added spring math

Runtime/Engine/Code/Foundation/MathUtility.cs

@@ -0,0 +1,44 @@
+using UnityEngine;
+
+namespace RebootKit.Engine.Foundation {
+    public static class MathUtility {
+
+        // Spring math
+        // Source: https://allenchou.net/2015/04/game-math-precise-control-over-numeric-springing/
+        public static void Spring(ref float current,
+                                  ref float velocity,
+                                  float target,
+                                  float halfLife,
+                                  float frequency,
+                                  float timeStep) {
+            float dampingRatio = -Mathf.Log(0.5f) / (frequency * halfLife);
+            float f = 1.0f + 2.0f * timeStep * dampingRatio * frequency;
+            float oo = frequency * frequency;
+            float hoo = timeStep * oo;
+            float hhoo = timeStep * hoo;
+            float detInv = 1.0f / (f + hhoo);
+            float detX = f * current + timeStep * velocity + hhoo * target;
+            float detV = velocity + hoo * (target - current);
+            current = detX * detInv;
+            velocity = detV * detInv;
+        }
+
+        public static void Spring(ref Vector3 current,
+                                  ref Vector3 velocity,
+                                  Vector3 target,
+                                  float halfLife,
+                                  float frequency,
+                                  float timeStep) {
+            float dampingRatio = -Mathf.Log(0.5f) / (frequency * halfLife);
+            float f = 1.0f + 2.0f * timeStep * dampingRatio * frequency;
+            float oo = frequency * frequency;
+            float hoo = timeStep * oo;
+            float hhoo = timeStep * hoo;
+            float detInv = 1.0f / (f + hhoo);
+            Vector3 detX = f * current + timeStep * velocity + hhoo * target;
+            Vector3 detV = velocity + hoo * (target - current);
+            current = detX * detInv;
+            velocity = detV * detInv;
+        }
+    }
+}