+        private readonly string _changeCarFields = "vda5050/frldAGV/changeCarFields";
+
+        private IManagedMqttClient _client;
+        private IManagedMqttClient _visualizationClient;
+
+        public MQTTCommunication(string host, int port)
+        {
+            _host = host;
+            _port = port;
+            InitializeClient();
+            InitializeVisualizationClient();
+        }
+
+        private void InitializeClient()
+        {
+            var willMessage = new connectionMessage()
+            {
+                headerId = 1,
+                timestamp = DateTime.Now,
+                version = "00",
+                manufacturer = "frld",
+                serialNumber = "test-01",
+                connectionState = "CONNECTIONBROKEN"
+            };
+
+            var mqttClientOptions = new MqttClientOptionsBuilder()
+                .WithClientId("AGV-Client-frldAGV")
+                .WithTcpServer(_host, _port)
+                .WithWillTopic(_connectionTopic)
+                .WithWillPayload(JsonConvert.SerializeObject(willMessage))
+                 .WithWillRetain(true)
+                .Build();
+
+            var managedMqttClientOptions = new ManagedMqttClientOptionsBuilder()
+                .WithClientOptions(mqttClientOptions)
+                .WithMaxPendingMessages(20)
+                .WithPendingMessagesOverflowStrategy(MqttPendingMessagesOverflowStrategy.DropOldestQueuedMessage)
+                .Build();
+
+            _client = new MqttFactory().CreateManagedMqttClient();
+            _client.StartAsync(managedMqttClientOptions).GetAwaiter().GetResult();
+            Console.WriteLine($" >> MQTT client initialized and connected to broker at {_host} - {_port}");
+        }
+
+        private void InitializeVisualizationClient()
+        {
+            var mqttClientOptions = new MqttClientOptionsBuilder()
+                .WithClientId("AGV-Visualization")
+                .WithTcpServer(_host, _port)
+                .Build();
+
+            var managedMqttClientOptions = new ManagedMqttClientOptionsBuilder()
+                .WithClientOptions(mqttClientOptions)
+                .WithMaxPendingMessages(10) // Prevent overloading
+                .WithPendingMessagesOverflowStrategy(MqttPendingMessagesOverflowStrategy.DropOldestQueuedMessage)
+                .Build();
+
+            _visualizationClient = new MqttFactory().CreateManagedMqttClient();
+            _visualizationClient.StartAsync(managedMqttClientOptions).GetAwaiter().GetResult();
+            Console.WriteLine("MQTT Visualization client initialized.");
+        }
+
+        public void SetUpImmediateCommandListener(Action<string> onChangeCarFieldsReceived)
+        {
+            Console.WriteLine($"Subscribed to the topic: {_changeCarFields}");
+            _client.SubscribeAsync(_changeCarFields).GetAwaiter().GetResult();
+
+            _client.ApplicationMessageReceivedAsync += async e =>
+            {
+                if (e.ApplicationMessage.Topic == _changeCarFields)
+                {
+                    var payload = Encoding.UTF8.GetString(e.ApplicationMessage.Payload);
+                    LogMessage($"RECEIVE-{e.ApplicationMessage.Topic}", e.ApplicationMessage.Topic, payload);
+                    //var script = JsonConvert.DeserializeObject<string>(payload);
+                    Console.WriteLine($"Change car field: {payload}");
+                    onChangeCarFieldsReceived(payload);
+                }
+            };
+        }
+
+
+        public void SetUpInstanActionListener(Action<instanceAction> onInstanceActionReceived)
+        {
+            Console.WriteLine($"Subscribed to the topic: {_instanceAction}");
+
+            // Subscribe to the instanceAction topic
+            _client.SubscribeAsync(_instanceAction).GetAwaiter().GetResult();
+
+            _client.ApplicationMessageReceivedAsync += async e =>
+            {
+                if (e.ApplicationMessage.Topic == _instanceAction)
+                {
+                    var payload = Encoding.UTF8.GetString(e.ApplicationMessage.Payload);
+                    LogMessage($"RECEIVE-{e.ApplicationMessage.Topic}", e.ApplicationMessage.Topic, payload);
+                    var actions = JsonConvert.DeserializeObject<instanceAction>(payload);
+                    Console.WriteLine($"Received instance action: Header ID = {actions.headerId}, Timestamp = {actions.timestamp}");
+                    foreach (var action in actions.actions)
+                    {
+                        Console.WriteLine($"Action ID: {action.actionId}, Type: {action.actionType}");
+                    }
+
+                    onInstanceActionReceived(actions);
+                }
+            };
+        }
+
+        public async Task PublishConnectionStatus(string status)
+        {
+            var message = new connectionMessage()
+            {
+                headerId = 1,
+                timestamp = DateTime.Now,
+                version = "00",
+                manufacturer = "frld",
+                serialNumber = "test-01",
+                connectionState = status
+            };
+
+            var payload = JsonConvert.SerializeObject(message);
+
+            var content = new MqttApplicationMessageBuilder()
+                .WithTopic(_connectionTopic)
+                .WithPayload(payload)
+                .WithQualityOfServiceLevel(MqttQualityOfServiceLevel.AtLeastOnce)
+                .WithRetainFlag(true)
+                .Build();
+
+            await _client.EnqueueAsync(content);
+            LogMessage($"SEND-{_connectionTopic}", _connectionTopic, payload);
+
+            //await SendMessageAsync(message, _connectionTopic);
+        }
+
+        public async Task PublishFactSheet(factsheetMessage message)
+        {
+         
+            //await SendMessageAsync(message, _factsheet);
+            var payload = JsonConvert.SerializeObject(message);
+
+            var content = new MqttApplicationMessageBuilder()
+                .WithTopic(_factsheet)
+                .WithPayload(payload)
+                .WithQualityOfServiceLevel(MqttQualityOfServiceLevel.AtMostOnce)
+                //.WithRetainFlag(true)
+                .Build();
+
+            await _client.EnqueueAsync(content);
+            LogMessage($"SEND-{_factsheet}", _factsheet, payload);
+
+        }
+
+        public void SetupOrderListener(Action<orderMessage> orderReceived)
+        {
+            // Subscribe to the orders topic
+            _client.SubscribeAsync(_orderTopic, MqttQualityOfServiceLevel.AtMostOnce).GetAwaiter().GetResult();
+            _client.ApplicationMessageReceivedAsync += async e =>
+            {
+                if (e.ApplicationMessage.Topic == _orderTopic)
+                {
+                    var payload = Encoding.UTF8.GetString(e.ApplicationMessage.Payload);
+                    LogMessage($"RECEIVE-{e.ApplicationMessage.Topic}", e.ApplicationMessage.Topic, payload);
+                    var order = JsonConvert.DeserializeObject<orderMessage>(payload);
+
+                    // Save the order message to a file for debugging
+                    // SaveOrderToFile(payload);
+                    orderReceived(order);
+                }
+                await Task.CompletedTask;
+            };
+        }
+
+        private void SaveOrderToFile(string orderJson)
+        {
+            try
+            {
+                // Specify the file path (e.g., orders_log.txt in the current directory)
+                string filePath = "orders_log.txt";
+
+                // Append the order JSON along with a timestamp
+                File.AppendAllText(filePath, $"{DateTime.UtcNow:yyyy-MM-dd HH:mm:ss} - {orderJson}{Environment.NewLine}");
+            }
+            catch (Exception ex)
+            {
+                // Handle any exceptions that occur while writing to the file
+                Console.WriteLine($"Failed to save order to file: {ex.Message}");
+            }
+        }
+
+        public async Task SendMessageAsync<T>(T message, string topic)
+        {
+
+            var payload = JsonConvert.SerializeObject(message);
+
+            var content = new MqttApplicationMessageBuilder()
+                .WithTopic(topic)
+                .WithPayload(payload)
+                .WithQualityOfServiceLevel(MqttQualityOfServiceLevel.AtMostOnce)
+                .Build();
+
+            await _client.EnqueueAsync(content);
+
+            if (topic != "vda5050/frldAGV/visualization")
+            {
+
+                LogMessage($"SEND-{topic}", topic, payload);
+            }
+           
+        }
+
+        public async Task SendVisualizationMessageAsync<T>(T message, string topic)
+        {
+            if (_visualizationClient == null) return; // Ensure client is initialized
+
+            var payload = JsonConvert.SerializeObject(message);
+
+            var content = new MqttApplicationMessageBuilder()
+                .WithTopic(topic)
+                .WithPayload(payload)
+                .WithQualityOfServiceLevel(MqttQualityOfServiceLevel.AtMostOnce) // QoS 0 for lightweight visualization
+                .Build();
+
+            if (_visualizationClient.PendingApplicationMessagesCount < 5) // Prevent flooding
+            {
+                await _visualizationClient.EnqueueAsync(content);
+            }
+            else
+            {
+                Console.WriteLine("Skipping visualization update to avoid MQTT congestion.");
+            }
+        }
+
+
+        public void LogMessage(string direction, string topic, string payload)
+        {
+            string formattedPayload = payload;
+            string logDirectory = "Logs"; // Directory for log files
+            var filePreName = direction;
+            filePreName = filePreName.Replace("/", "_");
+            string logFilePath = Path.Combine(logDirectory, filePreName + $"-{DateTime.Now:yyyy-MM-dd}.log");
+
+            if(!Directory.Exists(logDirectory)) Directory.CreateDirectory(logDirectory);
+            // Try to parse the payload as JSON and pretty-print it
+            try
+            {
+                var jsonObject = JsonConvert.DeserializeObject(payload);
+                formattedPayload = JsonConvert.SerializeObject(jsonObject, Formatting.Indented);
+            }
+            catch (JsonReaderException)
+            {
+                // If the payload is not valid JSON, just leave it as is
+                formattedPayload = payload;
+            }
+
+            string logMessage = $"[{DateTime.Now:HH:mm:ss}] [{direction}] Topic: {topic}, Payload:\n{formattedPayload}\n";
+            RotateLogFile(logFilePath, logDirectory);
+
+            try
+            {
+                File.AppendAllText(logFilePath, logMessage + Environment.NewLine);
+            }
+            catch (Exception ex)
+            {
+                Console.WriteLine($"Error writing to log file: {ex.Message}");
+            }
+            // Console.WriteLine($"[{DateTime.Now:HH:mm:ss}] [{direction}] Topic: {topic}, Payload: {formattedPayload}");
+            // DLog.Log($"[{DateTime.Now:HH:mm:ss}] [{direction}] Topic: {topic}, Payload: {formattedPayload}");
+        }
+
+
+        private void RotateLogFile(string logFilePath, string logDirectory)
+        {
+            const long maxFileSize = 10 * 1024 * 1024; // 10 MB in bytes
+
+            FileInfo fileInfo = new FileInfo(logFilePath);
+            if (fileInfo.Exists && fileInfo.Length > maxFileSize)
+            {
+                string archivePath = Path.Combine(logDirectory, $"log_{DateTime.Now:yyyy-MM-dd_HH-mm-ss}.log");
+
+                try
+                {
+                    File.Move(logFilePath, archivePath); // Rename the current log file
+                    Console.WriteLine($"Log file rotated: {archivePath}");
+                }
+                catch (Exception ex)
+                {
+                    Console.WriteLine($"Error rotating log file: {ex.Message}");
+                }
+            }
+        }
+    }
+}
@@ -0,0 +1,18 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Messages
+{
+    public class connectionMessage
+    {
+        public int headerId;
+        public DateTime timestamp;
+        public string version = "";
+        public string manufacturer = "";
+        public string serialNumber = "";
+        public string connectionState = "";  // Enum: {'ONLINE', 'OFFLINE', 'CONNECTIONBROKEN'}
+        
+    }
+
+}
@@ -0,0 +1,16 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Messages
+{
+    public class errorMessage
+    {
+        public string serialNumber = "";
+        public string errorCode = "";  // Unique error code
+        public string description = "";  // Error description
+        public string severity = "";  // Enum {'WARNING', 'FATAL'}
+        public DateTime timestamp;  // Time of the error
+    }
+
+}
@@ -0,0 +1,23 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+using CommonUsage.Protocols.VDA5050.Objects;
+
+namespace CommonUsage.Protocols.VDA5050.Messages
+{
+    public class factsheetMessage
+    {
+        public int headerId;
+        public DateTime timestamp;
+        public string version = "";
+        public string manufacturer = "";
+        public string serialNumber = "";
+
+        public typeSpecification typeSpecification;
+        public physicalParameters physicalParameters;
+        public protocolLimits protocolLimits;
+        public protocolFeatures protocolFeatures;
+        public agvGeometry agvGeometry;
+    }
+
+}
@@ -0,0 +1,19 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+using CommonUsage.Protocols.VDA5050.Objects;
+
+namespace CommonUsage.Protocols.VDA5050.Messages
+{
+    public class instanceAction
+    {
+
+        public uint headerId { get; set; } // Incremented for each new message.
+        public string timestamp { get; set; } // ISO 8601 UTC timestamp.
+        public string version { get; set; } // Protocol version.
+        public string manufacturer { get; set; } // AGV manufacturer.
+        public string serialNumber { get; set; } // Unique AGV serial number.
+
+        public List<actionState> actions { get; set; }
+    }
+}
@@ -0,0 +1,27 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+using CommonUsage.Protocols.VDA5050.Objects;
+
+namespace CommonUsage.Protocols.VDA5050.Messages
+{
+    public class orderMessage
+    {
+        public uint headerId;
+        public string timestamp = "";
+        public string version = "";
+        public string manufacturer = "";
+        public string serialNumber = "";
+
+        public string orderId { get; set; }
+
+        public uint orderUpdateId { get; set; }
+
+        public node[] nodes { get; set; }
+
+        public edge[] edges { get; set; }
+
+        //public action[] action { get; set; }
+    }
+}
+
@@ -0,0 +1,69 @@
+using System;
+using System.Collections.Generic;
+using System.ComponentModel;
+using CommonUsage.Protocols.VDA5050.Objects;
+
+namespace CommonUsage.Protocols.VDA5050.Messages
+{
+    /// <summary>
+    /// 6.10 Topic: "state" (from AGV to master control)
+    /// todo: complete all fields required by VDA5050
+    /// </summary>
+    public class stateMessage
+    {
+        public uint headerId;
+        public string timestamp = "";
+        public string version = "";
+        public string manufacturer = "";
+        public string serialNumber = "";
+        /// <summary>
+        /// Unique order identification of the current order or the previously finished order.
+        /// The orderId is kept until a new order is received.
+        /// Empty string (""), if no previous orderId is available.
+        /// </summary>
+        public string orderId = "";
+
+        /// <summary>
+        /// Order update identification to identify, that an order update has been accepted by the AGV.
+        /// "0" if no previous orderUpdateId is available.
+        /// </summary>
+        public uint orderUpdatedId = 0;
+
+        public string lastNodeId;
+
+        public uint lastNodeSequenceId;
+
+        /// <summary>
+        /// Array of nodeState objects that need to be traversed for fulfilling the order (empty array if idle)
+        /// </summary>
+        public nodeState[] nodeStates = [];
+
+        /// <summary>
+        /// Array of edgeState objects that need to be traversed for fulfilling the order (empty array if idle)
+        /// </summary>
+        public edgeState[] edgeStates = [];
+
+        public agvPosition agvPosition;
+
+        public velocity velocity;
+        public load[] loads = [];
+
+        public bool driving;
+
+        public bool paused;
+
+        public bool newBaseRequest;
+
+        public double distanceSinceLastNode;
+
+        public batteryState batteryState;
+
+        public actionState[] actionStates = Array.Empty<actionState>();
+        public string operatingMode = "";
+        public List<errorState> errors { get; set; } = new List<errorState>(); // Array of errorState objects
+
+        public info[] information = [];
+        public safetyState safetyState;
+
+    }
+}
@@ -0,0 +1,12 @@
+using CommonUsage.Protocols.VDA5050.Objects;
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Messages
+{
+    public class visualizationMessage
+    {
+        public agvPosition agvPosition;
+    }
+}
@@ -0,0 +1,18 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class action
+    {
+
+        public string actionId { get; set; }
+
+        public string actionType { get; set; }
+        public string actionDescription { get; set; }
+
+        public string blockingType { get; set; }
+
+    }
+}
@@ -0,0 +1,45 @@
+using Newtonsoft.Json.Converters;
+using Newtonsoft.Json;
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class actionState
+    {
+        public actionState(action action,ActionStateEnum state)
+        {
+            actionId = action.actionId;
+            actionDescription = action.actionDescription;
+            actionType = action.actionType;
+            actionStatus = state;
+        }
+
+        public actionState()
+        {
+        }
+
+        public string actionId { get; set; }
+
+        public string actionType { get; set; }
+        public string actionDescription { get; set; }
+
+        [JsonConverter(typeof(StringEnumConverter))]
+        public ActionStateEnum actionStatus { get; set; }
+
+        public string resultDescription { get; set; }
+
+        public enum ActionStateEnum
+        {
+            WAITING,
+            INITIALIZING,
+            RUNNING,
+            PAUSED,
+            FINISHED,
+            FAILED
+        }
+
+    }
+
+}
@@ -0,0 +1,63 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+using static CommonUsage.Protocols.VDA5050.Objects.agvGeometry;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class agvGeometry
+    {
+        // Wheel Definitions
+        public List<wheelDefinition> wheelDefinitions { get; set; } = new List<wheelDefinition>();
+
+        // 2D Envelopes
+        public List<envelope2D> envelopes2D { get; set; } = new List<envelope2D>();
+
+        // 3D Envelopes
+        public List<envelope3D> envelopes3D { get; set; } = new List<envelope3D>();
+
+        public class wheelDefinition
+        {
+            public enum WheelType { DRIVE, CASTER, FIXED, MECANUM }
+
+            public WheelType type { get; set; }
+            public bool isActiveDriven { get; set; }
+            public bool isActiveSteered { get; set; }
+
+            // Wheel Position
+            public double positionX { get; set; }
+            public double positionY { get; set; }
+            public double positionTheta { get; set; }  // Required for fixed wheels
+
+            // Wheel Properties
+            public double diameter { get; set; }
+            public double width { get; set; }
+            public double centerDisplacement { get; set; } = 0;  // Default to 0 if not defined
+            public string constraints { get; set; }
+        }
+
+        public class envelope2D
+        {
+            public string set { get; set; }
+            public List<polygonPoint> polygonPoints { get; set; } = new List<polygonPoint>();
+            public string description { get; set; }
+
+            public class polygonPoint
+            {
+                public double x { get; set; }
+                public double y { get; set; }
+            }
+        }
+
+        public class envelope3D
+        {
+            public string set { get; set; }
+            public string format { get; set; }
+            public object data { get; set; }  // JSON object for 3D envelope data
+            public string url { get; set; }
+            public string description { get; set; }
+        }
+    }
+
+}
+
@@ -0,0 +1,21 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class agvPosition
+    {
+        public bool positionInitialized;
+
+        public double x;
+
+        public double y;
+
+        public double theta;
+        public double localizationScore;
+        public double deviationRange;
+        public string mapId = "";
+        public string mapDescription = "";
+    }
+}
@@ -0,0 +1,15 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class batteryState
+    {
+        public double batteryCharge;
+        public double batteryVoltage;
+        public double batteryHealth;
+        public bool charging;
+        public int reach;
+    }
+}
@@ -0,0 +1,14 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class boundingBoxReference
+    {
+        public double X { get; set; } // Reference point X in AGV coordinate system
+        public double Y { get; set; } // Reference point Y in AGV coordinate system
+        public double Z { get; set; } // Reference point Z in AGV coordinate system
+        public double Theta { get; set; } // Orientation of the load bounding box
+    }
+}
@@ -0,0 +1,21 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class controlPoint
+    {
+        public float x;
+
+        public float y;
+
+        public float weight;
+        public controlPoint(float x, float y, float weight)
+        {
+            this.x = x;
+            this.y = y;
+            this.weight = weight;
+        }
+    }
+}
@@ -0,0 +1,31 @@
+using System;
+using System.Collections.Generic;
+using System.Numerics;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class edge : sequenceItem
+    {
+        public string edgeId;
+
+        public string edgeDescription;
+
+        public string startNodeId;
+
+        public string endNodeId;
+
+        public double maxSpeed;
+
+        public double orientation;
+
+        public trajectory? trajectory;
+
+        public float[] trackTypeInfo;
+        // public List<Vector2> controlPoints;
+        //
+        // public List<float> weights;
+
+        public action[] action = [];
+    }
+}
@@ -0,0 +1,15 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class edgeState : sequenceItem
+    {
+        public string edgeId;
+
+        public string edgeDescription;
+
+        public trajectory trajectory;
+    }
+}
@@ -0,0 +1,12 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class errorReference
+    {
+        public string referenceKey { get; set; } // Type of reference (e.g., nodeId, edgeId, actionId)
+        public string referenceValue { get; set; } // Value corresponding to the referenceKey
+    }
+}
@@ -0,0 +1,15 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class errorState
+    {
+        public List<errorReference> errorReferences { get; set; } = new List<errorReference>(); // Array of references
+        public string errorType { get; set; } // Required: Type/name of the error
+        public string errorDescription { get; set; } // Verbose description of the error
+        public string errorHint { get; set; } // Hint for resolving the error
+        public string errorLevel { get; set; } // Required: WARNING or FATAL
+    }
+}
@@ -0,0 +1,26 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class info
+    {
+        public string infoType { get; set; } // Type/name of the information
+        public List<infoReference> infoReferences { get; set; } = new List<infoReference>(); // List of references
+        public string infoDescription { get; set; } // Description of the information
+        public infoLevelEnum infoLevel { get; set; } // Debugging or visualization level
+
+        public class infoReference
+        {
+            public string ReferenceKey { get; set; } // Reference type (e.g., headerId, orderId)
+            public string ReferenceValue { get; set; } // The actual referenced field value
+        }
+
+        public enum infoLevelEnum
+        {
+            DEBUG, // Used for debugging
+            INFO   // Used for visualization
+        }
+    }
+}
@@ -0,0 +1,16 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class load
+    {
+        public string loadId { get; set; } // Unique ID (barcode, RFID, etc.)
+        public string loadType { get; set; } // Type of load
+        public string loadPosition { get; set; } // Load handling position (e.g., "front", "back")
+        public boundingBoxReference boundingBoxReference { get; set; } = new boundingBoxReference();
+        public loadDimensions loadDimensions { get; set; } = new loadDimensions();
+        public double weight { get; set; } // Weight of load in kg (0.0 to ∞)  
+    }
+}
@@ -0,0 +1,13 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class loadDimensions
+    {
+        public double Length { get; set; } // Length of the bounding box
+        public double Width { get; set; } // Width of the bounding box
+        public double Height { get; set; } // Height of the bounding box (optional)
+    }
+}
@@ -0,0 +1,17 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class node : sequenceItem
+    {
+        public string nodeId;
+
+        public string nodeDescription;
+
+        public nodePosition nodePosition;
+
+        public action[] actions = [];
+    }
+}
@@ -0,0 +1,36 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    /// <summary>
+    /// Defines the position on a map in a global project-specific world coordinate system.
+    /// Each floor has its own map.
+    /// All maps shall use the same project-specific global origin.
+    /// </summary>
+    public class nodePosition
+    {
+        /// <summary>
+        /// X-position on the map in reference to the map coordinate system.
+        /// Precision is up to the specific implementation.
+        /// </summary>
+        public double x;
+
+        /// <summary>
+        /// Y-position on the map in reference to the map coordinate system.
+        /// Precision is up to the specific implementation.
+        /// </summary>
+        public double y;
+
+        /// <summary>
+        /// Range: [-Pi ... Pi]
+        /// Absolute orientation of the AGV on the node.
+        /// Optional: vehicle can plan the path by itself. If defined, the AGV has to assume the theta angle on this node.
+        /// If previous edge disallows rotation, the AGV shall rotate on the node.
+        /// If following edge has a differing orientation defined but disallows rotation,
+        /// the AGV is to rotate on the node to the edges desired rotation before entering the edge.
+        /// </summary>
+        public double theta;
+    }
+}
@@ -0,0 +1,26 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class nodeState : sequenceItem
+    {
+        /// <summary>
+        /// Unique node identification.
+        /// </summary>
+        public string nodeId;
+
+        /// <summary>
+        /// Additional information on the node.
+        /// </summary>
+        public string nodeDescription;
+
+        /// <summary>
+        /// Node position.
+        /// The object is defined in 6.6 Topic: "order" (from master control to AGV)
+        /// Optional: Master control has this information. Can be sent additionally, e.g., for debugging purposes.
+        /// </summary>
+        public nodePosition nodePosition;
+    }
+}
@@ -0,0 +1,20 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class physicalParameters
+    {
+        public double speedMin;
+        public double speedMax;
+        public double angularSpeedMin;
+        public double angularSpeedMax;
+        public double accelerationMax;
+        public double decelerationMax;
+        public double heightMin;
+        public double heightMax;
+        public double width;
+        public double length;
+    }
+}
@@ -0,0 +1,10 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class protocolFeatures
+    {
+    }
+}
@@ -0,0 +1,10 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class protocolLimits
+    {
+    }
+}
@@ -0,0 +1,20 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class safetyState
+    {
+        public eStopEnum eStop { get; set; } // Emergency stop status
+        public bool fieldViolation { get; set; } // "true" if a safety field is violated, "false" otherwise
+
+        public enum eStopEnum
+        {
+            AUTOACK, // Auto-acknowledged emergency stop (e.g., triggered by a bumper)
+            MANUAL,  // Manually confirmed emergency stop
+            REMOTE,  // Remote-confirmed emergency stop
+            NONE     // No emergency stop activated
+        }
+    }
+}
@@ -0,0 +1,13 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class sequenceItem
+    {
+        public uint sequenceId;
+
+        public bool released;
+    }
+}
@@ -0,0 +1,15 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class trajectory
+    {
+        public float degree;
+
+        public float[] knotVector;
+
+        public controlPoint[] controlPoints;
+    }
+}
@@ -0,0 +1,15 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class typeSpecification
+    {
+        public string agvKinemantic = "";
+        public string agvClass = "";
+        public double maxLoadMass;
+        public string[] localizationTypes; // Simplified description of localization type (e.g., NATURAL, REFLECTOR, RFID, DMC, GRID)
+        public string[] navigationTypes;  // Path planning types (e.g., 'AUTONOMOUS', 'VIRTUAL_LINE_GUIDED')
+    }
+}
@@ -0,0 +1,15 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050.Objects
+{
+    public class velocity
+    {
+        public double vx;
+
+        public double vy;
+
+        public double omega;
+    }
+}
@@ -0,0 +1,118 @@
+//using CommonUsage.Protocols.VDA5050.Messages;
+//using System;
+//using System.Collections.Generic;
+//using System.Net.Http.Headers;
+//using System.Runtime.CompilerServices;
+//using System.Text;
+//using System.Threading;
+//using System.Threading.Tasks;
+//using CommonUsage.Protocols.VDA5050.Objects;
+//using ClumsyCore.Utilities;
+//using System.Linq;
+//using ClumsyCore.Pilot;
+//using System.Numerics;
+
+//namespace CommonUsage.Protocols.VDA5050
+//{
+//    public abstract class VDA5050Basic
+//    {
+//        protected static IVDACommunicationProtocol _communicationProtocol;
+
+//        public void Enable(IVDACommunicationProtocol protocol)
+//        {
+//            _communicationProtocol = protocol;
+//            Task.Run(() => ManageConnection());
+//            StartVisualizationLoop();
+//        }
+//        private void StartVisualizationLoop()
+//        {
+//            Console.WriteLine("Visualization in CommonUsage");
+//            new Thread(async () =>
+//                {
+//                    while (true)
+//                    {
+//                        var position = GetAGVPosition();
+//                        if (position != null)
+//                        {
+//                            var msg = new stateMessage()
+//                            {
+//                                serialNumber = "test-01",
+//                                agvPosition = new()
+//                                {
+//                                    x = position.Value.X,
+//                                    y = position.Value.Y,
+//                                    theta = position.Value.Theta,
+//                                    positionInitialized = true
+//                                }
+
+//                            };
+//                            await _communicationProtocol.SendMessageAsync(msg, "vda5050/frldAGV/visualization");
+//                        }
+
+//                        Thread.Sleep(100);
+//                    }
+//                })
+//            { Name = "VDA5050TopicVisualization" }.Start();
+//        }
+
+//        private void ManageConnection()
+//        {
+//            while (true)
+//            {
+//                var status = CheckConnectionStatus() ? "ONLINE" : "OFFLINE";
+//                _communicationProtocol.PublishConnectionStatus(status);
+//                Thread.Sleep(1000);
+//            }
+//        }
+
+//        protected List<sequenceItem> OrganizeReceivedSequence(orderMessage order)
+//        {
+//            List<sequenceItem> receivedSequence = new();
+
+//            int ii = 0, jj = 0;
+//            while (true)
+//            {
+//                var edge = order.edges[ii];
+//                var node = order.nodes[jj];
+//                var takeEdge = edge.sequenceId < node.sequenceId;
+
+//                if (takeEdge)
+//                {
+//                    receivedSequence.Add(edge);
+//                    ii++;
+//                    if (ii == order.edges.Length) break;
+//                }
+//                else
+//                {
+//                    receivedSequence.Add(node);
+//                    jj++;
+//                    if (jj == order.nodes.Length) break;
+//                }
+//            }
+//            for (var i = ii; i < order.edges.Length; ++i) receivedSequence.Add(order.edges[i]);
+//            for (var j = jj; j < order.nodes.Length; ++j) receivedSequence.Add(order.nodes[j]);
+
+//            for (var i = 1; i < receivedSequence.Count; i++)
+//            {
+//                if (receivedSequence[i - 1].sequenceId + 1 != receivedSequence[i].sequenceId)
+//                    throw new Exception("stateMessage not continuous!");
+//            }
+
+//            return receivedSequence;
+//        }
+
+//        public virtual bool CheckConnectionStatus()
+//        {
+//            return false;
+//        }
+
+//        protected abstract Vector3? GetAGVPosition();
+//        public struct Vector3
+//        {
+//            public double X;
+//            public double Y;
+//            public double Theta;
+//        }
+//    }
+
+//}
@@ -0,0 +1,11 @@
+using System;
+using System.Collections.Generic;
+using System.Text;
+
+namespace CommonUsage.Protocols.VDA5050
+{
+    public class VDA5050Helper
+    {
+
+    }
+}
@@ -0,0 +1,28 @@
+using System;
+using System.Collections.Generic;
+using System.Drawing;
+using System.Numerics;
+using System.Text;
+
+namespace CommonUsage
+{
+    public class Visualizer
+    {
+        public Action<Color, Vector2, Vector2, bool, bool, int> LineAction;
+
+        public Action<Color, string, Vector2> TextAction;
+
+        public Action Clear;
+
+        public void DrawLine(Color color, Vector2 src, Vector2 dst, bool startArrow = false, bool endArrow = false,
+            int width = 1)
+        {
+            LineAction?.Invoke(color, src, dst, startArrow, endArrow, width);
+        }
+
+        public void DrawText(Color color, string text, Vector2 pos)
+        {
+            TextAction?.Invoke(color, text, pos);
+        }
+    }
+}
@@ -27,11 +27,6 @@
      <Private>false</Private>
    </Reference>

-    <Reference Include="CommonUsage">
-      <HintPath>ref\CommonUsage.dll</HintPath>
-      <Private>false</Private>
-    </Reference>
-
    <Reference Include="MDCSToolBox">
      <HintPath>ref\MDCSToolBox.dll</HintPath>
      <Private>false</Private>
@@ -41,6 +36,9 @@
      <HintPath>ref\CycleGUI.dll</HintPath>
      <Private>false</Private>
    </Reference>
+    <Reference Include="CommonUsage">
+      <HintPath>..\ref\CommonUsage.dll</HintPath>
+    </Reference>
  </ItemGroup>

  <ItemGroup>
@@ -7,9 +7,20 @@
  "targets": {
    ".NETCoreApp,Version=v8.0": {
      "MedullaAdapter/1.0.0": {
+        "dependencies": {
+          "CommonUsage": "1.0.0.0"
+        },
        "runtime": {
          "MedullaAdapter.dll": {}
        }
+      },
+      "CommonUsage/1.0.0.0": {
+        "runtime": {
+          "CommonUsage.dll": {
+            "assemblyVersion": "1.0.0.0",
+            "fileVersion": "1.0.0.0"
+          }
+        }
      }
    }
  },
@@ -18,6 +29,11 @@
      "type": "project",
      "serviceable": false,
      "sha512": ""
+    },
+    "CommonUsage/1.0.0.0": {
+      "type": "reference",
+      "serviceable": false,
+      "sha512": ""
    }
  }
 }
@@ -119,6 +119,10 @@ namespace MyParking.Shared
            // 禁用旧版DirectionAngle/ZeroDirection坐标偏置，
            // 保证SendXYThSpeed直接使用真实车体坐标系。
            ResetToBodyFrame();
+
+            // 停车机器人优先保持当前机械舵角，通过反转轮速表达反向运动，
+            // 避免蟹行正反切换时四个舵轮无意义地旋转180°。
+            _chassis.PreferMinimumSteeringTravel = true;
        }