Transitioning - Done!

Assets/Scenes/SampleScene.unity

@@ -154,6 +154,9 @@ MonoBehaviour:
     type: 3}
   resolution: 50
   function: 4
+  transitionMode: 2
+  functionDuration: 1
+  transitionDuration: 1
 --- !u!4 &75389716
 Transform:
   m_ObjectHideFlags: 0
@@ -768,3 +771,5 @@ MonoBehaviour:
   m_Name: 
   m_EditorClassIdentifier: 
   display: {fileID: 1844483591}
+  displayMode: 0
+  sampleDuration: 1

Assets/Script/FunctionLibrary.cs

@@ -3,7 +3,7 @@ using static UnityEngine.Mathf;
 
 public static class FunctionLibrary
 {
-    public delegate Vector3 Function(float u, float v, float y);
+    public delegate Vector3 Function(float u, float v, float t);
 
     public enum FunctionName { Wave, MultiWave, Ripple, Sphere, Torus }
 
@@ -84,4 +84,9 @@ public static class FunctionLibrary
         p.z = s * Cos(PI * u);
         return p;
     }
+
+    public static Vector3 Morph(float u, float v, float t, Function from, Function to, float progress)
+    {
+        return Vector3.LerpUnclamped(from(u, v, t), to(u, v, t), SmoothStep(0.0f, 1.0f, progress));
+    }
 }

Assets/Script/Graph.cs

@@ -19,10 +19,17 @@ public class Graph : MonoBehaviour
     [SerializeField, Min(0.0f)]
     float functionDuration = 1.0f;
 
+    [SerializeField, Min(0.0f)]
+    float transitionDuration = 1.0f;
+
     Transform[] points;
 
     float duration = 0.0f;
 
+    bool transitioning;
+
+    FunctionLibrary.FunctionName transitionFunction;
+
     private void Awake()
     {
         var step = 2f / resolution;
@@ -40,12 +47,29 @@ public class Graph : MonoBehaviour
     private void Update()
     {
         duration += Time.deltaTime;
-        if (duration >= functionDuration)
+        if (transitioning)
+        {
+            if (duration >= transitionDuration)
+            {
+                duration -= transitionDuration;
+                transitioning = false;
+            }
+        }
+        else if (duration >= functionDuration)
         {
             duration -= functionDuration;
+            transitioning = true;
+            transitionFunction = function;
             PickNextFunction();
         }
-        UpdateFunction();
+        if (transitioning)
+        {
+            UpdateFunctionTransition();
+        }
+        else
+        {
+            UpdateFunction();
+        }
     }
 
     private void PickNextFunction()
@@ -54,7 +78,6 @@ public class Graph : MonoBehaviour
         function = transitionMode == TransitionMode.Cycle ?
             FunctionLibrary.GetNextFunctionName(function) :
             FunctionLibrary.GetRandomFunctionNameOtherThan(function);
-
     }
 
     private void UpdateFunction()
@@ -75,5 +98,26 @@ public class Graph : MonoBehaviour
             points[i].localPosition = f(u, v, time);
         }
     }
-    
+
+    private void UpdateFunctionTransition()
+    {
+        FunctionLibrary.Function
+            from = FunctionLibrary.GetFunction(transitionFunction),
+            to = FunctionLibrary.GetFunction(function);
+        float progress = duration / transitionDuration;
+        float time = Time.time;
+        float step = 2f / resolution;
+        float v = 0.5f * step - 1f;
+        for (int i = 0, x = 0, z = 0; i < points.Length; i++, x++)
+        {
+            if (x == resolution)
+            {
+                x = 0;
+                z += 1;
+                v = (z + 0.5f) * step - 1f;
+            }
+            float u = (x + 0.5f) * step - 1f;
+            points[i].localPosition = FunctionLibrary.Morph(u, v, time, from, to, progress);
+        }
+    }
 }