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研究生:王仁傑
研究生(外文):Ren-Jie Wang
論文名稱:以自然法則為基礎的水墨擴散
論文名稱(外文):Toward a Physically-Based Ink Diffusion
指導教授:王宗銘王宗銘引用關係
指導教授(外文):C. M. Wang
學位類別:碩士
校院名稱:國立中興大學
系所名稱:資訊科學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:93
中文關鍵詞:圖學宣紙吸水性墨汁擴散以自然法則為基礎以影像基礎的水墨擴散成圖法水墨渲染效果多維度擴散模型
外文關鍵詞:non-photorealistic renderingChinese calligraphy and ink paintingink diffusionphysically-basedpaper structuremultidimensional diffusion modelgravityimage-based ink diffusion rendering
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  在中國書法水墨畫(Chinese calligraphy and ink painting)方面的相關研究,從最早的毛刷(hairy brushes)開始,研究的方向主要是談如何「做」一枝好的虛擬筆刷(virtual brush),去產生接近真實毛筆筆觸(stroke)的效果。某些學者則研究如何利用貼圖(texture mapping)的方法,讓三維的模型(3D model)或二維的影像(2D image)產生中國水墨畫的風格。這些研究部分對於擴散現象大多不予解釋,或者只是用特定演算法來產生類似的效果。然而,仔細觀察中國的水墨畫,可以發現,畫家們透過熟練的技巧,可以讓單色的墨在畫紙上呈現變化萬千的效果,這是由於墨汁和紙張之間會有交互作用,不同濃淡的墨色,不同多寡的墨量,在畫紙上都會有不同的墨韻和擴散現象。這種複雜的水墨擴散現象,不是有限效果的貼圖演算法或是特定演算法所可以模擬的。
Knuii的多維度擴散模型(multidimensional diffusion model),對水墨的擴散現象提出了合理的解釋,也提出了一個數學表示式(mathematical formalisation)來模擬擴散現象,這是一個比較有學理依據的方法。我們重做了Kunii的結果,發現在視覺上仍不夠逼真,而且對於其他影響水墨擴散的因素,如紙張特性、重力等,並沒有深入研究和實作,也沒有談到任何應用。為了改進這些缺點,我們先對中國書法水墨畫最常用的紙材-宣紙進行研究並模擬。我們分析了宣紙的基本特性,發現宣紙的基重、厚度、密度、平滑度、吸水度、柔軟度、白度及紙力等特性與作畫時之運筆及墨色有密切的關係,而其中吸水度與墨汁的擴散更是息息相關。吸水度愈大者,其吸墨性愈強。可見紙張結構除了傳統纖維交織的紋路之外,吸水性應該是最重要的特性。為此,我們提出了更好的紙張結構,除了外觀可視的紋路之外,還具有吸水性這項重要特徵。我們使用傳統紙張結構演算法,製造了三種纖維束交織的紋路;而且根據研究結果,將紙張紋路和紙張密度、吸水性之間的關係建立起來。多了更好的紙張結構,我們得到了更真實的墨漬成像。
傳統書法一般都在水平的桌面上進行,可是水墨繪畫有可能是在傾斜的畫板上完成的。為了讓擴散動作能感應紙張傾斜所造成的重力變化,我們實際觀察墨汁在垂直宣紙上的擴散情形,仿照重力在斜面方向分力的概念來處理擴散表示式中的p、q參數,並且分別定義了X、Y兩方向的傾斜度。我們的方法能讓紙張在三度空間上從水平到垂直,以任意方式傾斜,擴散動作都可以正確地被模擬。
我們的系統能成功地以動畫方式來模擬重要的擴散現象,這些現象都是由同一個負責擴散的模組,從使用者選擇的宣紙,給予的墨量、墨色這三個設定值中,自動計算出來的,不需要個別不同的演算法來產生。例如:在墨量多、墨色較淡(即water rate值較大的墨汁)的情況下,由於水量多,墨漬會擴散開來,而邊緣會隨著紙張紋路產生不規則的羽化現象;如果墨量少,乾刷現象就會出現;如果將濃墨刷過淡墨上面,在濃墨、淡墨的交界附近,會產生類似濕紙效果的渲染現象等等。只要有紙、有墨,我們的系統就會自動算出墨漬的樣子,不像傳統的貼圖法,不同的效果,必須透過不同的演算法來產生貼圖。
這個以自然法則為基礎的水墨擴散法,是與成圖演算法無關(render algorithm independent)的。除了可以產生更逼真的墨漬成像之外,也很容易加以推廣應用。我們舉了兩個應用實例來加以說明-中國書法水墨畫的模擬和以影像為基礎的水墨渲染成圖(image-based ink diffusion render)。想要以動畫的方式來呈現書法或水墨畫在運筆過程中,墨漬的變化情形,事先取得字或畫的下筆順序是必需的。相關學者的研究告訴我們,用毛筆運筆時,可以將筆毛和紙張的切面視為橢圓,所以,可以利用橢圓來組成任意筆劃(stroke)。我們利用滑鼠在字跡的影像上擷取橢圓以取得筆劃的資訊,產生筆跡檔,並利用對橢圓做隨機取樣來取得筆跡,然後將筆跡轉成宣紙上的墨滴,再利用上述的擴散技巧造成筆跡邊緣的擴散,來達成我們用動畫來模擬、合成中國書法、水墨畫的目標。
另一個應用是以影像為基礎的水墨擴散成圖(image-based ink diffusion render)法,這是一個全新的方法,目前一般的商業影像處理軟體無法提供這個功能,也無法產生類似的效果。這個方法可以讓影像呈現令人激賞的水墨渲染風格,得到比傳統的貼圖演算法更好的視覺效果。我們將影像檔(image file)中每一個圖素(pixel)的RGB資訊,轉成單色的黑白資訊,然後從中取得墨量和墨色(即水和碳)的大小值,將墨滴滴在紙上同樣座標點上,讓擴散模組進行擴散計算,一直到水乾為止,一張水墨渲染風格的影像即可產生。基本上,我們在影像顏色較黑的地方,給予較少的墨量和較黑的墨色,使得擴散較小,以維持影像重要特徵不模糊;影像較淡的地方,給予較多的墨量和較淡的墨色,則擴散較大,以產生水墨渲染效果。
綜觀本研究,我們以Kunii的多維度擴散模型為基礎,將其缺失或未完成之部分予以具體化,提出了可行的辦法來模擬紙張的結構,並且考慮了重力對擴散過程的影響,得以完成這個以自然為基礎的水墨擴散技術。此外,我們還以動畫模擬和影像基礎之水墨擴散成圖兩個應用,來展示這個技術的水墨擴散效果。總結本文,我們認為,由於採用合乎自然法則的方法,我們所提出的技術,能使水墨擴散的模擬更真實、逼真。
Non-photorealistic rendering is a popular subject in computer graphics which has recently been intensively studied. Chinese calligraphy and black ink painting is a category of non-photorealistic rendering where the ink diffusion phenomenon is an import feature. Previous approaches for simulating or synthesizing this phenomenon were either based on texture mapping techniques or developing some specific, not general- purpose algorithms. Besides, they normally did not take paper into consideration, nor did they try to simulate the ink diffusion effect due to the existing of outer forces, such as gravity. In this thesis, we present several techniques to outcome the drawbacks of previous approaches. We investigate the multidimensional diffusion model proposed by Kunii and take it as a basis for synthesizing the ink diffusion. We first apply finite difference technique to solve the partial equation embedded in the multidimensional diffusion model. We later present a technique to simulate three types of paper which have normally been utilized in the Chinese calligraphy and black ink painting. Finally, we consider the effect of gravity in terms of vertical and horizontal forces, and apply them to our diffusion model to simulate the reaction between water and carbon. The simulation results are visual plausive since the black border of ink diffusion is successfully simulated. We later apply the ink diffusion techniques to two other applications: Chinese calligraphy & ink painting and image-based ink diffusion rendering. Experimental results demonstrate that various visual effects can be achieved using various kinds of paper, ink quantities and the effect of gravity. Besides, the image-based ink diffusion rendering presents an impressive effect where current commercial software are not able to do so. In conclusion, we present a physically-based approach for synthesizing the effects of ink diffusion. Experimental results demonstrate that this approach is superior to other approaches with more visually plausible effects.
第一章 緒論    1
1.1 研究動機…………………………………………………………………….1
1.2 研究目標…………………………………………………………………….4
1.3 論文大綱…………………………………………………………………….5
第二章 相關研究 7
2.1 粒子擴散模型(Particle Diffusion Model)……………………………….….7
2.2 熱力學運動(Thermal Motion)擴散模型…………………………………. 11
2.3 其他相關研究…………………………..……………………………… 16
2.4中國書法的合成………………………………………………………… 20
2.5相關研究之優缺點……………………..……………………………… ..22
第三章 以自然法則為基礎的水墨擴散 25
3.1 相關物理特性的探討…………………………………..…………………25
3.2 多維度擴散模型之數值解………………………………………………30
3.3 宣紙的產生………………………………………………………….……35
3.4 考慮重力因素……………………………………………………….…….40
3.5 中國書法繪畫的模擬……………………………………………….……42
3.5.1 用橢圓來擷取筆劃………………………………………….……42
3.5.2 橢圓上取樣本………………………………………………………44
3.5.3 將橢圓筆跡轉換成墨跡……………………………………………46
3.6 具有水墨渲染風格的影像處理……………………………………….…48
3.7 整體架構與系統實作…………………………………………………….51
第四章 實作結果 57
4.1 量的分析…………………………………..…………………………….…57
4.2 模擬結果…………………………………..…………………………….…64
4.3 應用實例…………………………………..…………………………….…68
第五章 結論與未來工作 80
5.1 結論..…………………………………..…………………………….…80
5.2 未來工作…………………………………..…………………………….…82
參考資料 84
詞彙索引
中英對照表……………………………………………………………………88
英中對照表……………………………………………………………………91
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