trajectory movement WIP

Assets/Scenes/Test.unity

@@ -649,7 +649,6 @@ MonoBehaviour:
   m_Name: 
   m_EditorClassIdentifier: 
   square: {fileID: 934514725}
-  pathrenderer: {fileID: 948598108}
   playercamera: {fileID: 1661408489}
   velocityslider: {fileID: 260633610}
   accelslider: {fileID: 1086622590}
@@ -1013,6 +1012,7 @@ MonoBehaviour:
   m_Script: {fileID: 11500000, guid: 0bf826b8a4774ba4b9c6a1cff6925667, type: 3}
   m_Name: 
   m_EditorClassIdentifier: 
+  beta: 0
   alpha: {x: 0, y: 0, z: 0}
   v: {x: 0, y: 0, z: 0}
   orientation: {x: 0, y: 0, z: 0}
@@ -1332,6 +1332,7 @@ MonoBehaviour:
   m_Script: {fileID: 11500000, guid: 9cbe363fdf02257478cb799cdf2190b3, type: 3}
   m_Name: 
   m_EditorClassIdentifier: 
+  beta: 0
   alpha: {x: 0, y: 0, z: 0}
   v: {x: 0, y: 0, z: 0}
   orientation: {x: 0, y: 0, z: 0}
@@ -1339,6 +1340,7 @@ MonoBehaviour:
   gamma: 1
   time: 0
   theobject: {fileID: 1320474661}
+  background: {fileID: 1713675711}
 --- !u!4 &739347347
 Transform:
   m_ObjectHideFlags: 0
@@ -1351,6 +1353,7 @@ Transform:
   m_LocalScale: {x: 1, y: 1, z: 1}
   m_Children:
   - {fileID: 1320474668}
+  - {fileID: 1713675712}
   m_Father: {fileID: 0}
   m_RootOrder: 2
   m_LocalEulerAnglesHint: {x: 0, y: 0, z: 0}
@@ -2557,6 +2560,7 @@ MonoBehaviour:
   m_Script: {fileID: 11500000, guid: 0bf826b8a4774ba4b9c6a1cff6925667, type: 3}
   m_Name: 
   m_EditorClassIdentifier: 
+  beta: 0
   alpha: {x: 0, y: 0, z: 0}
   v: {x: 0, y: 0, z: 0}
   orientation: {x: 0, y: 0, z: 0}
@@ -3665,13 +3669,13 @@ Transform:
   m_PrefabInstance: {fileID: 0}
   m_PrefabAsset: {fileID: 0}
   m_GameObject: {fileID: 1713675711}
-  m_LocalRotation: {x: -0, y: -0, z: -0, w: 1}
+  m_LocalRotation: {x: 0.7071068, y: -0, z: -0, w: 0.7071068}
   m_LocalPosition: {x: 0, y: 0, z: 0}
-  m_LocalScale: {x: 500, y: 500, z: 1}
+  m_LocalScale: {x: 500, y: 500.00024, z: 1}
   m_Children:
   - {fileID: 948598109}
-  m_Father: {fileID: 1756789505}
-  m_RootOrder: 0
+  m_Father: {fileID: 739347347}
+  m_RootOrder: 1
   m_LocalEulerAnglesHint: {x: 0, y: 0, z: 0}
 --- !u!64 &1713675713
 MeshCollider:
@@ -3748,8 +3752,7 @@ MonoBehaviour:
   m_Script: {fileID: 11500000, guid: a937b7b15233ade4b8c2766ff3695fb7, type: 3}
   m_Name: 
   m_EditorClassIdentifier: 
-  Cone: {fileID: 1756789504}
-  Levelmanager: {fileID: 279236944}
+  levelManager: {fileID: 279236944}
   starttime: 0
   gamma: 1
 --- !u!1 &1751424968
@@ -3869,8 +3872,7 @@ Transform:
   m_LocalRotation: {x: 0.7071068, y: -0, z: -0, w: 0.7071068}
   m_LocalPosition: {x: 0, y: 0, z: 0}
   m_LocalScale: {x: 1, y: 1, z: 1}
-  m_Children:
-  - {fileID: 1713675712}
+  m_Children: []
   m_Father: {fileID: 0}
   m_RootOrder: 8
   m_LocalEulerAnglesHint: {x: 90, y: 0, z: 0}

Assets/Scripts/BackgroundMovement.cs

@@ -4,14 +4,12 @@ using UnityEngine;
 
 public class BackgroundMovement : MonoBehaviour
 {
-    [SerializeField]
-    GameObject Cone;
     bool grabbed = false;
     int cnt = 0;
     double beta = 0.5f; // v/c
     Vector3 alpha = new Vector3(0.1f, 0.0f, 0.0f); // proper acceleration
     Vector3 v;
-    public LevelManager Levelmanager;
+    public LevelManager levelManager;
     public double starttime = 0.0f;
     public double gamma = 1.0f;
     Vector3 orientation;
@@ -26,11 +24,11 @@ public class BackgroundMovement : MonoBehaviour
         set
         {
             if(value)
-                transform.parent = Cone.transform;
+                transform.parent = levelManager.player.transform;
             else
             {
                 transform.parent = null;
-                v = Levelmanager.player.v;
+                v = levelManager.player.v;
             }
 
             toggle = value;
@@ -52,8 +50,8 @@ public class BackgroundMovement : MonoBehaviour
         }
         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);
+            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/FlatlandMovement.cs

@@ -193,29 +193,9 @@ public class FlatlandMovement : MonoBehaviour
 
         if (startv.magnitude > 0.0f)
         {
-            deltav = Constants.BoostMatrix(startv) * deltav;
-
-            var deltavsize = Mathf.Sqrt((float)(deltav[1] * deltav[1] + deltav[2] * deltav[2]));
-
-            deltav = atmp / deltavsize * deltav;
-
-            deltav[0] = Constants.Gamma(atmp) * Constants.c;
-            deltav[1] *= Constants.Gamma(atmp);
-            deltav[2] *= Constants.Gamma(atmp);
-
             deltav = Constants.BoostMatrix(-startv) * deltav;
         }
-        else
-        {
-            var deltavsize = Mathf.Sqrt((float)(deltav[1] * deltav[1] + deltav[2] * deltav[2]));
-
-            deltav = atmp / deltavsize * deltav;
-
-            deltav[0] = Constants.Gamma(atmp) * Constants.c;
-            deltav[1] *= Constants.Gamma(atmp);
-            deltav[2] *= Constants.Gamma(atmp);
-        }
-
+        
         var tt = deltav[0] / Constants.c;
 
         Vector3 finaldeltav = new Vector3((float)(deltav[1] / tt), 0.0f, (float)(deltav[2] / tt));

Assets/Scripts/LogScaleSlider.cs

@@ -19,7 +19,7 @@ public class LogScaleSlider : MonoBehaviour
     
     public float GetLogScaleValue()
     {
-        return (-1) * Mathf.Pow(10, slider.value * (-5)) + 1;
+        return (-1) * Mathf.Pow(10, slider.value * (-4)) + 1;
     }
 
     public void UpdateLogScaleText()
@@ -29,7 +29,7 @@ public class LogScaleSlider : MonoBehaviour
 
     public void UpdateValuebyVelocity(float v)
     {
-        slider.value = Mathf.Log10(1 - v) * -(1.0f/5.0f);
+        slider.value = Mathf.Log10(1 - v) * -(1.0f/4.0f);
     }
 
 }

Assets/Scripts/PathRenderer.cs

@@ -4,6 +4,8 @@ using UnityEngine;
 using System.Linq;
 using UnityEngine.UI;
 using System;
+using MathNet.Numerics.LinearAlgebra;
+using MathNet.Numerics.LinearAlgebra.Double;
 
 public class PathRenderer : MonoBehaviour
 {
@@ -197,13 +199,121 @@ public class PathRenderer : MonoBehaviour
         int i = 0;
         var u = levelManager.player.v;
         int tinterval = Constants.alphatinterval;
+        VectorBuilder<double> V = Vector<double>.Build;
 
         while (i <= finalPathNum)
         {
-            Vector3 acceleration = new Vector3(square.GetNthPath(i).x, 0f, square.GetNthPath(i).y);
+            Vector3 startpos = new Vector3(levelManager.player.transform.position.x, 0, levelManager.player.transform.position.z);
+            Vector3 dest = new Vector3(square.GetNthPath(i).x, 0f, square.GetNthPath(i).y);
+            Vector3 acceleration = dest.normalized;
 
-            var offsetstartpos = Background.transform.position;
-            var startpos = levelManager.player.transform.position;
+            var v = square.GetPathVelocity(i);
+
+            var atmp = (float)(v * Constants.c);
+
+            double[] vtmp = { (atmp * (acceleration.x / acceleration.magnitude)), 0.0, (atmp * (acceleration.z / acceleration.magnitude)) };
+            double[] xtmp = { dest.magnitude / (v * Constants.c), dest.x, dest.z };
+            var deltavnaive = V.DenseOfArray(vtmp);
+            var deltaxnaive = V.DenseOfArray(xtmp);
+
+            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);
+
+            Vector<double> deltax = deltaxnaive;
+
+            if (u.magnitude > 0.0f)
+            {
+                deltav = Constants.BoostMatrix(-u) * deltav;
+                deltax = Constants.BoostMatrix(-u) * deltaxnaive;
+            }
+
+            var tt = deltav[0] / Constants.c;
+
+            Vector3 finaldeltav = new Vector3((float)(deltav[1] / tt), 0.0f, (float)(deltav[2] / tt));
+            Vector3 finaldeltax = new Vector3((float)deltax[1], 0.0f, (float)deltax[2]);
+
+            levelManager.player.v = finaldeltav;
+
+            while(true)
+            {
+                var currentpos = new Vector3(levelManager.player.transform.position.x, 0, levelManager.player.transform.position.z);
+                var traveledpos = currentpos - startpos;
+                if (traveledpos.magnitude >= finaldeltax.magnitude)
+                {
+                    break;
+                }
+                yield return new WaitForFixedUpdate();
+            }
+            /*
+            levelManager.player.alpha = new Vector3(0, 0, 0);
+
+            var v = square.GetPathVelocity(i);
+
+            var atmp = (float)(v * Constants.c);
+
+            double[] vtmp = { ((acceleration.x / acceleration.magnitude)), 0.0, ((acceleration.z / acceleration.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 (u.magnitude > 0.0f)
+            {
+                deltav = Constants.BoostMatrix(u) * deltav;
+
+                var deltavsize = Mathf.Sqrt((float)(deltav[1] * deltav[1] + deltav[2] * deltav[2]));
+
+                deltav = atmp / deltavsize * deltav;
+
+                deltav[0] = Constants.Gamma(atmp) * Constants.c;
+                deltav[1] *= Constants.Gamma(atmp);
+                deltav[2] *= Constants.Gamma(atmp);
+
+                deltav = Constants.BoostMatrix(-u) * deltav;
+            }
+            else
+            {
+                var deltavsize = Mathf.Sqrt((float)(deltav[1] * deltav[1] + deltav[2] * deltav[2]));
+
+                deltav = atmp / deltavsize * deltav;
+
+                deltav[0] = Constants.Gamma(atmp) * Constants.c;
+                deltav[1] *= Constants.Gamma(atmp);
+                deltav[2] *= Constants.Gamma(atmp);
+            }
+
+            var tt = deltav[0] / Constants.c;
+
+            Vector3 finaldeltav = new Vector3((float)(deltav[1] / tt), 0.0f, (float)(deltav[2] / tt));
+
+            levelManager.player.v = finaldeltav;
+            var prevdistance = (dest
+                    + (new Vector3(Background.transform.position.x, 0, Background.transform.position.z))
+                    - (new Vector3(levelManager.player.transform.position.x, 0, levelManager.player.transform.position.z)));
+
+            yield return new WaitForFixedUpdate();
+
+            while (true)
+            {
+                var distanceleft = (dest
+                    + (new Vector3(Background.transform.position.x, 0, Background.transform.position.z))
+                    - (new Vector3(levelManager.player.transform.position.x, 0, levelManager.player.transform.position.z)));
+                if (distanceleft.magnitude - prevdistance.magnitude >= 0.0f)
+                    break;
+                prevdistance = distanceleft;
+                yield return new WaitForFixedUpdate();
+            }*/
+
+
+            /*
+            var offsetstartpos = new Vector3(Background.transform.position.x, 0, Background.transform.position.z);
+            var startpos = new Vector3(levelManager.player.transform.position.x, 0, levelManager.player.transform.position.z);
 
             acceleration = acceleration.normalized;
 
@@ -220,11 +330,14 @@ public class PathRenderer : MonoBehaviour
 
             for (var j = 0; j < tinterval; ++j)
             {
+                var tmp = (dest
+                    + (new Vector3(Background.transform.position.x, 0, Background.transform.position.z))
+                    - (new Vector3(levelManager.player.transform.position.x, 0, levelManager.player.transform.position.z)));
                 yield return new WaitForFixedUpdate();
             }
             levelManager.player.alpha = new Vector3(0, 0, 0);
-            var offsetnewpos = Background.transform.position;
-            var newpos = levelManager.player.transform.position;
+            var offsetnewpos = new Vector3(Background.transform.position.x, 0, Background.transform.position.z);
+            var newpos = new Vector3(levelManager.player.transform.position.x, 0, levelManager.player.transform.position.z);
 
             var posdiff = newpos - startpos;
             var offset = offsetnewpos - offsetstartpos;
@@ -233,8 +346,10 @@ public class PathRenderer : MonoBehaviour
              
             while(true)
             {
-                var tmp = (square.GetDestPoint(i) + Background.transform.position - levelManager.player.transform.position);
-                if ((posdiff - tmp).magnitude < 0.01f)
+                var tmp = (dest
+                    + (new Vector3(Background.transform.position.x, 0, Background.transform.position.z)) 
+                    - (new Vector3(levelManager.player.transform.position.x, 0, levelManager.player.transform.position.z)));
+                if (tmp.magnitude - posdiff.magnitude < 0.0f)
                     break;
                 yield return new WaitForFixedUpdate();
             }
@@ -248,15 +363,20 @@ public class PathRenderer : MonoBehaviour
                 yield return new WaitForFixedUpdate();
             }
             levelManager.player.alpha = new Vector3(0, 0, 0);
+            */
 
+            levelManager.player.v = u;
+            levelManager.player.transform.position = new Vector3(startpos.x + finaldeltax.x
+                                                               , levelManager.player.transform.position.y
+                                                               , startpos.z + finaldeltax.z);
 
-            Background.Toggle = true;
 
-            break;
 
             i++;
         }
 
+        Background.Toggle = true;
+
     }
 
     public void DeletePathsAfterNthPath(int n)

Assets/Scripts/PlayerMovement.cs

@@ -8,6 +8,8 @@ public class PlayerMovement : FlatlandMovement
 {
     bool isinertial = true;
 
+    public GameObject background;
+
     // Start is called before the first frame update
     void Start()
     {
@@ -30,6 +32,15 @@ public class PlayerMovement : FlatlandMovement
     {
         base.FixedUpdate();
 
+        if (v.magnitude > 0.0f)
+        {
+            Time.fixedDeltaTime = 0.02f / (float)Constants.Gamma(v.magnitude);
+
+            if (Time.fixedDeltaTime < 0.002f)
+                Time.fixedDeltaTime = 0.002f;
+
+        }
+
         var prevup = transform.up;
         var prevfor = transform.forward;
         var prevorient = orientation;
@@ -78,7 +89,7 @@ public class PlayerMovement : FlatlandMovement
         }
 
         if (v.magnitude >= Constants.c) // if floating point errors makes object ftl
-            v = v.normalized * (float)(0.999999f * Constants.c);
+            v = v.normalized * (float)(0.999995f * Constants.c);
 
         beta = v.magnitude / (float)Constants.c;
 
@@ -102,14 +113,20 @@ public class PlayerMovement : FlatlandMovement
         var neworientation = (Quaternion.FromToRotation(Vector3.up, vt)) * orientation;
 
         theobject.transform.rotation = Quaternion.LookRotation(neworientation, vt);
+        if(background.GetComponent<BackgroundMovement>().Toggle)
+            background.transform.rotation = Quaternion.LookRotation(-vt, neworientation);
 
         theobject.transform.parent = null;
+        if (background.GetComponent<BackgroundMovement>().Toggle)
+            background.transform.parent = null;
 
         Vector3 newforward = new Vector3(vt.y * (v.x / v.magnitude), Mathf.Sqrt(vt.x * vt.x + vt.z * vt.z), vt.y * (v.z / v.magnitude));
 
         transform.rotation = Quaternion.LookRotation(newforward, vt);
 
         theobject.transform.parent = transform;
+        if (background.GetComponent<BackgroundMovement>().Toggle)
+            background.transform.parent = transform;
 
         transform.localScale = new Vector3(1.0f, 1.0f, (float)gamma); // scale x'-axis scale (distance dilation)
 

Assets/Scripts/UIManager.cs

@@ -11,8 +11,6 @@ public class UIManager : MonoBehaviour
     [SerializeField]
     Square square;
     [SerializeField]
-    PathRenderer pathrenderer;
-    [SerializeField]
     Camera playercamera;
     [SerializeField]
     LogScaleSlider velocityslider;
@@ -117,22 +115,22 @@ public class UIManager : MonoBehaviour
 
         if(Input.GetKeyDown("w"))
         {
-            var tmp = accelslider.GetLogScaleValue() * (float)Constants.c * 10;
+            var tmp = accelslider.GetLogScaleValue() * (float)Constants.c;
             levelManager.player.alpha += new Vector3(0, 0, tmp);
         }
         else if(Input.GetKeyDown("a"))
         {
-            var tmp = accelslider.GetLogScaleValue() * (float)Constants.c * 10;
+            var tmp = accelslider.GetLogScaleValue() * (float)Constants.c;
             levelManager.player.alpha += new Vector3(-tmp, 0, 0);
         }
         else if(Input.GetKeyDown("s"))
         {
-            var tmp = accelslider.GetLogScaleValue() * (float)Constants.c * 10;
+            var tmp = accelslider.GetLogScaleValue() * (float)Constants.c;
             levelManager.player.alpha += new Vector3(0, 0, -tmp);
         }
         else if(Input.GetKeyDown("d"))
         {
-            var tmp = accelslider.GetLogScaleValue() * (float)Constants.c * 10;
+            var tmp = accelslider.GetLogScaleValue() * (float)Constants.c;
             levelManager.player.alpha += new Vector3(tmp, 0, 0);
         }
 
@@ -229,7 +227,7 @@ public class UIManager : MonoBehaviour
 
     public void PathCancel()
     {
-        pathrenderer.DeletePathsAfterNthPath(prevSelectPathNum + 1);
+        pathRenderer.DeletePathsAfterNthPath(prevSelectPathNum + 1);
         _pathUI.SetActive(false);
         prevSelectPathNum = -1;
     }