Added wasd key acceleration movement

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Assets/Scripts/BackgroundMovement.cs

@@ -4,7 +4,8 @@ using UnityEngine;
 
 public class BackgroundMovement : MonoBehaviour
 {
-    bool toggle = false;
+    [SerializeField]
+    GameObject Cone;
     bool grabbed = false;
     int cnt = 0;
     double beta = 0.5f; // v/c
@@ -15,15 +16,44 @@ public class BackgroundMovement : MonoBehaviour
     public double gamma = 1.0f;
     Vector3 orientation;
 
+    bool toggle = false;
+    public bool Toggle
+    {
+        get
+        {
+            return toggle;
+        }
+        set
+        {
+            if(value)
+                transform.parent = Cone.transform;
+            else
+            {
+                transform.parent = null;
+                v = Levelmanager.player.v;
+            }
+
+            toggle = value;
+        }
+    }
+
     // Start is called before the first frame update
     void Start()
     {
-        
+        toggle = false;
+        v = new Vector3(0, 0, 0);
     }
 
-    // Update is called once per frame
-    void Update()
+    void FixedUpdate()
     {
-        
+        if(!toggle)
+        {
+            transform.localPosition = new Vector3(0, 0, 0);
+        }
+        else
+        {
+            transform.Translate((float)Constants.c * Vector3.up * Time.fixedDeltaTime * (float)Levelmanager.player.gamma, Space.World); // move up by 1 second
+            transform.Translate(v * Time.fixedDeltaTime * (float)Levelmanager.player.gamma, Space.World);
+        }
     }
 }

Assets/Scripts/Constants.cs

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
+using MathNet.Numerics.LinearAlgebra;
+using MathNet.Numerics.LinearAlgebra.Double;
 
 public static class Constants
 {
     public static double c => 5; // speed of light.
     public static double Gamma(double v)
     {
-        return 1.0f / Mathf.Sqrt((1 - (float)((v / c) * (v / c))));
+        return 1.0f / Mathf.Sqrt((float)(1 - ((v / c) * (v / c))));
     }
 
     public static double RadianToDegree(double r)
     {
         return r * 180 / Mathf.PI;
     }
+
+    public static Matrix<double> BoostMatrix(Vector3 velocity)
+    {
+        var vmag = velocity.magnitude;
+        var gamma = Constants.Gamma(vmag);
+        var beta = vmag / Constants.c;
+        var betax = velocity.x / Constants.c;
+        var betay = velocity.z / Constants.c;
+        double[,] tmp = { { gamma, -gamma * betax, -gamma * betay}, 
+                          { -gamma * betax, 1.0+(gamma - 1.0)*(betax*betax)/(beta*beta) , (gamma - 1.0) * (betax*betay)/(beta*beta)}, 
+                          { -gamma * betay, (gamma - 1.0) * (betay*betax)/(beta*beta), 1.0+(gamma - 1.0)*(betay*betay)/(beta*beta)} };
+        var M = Matrix<double>.Build;
+        var result = M.DenseOfArray(tmp);
+        return result;
+    }
+
 }

Assets/Scripts/PathRenderer.cs

@@ -16,7 +16,7 @@ public class PathRenderer : MonoBehaviour
     [SerializeField]
     LevelManager levelManager;
     [SerializeField]
-    GameObject background;
+    BackgroundMovement background;
     [SerializeField]
     LogScaleSlider velocityslider;
 

Assets/Scripts/Planemovement.cs

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
+using MathNet.Numerics.LinearAlgebra;
+using MathNet.Numerics.LinearAlgebra.Double;
 
 public class Planemovement : MonoBehaviour
 {
@@ -22,6 +24,9 @@ public class Planemovement : MonoBehaviour
 
     public Planemovement otherclock;
 
+    MatrixBuilder<double> M = Matrix<double>.Build;
+    VectorBuilder<double> V = Vector<double>.Build;
+
 
     void Start()
     {
@@ -50,19 +55,37 @@ public class Planemovement : MonoBehaviour
         {
             cnt = 0;
         }
-        //transform.Translate(Vector3.forward * Time.fixedDeltaTime, Space.World);
-        //transform.Translate(0.5f*Vector3.forward * Mathf.Cos(2*Mathf.PI*cnt/480) * Time.fixedDeltaTime, Space.World);
-        //transform.Translate(0.5f*Vector3.left * Mathf.Sin(2 * Mathf.PI * cnt / 480) * Time.fixedDeltaTime, Space.World);
+        if (alpha.magnitude > 0.0f)
+        {
+
+            var atmp = alpha.magnitude * Time.fixedDeltaTime;
+
+
+            double[] vtmp = { (atmp * (alpha.x / alpha.magnitude)), 0.0, (atmp * (alpha.z / alpha.magnitude)) };
+            var deltavnaive = V.DenseOfArray(vtmp);
+
+            double[] tmp = {Constants.c * Constants.Gamma(deltavnaive.L2Norm()),
+                      deltavnaive[0] * Constants.Gamma(deltavnaive.L2Norm()),
+                      deltavnaive[2] * Constants.Gamma(deltavnaive.L2Norm())};
 
-        //orientation = (float)beta * Vector3.forward * Mathf.Cos(2 * Mathf.PI * cnt / 480) + (float)beta * Vector3.left * Mathf.Sin(2 * Mathf.PI * cnt / 480);
+            var deltav = V.DenseOfArray(tmp);
 
-        //v = (float)beta * Vector3.forward * Mathf.Cos(2 * Mathf.PI * cnt / 480) + (float)beta * Vector3.left * Mathf.Sin(2 * Mathf.PI * cnt / 480);
 
-        //v = alpha.normalized * (alpha.magnitude * Time.time / Mathf.Sqrt(1.0f+(alpha.magnitude * Time.time)*(alpha.magnitude * Time.time)));
+            if (v.magnitude > 0.0f)
+            {
+                deltav = Constants.BoostMatrix(-v) * deltav;
+            }
+
+            var tt = deltav[0] / Constants.c;
 
-        //v = new Vector3(0, 0, 0);
+            Vector3 finaldeltav = new Vector3((float)(deltav[1] / tt), 0.0f, (float)(deltav[2] / tt));
+
+            var hmm = finaldeltav - v;
+
+            v = finaldeltav;
+        }
 
-        if((Levelmanager.player.transform.position - transform.position).magnitude < 0.5f)
+        if ((Levelmanager.player.transform.position - transform.position).magnitude < 1f)
         {
             toggle = true;
         }

Assets/Scripts/PlayerMovement.cs

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
+using MathNet.Numerics.LinearAlgebra;
+using MathNet.Numerics.LinearAlgebra.Double;
 
 public class PlayerMovement : MonoBehaviour
 {
     //int cnt = 0;
     double beta = 0.5f; // v/c
-    public Vector3 alpha = new Vector3(0.1f, 0.0f, 0.0f); // proper acceleration
+    public Vector3 alpha = new Vector3(0.0f, 0.0f, 0.0f); // proper acceleration
     public Vector3 v = new Vector3(0.0f, 0.0f, 0.0f);
     public double gamma = 1.0f;
     public GameObject theobject;
     public Vector3 orientation = new Vector3(0.0f, 0.0f, 0.0f);
     public double time = 0.0f;
+    MatrixBuilder<double> M = Matrix<double>.Build;
+    VectorBuilder<double> V = Vector<double>.Build;
 
     bool isinertial = true;
 
@@ -25,6 +29,7 @@ public class PlayerMovement : MonoBehaviour
         orientation = new Vector3(0.0f, 0.0f, 1.0f);
         time = 0.0f;
         isinertial = true;
+        alpha = new Vector3(0.0f, 0.0f, 0.0f);
     }
 
     // Update is called once per frame
@@ -46,10 +51,43 @@ public class PlayerMovement : MonoBehaviour
         //v = (float)beta * Vector3.forward * Mathf.Cos(2 * Mathf.PI * cnt / 480) + (float)beta * Vector3.left * Mathf.Sin(2 * Mathf.PI * cnt / 480);
         //v = alpha.normalized * (alpha.magnitude * Time.time / Mathf.Sqrt(1.0f + (alpha.magnitude * Time.time) * (alpha.magnitude * Time.time)));
         //v = new Vector3(0.7f, 0.0f, 0.0f);
+
+        if (alpha.magnitude > 0.0f)
+        {
+
+            var atmp = alpha.magnitude * Time.fixedDeltaTime;
+
+
+            double[] vtmp = { (atmp * (alpha.x / alpha.magnitude)), 0.0,(atmp * (alpha.z / alpha.magnitude)) };
+            var deltavnaive = V.DenseOfArray(vtmp);
+
+            double[] tmp = {Constants.c * Constants.Gamma(deltavnaive.L2Norm()),
+                      deltavnaive[0] * Constants.Gamma(deltavnaive.L2Norm()),
+                      deltavnaive[2] * Constants.Gamma(deltavnaive.L2Norm())};
+
+            var deltav = V.DenseOfArray(tmp);
+
+
+            if (v.magnitude > 0.0f)
+            {
+                deltav = Constants.BoostMatrix(-v) * deltav;
+            }
+
+            var tt = deltav[0] / Constants.c;
+
+            Vector3 finaldeltav = new Vector3((float)(deltav[1]/tt), 0.0f, (float)(deltav[2]/tt));
+
+            var hmm = finaldeltav - v;
+
+            v = finaldeltav;
+        }
+
         beta = v.magnitude / (float)Constants.c;
 
         gamma = Constants.Gamma(v.magnitude);
 
+
+
         transform.Translate(v * Time.fixedDeltaTime * (float)gamma, Space.World);
 
         var vt = v + (float)Constants.c * Vector3.up;

Assets/Scripts/Square.cs

@@ -26,7 +26,7 @@ public class Square : FlatLandObject
         return pathList[n+1];
     }
 
-    public float GetPathVeclocity(int n)
+    public float GetPathVelocity(int n)
     {
         return pathVelocity[n + 1];
     }

Assets/Scripts/UIManager.cs

@@ -14,6 +14,9 @@ public class UIManager : MonoBehaviour
     Camera playercamera;
     [SerializeField]
     LogScaleSlider velocityslider;
+    [SerializeField]
+    LogScaleSlider accelslider;
+
 
     public Canvas canvas;
     public Text mytime;
@@ -27,7 +30,7 @@ public class UIManager : MonoBehaviour
 
     private int prevSelectPathNum = -1;
     private Text pathName;
-    private Text pathVeclocity;
+    private Text pathVelocity;
     private Vector3 middlePoint;
     private Vector3 canvasSize;
     private int sliderflag = 0;
@@ -40,7 +43,7 @@ public class UIManager : MonoBehaviour
     {
         _pathUI.SetActive(false);
         pathName = _pathUI.transform.Find("Name").GetComponent<Text>();
-        pathVeclocity = _pathUI.transform.Find("Velocity").GetComponent<Text>();
+        pathVelocity = _pathUI.transform.Find("Velocity").GetComponent<Text>();
         middlePoint = _pathUI.transform.position;
         canvasSize = new Vector3(Screen.width, Screen.height, 0);
 
@@ -73,7 +76,7 @@ public class UIManager : MonoBehaviour
                     if (_pathUI.activeSelf == true && prevSelectPathNum != -1)
                     {
                         square.pathVelocity[prevSelectPathNum + 1] = velocityslider.GetLogScaleValue();
-                        pathVeclocity.text = "Velocity: " + square.GetPathVeclocity(prevSelectPathNum).ToString() + "c";
+                        pathVelocity.text = "Velocity: " + square.GetPathVelocity(prevSelectPathNum).ToString() + "c";
                     }
                 }
             }
@@ -129,7 +132,7 @@ public class UIManager : MonoBehaviour
             if (_pathUI.activeSelf == true && prevSelectPathNum != -1)
             {
                 square.pathVelocity[prevSelectPathNum + 1] = velocityslider.GetLogScaleValue();
-                pathVeclocity.text = "Velocity: " + square.GetPathVeclocity(prevSelectPathNum).ToString() + "c";
+                pathVelocity.text = "Velocity: " + square.GetPathVelocity(prevSelectPathNum).ToString() + "c";
             }
         }
         else if (Input.GetMouseButtonDown(1))
@@ -138,6 +141,44 @@ public class UIManager : MonoBehaviour
             prevSelectPathNum = -1;
             sliderflag = 0;
         }
+
+        if(Input.GetKeyDown("w"))
+        {
+            var tmp = accelslider.GetLogScaleValue();
+            Levelmanager.player.alpha += new Vector3(0, 0, tmp);
+        }
+        else if(Input.GetKeyDown("a"))
+        {
+            var tmp = accelslider.GetLogScaleValue();
+            Levelmanager.player.alpha += new Vector3(-tmp, 0, 0);
+        }
+        else if(Input.GetKeyDown("s"))
+        {
+            var tmp = accelslider.GetLogScaleValue();
+            Levelmanager.player.alpha += new Vector3(0, 0, -tmp);
+        }
+        else if(Input.GetKeyDown("d"))
+        {
+            var tmp = accelslider.GetLogScaleValue();
+            Levelmanager.player.alpha += new Vector3(tmp, 0, 0);
+        }
+
+        if (Input.GetKeyUp("w"))
+        {
+            Levelmanager.player.alpha -= new Vector3(0, 0, Levelmanager.player.alpha.z);
+        }
+        else if (Input.GetKeyUp("a"))
+        {
+            Levelmanager.player.alpha -= new Vector3(Levelmanager.player.alpha.x, 0, 0);
+        }
+        else if (Input.GetKeyUp("s"))
+        {
+            Levelmanager.player.alpha -= new Vector3(0, 0, Levelmanager.player.alpha.z);
+        }
+        else if (Input.GetKeyUp("d"))
+        {
+            Levelmanager.player.alpha -= new Vector3(Levelmanager.player.alpha.x, 0, 0);
+        }
     }
 
     private Vector3 getMouseClickPosition(RaycastHit hit)
@@ -158,7 +199,8 @@ public class UIManager : MonoBehaviour
     private void updatePathInfo(GameObject obj, int pathNum)
     {
         pathName.text = obj.name;
-        pathVeclocity.text = "Velocity: " + square.GetPathVeclocity(pathNum).ToString() + "c";
-        velocityslider.UpdateValuebyVelocity(square.GetPathVeclocity(pathNum));
+        pathVelocity.text = "Velocity: " + square.GetPathVelocity(pathNum).ToString() + "c";
+        velocityslider.UpdateValuebyVelocity(square.GetPathVelocity(pathNum));
     }
+
 }