├── ProjectSettings ├── ProjectVersion.txt ├── ClusterInputManager.asset ├── PresetManager.asset ├── EditorBuildSettings.asset ├── XRSettings.asset ├── TimeManager.asset ├── VFXManager.asset ├── AudioManager.asset ├── TagManager.asset ├── UnityConnectSettings.asset ├── PackageManagerSettings.asset ├── EditorSettings.asset ├── DynamicsManager.asset ├── NavMeshAreas.asset ├── Physics2DSettings.asset ├── GraphicsSettings.asset ├── InputManager.asset ├── QualitySettings.asset └── ProjectSettings.asset ├── .vsconfig ├── Assets ├── Scenes.meta ├── Scripts.meta ├── Materials.meta ├── Scenes │ ├── SampleDamper2DGraph.meta │ └── SampleDamper2DGraph │ │ ├── SampleDamper2DGraph.unity.meta │ │ ├── SampleDamper2DGraph.cs.meta │ │ ├── SampleDamper2DGraph.cs │ │ └── SampleDamper2DGraph.unity ├── Materials │ ├── SelfIllum-Blue.mat.meta │ ├── SelfIllum-Red.mat.meta │ ├── SelfIllum-Blue.mat │ └── SelfIllum-Red.mat └── Scripts │ ├── ToolDamper.cs.meta │ └── ToolDamper.cs ├── LICENSE ├── README.md ├── .gitignore └── Packages ├── manifest.json └── packages-lock.json /ProjectSettings/ProjectVersion.txt: -------------------------------------------------------------------------------- 1 | m_EditorVersion: 2019.4.21f1 2 | m_EditorVersionWithRevision: 2019.4.21f1 (b76dac84db26) 3 | -------------------------------------------------------------------------------- /.vsconfig: -------------------------------------------------------------------------------- 1 | { 2 | "version": "1.0", 3 | "components": [ 4 | "Microsoft.VisualStudio.Workload.ManagedGame" 5 | ] 6 | } 7 | -------------------------------------------------------------------------------- /ProjectSettings/ClusterInputManager.asset: -------------------------------------------------------------------------------- 1 | %YAML 1.1 2 | %TAG !u! 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tag:unity3d.com,2011: 3 | --- !u!114 &1 4 | MonoBehaviour: 5 | m_ObjectHideFlags: 61 6 | m_CorrespondingSourceObject: {fileID: 0} 7 | m_PrefabInstance: {fileID: 0} 8 | m_PrefabAsset: {fileID: 0} 9 | m_GameObject: {fileID: 0} 10 | m_Enabled: 1 11 | m_EditorHideFlags: 0 12 | m_Script: {fileID: 13964, guid: 0000000000000000e000000000000000, type: 0} 13 | m_Name: 14 | m_EditorClassIdentifier: 15 | m_ScopedRegistriesSettingsExpanded: 1 16 | oneTimeWarningShown: 0 17 | m_Registries: 18 | - m_Id: main 19 | m_Name: 20 | m_Url: https://packages.unity.com 21 | m_Scopes: [] 22 | m_IsDefault: 1 23 | m_UserSelectedRegistryName: 24 | m_UserAddingNewScopedRegistry: 0 25 | m_RegistryInfoDraft: 26 | m_ErrorMessage: 27 | m_Original: 28 | m_Id: 29 | m_Name: 30 | m_Url: 31 | m_Scopes: [] 32 | m_IsDefault: 0 33 | m_Modified: 0 34 | m_Name: 35 | m_Url: 36 | m_Scopes: 37 | - 38 | m_SelectedScopeIndex: 0 39 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2021 Meta 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # ArtOfDamping 2 | Unity code used for the article "The Art of Damping" at https://www.alexisbacot.com/blog/the-art-of-damping 3 | 4 | It includes two scripts: 5 | - ToolDamper.cs: with all the damping functions 6 | - SampleDamper2DGraph.cs: Script for the sample scene to control the goal with arrow key or mouse 7 | 8 | One scene: 9 | - SampleDamper2DGraph: Scene used to display two goal & follower points in red & blue 10 | 11 | How to Use: 12 | - Download Unity 2019 LTS (it's free) 13 | - Clone / Download this repository 14 | - Start Unity & select your local repository folder as your unity project 15 | - In Unity: There is only one scene right now so the SampleDamper2DGraph scene should be your current scene automatically 16 | - In Unity: Just click Play to test! Use the up & down arrow keys to move the goal point slowly, or the mouse to move it instantly 17 | - In Unity: Select the *** 2D Graph *** GameObject to change the damping function used and its parameters 18 | - In Unity: FEEL the damping, change the parameters, play with each function to understand what it does intuitively :) 19 | 20 | Most of the code is just a port to C# from Daniel Holden original article at http://theorangeduck.com/page/spring-roll-call#damper 21 | -------------------------------------------------------------------------------- /ProjectSettings/EditorSettings.asset: -------------------------------------------------------------------------------- 1 | %YAML 1.1 2 | %TAG !u! tag:unity3d.com,2011: 3 | --- !u!159 &1 4 | EditorSettings: 5 | m_ObjectHideFlags: 0 6 | serializedVersion: 9 7 | m_ExternalVersionControlSupport: Visible Meta Files 8 | m_SerializationMode: 2 9 | m_LineEndingsForNewScripts: 0 10 | m_DefaultBehaviorMode: 0 11 | m_PrefabRegularEnvironment: 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-------------------------------------------------------------------------------- 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/master/Unity.gitignore 4 | # 5 | /[Ll]ibrary/ 6 | /[Tt]emp/ 7 | /[Oo]bj/ 8 | /[Bb]uild/ 9 | /[Bb]uilds/ 10 | /[Ll]ogs/ 11 | /[Mm]emoryCaptures/ 12 | 13 | # Asset meta data should only be ignored when the corresponding asset is also ignored 14 | !/[Aa]ssets/**/*.meta 15 | 16 | # Uncomment this line if you wish to ignore the asset store tools plugin 17 | # /[Aa]ssets/AssetStoreTools* 18 | 19 | # Autogenerated Jetbrains Rider plugin 20 | [Aa]ssets/Plugins/Editor/JetBrains* 21 | 22 | # Visual Studio cache directory 23 | .vs/ 24 | 25 | # Gradle cache directory 26 | .gradle/ 27 | 28 | # Autogenerated VS/MD/Consulo solution and project files 29 | ExportedObj/ 30 | .consulo/ 31 | *.csproj 32 | *.unityproj 33 | *.sln 34 | *.suo 35 | *.tmp 36 | *.user 37 | 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//TimedCriticalNoGoalSpeed, 20 | } 21 | 22 | //-------------------------------------------------------------------- 23 | [Header("Damping Params")] 24 | public EnumDampingType DampingType = EnumDampingType.Spring; 25 | public float halflife = 0.5f; 26 | public float frequency = 0.5f; 27 | public float speedMoveRight = 20.0f; 28 | 29 | //[Header("Timed Damping Params")] 30 | //public float timeToGoal = 1.0f; 31 | //public float apprehension = 2.0f; 32 | 33 | [Header("Goals Params")] 34 | public float goalMinY; 35 | public float goalMaxY, goalMoveSpeed; 36 | 37 | [Header("Links")] 38 | public Transform tsfmGoal; 39 | public Transform tsfmFollowing; 40 | public Camera cam; 41 | 42 | // Internal 43 | private Vector3 _posFollower, _posGoal, _posCam; 44 | private float _speedFollower; 45 | private float _speedGoal; 46 | // Another set of position and speed used for the double damper 47 | private float posGoal2, speedGoal2; 48 | 49 | //-------------------------------------------------------------------- 50 | private void Update() 51 | { 52 | _posGoal = tsfmGoal.position; 53 | _posFollower = tsfmFollowing.position; 54 | _posCam = cam.transform.position; 55 | 56 | MoveGoal(); 57 | 58 | // While changing values in the editor sometimes these values will be 0, we want to skip these! 59 | if (halflife == 0 || frequency == 0) return; 60 | 61 | // DAMPING: Follower y pos tries to match goal y 62 | switch(DampingType) 63 | { 64 | case EnumDampingType.Normal: _posFollower.y = ToolDamper.damper(_posFollower.y, _posGoal.y, halflife, Time.deltaTime); break; 65 | case EnumDampingType.Spring: ToolDamper.damper_spring(ref _posFollower.y, ref _speedFollower, _posGoal.y, _speedGoal, frequency, halflife, Time.deltaTime); break; 66 | case EnumDampingType.UnitySmoothDamp: _posFollower.y = Mathf.SmoothDamp(_posFollower.y, _posGoal.y, ref _speedFollower, halflife); break; 67 | case EnumDampingType.SpringCritical: ToolDamper.damper_spring_critical(ref _posFollower.y, ref _speedFollower, _posGoal.y, _speedGoal, halflife, Time.deltaTime); break; 68 | case EnumDampingType.SpringCriticalNoGoalSpeed: ToolDamper.damper_spring_critical_noGoalSpeed(ref _posFollower.y, ref _speedFollower, _posGoal.y, halflife, Time.deltaTime); break; 69 | case EnumDampingType.DoubleCriticalNoGoalSpeed: ToolDamper.double_spring_damper_implicit(ref _posFollower.y, ref _speedFollower, ref posGoal2, ref speedGoal2, _posGoal.y, halflife, Time.deltaTime); break; 70 | //case EnumDampingType.TimedCriticalNoGoalSpeed: ToolDamper.timed_spring_damper_implicit(ref _posFollower.y, ref _speedFollower, ref posGoal2, _posGoal.y, timeToGoal, halflife, Time.deltaTime, apprehension); break; 71 | default: Debug.LogWarning("[SampleDamper] DampingType: " + DampingType + " is not supported"); break; 72 | } 73 | 74 | // Move all to the right to have some trails behind follower 75 | _posFollower.x += speedMoveRight * Time.deltaTime; 76 | _posGoal.x += speedMoveRight * Time.deltaTime; 77 | _posCam.x += speedMoveRight * Time.deltaTime; 78 | 79 | // Finalize 80 | tsfmFollowing.position = _posFollower; 81 | tsfmGoal.position = _posGoal; 82 | cam.transform.position = _posCam; 83 | } 84 | 85 | //-------------------------------------------------------------------- 86 | private void MoveGoal() 87 | { 88 | float newGoalY = 0; 89 | bool hasGoalChanged = false; 90 | 91 | // Use arrows to slowly change goal y position 92 | float inputVertical = Input.GetAxis("Vertical"); 93 | if (inputVertical != 0) 94 | { 95 | newGoalY = _posGoal.y + inputVertical * goalMoveSpeed * Time.deltaTime; 96 | hasGoalChanged = true; 97 | } 98 | 99 | // Click to change goal y position instantly 100 | if (Input.GetMouseButtonDown(0)) 101 | { 102 | newGoalY = cam.ScreenToWorldPoint(Input.mousePosition).y; 103 | hasGoalChanged = true; 104 | } 105 | 106 | if (hasGoalChanged) 107 | { 108 | newGoalY = Mathf.Clamp(newGoalY, goalMinY, goalMaxY); 109 | 110 | _speedGoal = (newGoalY - _posGoal.y) / Time.deltaTime; 111 | 112 | _posGoal.y = newGoalY; 113 | } 114 | else 115 | _speedGoal = 0.0f; 116 | } 117 | 118 | //-------------------------------------------------------------------- 119 | } 120 | 121 | //-------------------------------------------------------------------- -------------------------------------------------------------------------------- /ProjectSettings/InputManager.asset: -------------------------------------------------------------------------------- 1 | %YAML 1.1 2 | %TAG !u! tag:unity3d.com,2011: 3 | --- !u!13 &1 4 | InputManager: 5 | m_ObjectHideFlags: 0 6 | serializedVersion: 2 7 | m_Axes: 8 | - serializedVersion: 3 9 | m_Name: Horizontal 10 | descriptiveName: 11 | descriptiveNegativeName: 12 | negativeButton: left 13 | positiveButton: right 14 | altNegativeButton: a 15 | altPositiveButton: d 16 | gravity: 3 17 | dead: 0.001 18 | sensitivity: 3 19 | snap: 1 20 | invert: 0 21 | type: 0 22 | axis: 0 23 | joyNum: 0 24 | - 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-------------------------------------------------------------------------------- /Assets/Scripts/ToolDamper.cs: -------------------------------------------------------------------------------- 1 | //-------------------------------------------------------------------- 2 | // Ported by Alexis Bacot - 2021 - www.alexisbacot.com 3 | // From Daniel Holden (https://twitter.com/anorangeduck) 4 | // Original article http://theorangeduck.com/page/spring-roll-call#damper 5 | //-------------------------------------------------------------------- 6 | using UnityEngine; 7 | 8 | //-------------------------------------------------------------------- 9 | public class ToolDamper 10 | { 11 | //-------------------------------------------------------------------- 12 | public static float damper(float x, float g, float halflife, float dt) 13 | { 14 | return Mathf.Lerp(x, g, 1.0f - fast_negexp((0.69314718056f * dt) / (halflife + Mathf.Epsilon))); 15 | } 16 | 17 | //-------------------------------------------------------------------- 18 | private static float fast_negexp(float x) 19 | { 20 | return 1.0f / (1.0f + x + 0.48f * x * x + 0.235f * x * x * x); 21 | } 22 | 23 | //-------------------------------------------------------------------- 24 | private static float squaref(float x) { return x * x; } 25 | 26 | //-------------------------------------------------------------------- 27 | /// 28 | /// Damper spring 29 | /// 30 | /// how many oscillations are done 31 | /// how quick the goal is reached 32 | public static void damper_spring(ref float x, ref float v, float x_goal, float v_goal, float frequency, float halflife, float dt) 33 | { 34 | float g = x_goal; 35 | float q = v_goal; 36 | float s = frequency_to_stiffness(frequency); 37 | float d = halflife_to_damping(halflife); 38 | float c = g + (d * q) / (s + Mathf.Epsilon); 39 | float y = d / 2.0f; 40 | 41 | if (Mathf.Abs(s - (d * d) / 4.0f) < Mathf.Epsilon) // Critically Damped 42 | { 43 | float j0 = x - c; 44 | float j1 = v + j0 * y; 45 | 46 | float eydt = fast_negexp(y * dt); 47 | 48 | x = j0 * eydt + dt * j1 * eydt + c; 49 | v = -y * j0 * eydt - y * dt * j1 * eydt + j1 * eydt; 50 | } 51 | else if (s - (d * d) / 4.0f > 0.0) // Under Damped 52 | { 53 | float w = Mathf.Sqrt(s - (d * d) / 4.0f); 54 | float j = Mathf.Sqrt(squaref(v + y * (x - c)) / (w * w + Mathf.Epsilon) + squaref(x - c)); 55 | float p = Mathf.Atan((v + (x - c) * y) / (-(x - c) * w + Mathf.Epsilon)); 56 | 57 | j = (x - c) > 0.0f ? j : -j; 58 | 59 | float eydt = fast_negexp(y * dt); 60 | 61 | x = j * eydt * Mathf.Cos(w * dt + p) + c; 62 | v = -y * j * eydt * Mathf.Cos(w * dt + p) - w * j * eydt * Mathf.Sin(w * dt + p); 63 | } 64 | else if (s - (d * d) / 4.0f < 0.0) // Over Damped 65 | { 66 | float y0 = (d + Mathf.Sqrt(d * d - 4 * s)) / 2.0f; 67 | float y1 = (d - Mathf.Sqrt(d * d - 4 * s)) / 2.0f; 68 | float j1 = (c * y0 - x * y0 - v) / (y1 - y0); 69 | float j0 = x - j1 - c; 70 | 71 | float ey0dt = fast_negexp(y0 * dt); 72 | float ey1dt = fast_negexp(y1 * dt); 73 | 74 | x = j0 * ey0dt + j1 * ey1dt + c; 75 | v = -y0 * j0 * ey0dt - y1 * j1 * ey1dt; 76 | } 77 | } 78 | 79 | //-------------------------------------------------------------------- 80 | /// 81 | /// Damper spring set to critical (w = 0) spring goes to goal as fast as possible without oscillations, frequency is set by halflife 82 | /// 83 | public static void damper_spring_critical(ref float x, ref float v, float x_goal, float v_goal, float halflife, float dt) 84 | { 85 | float g = x_goal; 86 | float q = v_goal; 87 | float d = halflife_to_damping(halflife); 88 | float c = g + (d * q) / ((d * d) / 4.0f); 89 | float y = d / 2.0f; 90 | float j0 = x - c; 91 | float j1 = v + j0 * y; 92 | float eydt = fast_negexp(y * dt); 93 | 94 | x = eydt * (j0 + j1 * dt) + c; 95 | v = eydt * (v - j1 * y * dt); 96 | } 97 | 98 | //-------------------------------------------------------------------- 99 | /// 100 | /// Damper spring set to critical AND we assume the goal has no speed, very smooth! smoothness similar to unity smoothdamping 101 | /// 102 | public static void damper_spring_critical_noGoalSpeed( ref float x, ref float v, float x_goal, float halflife, float dt) 103 | { 104 | float y = halflife_to_damping(halflife) / 2.0f; 105 | float j0 = x - x_goal; 106 | float j1 = v + j0 * y; 107 | float eydt = fast_negexp(y * dt); 108 | 109 | x = eydt * (j0 + j1 * dt) + x_goal; 110 | v = eydt * (v - j1 * y * dt); 111 | } 112 | 113 | //-------------------------------------------------------------------- 114 | /// 115 | /// Double Damper spring set to critical, we assume goal has no speed 116 | /// Both follower and goal are damped, to achieve maximum smoothness 117 | /// 118 | public static void double_spring_damper_implicit( ref float x, ref float v, ref float xi, ref float vi, float x_goal, float halflife, float dt) 119 | { 120 | damper_spring_critical_noGoalSpeed(ref xi, ref vi, x_goal, 0.5f * halflife, dt); 121 | damper_spring_critical_noGoalSpeed(ref x, ref v, xi, 0.5f * halflife, dt); 122 | } 123 | 124 | //-------------------------------------------------------------------- 125 | /*public static void timed_spring_damper_implicit( ref float x, ref float v, ref float xi, float x_goal, float t_goal, float halflife, float dt, float apprehension = 2.0f) 126 | { 127 | float min_time = t_goal > dt ? t_goal : dt; 128 | 129 | float v_goal = (x_goal - xi) / min_time; 130 | 131 | float t_goal_future = dt + apprehension * halflife; 132 | float x_goal_future = t_goal_future < t_goal ? 133 | xi + v_goal * t_goal_future : x_goal; 134 | 135 | damper_spring_critical_noGoalSpeed(ref x, ref v, x_goal_future, halflife, dt); 136 | 137 | xi += v_goal * dt; 138 | }*/ 139 | 140 | //-------------------------------------------------------------------- 141 | public static float critical_halflife(float frequency) 142 | { 143 | return damping_to_halflife(Mathf.Sqrt(frequency_to_stiffness(frequency) * 4.0f)); 144 | } 145 | 146 | //-------------------------------------------------------------------- 147 | public static float critical_frequency(float halflife) 148 | { 149 | return stiffness_to_frequency(squaref(halflife_to_damping(halflife)) / 4.0f); 150 | } 151 | 152 | //-------------------------------------------------------------------- 153 | private static float frequency_to_stiffness(float frequency) 154 | { 155 | return squaref(2.0f * Mathf.PI * frequency); 156 | } 157 | 158 | //-------------------------------------------------------------------- 159 | private static float stiffness_to_frequency(float stiffness) 160 | { 161 | return Mathf.Sqrt(stiffness) / (2.0f * Mathf.PI); 162 | } 163 | 164 | //-------------------------------------------------------------------- 165 | private static float halflife_to_damping(float halflife) 166 | { 167 | return (4.0f * 0.69314718056f) / (halflife + Mathf.Epsilon); 168 | } 169 | 170 | //-------------------------------------------------------------------- 171 | private static float damping_to_halflife(float damping) 172 | { 173 | return (4.0f * 0.69314718056f) / (damping + Mathf.Epsilon); 174 | } 175 | 176 | //-------------------------------------------------------------------- 177 | } 178 | 179 | //-------------------------------------------------------------------- 180 | -------------------------------------------------------------------------------- /Packages/packages-lock.json: -------------------------------------------------------------------------------- 1 | { 2 | "dependencies": { 3 | "com.unity.ide.vscode": { 4 | "version": "1.2.3", 5 | "depth": 0, 6 | "source": "registry", 7 | "dependencies": {}, 8 | "url": "https://packages.unity.com" 9 | }, 10 | "com.unity.sysroot": { 11 | "version": "0.1.19-preview", 12 | "depth": 1, 13 | "source": "registry", 14 | "dependencies": {}, 15 | "url": "https://packages.unity.com" 16 | }, 17 | "com.unity.sysroot.linux-x86_64": { 18 | "version": "0.1.14-preview", 19 | "depth": 1, 20 | "source": 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