本文選題：四邊形網(wǎng)格生成 + 方向場　； 參考：《清華大學(xué)》2016年碩士論文

【摘要】：四邊形網(wǎng)格在幾何造型、紋理映射、有限元模擬仿真、計(jì)算機(jī)動(dòng)畫以及建筑學(xué)等領(lǐng)域都有著大量廣泛的應(yīng)用。相比于傳統(tǒng)的三角形網(wǎng)格,四邊形網(wǎng)格擁有很多優(yōu)良的特性,如天然地具有張量積性質(zhì),其網(wǎng)格面片能夠非常自然地與矩形紋理保持一致對齊,而且可以直觀地捕獲模型的幾何特征與語義特征。因此,四邊形網(wǎng)格生成算法已經(jīng)成為了當(dāng)今國內(nèi)外研究的熱點(diǎn)內(nèi)容。然而,如何生成符合用戶設(shè)計(jì)意圖、奇異點(diǎn)少且分布良好的各向異性高質(zhì)量四邊形網(wǎng)格模型仍然是一個(gè)開放性的問題,其主要困難在于:1)在不同的應(yīng)用領(lǐng)域中,用戶對四邊形網(wǎng)格質(zhì)量的控制需求往往不盡相同。而這些控制需求常常又是相互制約,甚至相互矛盾的。2)當(dāng)今主流的全自動(dòng)生成算法缺乏對奇異點(diǎn)的控制,而用戶輔助的生成算法又對用戶的手工建模能力提出了過高的要求。因此,如何結(jié)合這兩類四邊形網(wǎng)格生成算法的各自優(yōu)勢是一項(xiàng)很大的挑戰(zhàn)。于是,針對目前四邊形網(wǎng)格生成算法存在的這些問題,本文提出了相應(yīng)的解決方案:1)提出了一種基于方向場的可控四邊形網(wǎng)格生成算法。本文在前人的基礎(chǔ)上提高了用戶的可控性:通過引入測地線技術(shù)和三維草繪技術(shù),允許用戶對方向場的方向進(jìn)行自由直觀的控制,同時(shí)為了處理用戶在控制方向場時(shí)產(chǎn)生的沖突和誤差,本文提出了相應(yīng)的解決方向約束沖突以及修正用戶交互不精確性問題的處理方案,進(jìn)而擴(kuò)展優(yōu)化了正交場的光滑能量函數(shù),使其能夠插值生成用戶可控的全局光滑正交場,從而能夠控制決定最終四邊形網(wǎng)格的網(wǎng)格邊方向、以及奇異點(diǎn)分布。2)提出了一種基于模式的用戶輔助四邊形網(wǎng)格生成算法。針對前人方法中拓?fù)淠Ｊ椒N類過少的問題,本文提出了一種面片松弛分解操作,通過面流塌縮處理可將原始輸入的多邊形面片進(jìn)行分解化簡,然后根據(jù)大量簡化的面片,設(shè)計(jì)出了多種更加復(fù)雜的拓?fù)淠Ｊ?進(jìn)而再通過面片填補(bǔ)操作便能夠生成拓?fù)浣Y(jié)構(gòu)更加豐富的四邊形網(wǎng)格,即擴(kuò)展了四邊形網(wǎng)格生成的解空間。3)結(jié)合全自動(dòng)生成算法與用戶輔助生成算法的各自優(yōu)勢,本文將上述兩種算法進(jìn)行了整合,設(shè)計(jì)開發(fā)出了一套完整的四邊形網(wǎng)格生成與編輯系統(tǒng),可以快速方便地生成符合用戶需求、且具有各向異性的高質(zhì)量四邊形網(wǎng)格模型。
[Abstract]:Quadrilateral mesh is widely used in geometry modeling, texture mapping, finite element simulation, computer animation and architecture. Compared with traditional triangular meshes, quadrilateral meshes have many excellent properties, such as natural tensor product properties, and their meshes are naturally aligned with rectangular textures. Moreover, the geometric and semantic features of the model can be captured intuitively. Therefore, quadrilateral mesh generation algorithm has become a hot topic at home and abroad. However, how to generate anisotropic high quality quadrilateral mesh models with few singular points and good distribution is still an open problem. The main difficulty is that: 1) in different application fields. Users' requirements for quadrilateral mesh quality control are often different. However, these control requirements are often restricted to each other, or even contradictory. 2) nowadays, the mainstream automatic generation algorithms lack the control of singularity points, and the user-aided generation algorithms require too much on the manual modeling ability of users. Therefore, how to combine the advantages of these two quadrilateral mesh generation algorithms is a great challenge. Therefore, aiming at these problems existing in the current quadrilateral mesh generation algorithm, this paper proposes a corresponding solution: 1) A controllable quadrilateral mesh generation algorithm based on directional field is proposed. This paper improves the controllability of users on the basis of predecessors: by introducing geodesic technology and 3D sketching technology, the user is allowed to control freely and intuitively in the direction of the field. At the same time, in order to deal with the conflicts and errors caused by the user in controlling the direction field, this paper proposes a corresponding solution to the direction constraint conflict and to correct the inaccuracy of user interaction. Furthermore, the smooth energy function of orthogonal field is optimized, which can interpolate and generate the globally smooth orthogonal field which is controllable by the user, so that the edge direction of the final quadrilateral grid can be controlled. And singular point distribution .2) A user-aided quadrilateral mesh generation algorithm based on patterns is proposed. In order to solve the problem of too few topological patterns in previous methods, a relaxation decomposition operation is proposed in this paper, in which the original input polygonal surface slices can be decomposed and simplified by surface flow collapse processing, and then according to a large number of simplified facets, A variety of more complex topology patterns are designed, and then the quadrilateral mesh with more abundant topology can be generated by the patch filling operation. That is, the solution space of quadrilateral mesh generation is expanded. 3) combining the advantages of automatic generation algorithm and user-aided generation algorithm, the two algorithms are integrated in this paper. A complete quadrilateral mesh generation and editing system is designed and developed. The quadrilateral mesh model with high quality and anisotropy can be generated quickly and conveniently.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：TP391.7

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 郭鳳華;張彩明;焦文江;;網(wǎng)格參數(shù)化研究進(jìn)展[J];軟件學(xué)報(bào);2016年01期

相關(guān)博士學(xué)位論文 前1條

1 張沐陽;高質(zhì)量可控四邊網(wǎng)格生成技術(shù)[D];浙江大學(xué);2011年

，

本文編號：2117942