三維模型的使用過去主要用於平台遊戲與電影工業等，
但是，隨著硬體的進步帶來的運算效能大量增長而延伸到了移動式設備上。
同時許多能夠節省三維模型之網格量與計算量演算法被提出，在這些演算法中與本研究相關的便是法向量貼圖(Normal map)。
藉由點陣圖(Raster image)來儲存高網格量三維模型法向量變化，
並且在低網格量三維模型上加以還原，得以在視覺上逼近高網格量三維模型之渲染結果。
其中重複樣式(Repeat pattern)法向量貼圖(Normal map)重覆紀錄相似資訊，造成檔案量巨大，根據重複次數鋸齒嚴重等問題，即使以高達二千解析度貼圖依然在放大時明顯可見。
本研究觀察發現重複樣式(Repeat pattern)有生長方向大略與骨架前進方向一致，且鄰近重複樣式(Repeat pattern)大小、形狀與方向相似之特性，利用基於骨架之四路旋轉對稱流場(4-RoSy flow field)與樣式起始位置、密度產生之座標去擺放重複樣式(Repeat pattern)以省去儲存大量重複樣式(Repeat pattern)之資訊。同時，也設計出專為樣式法向量貼圖(Normal map)設計的向量化方法，以克服傳統點陣法向貼圖大量密鋪時的貼圖解析度限制及精準度不夠失真問題。
本研究使用法向量貼圖(Normal map)以擴散曲線(Diffusion curve)表示式向量化之方法，以減少描述法向量平滑區域的使用量，
同時使用法向量旋轉四元數(Quaternation)來計算法向量貼圖(Normal map)像素間的差別。
能夠比傳統顏色色差法保留更多細節，
並且能準確找出向量變化較大的位置。
因此能產生較為符合需求之擴散曲線(Diffusion curve)，
並利用格林涵式(Green's function)來計算擴散曲線(Diffusion curve)之顏色。
此外傳統法向量貼圖(Normal map)製作過程繁雜，一但圖像成型則難以調整，
而擴散曲線(Diffusion curve)提供了再次編輯的便利性。
本論文設計針對法向量貼圖(Normal map)的峰值信噪比(PSNR)來驗證研究結果，並且比較本論文輸出檔案容量大小。結果在容量上大幅減少，並且保有高還原程度。本論文結合擴散式曲線向量化方法與自動化流場骨架貼圖座標計算，產出符合骨架走向重複區塊向量貼圖，大幅節省資料儲存及傳輸量。

3D models are mainly used in console games and movie industries, but recently, with the significant increase of computing performance, are also used on mobile devices. Simultaneously, many rendering methods are introduced to save the data storage and computation of 3D models, and our research is related to normal mapping.Using raster images to store the normal difference on high-polygon 3D models and texturing to low-polygon 3D models can get a result that visually close enough to high-polygon 3D models.Repeat pattern normal maps contain repeat information, result in huge data storage and the aliasing become severe depend on the repeat times.Even with 2K resolution texture, the aliasing in render result is still obvious when zoomed in. In our study, we found that repeat patterns grow directions are similar to skeleton's.Nearby patterns' shape, direction, size are similar.In order to save data storage of huge amount of repeat pattern,we generate texture coordinate by using skeleton-based 4-RoSy flow field and repeat pattern start position, density to place patterns.Also, we design a method to vectoring normal map, to solve the problem of traditional raster image resolution limitation and aliasing problems.Our research propose a method to vectoring normal maps by using diffusion curves, which can use less data to represent the smooth areas of the images, then calculate the difference of pixels by using normal rotation quaternions.Normal rotation quaternions are better at reserving the detail information than traditional color differential method, and can precisely find positions of larger difference of normal.Therefore, our research can produce diffusion curves qualify the normal difference, and then use green function to compute the color on each side of diffusion curves.Besides, traditional normal map generated methods are complicating, and it is hard to modify once the normal map is produced.And diffusion curves are convenient to be modified.We design a method to measure the error of normal map reconstruction result by using quaternions rotation angle difference and then calculate PSNR and compare data storage of our method with input data storage.Our research reduce huge amount of data storage and remains high quality.We combine diffusion curve vectoring method and texture coordinate generation method based on flow field, to reduce the data storage.

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