2D Object Metamorphosis Based On Continued Fractions Interpolation

In recent years,the technology of 2D object metamorphosis has got rapid development in the field of industrial simulation,virtual reality,scientific computing visualization, biomedicine project, advertising and entertainment and so on.This technology principally consists of two parts:2D shape morphing(blending) and image morphing(or metamorphosis). There are a lot of methods of 2D object metamorphosis.The current algorithms have advantages and disadvantages.Whether the shape morphing algorithms or image morphing algorithms are concerned,most of them deal with the morphing between two objects.In this thesis, an algorithm of the morphing among multiple 2D objects is presented with the aid of theory of continued fractions.First,the technology of 2D object metamorphosis is discussed in detail and two main parts are presented in this thesis.In the first part are the principal methods of 2D shape blending. And in this part,the algorithm of polygons is emphasized.The second part is focused on image morphing.After expatiating its principal algorithms and mature methods,a method among multiple images is presented and analysed in detail.Second,in the second chapter of this thesis,the basic theories and methods are systematically discussed ,especially Thiele continued fractions,because it is the main interpolation tool in the experiments.And finally,the processes and results of experiments in the application of continued fractions to 2D object metamorphosis are given,and detailed analyzing and discussing are made.The experiments show that the results are good .This demonstrates that it is successful for continued fractions to be applied in the processes of 2D object metamorphosis.