├── .gitignore ├── .idea └── .idea.UnityVerletRope │ └── .idea │ ├── .gitignore │ ├── encodings.xml │ ├── indexLayout.xml │ └── vcs.xml ├── Assets ├── Materials.meta ├── Materials │ ├── RopeMaterial.mat │ └── RopeMaterial.mat.meta ├── Prefabs.meta ├── Prefabs │ ├── Rope.prefab │ └── Rope.prefab.meta ├── Scenes.meta ├── Scenes │ ├── SampleScene.unity │ └── SampleScene.unity.meta ├── Scripts.meta └── Scripts │ ├── RopeRenderer.cs │ ├── RopeRenderer.cs.meta │ ├── VerletRope.cs │ └── VerletRope.cs.meta ├── Packages ├── manifest.json └── packages-lock.json ├── ProjectSettings ├── AudioManager.asset ├── ClusterInputManager.asset ├── DynamicsManager.asset ├── EditorBuildSettings.asset ├── EditorSettings.asset ├── GraphicsSettings.asset ├── InputManager.asset ├── MemorySettings.asset ├── NavMeshAreas.asset ├── PackageManagerSettings.asset ├── Packages │ └── com.unity.testtools.codecoverage │ │ └── Settings.json ├── Physics2DSettings.asset ├── PresetManager.asset ├── ProjectSettings.asset ├── ProjectVersion.txt ├── QualitySettings.asset ├── SceneTemplateSettings.json ├── TagManager.asset ├── TimeManager.asset ├── TimelineSettings.asset ├── UnityConnectSettings.asset ├── VFXManager.asset ├── VersionControlSettings.asset └── XRSettings.asset ├── README.md ├── RopeRenderer.png ├── SampleGIF.gif └── VerletRope.png /.gitignore: -------------------------------------------------------------------------------- 1 | # This .gitignore file should be placed at the root of your Unity project directory 2 | # 3 | # Get latest from https://github.com/github/gitignore/blob/main/Unity.gitignore 4 | # 5 | /[Ll]ibrary/ 6 | /[Tt]emp/ 7 | /[Oo]bj/ 8 | /[Bb]uild/ 9 | /[Bb]uilds/ 10 | /[Ll]ogs/ 11 | /[Uu]ser[Ss]ettings/ 12 | 13 | # MemoryCaptures can get excessive in size. 14 | # They also could contain extremely sensitive data 15 | /[Mm]emoryCaptures/ 16 | 17 | # Recordings can get excessive in size 18 | /[Rr]ecordings/ 19 | 20 | # Uncomment this line if you wish to ignore the asset store tools plugin 21 | # /[Aa]ssets/AssetStoreTools* 22 | 23 | # Autogenerated Jetbrains Rider plugin 24 | /[Aa]ssets/Plugins/Editor/JetBrains* 25 | 26 | # Visual Studio cache directory 27 | .vs/ 28 | 29 | # Gradle cache directory 30 | .gradle/ 31 | 32 | # Autogenerated VS/MD/Consulo solution and project files 33 | ExportedObj/ 34 | .consulo/ 35 | *.csproj 36 | *.unityproj 37 | *.sln 38 | *.suo 39 | *.tmp 40 | *.user 41 | *.userprefs 42 | *.pidb 43 | *.booproj 44 | *.svd 45 | *.pdb 46 | *.mdb 47 | *.opendb 48 | *.VC.db 49 | 50 | # Unity3D generated meta files 51 | *.pidb.meta 52 | *.pdb.meta 53 | *.mdb.meta 54 | 55 | # Unity3D generated file on crash reports 56 | sysinfo.txt 57 | 58 | # Builds 59 | *.apk 60 | *.aab 61 | *.unitypackage 62 | *.app 63 | 64 | # Crashlytics generated file 65 | crashlytics-build.properties 66 | 67 | # Packed Addressables 68 | /[Aa]ssets/[Aa]ddressable[Aa]ssets[Dd]ata/*/*.bin* 69 | 70 | # Temporary auto-generated Android Assets 71 | /[Aa]ssets/[Ss]treamingAssets/aa.meta 72 | /[Aa]ssets/[Ss]treamingAssets/aa/* -------------------------------------------------------------------------------- /.idea/.idea.UnityVerletRope/.idea/.gitignore: -------------------------------------------------------------------------------- 1 | # Default ignored files 2 | /shelf/ 3 | /workspace.xml 4 | # Rider ignored files 5 | /contentModel.xml 6 | /.idea.UnityVerletRope.iml 7 | /projectSettingsUpdater.xml 8 | /modules.xml 9 | # Editor-based HTTP Client requests 10 | /httpRequests/ 11 | # Datasource local storage ignored files 12 | /dataSources/ 13 | /dataSources.local.xml 14 | -------------------------------------------------------------------------------- /.idea/.idea.UnityVerletRope/.idea/encodings.xml: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | -------------------------------------------------------------------------------- /.idea/.idea.UnityVerletRope/.idea/indexLayout.xml: 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-------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: 99913f7b4d13b2a47a60c72fd79d03d3 3 | folderAsset: yes 4 | DefaultImporter: 5 | externalObjects: {} 6 | userData: 7 | assetBundleName: 8 | assetBundleVariant: 9 | -------------------------------------------------------------------------------- /Assets/Scripts/RopeRenderer.cs: -------------------------------------------------------------------------------- 1 | using System; 2 | using System.Collections; 3 | using System.Collections.Generic; 4 | using UnityEngine; 5 | 6 | [RequireComponent(typeof(MeshRenderer))] 7 | [RequireComponent(typeof(MeshFilter))] 8 | [RequireComponent(typeof(VerletRope))] 9 | public class RopeRenderer : MonoBehaviour 10 | { 11 | [Min(3)] [SerializeField] private int m_RopeSegmentSides; 12 | 13 | private MeshFilter m_MeshFilter; 14 | private MeshRenderer m_MeshRenderer; 15 | private Mesh m_RopeMesh; 16 | private VerletRope m_Rope; 17 | private Vector3[] m_Vertices; 18 | private int[] m_Triangles; 19 | 20 | private float m_Angle; 21 | private int m_NodeCount; 22 | private bool m_IsInitialized; 23 | 24 | private void Awake() 25 | { 26 | m_MeshFilter = GetComponent(); 27 | m_MeshRenderer = GetComponent(); 28 | 29 | m_RopeMesh = new Mesh(); 30 | m_Angle = ((m_RopeSegmentSides - 2) * 180) / m_RopeSegmentSides; 31 | m_IsInitialized = false; 32 | } 33 | 34 | private void Start() 35 | { 36 | m_Rope = GetComponent(); 37 | m_Vertices = new Vector3[m_Rope.GetNodeCount() * m_RopeSegmentSides]; 38 | m_Triangles = new int[m_RopeSegmentSides * (m_Rope.GetNodeCount() - 1) * 6]; 39 | } 40 | 41 | // private void OnDrawGizmos() 42 | // { 43 | // if (!Application.isPlaying) 44 | // return; 45 | // 46 | // if (m_Vertices is null || m_Triangles is null) 47 | // return; 48 | // 49 | // 50 | // foreach (var vert in m_Vertices) 51 | // { 52 | // Gizmos.color = Color.white; 53 | // Gizmos.DrawSphere(vert, 0.01f); 54 | // } 55 | // 56 | // for (int i = 0; i < m_Triangles.Length - 3; i += 3) 57 | // { 58 | // Gizmos.DrawLine(m_Vertices[m_Triangles[i]], m_Vertices[m_Triangles[i + 1]]); 59 | // Gizmos.DrawLine(m_Vertices[m_Triangles[i + 1]], m_Vertices[m_Triangles[i + 2]]); 60 | // Gizmos.DrawLine(m_Vertices[m_Triangles[i + 2]], m_Vertices[m_Triangles[i]]); 61 | // } 62 | // } 63 | 64 | public void RenderRope(VerletNode[] nodes, float radius) 65 | { 66 | if (m_Vertices is null || m_Triangles is null) 67 | return; 68 | 69 | ComputeVertices(nodes, radius); 70 | 71 | if(!m_IsInitialized){ 72 | ComputeTriangles(); 73 | m_IsInitialized = true; 74 | } 75 | 76 | SetupMeshFilter(); 77 | } 78 | 79 | private void ComputeVertices(VerletNode[] nodes, float radius) 80 | { 81 | var angle = (360f / m_RopeSegmentSides) * Mathf.Deg2Rad; 82 | 83 | for (int i = 0; i < m_Vertices.Length; i++) 84 | { 85 | var nodeindex = i / m_RopeSegmentSides; 86 | var sign = nodeindex == nodes.Length - 1 ? -1 : 1; 87 | Debug.Log($"Node Index: {nodeindex}, Vert Index: {i} , {m_Vertices[i]}"); 88 | 89 | var currNodePosition = nodes[nodeindex].Position; 90 | var normalOfPlane = 91 | (sign * nodes[nodeindex].Position + -sign * nodes[nodeindex + (nodeindex == nodes.Length - 1 ? -1 : 1)].Position) 92 | .normalized; 93 | 94 | var u = Vector3.Cross(normalOfPlane, Vector3.forward).normalized; 95 | var v = Vector3.Cross(u, normalOfPlane).normalized; 96 | 97 | m_Vertices[i] = currNodePosition + radius * (float)Math.Cos(angle * (i % m_RopeSegmentSides)) * u + 98 | radius * (float)Math.Sin(angle * (i % m_RopeSegmentSides)) * v; 99 | } 100 | } 101 | 102 | private void ComputeTriangles() 103 | { 104 | var tn = 0; 105 | 106 | for (int i = 0; i < m_Vertices.Length - m_RopeSegmentSides; i++) 107 | { 108 | var nexti = (i + 1) % m_RopeSegmentSides == 0 ? i - m_RopeSegmentSides + 1 : i + 1; 109 | 110 | m_Triangles[tn] = i; 111 | m_Triangles[tn + 1] = nexti + m_RopeSegmentSides; 112 | m_Triangles[tn + 2] = i + m_RopeSegmentSides; 113 | 114 | m_Triangles[tn + 3] = i; 115 | m_Triangles[tn + 4] = nexti; 116 | m_Triangles[tn + 5] = nexti + m_RopeSegmentSides; 117 | 118 | tn += 6; 119 | } 120 | } 121 | 122 | private void SetupMeshFilter() 123 | { 124 | for (int i = 0; i < m_Vertices.Length; i++) 125 | { 126 | m_Vertices[i] -= transform.position; 127 | } 128 | 129 | m_RopeMesh.Clear(); 130 | m_RopeMesh.vertices = m_Vertices; 131 | m_RopeMesh.triangles = m_Triangles; 132 | 133 | m_MeshFilter.mesh = m_RopeMesh; 134 | m_MeshFilter.mesh.RecalculateBounds(); 135 | m_MeshFilter.mesh.RecalculateNormals(); 136 | } 137 | } -------------------------------------------------------------------------------- /Assets/Scripts/RopeRenderer.cs.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: f419a5bb03a6cc941a638acaaf0211c8 3 | MonoImporter: 4 | externalObjects: {} 5 | serializedVersion: 2 6 | defaultReferences: [] 7 | executionOrder: 0 8 | icon: {instanceID: 0} 9 | userData: 10 | assetBundleName: 11 | assetBundleVariant: 12 | -------------------------------------------------------------------------------- /Assets/Scripts/VerletRope.cs: -------------------------------------------------------------------------------- 1 | using UnityEngine; 2 | using UnityEngine.Serialization; 3 | 4 | public struct VerletNode 5 | { 6 | public Vector3 Position; 7 | public Vector3 PrevoiusPosition; 8 | } 9 | 10 | public class VerletRope : MonoBehaviour 11 | { 12 | private VerletNode[] m_VerletNodes; 13 | [SerializeField] private float m_RopeLength; 14 | [SerializeField] private int m_NumberOfNodes; 15 | [SerializeField] private int m_ConstraintIterationCount; 16 | [SerializeField] private Vector3 m_Gravity; 17 | private float m_DistanceBetweenNodes; 18 | [SerializeField] private float m_RopeRadius; 19 | [SerializeField] private int m_SubSteps = 4; 20 | 21 | private RopeRenderer m_RopeRenderer; 22 | 23 | private void Awake() 24 | { 25 | m_VerletNodes = new VerletNode[(int)(m_NumberOfNodes)]; 26 | m_DistanceBetweenNodes = m_RopeLength / m_NumberOfNodes; 27 | 28 | for (int i = 0; i < m_VerletNodes.Length; i++) 29 | { 30 | m_VerletNodes[i].Position = transform.position - new Vector3(0f, (m_DistanceBetweenNodes * i), 0f); 31 | m_VerletNodes[i].PrevoiusPosition = m_VerletNodes[i].Position; 32 | } 33 | } 34 | 35 | private void Start() 36 | { 37 | m_RopeRenderer = GetComponent(); 38 | } 39 | 40 | private void FixedUpdate() 41 | { 42 | for (int step = 0; step < m_SubSteps; step++) 43 | { 44 | CalculateNewPositions(Time.fixedDeltaTime / m_SubSteps); 45 | for (int i = 0; i < m_ConstraintIterationCount; i++) 46 | { 47 | FixNodeDistances(); 48 | if (i % 2 == 0) 49 | ApplyCollision(); 50 | } 51 | } 52 | 53 | m_RopeRenderer.RenderRope(m_VerletNodes, m_RopeRadius); 54 | } 55 | 56 | // private void OnDrawGizmos() 57 | // { 58 | // if (!Application.isPlaying) 59 | // return; 60 | // 61 | // for (int i = 0; i < m_VerletNodes.Length; i++) 62 | // { 63 | // if (i != m_VerletNodes.Length - 1) 64 | // { 65 | // Gizmos.color = Color.green; 66 | // Gizmos.DrawLine(m_VerletNodes[i].Position, m_VerletNodes[i + 1].Position); 67 | // } 68 | // 69 | // Gizmos.color = Color.blue; 70 | // Gizmos.DrawLine(m_VerletNodes[i].Position, m_VerletNodes[i].PrevoiusPosition); 71 | // } 72 | // } 73 | 74 | private void CalculateNewPositions(float deltaTime) 75 | { 76 | Vector3 gravityStep = m_Gravity * (deltaTime * deltaTime); 77 | 78 | for (int i = 0; i < m_VerletNodes.Length; i++) 79 | { 80 | var currNode = m_VerletNodes[i]; 81 | var newPreviousPosition = currNode.Position; 82 | 83 | var newPosition = (2 * currNode.Position) - currNode.PrevoiusPosition + gravityStep; 84 | 85 | Vector3 direction = newPosition - currNode.Position; 86 | float distance = direction.magnitude; 87 | direction.Normalize(); 88 | 89 | if (Physics.SphereCast(currNode.Position, m_RopeRadius, direction, out RaycastHit hit, distance)) 90 | { 91 | newPosition = hit.point + hit.normal * m_RopeRadius; 92 | } 93 | 94 | m_VerletNodes[i].PrevoiusPosition = newPreviousPosition; 95 | m_VerletNodes[i].Position = newPosition; 96 | } 97 | } 98 | 99 | private void FixNodeDistances() 100 | { 101 | m_VerletNodes[0].Position = transform.position; 102 | 103 | for (int i = 0; i < m_VerletNodes.Length - 1; i++) 104 | { 105 | var n1 = m_VerletNodes[i]; 106 | var n2 = m_VerletNodes[i + 1]; 107 | 108 | var d1 = n1.Position - n2.Position; 109 | var d2 = d1.magnitude; 110 | var d3 = (d2 - m_DistanceBetweenNodes) / d2; 111 | 112 | m_VerletNodes[i].Position -= (d1 * (0.5f * d3)); 113 | m_VerletNodes[i + 1].Position += (d1 * (0.5f * d3)); 114 | } 115 | } 116 | 117 | private void ApplyCollision() 118 | { 119 | for (int i = 0; i < m_VerletNodes.Length; i++) 120 | { 121 | ResolveCollision(ref m_VerletNodes[i]); 122 | } 123 | } 124 | 125 | private void ResolveCollision(ref VerletNode node) 126 | { 127 | var colliders = Physics.OverlapSphere(node.Position, m_RopeRadius); 128 | 129 | foreach (var col in colliders) 130 | { 131 | 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-------------------------------------------------------------------------------- /ProjectSettings/VersionControlSettings.asset: -------------------------------------------------------------------------------- 1 | %YAML 1.1 2 | %TAG !u! tag:unity3d.com,2011: 3 | --- !u!890905787 &1 4 | VersionControlSettings: 5 | m_ObjectHideFlags: 0 6 | m_Mode: Visible Meta Files 7 | m_CollabEditorSettings: 8 | inProgressEnabled: 1 9 | -------------------------------------------------------------------------------- /ProjectSettings/XRSettings.asset: -------------------------------------------------------------------------------- 1 | { 2 | "m_SettingKeys": [ 3 | "VR Device Disabled", 4 | "VR Device User Alert" 5 | ], 6 | "m_SettingValues": [ 7 | "False", 8 | "False" 9 | ] 10 | } -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Rope Physics Using Verlet Integration in Unity 2 | ![Verlet Demo GIF](./SampleGIF.gif) 3 | ## What is Verlet Integration? 4 | [Verlet integration](https://en.wikipedia.org/wiki/Verlet_integration) is a numerical method used to calculate the trajectory of particles in molecular dynamics. But it's widely used in computer graphics and software simulations to simulate physical phenomena and visual effects. 5 | 6 | In each time step, it calculates the position of the particle in the next time step using current position, previous position and its accelaration. Then it applies constraints (if there's any) to maintain the right position of each particle. 7 | 8 | ## How Is It Used to Simulate a Rope? 9 | We see a rope as a string of particles/nodes connected to each other with a fixed distance from each other. By running the Verlet integration for each node in the rope, we can simualte its physics with good accuracy. 10 | 11 | We apply the constraint of nodes having the same distance from each other in each frame, and resolve collisions. 12 | 13 | I also render a cylender-like mesh for the rope, which is generated procedurally in each timestep. 14 | 15 | ## How to Use This Project? 16 | 17 | 1. Clone this repository. 18 | 2. Open the project in Unity 2022.3.16 (Other versions are not tested but they might work). 19 | 3. Open `SampleScene` scene in the scenes folder. 20 | 4. Press play. After pressing Play, the rope appears. 21 | 5. Move the rope around in the scene view and see how it goes (I haven't implemented any control for it to use in the game view. Sorry :( ) 22 | 23 | In the `Prefabs` folder you can find the `Rope` prefab which has two components. 24 | 25 | The first is the `Verlet Rope` component. It has some fields: 26 | 27 | ![Verlet Rope Component](./VerletRope.png) 28 | * **Rope Length:** The length of the rope. 29 | * **Number of Nodes:** How many nodes the rope consists of. the more the nodes are, the more accurate the simualtion is, but it will be computationally heavier. 30 | * **Constraint Iteration Count:** How many times the constraints are applied in each timestep. The more the iterations, the stiffer the rope becomes. 31 | * **Gravity:** The gravity vector. 32 | * **Rope Radius:** The radius of the rope. 33 | * **Substeps:** Each fixed delta time is divided into smaller time steps called substeps for better accuracy. This field sets the number of substeps. 34 | 35 | The other component is the `Rope Renderer`. It has only one field: 36 | 37 | ![Rope Renderer Component](./RopeRenderer.png) 38 | 39 | * **Rope Segment Sides:** The number of sides the rope will have when the 3D mesh is rendered. 40 | --- 41 | You can read the detailed breakdown of this implementation [here](https://alirezaft98.medium.com/verlet-integration-simulating-rope-physics-in-unity-b4f0ffde38fb) and you can read about how the rope is rendered [here](https://alirezaft98.medium.com/verlet-integration-rendering-the-rope-97dae2832dce). 42 | 43 | -------------------------------------------------------------------------------- /RopeRenderer.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alirezaft/UnityVerletRope/65fda4500ced517a33819ed62e97042e4528f2a4/RopeRenderer.png -------------------------------------------------------------------------------- /SampleGIF.gif: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alirezaft/UnityVerletRope/65fda4500ced517a33819ed62e97042e4528f2a4/SampleGIF.gif -------------------------------------------------------------------------------- /VerletRope.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/alirezaft/UnityVerletRope/65fda4500ced517a33819ed62e97042e4528f2a4/VerletRope.png --------------------------------------------------------------------------------