點陣圖(Bitmap)是一種簡單利用位元值(bit)來表示圖形的一種方法， 而每個位元值為0或1。點陣文字(Bitmap Font)也是利用點陣圖形的方式來呈現文字。而我們更是容易在電腦或是其他電子設備中看見點陣文字的出現。一般而言，點陣圖的優點在於不是一種壓縮過的圖形，所以更好的被拿來應用在各種處理上。漸變式演算法是一種連續性的變形過程。被廣泛的被使用在動畫或是電影的變形效果中，使某一件物體變形成另一種物體，或是由人變成另一個人。而最常見的漸變式算法即是用內插法來呈現，然而使用內插法得到的結果往往產生斷裂或是不連續性破壞了整個圖形的結構。因此我們想去設計一個算法在圖形的漸變過程中可以盡量保持連接與維持相似的結構不被破壞。我們在此提出了一種在各種電子產品、網頁製作、或是電子書集中更好的呈現方式。而在本篇的論文當中，我們專注於雙色的點陣圖(黑與白)，我們得到不錯且平滑的執行結果。此外，這個演算法也可以是用在小尺寸的顯示裝備或是移動裝置中。

在本篇論文裡，我們應用在希臘文字、英文文字、中國文字還有一些圖形中，例如插圖或是多邊形。

A bitmap can represent a image by using bits, and the value which are zero or one. Bitmap fonts consist of a matrix of dots or pixels representing the image of each glyph in each face and size. The bitmap font is a common format for printing and displaying on computers, and it is widely used to display characters or pictures. Generally speaking, the advantage of bitmap format is that bitmap will not compose the data and with no distortion after applying any operations. Morphing is a transforming process changes one image or shape into another. The fundamental method to morph an image is mapping the points one by one, and interpolation the points to get the result. However, the drawback with one-by-one point-mapping method is that points can be mapped randomly, the corresponding character may be broken into pieces and then the architecture is destroyed. Thus we want to design an algorithm which morphs the bitmap font from one input data to another, such that creating an animation of bitmap data, and more details are kept than mapping points one by one. Here we present an alternate real-time method which displays characters on electronics products, web-page, computer games, and electronic books(e-books). We only use monotone bitmap font and we expect the morphing processes to run smoothly. In this way we can overcome the drawbacks of one by one mapping method. Moreover, it is appropriate to apply bitmap font to small-size monitors or mobile devices.

In this thesis, we apply this method on English characters, Chinese characters, and some bitmap images, such as illustration and polygons.

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