Collision WIP

Assets/Scripts/FlatlandMovement.cs

@@ -249,6 +249,28 @@ public class FlatlandMovement : MonoBehaviour
         this.v = finaldeltav;
 
 
+    }
+
+    public IEnumerator _AcceleratetoConstantVelocityWithoutCorrection(Vector3 dest, float v)
+    {
+        Vector3 acceleration = new Vector3(dest.x, 0f, dest.y);
+        var tinterval = Constants.alphatinterval;
+
+        acceleration = acceleration.normalized;
+
+        var deltat = Time.fixedDeltaTime * tinterval;
+
+        acceleration = (float)((Constants.c / deltat) * MathNet.Numerics.Trig.Asinh(v * Constants.Gamma(v * Constants.c))) * acceleration;
+        // acceleration required to accelerate to v in deltat seconds: see https://en.wikiversity.org/wiki/Theory_of_relativity/Rindler_coordinates
+
+        this.alpha += acceleration;
+
+        for (var j = 0; j < tinterval; ++j)
+        {
+            yield return new WaitForFixedUpdate();
+        }
+        this.alpha -= acceleration;
+
     }
 
         public bool SetVelecityToAbPosition(Vector3 dest, float v)
@@ -340,21 +362,46 @@ public class FlatlandMovement : MonoBehaviour
 
         Vector3 col = (other.v - this.v);
 
-        var totalThreeMomentum = this.GetThreeMomentum() + other.GetThreeMomentum();
+        var totalThreeMomentum = Constants.BoostMatrix(v) * other.GetThreeMomentum();
         
         var tmp = collision.GetContact(0).normal;
         tmp = new Vector3(tmp.x, 0, tmp.z);
 
         tmp = tmp.normalized;
 
-        float inner = SpaceInnerPorduct(tmp, col.normalized);
+        double[] tmpx = {0,tmp.x, tmp.z };
+        double[] tmpv = { Constants.Gamma(other.v.magnitude) * Constants.c, Constants.Gamma(other.v.magnitude) * other.v.x, Constants.Gamma(other.v.magnitude) * other.v.z };
+
+        var direction = V.DenseOfArray(tmpx);
+        var collisionvelocity = V.DenseOfArray(tmpv);
+
+        if(v.magnitude > 0)
+        {
+            direction = Constants.BoostMatrix(v) * direction;
+            collisionvelocity = Constants.BoostMatrix(v) * collisionvelocity;
+        }
+
+
+        Vector3 finalcollisionforcedirection = new Vector3((float)direction[1], 0, (float)direction[2]);
+        var finalcollisionvelocitygamma = collisionvelocity[0] / Constants.c;
+        Vector3 finalcollisionvelocity = new Vector3((float)(collisionvelocity[1] / finalcollisionvelocitygamma), 0, (float)(collisionvelocity[2] / finalcollisionvelocitygamma));
+
+        finalcollisionforcedirection = finalcollisionforcedirection.normalized;
+
+        var a = mass + other.mass * finalcollisionvelocitygamma;
+        var b = other.mass * finalcollisionvelocitygamma * SpaceInnerPorduct(finalcollisionvelocity, finalcollisionforcedirection) / Constants.c;
+        var c = other.mass * finalcollisionvelocitygamma;
 
-        inner = Mathf.Abs(inner);
+        var resultvgamma = ((2.0 * a * c) + Math.Sqrt((4 * a * a * c * c ) - 4.0 * (a * a - b * b) * (b * b + c * c))) / (2.0 * (a * a - b * b));
+
+        if(resultvgamma < 1.0)
+        {
+            resultvgamma = -resultvgamma;
+        }
 
-        tmp *= col.magnitude*inner*other.mass;
+        var resultvbetamagnitude = Math.Sqrt(1.0 - (1.0/resultvgamma));
 
-        collisionforce = tmp;
-        alpha += collisionforce;
+        StartCoroutine(_AcceleratetoConstantVelocityWithoutCorrection(finalcollisionforcedirection,(float)resultvbetamagnitude));
 
         Debug.Log(collisions.Count);
     }
@@ -376,8 +423,8 @@ public class FlatlandMovement : MonoBehaviour
 
         collisions.Remove(collision.gameObject.GetComponent<ExtrudedMesh>().hash);
 
-        alpha -= collisionforce;
-        collisionforce = new Vector3(0, 0, 0);
+        //alpha -= collisionforce;
+        //collisionforce = new Vector3(0, 0, 0);
     }
 
     public double GetEnergy()