Morphing is the transformation from a source shape to a target shape. Conventional approaches to this problem often require the user to indicate a correspondence between the source and target shapes. A new framework is recently proposed by Edelsbrunner and Fu based on alpha shapes. It overcomes several limitations and the correspondence between source and target shapes is established automatically. It also allows all intermediate shapes be specified using a combinatorial structure: an arrangement of parabolas. Thus, it becomes possible to control the morphing directly. In this thesis, we design and implement a morphing system based on this new framework. We incorporate the skin of alpha shape proposed by Edelsbrunner to smooth out the transitions between intermediate shapes. We also stu...[ Read more ]

Morphing is the transformation from a source shape to a target shape. Conventional approaches to this problem often require the user to indicate a correspondence between the source and target shapes. A new framework is recently proposed by Edelsbrunner and Fu based on alpha shapes. It overcomes several limitations and the correspondence between source and target shapes is established automatically. It also allows all intermediate shapes be specified using a combinatorial structure: an arrangement of parabolas. Thus, it becomes possible to control the morphing directly. In this thesis, we design and implement a morphing system based on this new framework. We incorporate the skin of alpha shape proposed by Edelsbrunner to smooth out the transitions between intermediate shapes. We also study an objective criterion for measuring the complexity of morphing and prove a monotonicity property. This is a step towards comparing different morphings and constructing a desirable one.