| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 101 === Morphing is the process of changing one figure into another. In this study, we show some numerical methods of surface morphing by using the conformal mapping and the idea of homotopy. We uniformize the structure of each mesh by using the conformal parameterization, and construct the morphing process by using cubic spline homotopy.
In order to control the morphing process as our desire, here comes a surface matching problem. From the Riemann mapping theorem, we know that there exists a unique Riemann conformal mapping from a simply connected surface into a unit disk. Therefore, we reduce a surface matching problem into a unit disk matching problem and solve this problem by using the biharmonic weighted least square method.
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