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Blog de Gilles Vasseur - Pascal et compagnie

[Actualité] Les interpolations et fonctions d'easing avec Lazarus IX - L'application pour le test des fonctions d'easing

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par , 06/02/2019 à 11h13 (624 Affichages)
L'interface de l'application de test

Maintenant que nous avons fait le tour des fonctions d'easing nécessaires, il est temps de proposer une application de test : nous allons enfin voir ces fonctions à l’œuvre ! L'objectif de l'application sera simple : des boutons feront l'aller et retour d'une zone de déplacement selon la fonction d'easing qui leur sera affectée.

Pour un aperçu efficace des courbes d'easing, nous allons créer une application sans prétention dont l'interface ressemblera à ceci :

Nom : easing01.png
Affichages : 437
Taille : 18,1 Ko

Nous reconnaissons :
  • trois zones délimitées par des panneaux TPanel (un pour les contrôles de types Out ou In, un pour les contrôles de types InOut ou OutIn et un pour un composant TTrackbar afin d'ajuster la vitesse de l'animation ;
  • une séparation ajustable TSplitter entre les deux panneaux supérieurs afin de moduler les distances à parcourir par les contrôles animés (elle est à deviner ) ;
  • des boutons TButton qui serviront d'objets animés (21 dans chaque panneau : 1 pour un repère linéaire et 10 pour chaque type).



Voici le fichier LFM correspondant :

Code : Sélectionner tout - Visualiser dans une fenêtre à part
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object MainForm: TMainForm
  Left = 304
  Height = 623
  Top = 197
  Width = 953
  Caption = 'Test des interpolations - © G. Vasseur 2019'
  ClientHeight = 623
  ClientWidth = 953
  OnCreate = FormCreate
  LCLVersion = '1.8.2.0'
  object pnlMain: TPanel
    Left = 10
    Height = 553
    Top = 10
    Width = 933
    Align = alClient
    BorderSpacing.Around = 10
    ClientHeight = 553
    ClientWidth = 933
    TabOrder = 0
    OnClick = btnLinear2Click
    object pnlLeft: TPanel
      Left = 1
      Height = 551
      Top = 1
      Width = 474
      Align = alLeft
      ClientHeight = 551
      ClientWidth = 474
      TabOrder = 0
      OnClick = btnLinear2Click
      object btnEaseOutBounce: TButton
        Left = 0
        Height = 25
        Top = 256
        Width = 120
        Caption = 'EaseOutBounce'
        OnClick = btnEaseOutQuadClick
        TabOrder = 0
      end
      object btnEaseOutBack: TButton
        Left = 0
        Height = 25
        Top = 232
        Width = 120
        Caption = 'EaseOutBack'
        OnClick = btnEaseOutQuadClick
        TabOrder = 1
      end
      object btnEaseOutElastic: TButton
        Left = 0
        Height = 25
        Top = 208
        Width = 120
        Caption = 'EaseOutElastic'
        OnClick = btnEaseOutQuadClick
        TabOrder = 2
      end
      object btnEaseOutCirc: TButton
        Left = 0
        Height = 25
        Top = 184
        Width = 120
        Caption = 'EaseOutCirc'
        OnClick = btnEaseOutQuadClick
        TabOrder = 3
      end
      object btnEaseOutSine: TButton
        Left = 0
        Height = 25
        Top = 136
        Width = 120
        Caption = 'EaseOutSine'
        OnClick = btnEaseOutQuadClick
        TabOrder = 4
      end
      object btnEaseOutQuint: TButton
        Left = 0
        Height = 25
        Top = 112
        Width = 120
        Caption = 'EaseOutQuint'
        OnClick = btnEaseOutQuadClick
        TabOrder = 5
      end
      object btnEaseOutQuad: TButton
        Left = 0
        Height = 25
        Top = 40
        Width = 120
        Caption = 'EaseOutQuad'
        OnClick = btnEaseOutQuadClick
        TabOrder = 6
      end
      object btnEaseOutCubic: TButton
        Left = 0
        Height = 25
        Top = 64
        Width = 120
        Caption = 'EaseOutCubic'
        OnClick = btnEaseOutQuadClick
        TabOrder = 7
      end
      object btnEaseOutQuart: TButton
        Left = 0
        Height = 25
        Top = 88
        Width = 120
        Caption = 'EaseOutQuart'
        OnClick = btnEaseOutQuadClick
        TabOrder = 8
      end
      object btnEaseOutExpo: TButton
        Left = 0
        Height = 25
        Top = 160
        Width = 120
        Caption = 'EaseOutExpo'
        OnClick = btnEaseOutQuadClick
        TabOrder = 9
      end
      object btnEaseInQuad: TButton
        Left = 1
        Height = 25
        Top = 296
        Width = 120
        Caption = 'EaseInQuad'
        OnClick = btnEaseInQuadClick
        TabOrder = 10
      end
      object btnEaseInCubic: TButton
        Left = 1
        Height = 25
        Top = 320
        Width = 120
        Caption = 'EaseInCubic'
        OnClick = btnEaseInQuadClick
        TabOrder = 11
      end
      object btnEaseInQuart: TButton
        Left = 1
        Height = 25
        Top = 344
        Width = 120
        Caption = 'EaseInQuart'
        OnClick = btnEaseInQuadClick
        TabOrder = 12
      end
      object btnEaseInQuint: TButton
        Left = 1
        Height = 25
        Top = 368
        Width = 120
        Caption = 'EaseInQuint'
        OnClick = btnEaseInQuadClick
        TabOrder = 13
      end
      object btnEaseInSine: TButton
        Left = 1
        Height = 25
        Top = 392
        Width = 120
        Caption = 'EaseInSine'
        OnClick = btnEaseInQuadClick
        TabOrder = 14
      end
      object btnEaseInExpo: TButton
        Left = 1
        Height = 25
        Top = 416
        Width = 120
        Caption = 'EaseInExpo'
        OnClick = btnEaseInQuadClick
        TabOrder = 15
      end
      object btnEaseInCirc: TButton
        Left = 1
        Height = 25
        Top = 440
        Width = 120
        Caption = 'EaseInCirc'
        OnClick = btnEaseInQuadClick
        TabOrder = 16
      end
      object btnEaseInElastic: TButton
        Left = 1
        Height = 25
        Top = 464
        Width = 120
        Caption = 'EaseInElastic'
        OnClick = btnEaseInQuadClick
        TabOrder = 17
      end
      object btnEaseInBack: TButton
        Left = 1
        Height = 25
        Top = 488
        Width = 120
        Caption = 'EaseInBack'
        OnClick = btnEaseInQuadClick
        TabOrder = 18
      end
      object btnEaseInBounce: TButton
        Left = 1
        Height = 25
        Top = 512
        Width = 120
        Caption = 'EaseInBounce'
        OnClick = btnEaseInQuadClick
        TabOrder = 19
      end
      object btnLinear: TButton
        Left = 0
        Height = 25
        Top = 8
        Width = 120
        Caption = 'Linear'
        Font.Style = [fsBold]
        OnClick = btnLinear2Click
        ParentFont = False
        TabOrder = 20
      end
    end
    object pnlRight: TPanel
      Left = 480
      Height = 551
      Top = 1
      Width = 452
      Align = alClient
      ClientHeight = 551
      ClientWidth = 452
      TabOrder = 1
      OnClick = btnLinear2Click
      object btnLinear2: TButton
        Left = 0
        Height = 25
        Top = 8
        Width = 120
        Caption = 'Linear'
        Font.Style = [fsBold]
        OnClick = btnLinear2Click
        ParentFont = False
        TabOrder = 0
      end
      object btnEaseInOutCubic: TButton
        Left = 0
        Height = 25
        Top = 320
        Width = 120
        Caption = 'EaseInOutCubic'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 1
      end
      object btnEaseInOutQuart: TButton
        Left = 0
        Height = 25
        Top = 344
        Width = 120
        Caption = 'EaseInOutQuart'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 2
      end
      object btnEaseOutInQuart: TButton
        Left = 0
        Height = 25
        Top = 88
        Width = 120
        Caption = 'EaseOutInQuart'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 3
      end
      object btnEaseOutInCubic: TButton
        Left = 0
        Height = 25
        Top = 64
        Width = 120
        Caption = 'EaseOutInCubic'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 4
      end
      object btnEaseOutInQuint: TButton
        Left = 0
        Height = 25
        Top = 112
        Width = 120
        Caption = 'EaseOutInQuint'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 5
      end
      object btnEaseInOutQuint: TButton
        Left = 0
        Height = 25
        Top = 368
        Width = 120
        Caption = 'EaseInOutQuint'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 6
      end
      object btnEaseOutInSine: TButton
        Left = 0
        Height = 25
        Top = 136
        Width = 120
        Caption = 'EaseOutInSine'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 7
      end
      object btnEaseInOutQuad: TButton
        Left = 0
        Height = 25
        Top = 296
        Width = 120
        Caption = 'EaseInOutQuad'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 8
      end
      object btnEaseOutInQuad: TButton
        Left = 0
        Height = 25
        Top = 40
        Width = 120
        Caption = 'EaseOutInQuad'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 9
      end
      object btnEaseInOutSine: TButton
        Left = 0
        Height = 25
        Top = 392
        Width = 120
        Caption = 'EaseInOutSine'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 10
      end
      object btnEaseOutInCirc: TButton
        Left = 0
        Height = 25
        Top = 184
        Width = 120
        Caption = 'EaseOutInCirc'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 11
      end
      object btnEaseOutInElastic: TButton
        Left = 0
        Height = 25
        Top = 208
        Width = 120
        Caption = 'EaseOutInElastic'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 12
      end
      object btnEaseOutInBack: TButton
        Left = 0
        Height = 25
        Top = 232
        Width = 120
        Caption = 'EaseOutInBack'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 13
      end
      object btnEaseOutInBounce: TButton
        Left = 0
        Height = 25
        Top = 256
        Width = 120
        Caption = 'EaseOutInBounce'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 14
      end
      object btnEaseOutInExpo: TButton
        Left = 0
        Height = 25
        Top = 160
        Width = 120
        Caption = 'EaseOutInExpo'
        OnClick = btnEaseOutInQuadClick
        TabOrder = 15
      end
      object btnEaseInOutExpo: TButton
        Left = 0
        Height = 25
        Top = 416
        Width = 120
        Caption = 'EaseInOutExpo'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 16
      end
      object btnEaseInOutCirc: TButton
        Left = 0
        Height = 25
        Top = 440
        Width = 120
        Caption = 'EaseInOutCirc'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 17
      end
      object btnEaseInOutElastic: TButton
        Left = 0
        Height = 25
        Top = 464
        Width = 120
        Caption = 'EaseInOutElastic'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 18
      end
      object btnEaseInOutBack: TButton
        Left = 0
        Height = 25
        Top = 488
        Width = 120
        Caption = 'EaseInOutBack'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 19
      end
      object btnEaseInOutBounce: TButton
        Left = 0
        Height = 25
        Top = 512
        Width = 120
        Caption = 'EaseInOutBounce'
        OnClick = btnEaseInOutQuadClick
        TabOrder = 20
      end
    end
    object Splitter1: TSplitter
      Left = 475
      Height = 551
      Top = 1
      Width = 5
    end
  end
  object pnlBottom: TPanel
    Left = 0
    Height = 50
    Top = 573
    Width = 953
    Align = alBottom
    BorderSpacing.InnerBorder = 10
    ClientHeight = 50
    ClientWidth = 953
    TabOrder = 1
    object tbarWait: TTrackBar
      Left = 11
      Height = 28
      Top = 11
      Width = 301
      Max = 100
      OnChange = tbarWaitChange
      Position = 0
      Align = alLeft
      BorderSpacing.Around = 10
      TabOrder = 0
    end
  end
end
Ce long listing ne doit pas effrayer : en fait, il indique où sont placés les composants (ce qui peut varier selon vos goûts), leur intitulé (qui correspond pour les boutons à la fonction représentée), leur taille (les boutons ont tous une largeur de 120, mais cette valeur est indicative) ainsi que le gestionnaire d'événement OnClick associé (les boutons sont regroupés par catégories comme le montrera le code). De toute façon, le code source complet de l'unité est fourni à la fin de billet.

Comme annoncé, vous noterez la présence d'un TTrackbar qui déterminera la vitesse (de manière très grossière pour le moment) d'exécution des interpolations, ainsi que d'un TSplitter dont la fonction sera de modifier à volonté la largeur des zones de déplacement afin de voir comment se comportent les fonctions sur des trajets plus ou moins longs.

Aucune action n'est nécessaire pour le TSplitter qui saura dimensionner les panneaux suivant le choix de l'utilisateur final.

Le code associé à l'application

Le code reprend celui décrit dans les billets précédents, mais il ajoute la gestion des clics sur les boutons. Sachant que les coordonnées des boutons sont des entiers, on a simplement introduit une variante à valeur entière des différentes interpolations qui utilisaient des nombres flottants Single.

Une fois toutes les fonctions solidement définies, le reste de l'application ne met en œuvre que des techniques habituelles.
Nous déclarons des constantes pour la valeur de fin à atteindre et la durée par défaut ainsi qu'une énumération afin de différencier les interpolations :

Code delphi : Sélectionner tout - Visualiser dans une fenêtre à part
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const
 C_DefaultDuration = 100;
 C_End = 200;
 
type
 
 TInterpolation = (intLinear,
    intEaseInQuad, intEaseOutQuad, intEaseInOutQuad, intEaseOutInQuad,
    intEaseInCubic, intEaseOutCubic, intEaseInOutCubic, intEaseOutInCubic,
    intEaseInQuart, intEaseOutQuart, intEaseInOutQuart, intEaseOutInQuart,
    intEaseInQuint, intEaseOutQuint, intEaseInOutQuint, intEaseOutInQuint,
    intEaseInSine, intEaseOutSine, intEaseInOutSine, intEaseOutInSine,
    intEaseInExpo, intEaseOutExpo, intEaseInOutExpo, intEaseOutInExpo,
    intEaseInCirc, intEaseOutCirc, intEaseInOutCirc, intEaseOutInCirc,
    intEaseInElastic, intEaseOutElastic, intEaseInOutElastic, intEaseOutInElastic,
    intEaseInBack, intEaseOutBack, intEaseInOutBack, intEaseOutInBack,
    intEaseInBounce, intEaseOutBounce, intEaseInOutBounce, intEaseOutInBounce
    );

Les clics ont été modulés ainsi : un clic sur un des boutons de référence (btnLinear et btnLinear2), c'est-à-dire suivant un parcours linéaire, provoque le déplacement des tous les boutons. En revanche, un clic sur un autre bouton provoque seulement le déplacement de son groupe (Out, In, OutIn ou InOut).

Voici le code associé aux premiers boutons dits de référence :

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procedure TMainForm.btnLinear2Click(Sender: TObject);
// *** lancement des animations ***
var
  Li, LWidth, LWidth2: Integer;
  LBack: Boolean;
begin
  tbarWait.Enabled := False;
  LWidth := pnlLeft.Width - btnLinear2.Width;
  LWidth2 := pnlRight.Width - btnLinear.Width;
  for LBack := False to True do
    for Li := 1 to fDuration do
    begin
      btnLinear.Left := ComputeInterpolationInt(0, LWidth, Li, intLinear, LBack);
      btnLinear2.Left := ComputeInterpolationInt(0, LWidth2, Li, intLinear, LBack);
 
      btnEaseInQuad.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuad, LBack);
      btnEaseOutQuad.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutQuad, LBack);
      btnEaseInOutQuad.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutQuad, LBack);
      btnEaseOutInQuad.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInQuad, LBack);
 
      btnEaseInCubic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInCubic, LBack);
      btnEaseOutCubic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutCubic, LBack);
      btnEaseInOutCubic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutCubic, LBack);
      btnEaseOutInCubic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInCubic, LBack);
 
      btnEaseInQuart.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuart, LBack);
      btnEaseOutQuart.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutQuart, LBack);
      btnEaseInOutQuart.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutQuart, LBack);
      btnEaseOutInQuart.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInQuart, LBack);
 
      btnEaseInQuint.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuint, LBack);
      btnEaseOutQuint.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutQuint, LBack);
      btnEaseInOutQuint.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutQuint, LBack);
      btnEaseOutInQuint.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInQuint, LBack);
 
      btnEaseInSine.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInSine, LBack);
      btnEaseOutSine.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutSine, LBack);
      btnEaseInOutSine.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutSine, LBack);
      btnEaseOutInSine.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInSine, LBack);
 
      btnEaseInExpo.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInExpo, LBack);
      btnEaseOutExpo.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutExpo, LBack);
      btnEaseInOutExpo.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutExpo, LBack);
      btnEaseOutInExpo.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInExpo, LBack);
 
      btnEaseInCirc.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInCirc, LBack);
      btnEaseOutCirc.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutCirc, LBack);
      btnEaseInOutCirc.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutCirc, LBack);
      btnEaseOutInCirc.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInCirc, LBack);
 
      btnEaseInElastic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInElastic, LBack);
      btnEaseOutElastic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutElastic, LBack);
      btnEaseInOutElastic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutElastic, LBack);
      btnEaseOutInElastic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInElastic, LBack);
 
      btnEaseInBack.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInBack, LBack);
      btnEaseOutBack.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutBack, LBack);
      btnEaseInOutBack.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutBack, LBack);
      btnEaseOutInBack.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInBack, LBack);
 
      btnEaseInBounce.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInBounce, LBack);
      btnEaseOutBounce.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutBounce, LBack);
      btnEaseInOutBounce.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutBounce, LBack);
      btnEaseOutInBounce.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInBounce, LBack);
 
      sleep(10);
      Repaint;
      Application.ProcessMessages;
    end;
  tbarWait.Enabled := True;
end;

Dans deux boucles imbriquées qui prennent en compte le sens du déplacement (booléen Back) et la portion de durée effectuée (Li pour fDuration), les boutons sont tous déplacés grâce à la modification de leur propriété Left.
C'est le résultat entier de la fonction ComputeInterpolationInt qui est affecté à cette propriété Left de chaque bouton. La fonction calcule la valeur à retourner en fonction du point de départ, du point d'arrivée, du type d'interpolation et du sens de déplacement.

Après le déplacement, un temps d'arrêt est donné via sleep pour éviter une exécution trop rapide, la zone d'affichage est repeinte avec Repaint pour prendre en compte les changements et un appel est fait à Application.ProcessMessages pour répondre aux éventuels messages non traités (comme l'arrêt de l'application par exemple).

Vous remarquerez que le TTrackBar est désactivé pendant les mouvements afin de garantir l'homogénéité des données durant le processus d'interpolation.

De la même manière, voici le code correspondant aux clics sur les boutons de type In :

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procedure TMainForm.btnEaseInQuadClick(Sender: TObject);
// *** fonctions IN ***
var
  Li, LWidth: Integer;
  LBack: Boolean;
begin
  tbarWait.Enabled := False;
  LWidth := pnlLeft.Width - btnLinear2.Width;
  for LBack := False to True do
    for Li := 1 to fDuration do
    begin
      btnLinear.Left := ComputeInterpolationInt(0, LWidth, Li, intLinear, LBack);
      btnEaseInQuad.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuad, LBack);
      btnEaseInCubic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInCubic, LBack);
      btnEaseInQuart.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuart, LBack);
      btnEaseInQuint.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuint, LBack);
      btnEaseInSine.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInSine, LBack);
      btnEaseInExpo.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInExpo, LBack);
      btnEaseInCirc.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInCirc, LBack);
      btnEaseInElastic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInElastic, LBack);
      btnEaseInBack.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInBack, LBack);
      btnEaseInBounce.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInBounce, LBack);
      sleep(10);
      pnlLeft.Repaint;
      Application.ProcessMessages;
    end;
  tbarWait.Enabled := True;
end;

Le code est similaire au précédent sinon que seuls sont affectés les boutons visés et que la méthode Repaint n'affecte que le panneau modifié. Nous renvoyons au code fourni à la fin de ce billet pour les autres types de fonction : il est évidemment construit sur le même modèle.

Reste à gérer la durée qui est une propriété nommée Duration qui elle-même fait référence à un champ privé fDuration à travers un setter :

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property Duration: Cardinal read fDuration write SetDuration default C_DefaultDuration;

Le setter peut sembler superflu, mais il prépare une meilleure gestion de la durée qui n'est pour le moment qu'une suite linéaire de valeurs entières.

Les méthodes associées sont simples et en relation avec le composant TTrackbar qui fournit la valeur brute de la durée :

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procedure TMainForm.tbarWaitChange(Sender: TObject);
// *** changement de la vitesse ***
begin
  Duration := tbarWait.Position;
end;
 
procedure TMainForm.SetDuration(AValue: Cardinal);
// *** détermination de la durée d'interpolation ***
begin
  if fDuration = C_End - AValue then
    Exit;
  fDuration := C_End - AValue;
end;

Il ne reste que la création de la fiche à compléter pour obtenir une application fonctionnelle :

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procedure TMainForm.FormCreate(Sender: TObject);
// *** création de la fiche ***
begin
  Duration := C_DefaultDuration;
  tbarWait.Max := C_End;
  tbarWait.Position := fDuration;
end;

Nous devons en effet renseigner la valeur de la durée par défaut et ajuster correctement les propriétés du composant TTrackbar.

La méthode ComputeInterpolationInt renvoie à une méthode ComputeInterpolation calquée sur les fonctions que nous avions déjà produites :

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function TMainForm.ComputeInterpolationInt(AStart, AEnd: Integer;
  AStep: Integer; AInter: TInterpolation; ABack: Boolean): Integer;
// *** interpolation entière ***
begin
  Result := Round(ComputeInterpolation(AStart, AEnd, AStep, AInter, ABack));
end;

Voici le code de cette méthode ComputeInterpolation :

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function TMainForm.ComputeInterpolation(AStart, AEnd, AStep: Single;
  AInter: TInterpolation; ABack: Boolean): Single;
// *** calcul des interpolations ***
begin
  case AInter of
    // linéaire
    intLinear: Result := EaseNone(AStart, AEnd, AStep);
    // quadratique
    intEaseInQuad: Result := EaseInQuad(AStart, AEnd, AStep);
    intEaseOutQuad: Result := EaseOutQuad(AStart, AEnd, AStep);
    intEaseInOutQuad: Result := EaseInOutQuad(AStart, AEnd, AStep);
    intEaseOutInQuad: Result := EaseOutInQuad(AStart, AEnd, AStep);
    // cubique
    intEaseInCubic: Result := EaseInCubic(AStart, AEnd, AStep);
    intEaseOutCubic: Result := EaseOutCubic(AStart, AEnd, AStep);
    intEaseInOutCubic: Result := EaseInOutCubic(AStart, AEnd, AStep);
    intEaseOutInCubic: Result := EaseOutInCubic(AStart, AEnd, AStep);
    // quartique
    intEaseInQuart: Result := EaseInQuart(AStart, AEnd, AStep);
    intEaseOutQuart: Result := EaseOutQuart(AStart, AEnd, AStep);
    intEaseInOutQuart:  Result := EaseInOutQuart(AStart, AEnd, AStep);
    intEaseOutInQuart: Result := EaseOutInQuart(AStart, AEnd, AStep);
    // quintique
    intEaseInQuint: Result := EaseInQuint(AStart, AEnd, AStep);
    intEaseOutQuint: Result := EaseOutQuint(AStart, AEnd, AStep);
    intEaseInOutQuint:  Result := EaseInOutQuint(AStart, AEnd, AStep);
    intEaseOutInQuint: Result := EaseOutInQuint(AStart, AEnd, AStep);
    // sinus
    intEaseInSine: Result := EaseInSine(AStart, AEnd, AStep);
    intEaseOutSine: Result := EaseOutSine(AStart, AEnd, AStep);
    intEaseInOutSine: Result := EaseInOutSine(AStart, AEnd, AStep);
    intEaseOutInSine: Result := EaseOutInSine(AStart, AEnd, AStep);
    // exponentielle
    intEaseInExpo: Result := EaseInExpo(AStart, AEnd, AStep);
    intEaseOutExpo: Result := EaseOutExpo(AStart, AEnd, AStep);
    intEaseInOutExpo: Result := EaseInOutExpo(AStart, AEnd, AStep);
    intEaseOutInExpo: Result := EaseOutInExpo(AStart, AEnd, AStep);
    // cercle
    intEaseInCirc: Result := EaseInCirc(AStart, AEnd, AStep);
    intEaseOutCirc: Result := EaseOutCirc(AStart, AEnd, AStep);
    intEaseInOutCirc: Result := EaseInOutCirc(AStart, AEnd, AStep);
    intEaseOutInCirc: Result := EaseOutInCirc(AStart, AEnd, AStep);
    // élastique
    intEaseInElastic: Result := EaseInElastic(AStart, AEnd, AStep);
    intEaseOutElastic: Result := EaseOutElastic(AStart, AEnd, AStep);
    intEaseInOutElastic: Result := EaseInOutElastic(AStart, AEnd, AStep);
    intEaseOutInElastic: Result := EaseOutInElastic(AStart, AEnd, AStep);
    // retour
    intEaseInBack: Result := EaseInBack(AStart, AEnd, AStep);
    intEaseOutBack: Result := EaseOutBack(AStart, AEnd, AStep);
    intEaseInOutBack: Result := EaseInOutBack(AStart, AEnd, AStep);
    intEaseOutInBack: Result := EaseOutInBack(AStart, AEnd, AStep);
    // rebond
    intEaseInBounce: Result := EaseInBounce(AStart, AEnd, AStep);
    intEaseOutBounce: Result := EaseOutBounce(AStart, AEnd, AStep);
    intEaseInOutBounce: Result := EaseInOutBounce(AStart, AEnd, AStep);
    intEaseOutInBounce: Result := EaseOutInBounce(AStart, AEnd, AStep);
  end;
  if ABack then
    Result := AEnd - Result;
end;

Comme attendu, elle fonctionne à la manière d'une gare de triage selon la fonction d'easing voulue.

Finalement, l'unité complète donnera :
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{¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤@
@                                                                      @
@              Nom du produit : GVTransitions - interpolations 02      @
@              Nom du fichier : main.pas                               @
@              Copyright : G. Vasseur 2019                             @
@              Contact : gillesvasseur58@gmail.com                     @
@              Date/Heure : 05/02/2019 12:20:05                        @
@              Version : 1.0.0.14                                      @
@                                                                      @
@¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤¤}
 
{ Transitions entre deux images - interpolations
 
Copyright (C) 05/02/2019 12:20:05 G. Vasseur 2018 gillesvasseur58@gmail.com
 
This source is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your option)
any later version.
 
This code is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more
details.
 
A copy of the GNU General Public License is available on the World Wide Web
at <http://www.gnu.org/copyleft/gpl.html>. You can also obtain it by writing
to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA.
}
 
unit main;
 
{$mode objfpc}{$H+}
 
interface
 
uses
  Classes, SysUtils, FileUtil, Forms, Controls, Graphics, Dialogs, ExtCtrls,
  StdCtrls, ComCtrls;
 
const
 C_DefaultDuration = 100;
 C_End = 200;
 
type
 
 TInterpolation = (intLinear,
    intEaseInQuad, intEaseOutQuad, intEaseInOutQuad, intEaseOutInQuad,
    intEaseInCubic, intEaseOutCubic, intEaseInOutCubic, intEaseOutInCubic,
    intEaseInQuart, intEaseOutQuart, intEaseInOutQuart, intEaseOutInQuart,
    intEaseInQuint, intEaseOutQuint, intEaseInOutQuint, intEaseOutInQuint,
    intEaseInSine, intEaseOutSine, intEaseInOutSine, intEaseOutInSine,
    intEaseInExpo, intEaseOutExpo, intEaseInOutExpo, intEaseOutInExpo,
    intEaseInCirc, intEaseOutCirc, intEaseInOutCirc, intEaseOutInCirc,
    intEaseInElastic, intEaseOutElastic, intEaseInOutElastic, intEaseOutInElastic,
    intEaseInBack, intEaseOutBack, intEaseInOutBack, intEaseOutInBack,
    intEaseInBounce, intEaseOutBounce, intEaseInOutBounce, intEaseOutInBounce
    );
 
  { TMainForm }
 
  TMainForm = class(TForm)
    btnEaseOutInQuart: TButton;
    btnLinear2: TButton;
    btnEaseInQuad: TButton;
    btnEaseOutCubic: TButton;
    btnEaseInCubic: TButton;
    btnEaseOutQuad: TButton;
    btnEaseInOutCubic: TButton;
    btnEaseInOutQuart: TButton;
    btnEaseOutInCubic: TButton;
    btnEaseInQuart: TButton;
    btnEaseOutQuart: TButton;
    btnEaseInQuint: TButton;
    btnEaseOutQuint: TButton;
    btnEaseOutInQuint: TButton;
    btnEaseInOutQuint: TButton;
    btnEaseInSine: TButton;
    btnEaseOutSine: TButton;
    btnEaseInOutSine: TButton;
    btnEaseOutInSine: TButton;
    btnEaseInOutQuad: TButton;
    btnEaseOutInQuad: TButton;
    btnEaseInExpo: TButton;
    btnEaseInCirc: TButton;
    btnEaseInElastic: TButton;
    btnEaseInBack: TButton;
    btnEaseInBounce: TButton;
    btnEaseOutCirc: TButton;
    btnEaseOutElastic: TButton;
    btnEaseOutBack: TButton;
    btnEaseOutBounce: TButton;
    btnEaseOutExpo: TButton;
    btnLinear: TButton;
    btnEaseOutInCirc: TButton;
    btnEaseOutInElastic: TButton;
    btnEaseOutInBack: TButton;
    btnEaseOutInBounce: TButton;
    btnEaseInOutExpo: TButton;
    btnEaseInOutCirc: TButton;
    btnEaseInOutElastic: TButton;
    btnEaseInOutBack: TButton;
    btnEaseOutInExpo: TButton;
    btnEaseInOutBounce: TButton;
    pnlRight: TPanel;
    pnlLeft: TPanel;
    pnlBottom: TPanel;
    pnlMain: TPanel;
    Splitter1: TSplitter;
    tbarWait: TTrackBar;
    procedure btnEaseInOutQuadClick(Sender: TObject);
    procedure btnEaseInQuadClick(Sender: TObject);
    procedure btnEaseOutInQuadClick(Sender: TObject);
    procedure btnEaseOutQuadClick(Sender: TObject);
    procedure btnLinear2Click(Sender: TObject);
    procedure FormCreate(Sender: TObject);
    procedure tbarWaitChange(Sender: TObject);
  private
    fDuration: Cardinal;
    procedure SetDuration(AValue: Cardinal);
    function InPower(AStart, AChange, AStep: Single; APower: Integer): Single;
    function OutPower(AStart, AChange, AStep: Single; APower: Integer): Single;
    function InOutPower(AStart, AChange, AStep: Single; APower: Integer): Single;
  protected
    function EaseNone(AStart, AChange, AStep: Single): Single;
    function EaseInQuad(AStart, AChange, AStep: Single): Single;
    function EaseOutQuad(AStart, AChange, AStep: Single): Single;
    function EaseInOutQuad(AStart, AChange, AStep: Single): Single;
    function EaseOutInQuad(AStart, AChange, AStep: Single): Single;
    function EaseInCubic(AStart, AChange, AStep: Single): Single;
    function EaseOutCubic(AStart, AChange, AStep: Single): Single;
    function EaseInOutCubic(AStart, AChange, AStep: Single): Single;
    function EaseOutInCubic(AStart, AChange, AStep: Single): Single;
    function EaseInQuart(AStart, AChange, AStep: Single): Single;
    function EaseOutQuart(AStart, AChange, AStep: Single): Single;
    function EaseInOutQuart(AStart, AChange, AStep: Single): Single;
    function EaseOutInQuart(AStart, AChange, AStep: Single): Single;
    function EaseInQuint(AStart, AChange, AStep: Single): Single;
    function EaseOutQuint(AStart, AChange, AStep: Single): Single;
    function EaseInOutQuint(AStart, AChange, AStep: Single): Single;
    function EaseOutInQuint(AStart, AChange, AStep: Single): Single;
    function EaseInSine(AStart, AChange, AStep: Single): Single;
    function EaseOutSine(AStart, AChange, AStep: Single): Single;
    function EaseInOutSine(AStart, AChange, AStep: Single): Single;
    function EaseOutInSine(AStart, AChange, AStep: Single): Single;
    function EaseInExpo(AStart, AChange, AStep: Single): Single;
    function EaseOutExpo(AStart, AChange, AStep: Single): Single;
    function EaseInOutExpo(AStart, AChange, AStep: Single): Single;
    function EaseOutInExpo(AStart, AChange, AStep: Single): Single;
    function EaseInCirc(AStart, AChange, AStep: Single): Single;
    function EaseOutCirc(AStart, AChange, AStep: Single): Single;
    function EaseInOutCirc(AStart, AChange, AStep: Single): Single;
    function EaseOutInCirc(AStart, AChange, AStep: Single): Single;
    function EaseInElastic(AStart, AChange, AStep: Single): Single;
    function EaseOutElastic(AStart, AChange, AStep: Single): Single;
    function EaseInOutElastic(AStart, AChange, AStep: Single): Single;
    function EaseOutInElastic(AStart, AChange, AStep: Single): Single;
    function EaseInBack(AStart, AChange, AStep: Single): Single;
    function EaseOutBack(AStart, AChange, AStep: Single): Single;
    function EaseInOutBack(AStart, AChange, AStep: Single): Single;
    function EaseOutInBack(AStart, AChange, AStep: Single): Single;
    function EaseInOutBounce(AStart, AChange, AStep: Single): Single;
    function EaseOutInBounce(AStart, AChange, AStep: Single): Single;
    function EaseInBounce(AStart, AChange, AStep: Single): Single;
    function EaseOutBounce(AStart, AChange, AStep: Single): Single;
  public
    property Duration: Cardinal read fDuration write SetDuration default C_DefaultDuration;
    function ComputeInterpolation(AStart, AEnd, AStep: Single; AInter: TInterpolation;
      ABack: Boolean = False): Single;
    function ComputeInterpolationInt(AStart, AEnd: Integer; AStep: Integer; AInter: TInterpolation;
      ABack: Boolean = False): Integer;
  end;
 
var
  MainForm: TMainForm;
 
implementation
 
uses
  math;
 
{$R *.lfm}
 
{ TMainForm }
 
procedure TMainForm.btnLinear2Click(Sender: TObject);
// *** lancement des animations ***
var
  Li, LWidth, LWidth2: Integer;
  LBack: Boolean;
begin
  tbarWait.Enabled := False;
  LWidth := pnlLeft.Width - btnLinear2.Width;
  LWidth2 := pnlRight.Width - btnLinear.Width;
  for LBack := False to True do
    for Li := 1 to fDuration do
    begin
      btnLinear.Left := ComputeInterpolationInt(0, LWidth, Li, intLinear, LBack);
      btnLinear2.Left := ComputeInterpolationInt(0, LWidth2, Li, intLinear, LBack);
 
      btnEaseInQuad.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuad, LBack);
      btnEaseOutQuad.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutQuad, LBack);
      btnEaseInOutQuad.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutQuad, LBack);
      btnEaseOutInQuad.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInQuad, LBack);
 
      btnEaseInCubic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInCubic, LBack);
      btnEaseOutCubic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutCubic, LBack);
      btnEaseInOutCubic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutCubic, LBack);
      btnEaseOutInCubic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInCubic, LBack);
 
      btnEaseInQuart.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuart, LBack);
      btnEaseOutQuart.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutQuart, LBack);
      btnEaseInOutQuart.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutQuart, LBack);
      btnEaseOutInQuart.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInQuart, LBack);
 
      btnEaseInQuint.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuint, LBack);
      btnEaseOutQuint.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutQuint, LBack);
      btnEaseInOutQuint.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutQuint, LBack);
      btnEaseOutInQuint.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInQuint, LBack);
 
      btnEaseInSine.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInSine, LBack);
      btnEaseOutSine.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutSine, LBack);
      btnEaseInOutSine.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutSine, LBack);
      btnEaseOutInSine.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInSine, LBack);
 
      btnEaseInExpo.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInExpo, LBack);
      btnEaseOutExpo.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutExpo, LBack);
      btnEaseInOutExpo.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutExpo, LBack);
      btnEaseOutInExpo.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInExpo, LBack);
 
      btnEaseInCirc.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInCirc, LBack);
      btnEaseOutCirc.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutCirc, LBack);
      btnEaseInOutCirc.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutCirc, LBack);
      btnEaseOutInCirc.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInCirc, LBack);
 
      btnEaseInElastic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInElastic, LBack);
      btnEaseOutElastic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutElastic, LBack);
      btnEaseInOutElastic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutElastic, LBack);
      btnEaseOutInElastic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInElastic, LBack);
 
      btnEaseInBack.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInBack, LBack);
      btnEaseOutBack.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutBack, LBack);
      btnEaseInOutBack.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutBack, LBack);
      btnEaseOutInBack.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInBack, LBack);
 
      btnEaseInBounce.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInBounce, LBack);
      btnEaseOutBounce.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutBounce, LBack);
      btnEaseInOutBounce.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutBounce, LBack);
      btnEaseOutInBounce.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInBounce, LBack);
 
      sleep(10);
      Repaint;
      Application.ProcessMessages;
    end;
  tbarWait.Enabled := True;
end;
 
procedure TMainForm.btnEaseInQuadClick(Sender: TObject);
// *** fonctions IN ***
var
  Li, LWidth: Integer;
  LBack: Boolean;
begin
  tbarWait.Enabled := False;
  LWidth := pnlLeft.Width - btnLinear2.Width;
  for LBack := False to True do
    for Li := 1 to fDuration do
    begin
      btnLinear.Left := ComputeInterpolationInt(0, LWidth, Li, intLinear, LBack);
      btnEaseInQuad.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuad, LBack);
      btnEaseInCubic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInCubic, LBack);
      btnEaseInQuart.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuart, LBack);
      btnEaseInQuint.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInQuint, LBack);
      btnEaseInSine.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInSine, LBack);
      btnEaseInExpo.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInExpo, LBack);
      btnEaseInCirc.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInCirc, LBack);
      btnEaseInElastic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInElastic, LBack);
      btnEaseInBack.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInBack, LBack);
      btnEaseInBounce.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseInBounce, LBack);
      sleep(10);
      pnlLeft.Repaint;
      Application.ProcessMessages;
    end;
  tbarWait.Enabled := True;
end;
 
procedure TMainForm.btnEaseInOutQuadClick(Sender: TObject);
// *** fonctions INOUT ***
var
  Li, LWidth2: Integer;
  LBack: Boolean;
begin
  tbarWait.Enabled := False;
  LWidth2 := pnlRight.Width - btnLinear.Width;
  for LBack := False to True do
    for Li := 1 to fDuration do
    begin
      btnLinear2.Left := ComputeInterpolationInt(0, LWidth2, Li, intLinear, LBack);
      btnEaseInOutQuad.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutQuad, LBack);
      btnEaseInOutCubic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutCubic, LBack);
      btnEaseInOutQuart.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutQuart, LBack);
      btnEaseInOutQuint.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutQuint, LBack);
      btnEaseInOutSine.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutSine, LBack);
      btnEaseInOutExpo.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutExpo, LBack);
      btnEaseInOutCirc.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutCirc, LBack);
      btnEaseInOutElastic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutElastic, LBack);
      btnEaseInOutBack.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutBack, LBack);
      btnEaseInOutBounce.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseInOutBounce, LBack);
      sleep(10);
      pnlRight.Repaint;
      Application.ProcessMessages;
    end;
  tbarWait.Enabled := True;
end;
 
procedure TMainForm.btnEaseOutInQuadClick(Sender: TObject);
// *** fonctions OUTIN ***
var
  Li, LWidth2: Integer;
  LBack: Boolean;
begin
  tbarWait.Enabled := False;
  LWidth2 := pnlRight.Width - btnLinear.Width;
  for LBack := False to True do
    for Li := 1 to fDuration do
    begin
      btnLinear2.Left := ComputeInterpolationInt(0, LWidth2, Li, intLinear, LBack);
      btnEaseOutInQuad.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInQuad, LBack);
      btnEaseOutInCubic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInCubic, LBack);
      btnEaseOutInQuart.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInQuart, LBack);
      btnEaseOutInQuint.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInQuint, LBack);
      btnEaseOutInSine.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInSine, LBack);
      btnEaseOutInExpo.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInExpo, LBack);
      btnEaseOutInCirc.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInCirc, LBack);
      btnEaseOutInElastic.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInElastic, LBack);
      btnEaseOutInBack.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInBack, LBack);
      btnEaseOutInBounce.Left := ComputeInterpolationInt(0, LWidth2, Li, intEaseOutInBounce, LBack);
      sleep(10);
      pnlRight.Repaint;
      Application.ProcessMessages;
    end;
  tbarWait.Enabled := True;
end;
 
procedure TMainForm.btnEaseOutQuadClick(Sender: TObject);
// *** fonctions OUT ***
var
  Li, LWidth: Integer;
  LBack: Boolean;
begin
  tbarWait.Enabled := False;
  LWidth := pnlLeft.Width - btnLinear2.Width;
  for LBack := False to True do
    for Li := 1 to fDuration do
    begin
      btnLinear.Left := ComputeInterpolationInt(0, LWidth, Li, intLinear, LBack);
      btnEaseOutQuad.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutQuad, LBack);
      btnEaseOutCubic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutCubic, LBack);
      btnEaseOutQuart.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutQuart, LBack);
      btnEaseOutQuint.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutQuint, LBack);
      btnEaseOutSine.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutSine, LBack);
      btnEaseOutExpo.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutExpo, LBack);
      btnEaseOutCirc.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutCirc, LBack);
      btnEaseOutElastic.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutElastic, LBack);
      btnEaseOutBack.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutBack, LBack);
      btnEaseOutBounce.Left := ComputeInterpolationInt(0, LWidth, Li, intEaseOutBounce, LBack);
      sleep(10);
      pnlLeft.Repaint;
      Application.ProcessMessages;
    end;
  tbarWait.Enabled := True;
end;
 
procedure TMainForm.FormCreate(Sender: TObject);
// *** création de la fiche ***
begin
  Duration := C_DefaultDuration;
  tbarWait.Max := C_End;
  tbarWait.Position := fDuration;
end;
 
procedure TMainForm.tbarWaitChange(Sender: TObject);
// *** changement de la vitesse ***
begin
  Duration := tbarWait.Position;
end;
 
procedure TMainForm.SetDuration(AValue: Cardinal);
// *** détermination de la durée d'interpolation ***
begin
  if fDuration =AValue then
    Exit;
  fDuration := AValue;
end;
 
function TMainForm.InPower(AStart, AChange, AStep: Single; APower: Integer
  ): Single;
// *** calcul d'une interpolation de type IN pour les puissances ***
begin
  Result := AChange * Power(AStep / fDuration, APower) + AStart;
end;
 
function TMainForm.OutPower(AStart, AChange, AStep: Single; APower: Integer
  ): Single;
// *** calcul d'une interpolation de type OUT pour les puissances ***
var
  LSign: Integer;
begin
  LSign := ifthen(Odd(APower), 1, -1);
  Result := LSign * AChange * (Power(AStep / fDuration - 1, APower) + LSign) + AStart;
end;
 
function TMainForm.InOutPower(AStart, AChange, AStep: Single; APower: Integer
  ): Single;
// *** calcul d'une interpolation de type INOUT pour les puissances ***
var
  LSign: Integer;
begin
  LSign := ifthen(Odd(APower), 1, -1);
  AStep := AStep / fDuration * 2;
  if AStep < 1 then
    Result := AChange / 2 * Power(AStep, APower) + AStart
  else
    Result :=  LSign * AChange / 2 * (Power(AStep - 2, APower) + LSign * 2) + AStart;
end;
 
function TMainForm.EaseNone(AStart, AChange, AStep: Single): Single;
// *** pas de fonction ease ***
begin
  Result := AChange * AStep / fDuration + AStart;
end;
 
function TMainForm.EaseInQuad(AStart, AChange, AStep: Single): Single;
// *** INQUAD ***
begin
  Result := InPower(AStart, AChange, AStep, 2);
end;
 
function TMainForm.EaseOutQuad(AStart, AChange, AStep: Single): Single;
// *** OUTQUAD ***
begin
  Result := OutPower(AStart, AChange, AStep, 2);
end;
 
function TMainForm.EaseInOutQuad(AStart, AChange, AStep: Single): Single;
// *** INOUTQUAD ***
begin
  Result := InOutPower(AStart, AChange, AStep, 2);
end;
 
function TMainForm.EaseOutInQuad(AStart, AChange, AStep: Single): Single;
// *** OUTINQUAD ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutQuad(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInQuad(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInCubic(AStart, AChange, AStep: Single): Single;
// *** INCUBIC ***
begin
  Result := InPower(AStart, AChange, AStep, 3);
end;
 
function TMainForm.EaseOutCubic(AStart, AChange, AStep: Single): Single;
// *** OUTCUBIC ***
begin
  Result := OutPower(AStart, AChange, AStep, 3);
end;
 
function TMainForm.EaseInOutCubic(AStart, AChange, AStep: Single): Single;
// *** INOUTCUBIC ***
begin
  Result := InOutPower(AStart, AChange, AStep, 3);
end;
 
function TMainForm.EaseOutInCubic(AStart, AChange, AStep: Single): Single;
// *** OUTINCUBIC ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutCubic(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInCubic(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInQuart(AStart, AChange, AStep: Single): Single;
// *** INQUART ***
begin
  Result := InPower(AStart, AChange, AStep, 4);
end;
 
function TMainForm.EaseOutQuart(AStart, AChange, AStep: Single): Single;
// *** OUTQUART ***
begin
  Result := OutPower(AStart, AChange, AStep, 4);
end;
 
function TMainForm.EaseInOutQuart(AStart, AChange, AStep: Single): Single;
// *** INOUTQUART ***
begin
  Result := InOutPower(AStart, AChange, AStep, 4);
end;
 
function TMainForm.EaseOutInQuart(AStart, AChange, AStep: Single): Single;
// *** OUTINQUART ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutQuart(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInQuart(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInQuint(AStart, AChange, AStep: Single): Single;
// *** INQUINT ***
begin
  Result := InPower(AStart, AChange, AStep, 5);
end;
 
function TMainForm.EaseOutQuint(AStart, AChange, AStep: Single): Single;
// *** OUTQUINT ***
begin
  Result := OutPower(AStart, AChange, AStep, 5);
end;
 
function TMainForm.EaseInOutQuint(AStart, AChange, AStep: Single): Single;
// *** INOUTQUINT ***
begin
  Result := InOutPower(AStart, AChange, AStep, 5);
end;
 
function TMainForm.EaseOutInQuint(AStart, AChange, AStep: Single): Single;
// *** OUTINQUINT ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutQuint(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInQuint(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInSine(AStart, AChange, AStep: Single): Single;
// *** INSINE ***
begin
  Result := - AChange * cos(AStep / fDuration * Pi / 2) + AChange + AStart;
end;
 
function TMainForm.EaseOutSine(AStart, AChange, AStep: Single): Single;
// *** OUTSINE ***
begin
  Result := AChange * sin(AStep / fDuration * Pi / 2) + AStart;
end;
 
function TMainForm.EaseInOutSine(AStart, AChange, AStep: Single): Single;
// *** INOUTSINE ***
begin
  Result := - AChange / 2 * (cos(AStep / fDuration * Pi) - 1) + AStart;
end;
 
function TMainForm.EaseOutInSine(AStart, AChange, AStep: Single): Single;
// *** OUTINSINE ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutSine(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInSine(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInExpo(AStart, AChange, AStep: Single): Single;
// *** INEXPO ***
begin
  Result := ifthen(AStep = 0, AStart,
    AChange * Power(2, 10 * (AStep / fDuration - 1)) + AStart);
end;
 
function TMainForm.EaseOutExpo(AStart, AChange, AStep: Single): Single;
// *** OUTEXPO ***
begin
  Result := ifthen(AStep = fDuration, AChange + AStart,
    AChange * (- Power(2, -10 * AStep / fDuration) + 1) + AStart);
end;
 
function TMainForm.EaseInOutExpo(AStart, AChange, AStep: Single): Single;
// *** INOUTEXPO ***
begin
  if AStep = 0 then
    Result := AStart
  else
  if AStep = fDuration then
    Result := AChange + AStart
  else
  begin
    AStep := AStep / fDuration * 2;
    if AStep < 1 then
      Result := AChange / 2 * Power(2, 10 * (AStep - 1)) + AStart
    else
      Result := AChange / 2 * (- Power(2, - 10 * (AStep - 1)) + 2) + AStart;
  end;
end;
 
function TMainForm.EaseOutInExpo(AStart, AChange, AStep: Single): Single;
// *** OUTINEXPO ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutExpo(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInExpo(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInCirc(AStart, AChange, AStep: Single): Single;
// *** INCIRC ***
begin
  Result := - AChange * (Sqrt(1 - Power(AStep / fDuration, 2)) - 1) + AStart;
end;
 
function TMainForm.EaseOutCirc(AStart, AChange, AStep: Single): Single;
// *** OUTCIRC ***
begin
  Result := AChange * Sqrt(1 - Power(AStep / fDuration - 1, 2)) + AStart;
end;
 
function TMainForm.EaseInOutCirc(AStart, AChange, AStep: Single): Single;
// *** INOUTCIRC ***
begin
  AStep := AStep / fDuration * 2;
  if AStep < 1 then
    Result := - AChange / 2 * (Sqrt(1 - Power(AStep, 2)) - 1) + AStart
  else
    Result := AChange / 2 * (Sqrt(1 - Power(AStep - 2, 2)) + 1) + AStart;
end;
 
function TMainForm.EaseOutInCirc(AStart, AChange, AStep: Single): Single;
// *** OUTINCIRC ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutCirc(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInCirc(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInElastic(AStart, AChange, AStep: Single): Single;
// *** INELASTIC ***
begin
  if AStep = 0 then
    Result := AStart
  else
  begin
    AStep := AStep / fDuration;
    if AStep = 1 then
      Result := AChange + AStart
    else
    begin
      AStep := AStep - 1;
      Result := - (AChange * Power(2, 10 * AStep) * sin((AStep * fDuration
        - (fDuration * 0.3 / 4)) * 2 * Pi / (fDuration * 0.3))) + AStart;
    end;
  end;
end;
 
function TMainForm.EaseOutElastic(AStart, AChange, AStep: Single): Single;
// *** OUTELASTIC ***
begin
  if AStep = 0 then
    Result := AStart
  else
  begin
    AStep := AStep / fDuration;
    if AStep = 1 then
      Result := AChange + AStart
    else
      Result := AChange * Power(2, - 10 * AStep) * sin((AStep * fDuration -
        (fDuration * 0.3 / 4)) * 2 * Pi / (fDuration * 0.3)) + AChange + AStart;
   end;
end;
 
function TMainForm.EaseInOutElastic(AStart, AChange, AStep: Single): Single;
// *** INOUTELASTIC ***
begin
  if AStep = 0 then
    Result := AStart
  else
  begin
    AStep := AStep / fDuration * 2;
    if AStep = 2 then
      Result := AChange + AStart
    else
    begin
      // 0.45 = 0.3*1.5  0.1125 = 0.45 / 4
      if AStep < 1 then
      begin
        AStep := AStep - 1;
        Result := - (AChange * Power(2, 10 * AStep) * sin((AStep * fDuration -
          fDuration * 0.1125) * 2 * Pi / (fDuration * 0.45))) / 2 + AStart;
      end
      else
      begin
        AStep := AStep - 1;
        Result :=  AChange * Power(2, - 10 * AStep) * sin((AStep * fDuration -
          fDuration * 0.1125) * 2 * Pi / (fDuration * 0.45)) / 2 + AChange + AStart;
      end;
    end;
  end;
end;
 
function TMainForm.EaseOutInElastic(AStart, AChange, AStep: Single): Single;
// *** OUTINELASTIC ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutElastic(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInElastic(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInBack(AStart, AChange, AStep: Single): Single;
// *** INBACK ***
begin
  // 1.70158 = 10% 2.592389 = 20% 3.394051 = 30% 4.15574465 = 40%
  Result := AChange * Power(AStep / fDuration, 2) * (2.70158 *
    AStep / fDuration - 1.70158) + AStart;
end;
 
function TMainForm.EaseOutBack(AStart, AChange, AStep: Single): Single;
// *** OUTBACK ***
begin
  Result := AChange * (Power(AStep / fDuration - 1, 2) *
    (2.70158 * (AStep / fDuration - 1) + 1.70158) + 1) + AStart;
end;
 
function TMainForm.EaseInOutBack(AStart, AChange, AStep: Single): Single;
// *** INOUTBACK ***
begin
  // 2.5949095 = 1.70158 * 1.525
  AStep := AStep / fDuration * 2;
  if AStep < 1 then
    Result := AChange / 2 * Power(AStep, 2) * (3.594905 * AStep - 2.594905)
      + AStart
  else
    Result := AChange / 2 * (Power(AStep - 2, 2) * (3.594905 * (AStep - 2)
      + 2.594905) + 2) + AStart;
end;
 
function TMainForm.EaseOutInBack(AStart, AChange, AStep: Single): Single;
// *** OUTINBACK ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutBack(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInBack(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInOutBounce(AStart, AChange, AStep: Single): Single;
// *** INOUTBOUNCE ***
begin
  if AStep < fDuration / 2 then
    Result := EaseInBounce(0, AChange, AStep * 2) / 2 + AStart
  else
    Result := EaseOutBounce(0, AChange, AStep * 2 - fDuration) / 2 + AChange / 2
      + AStart;
end;
 
function TMainForm.EaseOutInBounce(AStart, AChange, AStep: Single): Single;
// *** OUTINBOUNCE ***
begin
  if AStep < fDuration / 2 then
    Result := EaseOutBounce(AStart, AChange / 2, AStep * 2)
  else
    Result := EaseInBounce(AStart + AChange / 2, AChange / 2, AStep * 2 - fDuration);
end;
 
function TMainForm.EaseInBounce(AStart, AChange, AStep: Single): Single;
// *** INBOUNCE ***
begin
  Result := AChange - EaseOutBounce(0, AChange, fDuration - AStep) + AStart;
end;
 
function TMainForm.EaseOutBounce(AStart, AChange, AStep: Single): Single;
// *** OUTBOUNCE ***
begin
  AStep := AStep / fDuration;
  if AStep < 1 / 2.75 then
    Result := AChange * 7.5625 * Power(AStep, 2) + AStart
  else
  if AStep < 2 / 2.75 then
  begin
    AStep := AStep - 1.5 / 2.75;
    Result := AChange * (7.5625 * Power(AStep, 2) + 0.75) + AStart;
  end
  else
  if AStep < 2.5 / 2.75 then
  begin
    AStep := AStep - 2.25 / 2.75;
    Result := AChange * (7.5625 * Power(AStep, 2) + 0.9375) + AStart;
  end
  else
  begin
    AStep := AStep - 2.625 / 2.75;
    Result := AChange * (7.5625 * Power(AStep, 2) + 0.984375) + AStart;
  end;
end;
 
function TMainForm.ComputeInterpolation(AStart, AEnd, AStep: Single;
  AInter: TInterpolation; ABack: Boolean): Single;
// *** calcul des interpolations ***
begin
  case AInter of
    // linéaire
    intLinear: Result := EaseNone(AStart, AEnd, AStep);
    // quadratique
    intEaseInQuad: Result := EaseInQuad(AStart, AEnd, AStep);
    intEaseOutQuad: Result := EaseOutQuad(AStart, AEnd, AStep);
    intEaseInOutQuad: Result := EaseInOutQuad(AStart, AEnd, AStep);
    intEaseOutInQuad: Result := EaseOutInQuad(AStart, AEnd, AStep);
    // cubique
    intEaseInCubic: Result := EaseInCubic(AStart, AEnd, AStep);
    intEaseOutCubic: Result := EaseOutCubic(AStart, AEnd, AStep);
    intEaseInOutCubic: Result := EaseInOutCubic(AStart, AEnd, AStep);
    intEaseOutInCubic: Result := EaseOutInCubic(AStart, AEnd, AStep);
    // quartique
    intEaseInQuart: Result := EaseInQuart(AStart, AEnd, AStep);
    intEaseOutQuart: Result := EaseOutQuart(AStart, AEnd, AStep);
    intEaseInOutQuart:  Result := EaseInOutQuart(AStart, AEnd, AStep);
    intEaseOutInQuart: Result := EaseOutInQuart(AStart, AEnd, AStep);
    // quintique
    intEaseInQuint: Result := EaseInQuint(AStart, AEnd, AStep);
    intEaseOutQuint: Result := EaseOutQuint(AStart, AEnd, AStep);
    intEaseInOutQuint:  Result := EaseInOutQuint(AStart, AEnd, AStep);
    intEaseOutInQuint: Result := EaseOutInQuint(AStart, AEnd, AStep);
    // sinus
    intEaseInSine: Result := EaseInSine(AStart, AEnd, AStep);
    intEaseOutSine: Result := EaseOutSine(AStart, AEnd, AStep);
    intEaseInOutSine: Result := EaseInOutSine(AStart, AEnd, AStep);
    intEaseOutInSine: Result := EaseOutInSine(AStart, AEnd, AStep);
    // exponentielle
    intEaseInExpo: Result := EaseInExpo(AStart, AEnd, AStep);
    intEaseOutExpo: Result := EaseOutExpo(AStart, AEnd, AStep);
    intEaseInOutExpo: Result := EaseInOutExpo(AStart, AEnd, AStep);
    intEaseOutInExpo: Result := EaseOutInExpo(AStart, AEnd, AStep);
    // cercle
    intEaseInCirc: Result := EaseInCirc(AStart, AEnd, AStep);
    intEaseOutCirc: Result := EaseOutCirc(AStart, AEnd, AStep);
    intEaseInOutCirc: Result := EaseInOutCirc(AStart, AEnd, AStep);
    intEaseOutInCirc: Result := EaseOutInCirc(AStart, AEnd, AStep);
    // élastique
    intEaseInElastic: Result := EaseInElastic(AStart, AEnd, AStep);
    intEaseOutElastic: Result := EaseOutElastic(AStart, AEnd, AStep);
    intEaseInOutElastic: Result := EaseInOutElastic(AStart, AEnd, AStep);
    intEaseOutInElastic: Result := EaseOutInElastic(AStart, AEnd, AStep);
    // retour
    intEaseInBack: Result := EaseInBack(AStart, AEnd, AStep);
    intEaseOutBack: Result := EaseOutBack(AStart, AEnd, AStep);
    intEaseInOutBack: Result := EaseInOutBack(AStart, AEnd, AStep);
    intEaseOutInBack: Result := EaseOutInBack(AStart, AEnd, AStep);
    // rebond
    intEaseInBounce: Result := EaseInBounce(AStart, AEnd, AStep);
    intEaseOutBounce: Result := EaseOutBounce(AStart, AEnd, AStep);
    intEaseInOutBounce: Result := EaseInOutBounce(AStart, AEnd, AStep);
    intEaseOutInBounce: Result := EaseOutInBounce(AStart, AEnd, AStep);
  end;
  if ABack then
    Result := AEnd - Result;
end;
 
function TMainForm.ComputeInterpolationInt(AStart, AEnd: Integer;
  AStep: Integer; AInter: TInterpolation; ABack: Boolean): Integer;
// *** interpolation entière ***
begin
  Result := Round(ComputeInterpolation(AStart, AEnd, AStep, AInter, ABack));
end;
 
end.

Voici une vidéo qui montre l'application en action :



Vous voici parvenus au bout de votre première exploration des interpolations, et plus spécifiquement des courbes d'easing. L'épisode suivant va formaliser ce travail préparatoire en proposant une série de classes à réutiliser dans vos projets à venir.

Le code source de l'application est ici : exemples.zip.

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