高虧格曲面共形參數(shù)化方法
發(fā)布時(shí)間：2018-10-11 12:43
【摘要】：共形映射又稱為保角映射,在計(jì)算機(jī)圖形學(xué)、幾何信息處理和參數(shù)化領(lǐng)域扮演著重要角色.調(diào)和映射易于計(jì)算并且有嚴(yán)密的理論基礎(chǔ),為了計(jì)算高虧格曲面的共形映射,提出一種基于調(diào)和映射的非線性擴(kuò)散方法.首先使用貪心算法在高虧格曲面上找到一個(gè)同倫群基底;然后通過(guò)求解一個(gè)線性系統(tǒng)來(lái)計(jì)算曲面的調(diào)和映射,將該映射的結(jié)果作為非線性擴(kuò)散計(jì)算的初始條件;再使用拉普拉斯切向法來(lái)調(diào)節(jié)曲面邊界的調(diào)和能量,調(diào)和能量下降的過(guò)程即非線性擴(kuò)散過(guò)程;最后最小化調(diào)和能量,以獲得曲面的共形映射.實(shí)驗(yàn)結(jié)果表明,文中方法是穩(wěn)定的,映射結(jié)果可以很好地保證曲面三角網(wǎng)格的角度關(guān)系;算法對(duì)模型網(wǎng)格質(zhì)量要求不高,具有更高的魯棒性;與經(jīng)典的共形映射方法相比,該方法得到的結(jié)果更均勻,共形效果更好.該方法可以在參數(shù)化、紋理映射、曲面注冊(cè)等領(lǐng)域得到很好應(yīng)用.
[Abstract]:Conformal mapping, also called conformal mapping, plays an important role in computer graphics, geometric information processing and parameterization. Harmonic maps are easy to calculate and have a strict theoretical basis. In order to calculate conformal maps of high genus surfaces, a nonlinear diffusion method based on harmonic maps is proposed. Firstly, the greedy algorithm is used to find a homotopy group base on the high genus surface, then the harmonic mapping of the surface is calculated by solving a linear system, and the result of the mapping is regarded as the initial condition of the nonlinear diffusion calculation. Then the Laplacian tangential method is used to adjust the harmonic energy of the surface boundary, the process of harmonic energy decreasing is called nonlinear diffusion process, and the harmonic energy is minimized to obtain the conformal mapping of the surface. The experimental results show that the proposed method is stable, and the mapping results can guarantee the angle relation of triangular mesh of curved surface. The algorithm is less robust to the mesh quality of the model, and compared with the classical conformal mapping method, the proposed algorithm is more robust than the classical conformal mapping method. The results obtained by this method are more uniform and the conformal effect is better. This method can be used in parameterization, texture mapping, surface registration and so on.
【作者單位】： 昆明理工大學(xué)建筑工程學(xué)院;昆明理工大學(xué)理學(xué)院;武漢大學(xué)計(jì)算機(jī)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(11461037,61772379)
【分類號(hào)】：TP391.41
本文編號(hào)：2264236
[Abstract]:Conformal mapping, also called conformal mapping, plays an important role in computer graphics, geometric information processing and parameterization. Harmonic maps are easy to calculate and have a strict theoretical basis. In order to calculate conformal maps of high genus surfaces, a nonlinear diffusion method based on harmonic maps is proposed. Firstly, the greedy algorithm is used to find a homotopy group base on the high genus surface, then the harmonic mapping of the surface is calculated by solving a linear system, and the result of the mapping is regarded as the initial condition of the nonlinear diffusion calculation. Then the Laplacian tangential method is used to adjust the harmonic energy of the surface boundary, the process of harmonic energy decreasing is called nonlinear diffusion process, and the harmonic energy is minimized to obtain the conformal mapping of the surface. The experimental results show that the proposed method is stable, and the mapping results can guarantee the angle relation of triangular mesh of curved surface. The algorithm is less robust to the mesh quality of the model, and compared with the classical conformal mapping method, the proposed algorithm is more robust than the classical conformal mapping method. The results obtained by this method are more uniform and the conformal effect is better. This method can be used in parameterization, texture mapping, surface registration and so on.
【作者單位】： 昆明理工大學(xué)建筑工程學(xué)院;昆明理工大學(xué)理學(xué)院;武漢大學(xué)計(jì)算機(jī)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(11461037,61772379)
【分類號(hào)】：TP391.41
【相似文獻(xiàn)】
相關(guān)期刊論文 前1條
1 董曉光;圖的色數(shù)與虧格的相對(duì)獨(dú)立性[J];國(guó)防科技大學(xué)學(xué)報(bào);1991年03期
，本文編號(hào)：2264236
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