Easing Functions in the New Form Based on Bézier Curves

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• 关键词：Easing function ; Tweening function ; Transition ; Keyframing ; CSS
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9972
• 期：1
• 页码：37-48
• 全文大小：1,388 KB
• 参考文献：1.Parent, R.: Computer Animation, 3rd edn. Morgan Kaufmann, Burlington (2012)
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  3.Robert Penner’s Easing Functions. http://​robertpenner.​com/​easing/​ . Accessed 10 Mar 2016
  4.Owen, M., Willis, P.: Modelling and interpolating cartoon characters. In: Proceedings of the Computer Animation 1994, Geneva, 25–28 May 1994, pp. 148–155. http://​ieeexplore.​ieee.​org/​iel2/​987/​7718/​00323996.​pdf . Accessed 10 Mar 2016
  5.Melikhov, K., Tian, F., Seah, H.S., Chen, Q., Qiu, J.: Frame skeleton based auto-inbetweening in computer assisted cel animation. In: Proceedings of the 2004 International Conference on Cyberworlds (CW 2004), 18–20 November 2004, Tokyo, Japan, pp. 216–223 (2004)
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  11.Easing Functions. In: .NET Framework v4 Documentation, https://​msdn.​microsoft.​com/​en-us/​library/​ee308751%28v=​vs.​100%29.​aspx . Accessed 10 Mar 2016
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  13.The secret of tweening: when and when not to. Broder Jakobs Flash. http://​www.​broderjakob.​se/​2007/​09/​07/​the-secret-of-tweening-using-it-when-you-need-it/​ . Accessed 10 Mar 2016
  14.Apt, D.: An Introduction to Tweening with ActionScript 3.0. (2009). http://​code.​tutsplus.​com/​tutorials/​an-introduction-to-tweening-with-actionscript-30--active-2022 . Accessed 10 Mar 2016
  15.Smith, J., Smith, C., Gerantabee, F.: How to Create a Motion Tween in Adobe Flash CS6. http://​www.​dummies.​com/​how-to/​content/​how-to-create-a-motion-tween-in-adobe-flash-cs6.​html . Accessed 10 Mar 2016
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  17.Lie, H.W.: Cascading HTML Style Sheets a Proposal. https://​www.​w3.​org/​People/​howcome/​p/​cascade.​html . Accessed 10 Mar 2016
  18.Ceaser CSS Easing Animation Tool. https://​matthewlein.​com/​ceaser/​ . Accessed 10 Mar 2016
  19.Tween Class. http://​www.​createjs.​com/​docs/​tweenjs/​classes/​Tween.​html . Accessed 10 Mar 2016
  20.AHEasing. A library of easing functions for C, C++ and Objective-C. https://​github.​com/​warrenm/​AHEasing . Accessed 10 Mar 2016
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  22.Tween-functions. Robert Penner’s easing functions, slightly modified. https://​www.​npmjs.​com/​package/​tween-functions . Accessed 10 Mar 2016
  
• 作者单位：Łukasz Izdebski (17)
  Dariusz Sawicki (17)
  
  17. Warsaw University of Technology, Pl. Politechniki 1, 00-661, Warsaw, Poland
  
• 丛书名：Computer Vision and Graphics
• ISBN：978-3-319-46418-3
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9972

文摘

The transition problem is one of the important problems of animation. The Penners easing functions solve this successfully. There are some well known and widely used approximations of these functions where Bézier curves have been used. However, the transition functions, obtained by such approximation differ substantially from the original. We proposed new form of approximation in the paper. Two class of easing functions are discussed. In first simple approximation allows obtaining sufficient effects. In the second the easing function is divided into two symmetric parts where the approximation is done. For every approximation the root mean square error (RMSE) has been determined and the animated transition using new solution is analyzed. The new approximation allows obtaining better RMSE as well as better visual effects in animation.