├── .gitattributes ├── .gitignore ├── Assets ├── Flask.meta ├── Flask │ ├── Tween.cs │ └── Tween.cs.meta ├── Test1D.meta ├── Test1D │ ├── Test1D.unity │ ├── Test1D.unity.meta │ ├── TestDTween.cs │ ├── TestDTween.cs.meta │ ├── TestDirect.cs │ ├── TestDirect.cs.meta │ ├── TestETween.cs │ └── TestETween.cs.meta ├── Test3D.meta ├── Test3D │ ├── Cyan.mat │ ├── Cyan.mat.meta │ ├── Dots.mat │ ├── Dots.mat.meta │ ├── RandomWalker.cs │ ├── RandomWalker.cs.meta │ ├── Red.mat │ ├── Red.mat.meta │ ├── Test3D.unity │ ├── Test3D.unity.meta │ ├── TestDTween.cs │ ├── TestDTween.cs.meta │ ├── TestETween.cs │ ├── TestETween.cs.meta │ ├── Yellow.mat │ └── Yellow.mat.meta ├── TestRotation.meta └── TestRotation │ ├── RandomRotation.cs │ ├── RandomRotation.cs.meta │ ├── Teapot.fbx │ ├── Teapot.fbx.meta │ ├── TestDTween.cs │ ├── TestDTween.cs.meta │ ├── TestETween.cs │ ├── TestETween.cs.meta │ ├── TestRotation.unity │ └── TestRotation.unity.meta ├── ProjectSettings ├── AudioManager.asset ├── DynamicsManager.asset ├── EditorBuildSettings.asset ├── EditorSettings.asset ├── GraphicsSettings.asset ├── InputManager.asset ├── NavMeshAreas.asset ├── NetworkManager.asset ├── Physics2DSettings.asset ├── ProjectSettings.asset ├── ProjectVersion.txt ├── QualitySettings.asset ├── TagManager.asset ├── TimeManager.asset ├── UnityAdsSettings.asset └── UnityAnalyticsManager.asset └── README.md /.gitattributes: -------------------------------------------------------------------------------- 1 | # Auto detect text files and perform LF normalization 2 | * text=auto 3 | 4 | # Custom for Visual Studio 5 | *.cs diff=csharp 6 | 7 | # Standard to msysgit 8 | *.doc diff=astextplain 9 | *.DOC diff=astextplain 10 | *.docx diff=astextplain 11 | *.DOCX diff=astextplain 12 | *.dot diff=astextplain 13 | *.DOT diff=astextplain 14 | *.pdf diff=astextplain 15 | *.PDF diff=astextplain 16 | *.rtf diff=astextplain 17 | *.RTF diff=astextplain 18 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | /[Ll]ibrary/ 2 | /[Tt]emp/ 3 | /[Oo]bj/ 4 | /[Bb]uild/ 5 | 6 | # Autogenerated VS/MD solution and project files 7 | *.csproj 8 | *.unityproj 9 | *.sln 10 | *.suo 11 | *.tmp 12 | *.user 13 | *.userprefs 14 | *.pidb 15 | *.booproj 16 | 17 | # Unity3D generated meta files 18 | *.pidb.meta 19 | 20 | # Unity3D Generated File On Crash Reports 21 | sysinfo.txt 22 | 23 | # ========================= 24 | # Operating System Files 25 | # ========================= 26 | 27 | # OSX 28 | # ========================= 29 | 30 | .DS_Store 31 | .AppleDouble 32 | .LSOverride 33 | 34 | # Thumbnails 35 | ._* 36 | 37 | # Files that might appear in the root of a volume 38 | .DocumentRevisions-V100 39 | .fseventsd 40 | .Spotlight-V100 41 | .TemporaryItems 42 | .Trashes 43 | .VolumeIcon.icns 44 | 45 | # Directories potentially created on remote AFP share 46 | .AppleDB 47 | .AppleDesktop 48 | Network Trash Folder 49 | Temporary Items 50 | .apdisk 51 | 52 | # Windows 53 | # ========================= 54 | 55 | # Windows image file caches 56 | Thumbs.db 57 | ehthumbs.db 58 | 59 | # Folder config file 60 | Desktop.ini 61 | 62 | # Recycle Bin used on file shares 63 | $RECYCLE.BIN/ 64 | 65 | # Windows Installer files 66 | *.cab 67 | *.msi 68 | *.msm 69 | *.msp 70 | 71 | # Windows shortcuts 72 | *.lnk 73 | -------------------------------------------------------------------------------- /Assets/Flask.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: 76c4c58d5cd13482898fabc0d54597d3 3 | folderAsset: yes 4 | timeCreated: 1452407696 5 | licenseType: Pro 6 | DefaultImporter: 7 | userData: 8 | assetBundleName: 9 | assetBundleVariant: 10 | -------------------------------------------------------------------------------- /Assets/Flask/Tween.cs: -------------------------------------------------------------------------------- 1 | using UnityEngine; 2 | using System.Runtime.InteropServices; 3 | 4 | namespace Flask 5 | { 6 | // exponential interpolation 7 | static class ETween 8 | { 9 | public static float Step(float current, float target, float omega) 10 | { 11 | return target - (target - current) * Mathf.Exp(-omega * Time.deltaTime); 12 | } 13 | 14 | public static float StepAngle(float current, float target, float omega) 15 | { 16 | return target - Mathf.DeltaAngle(current, target) * Mathf.Exp(-omega * Time.deltaTime); 17 | } 18 | 19 | public static Vector3 Step(Vector3 current, Vector3 target, float omega) 20 | { 21 | return Vector3.Lerp(target, current, Mathf.Exp(-omega * Time.deltaTime)); 22 | } 23 | 24 | public static Quaternion Step(Quaternion current, Quaternion target, float omega) 25 | { 26 | if (current == target) 27 | return target; 28 | else 29 | return Quaternion.Lerp(target, current, Mathf.Exp(-omega * Time.deltaTime)); 30 | } 31 | } 32 | 33 | // tweening with the critically damped sprint model 34 | struct DTween 35 | { 36 | public float position; 37 | public float velocity; 38 | public float omega; 39 | 40 | public DTween(float position, float omega) 41 | { 42 | this.position = position; 43 | this.velocity = 0; 44 | this.omega = omega; 45 | } 46 | 47 | public void Step(float target) 48 | { 49 | var dt = Time.deltaTime; 50 | var n1 = velocity - (position - target) * (omega * omega * dt); 51 | var n2 = 1 + omega * dt; 52 | velocity = n1 / (n2 * n2); 53 | position += velocity * dt; 54 | } 55 | 56 | public static implicit operator float(DTween m) 57 | { 58 | return m.position; 59 | } 60 | } 61 | 62 | struct DTweenVector2 63 | { 64 | public Vector2 position; 65 | public Vector2 velocity; 66 | public float omega; 67 | 68 | public DTweenVector2(Vector2 position, float omega) 69 | { 70 | this.position = position; 71 | this.velocity = Vector2.zero; 72 | this.omega = omega; 73 | } 74 | 75 | public void Step(Vector2 target) 76 | { 77 | var dt = Time.deltaTime; 78 | var n1 = velocity - (position - target) * (omega * omega * dt); 79 | var n2 = 1 + omega * dt; 80 | velocity = n1 / (n2 * n2); 81 | position += velocity * dt; 82 | } 83 | 84 | public static implicit operator Vector2(DTweenVector2 m) 85 | { 86 | return m.position; 87 | } 88 | } 89 | 90 | struct DTweenVector3 91 | { 92 | public Vector3 position; 93 | public Vector3 velocity; 94 | public float omega; 95 | 96 | public DTweenVector3(Vector3 position, float omega) 97 | { 98 | this.position = position; 99 | this.velocity = Vector3.zero; 100 | this.omega = omega; 101 | } 102 | 103 | public void Step(Vector3 target) 104 | { 105 | var dt = Time.deltaTime; 106 | var n1 = velocity - (position - target) * (omega * omega * dt); 107 | var n2 = 1 + omega * dt; 108 | velocity = n1 / (n2 * n2); 109 | position += velocity * dt; 110 | } 111 | 112 | public static implicit operator Vector3(DTweenVector3 m) 113 | { 114 | return m.position; 115 | } 116 | } 117 | 118 | struct DTweenVector4 119 | { 120 | public Vector4 position; 121 | public Vector4 velocity; 122 | public float omega; 123 | 124 | public DTweenVector4(Vector4 position, float omega) 125 | { 126 | this.position = position; 127 | this.velocity = Vector4.zero; 128 | this.omega = omega; 129 | } 130 | 131 | public void Step(Vector4 target) 132 | { 133 | var dt = Time.deltaTime; 134 | var n1 = velocity - (position - target) * (omega * omega * dt); 135 | var n2 = 1 + omega * dt; 136 | velocity = n1 / (n2 * n2); 137 | position += velocity * dt; 138 | } 139 | 140 | public static implicit operator Vector4(DTweenVector4 m) 141 | { 142 | return m.position; 143 | } 144 | } 145 | 146 | struct DTweenQuaternion 147 | { 148 | [StructLayout(LayoutKind.Explicit)] 149 | struct QVUnion 150 | { 151 | [FieldOffset(0)] public Vector4 v; 152 | [FieldOffset(0)] public Quaternion q; 153 | } 154 | 155 | static Vector4 q2v(Quaternion q) 156 | { 157 | return new Vector4(q.x, q.y, q.z, q.w); 158 | } 159 | 160 | QVUnion _rotation; 161 | 162 | public Quaternion rotation { 163 | get { return _rotation.q; } 164 | set { _rotation.q = value; } 165 | } 166 | 167 | public Vector4 velocity; 168 | public float omega; 169 | 170 | public DTweenQuaternion(Quaternion rotation, float omega) 171 | { 172 | _rotation.v = Vector4.zero; // needed for suppressing warnings 173 | _rotation.q = rotation; 174 | velocity = Vector4.zero; 175 | this.omega = omega; 176 | } 177 | 178 | public void Step(Quaternion target) 179 | { 180 | var vtarget = q2v(target); 181 | // We can use either of vtarget/-vtarget. Use closer one. 182 | if (Vector4.Dot(_rotation.v, vtarget) < 0) vtarget = -vtarget; 183 | var dt = Time.deltaTime; 184 | var n1 = velocity - (_rotation.v - vtarget) * (omega * omega * dt); 185 | var n2 = 1 + omega * dt; 186 | velocity = n1 / (n2 * n2); 187 | _rotation.v = (_rotation.v + velocity * dt).normalized; 188 | } 189 | 190 | public static implicit operator Quaternion(DTweenQuaternion m) 191 | { 192 | return m.rotation; 193 | } 194 | } 195 | } 196 | -------------------------------------------------------------------------------- /Assets/Flask/Tween.cs.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: c194b21ff1aaf4492b8e78c1dd410605 3 | timeCreated: 1452407447 4 | licenseType: Pro 5 | MonoImporter: 6 | serializedVersion: 2 7 | defaultReferences: [] 8 | executionOrder: 0 9 | icon: {instanceID: 0} 10 | userData: 11 | assetBundleName: 12 | assetBundleVariant: 13 | 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_width = 10; 9 | [SerializeField] float _omega = 1; 10 | 11 | Vector3 _origin; 12 | DTween _position = new DTween(0, 1); 13 | 14 | void Start() 15 | { 16 | _origin = transform.position; 17 | } 18 | 19 | void Update() 20 | { 21 | var target = Input.GetAxis("Horizontal") * _width; 22 | 23 | _position.omega = _omega; 24 | _position.Step(target); 25 | 26 | transform.position = _origin + Vector3.right * _position; 27 | } 28 | } 29 | } 30 | -------------------------------------------------------------------------------- /Assets/Test1D/TestDTween.cs.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: 5d61e6126118240daaf753f436b94d6f 3 | timeCreated: 1452407678 4 | licenseType: Pro 5 | MonoImporter: 6 | serializedVersion: 2 7 | defaultReferences: [] 8 | executionOrder: 0 9 | icon: {instanceID: 0} 10 | userData: 11 | assetBundleName: 12 | assetBundleVariant: 13 | -------------------------------------------------------------------------------- /Assets/Test1D/TestDirect.cs: -------------------------------------------------------------------------------- 1 | using UnityEngine; 2 | 3 | namespace Test1D 4 | { 5 | public class TestDirect : MonoBehaviour 6 | { 7 | [SerializeField] float _width = 10; 8 | 9 | Vector3 _origin; 10 | 11 | void Start() 12 | { 13 | _origin = transform.position; 14 | } 15 | 16 | void Update() 17 | { 18 | var position = Input.GetAxis("Horizontal") * _width; 19 | transform.position = _origin + Vector3.right * position; 20 | } 21 | } 22 | } 23 | -------------------------------------------------------------------------------- /Assets/Test1D/TestDirect.cs.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: 653322973e0bb4cccb87b7d3c1552c40 3 | timeCreated: 1452407678 4 | licenseType: Pro 5 | MonoImporter: 6 | serializedVersion: 2 7 | defaultReferences: [] 8 | executionOrder: 0 9 | icon: {instanceID: 0} 10 | userData: 11 | assetBundleName: 12 | assetBundleVariant: 13 | -------------------------------------------------------------------------------- /Assets/Test1D/TestETween.cs: -------------------------------------------------------------------------------- 1 | using UnityEngine; 2 | using Flask; 3 | 4 | namespace Test1D 5 | { 6 | public class TestETween : MonoBehaviour 7 | { 8 | [SerializeField] float _width = 10; 9 | [SerializeField] float _omega = 1; 10 | 11 | Vector3 _origin; 12 | float _position; 13 | 14 | void Start() 15 | { 16 | _origin = transform.position; 17 | } 18 | 19 | void Update() 20 | { 21 | var target = Input.GetAxis("Horizontal") * _width; 22 | 23 | _position = ETween.Step(_position, target, _omega); 24 | 25 | transform.position = _origin + Vector3.right * _position; 26 | } 27 | } 28 | } 29 | -------------------------------------------------------------------------------- /Assets/Test1D/TestETween.cs.meta: 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-------------------------------------------------------------------------------- /Assets/TestRotation/RandomRotation.cs: -------------------------------------------------------------------------------- 1 | using UnityEngine; 2 | using System.Collections; 3 | 4 | namespace TestRotation 5 | { 6 | public class RandomRotation : MonoBehaviour 7 | { 8 | [SerializeField] float _interval = 1; 9 | 10 | IEnumerator Start() 11 | { 12 | while (true) 13 | { 14 | transform.rotation = Random.rotation; 15 | yield return new WaitForSeconds(_interval); 16 | } 17 | } 18 | } 19 | } 20 | -------------------------------------------------------------------------------- /Assets/TestRotation/RandomRotation.cs.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: 3348306e81da844359a8718f62de32f0 3 | timeCreated: 1452411868 4 | licenseType: Pro 5 | MonoImporter: 6 | serializedVersion: 2 7 | defaultReferences: [] 8 | executionOrder: 0 9 | icon: {instanceID: 0} 10 | userData: 11 | assetBundleName: 12 | assetBundleVariant: 13 | -------------------------------------------------------------------------------- /Assets/TestRotation/Teapot.fbx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/keijiro/SmoothingTest/944963d9e1e022e3a160caf11838ef57a85a410c/Assets/TestRotation/Teapot.fbx -------------------------------------------------------------------------------- /Assets/TestRotation/Teapot.fbx.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: a4d72844ed18d40798216282d9143cfe 3 | timeCreated: 1452411767 4 | licenseType: Pro 5 | ModelImporter: 6 | serializedVersion: 18 7 | fileIDToRecycleName: 8 | 100000: //RootNode 9 | 400000: //RootNode 10 | 2300000: //RootNode 11 | 3300000: //RootNode 12 | 4300000: Teapot 13 | materials: 14 | importMaterials: 0 15 | materialName: 0 16 | materialSearch: 1 17 | 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normalImportMode: 0 55 | tangentImportMode: 1 56 | importAnimation: 0 57 | copyAvatar: 0 58 | humanDescription: 59 | human: [] 60 | skeleton: [] 61 | armTwist: .5 62 | foreArmTwist: .5 63 | upperLegTwist: .5 64 | legTwist: .5 65 | armStretch: .0500000007 66 | legStretch: .0500000007 67 | feetSpacing: 0 68 | rootMotionBoneName: 69 | hasTranslationDoF: 0 70 | lastHumanDescriptionAvatarSource: {instanceID: 0} 71 | animationType: 0 72 | humanoidOversampling: 1 73 | additionalBone: 0 74 | userData: 75 | assetBundleName: 76 | assetBundleVariant: 77 | -------------------------------------------------------------------------------- /Assets/TestRotation/TestDTween.cs: -------------------------------------------------------------------------------- 1 | using UnityEngine; 2 | using Flask; 3 | 4 | namespace TestRotation 5 | { 6 | public class TestDTween : MonoBehaviour 7 | { 8 | [SerializeField] Transform _target; 9 | [SerializeField] float _omega = 1; 10 | 11 | DTweenQuaternion _rotation = new DTweenQuaternion(Quaternion.identity, 1); 12 | 13 | void Update() 14 | { 15 | _rotation.omega = _omega; 16 | _rotation.Step(_target.rotation); 17 | transform.rotation = _rotation; 18 | } 19 | } 20 | } 21 | -------------------------------------------------------------------------------- /Assets/TestRotation/TestDTween.cs.meta: -------------------------------------------------------------------------------- 1 | fileFormatVersion: 2 2 | guid: 89e9b54a0f6894aa28788d8b02a58c1d 3 | timeCreated: 1452412078 4 | licenseType: Pro 5 | MonoImporter: 6 | serializedVersion: 2 7 | defaultReferences: [] 8 | executionOrder: 0 9 | icon: {instanceID: 0} 10 | userData: 11 | assetBundleName: 12 | assetBundleVariant: 13 | -------------------------------------------------------------------------------- /Assets/TestRotation/TestETween.cs: -------------------------------------------------------------------------------- 1 | using UnityEngine; 2 | using Flask; 3 | 4 | namespace TestRotation 5 | { 6 | public 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-------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | SmoothingTest 2 | ============= 3 | 4 | An example which tests [critically damped spring smoothing] 5 | (http://mathproofs.blogspot.jp/2013/07/critically-damped-spring-smoothing.html). 6 | 7 | ![gif](https://49.media.tumblr.com/4e1aa36b67b22d2702fcfa55b0a738eb/tumblr_o0oyn7SKep1qio469o1_400.gif) 8 | 9 | ![gif](https://49.media.tumblr.com/dfba0ff232f0bb76dc10a25026a888a2/tumblr_o0q7hmMfYU1qio469o1_400.gif) 10 | 11 | ![gif](http://45.media.tumblr.com/628d2b478edd67b560936ffbcff2918f/tumblr_o0qt2yfbpQ1qio469o1_400.gif) 12 | --------------------------------------------------------------------------------