The Visual Computer

, Volume 22, Issue 5, pp 346–356 | Cite as

Detection and classification of topological evolution for linear metamorphosis

  • Tomoyuki NiedaEmail author
  • Alexander Pasko
  • Tosiyasu L. Kunii
Special Issue Paper


The advantage of functional methods for shape metamorphosis is the automatic generation of intermediate shapes possible between the key shapes of different topology types. However, functional methods have a serious problem: shape interpolation is applied without topological information and thereby the time values of topological changes are not known. Thus, it is difficult to identify the time intervals for key frames of shape metamorphosis animation that faithfully visualize the topological evolution. Moreover, information on the types of topological changes is missing. To overcome the problem, we apply topological analysis to functional linear shape metamorphosis and classify the type of topological evolution by using a Hessian matrix. Our method is based on Morse theory and analyzes how the critical points appear. We classify the detected critical points into maximum point, minimum point, and saddle point types. Using the types of critical points, we can define the topological information for shape metamorphosis. We illustrate these methods using shape metamorphosis in 2D and 3D spaces.


Critical point classification Morse theory Shape metamorphosis Topological evolution 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Tomoyuki Nieda
    • 1
    Email author
  • Alexander Pasko
    • 1
    • 2
  • Tosiyasu L. Kunii
    • 2
  1. 1.Graduate School of Computer and Information SciencesHosei UniversityKoganei-shiJapan
  2. 2.IT InstituteKanazawa Institute of TechnologyShibuya-kuJapan

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