【摘要】：正方形堆積是一個古老的經(jīng)典問題,在圖的可視化方面有很好的應(yīng)用,也有多種不同的計算方法。本文考慮的是三角網(wǎng)格曲面的正方形堆積問題,采用極值長度的算法。極值長度是曲面的一個共形不變量,通過極值長度計算出的曲面度量叫極值度量,可以給出曲面的一種平面參數(shù)化。文中用三種曲面的離散化三角網(wǎng)格為例,展示了其上的離散極值度量。文章給出了計算拓?fù)渌倪呅吻嫒蔷W(wǎng)格和拓?fù)鋱A柱曲面三角網(wǎng)格的離散極值度量算法,從而為拓?fù)渌倪呅吻嫒蔷W(wǎng)格和拓?fù)鋱A柱曲面三角網(wǎng)格的每個點(diǎn)附加一個離散極值度量m(v);根據(jù)三角網(wǎng)格中點(diǎn)的極值度量以及網(wǎng)格中點(diǎn)與點(diǎn)的連接方式,給出了上述兩種曲面三角網(wǎng)格的正方形堆積方法。正方形堆積中的一個正方形對應(yīng)了原三角網(wǎng)格中的一個點(diǎn),正方形的邊長為對應(yīng)點(diǎn)的離散極值度量的值,在原三角網(wǎng)格中相鄰的兩點(diǎn)對應(yīng)的正方形在正方形堆積中是相鄰的。正方形堆積的結(jié)果本質(zhì)上來講是三角網(wǎng)格的離散極值度量被以歐式度量的方式在歐式空間中可視化的結(jié)果。同時文中也給出了拓?fù)鋱A環(huán)曲面三角網(wǎng)格的離散極值度量的計算算法,并對拓?fù)鋱A環(huán)曲面三角網(wǎng)格進(jìn)行了近似的正方形堆積。
[Abstract]:Square packing is an ancient classical problem, which has a good application in the visualization of graphs, and also has many different calculation methods. The problem of square packing of triangular mesh surfaces is considered in this paper, and the algorithm of extremum length is adopted. The extreme length is a conformal invariant of the surface. The surface metric calculated by the extreme length is called the extreme value metric, and a planar parameterization of the surface can be obtained. In this paper, the discretized triangular mesh of three surfaces is used as an example to show the discrete extremum measurement on it. In this paper, the discrete extremum measurement algorithm for calculating triangular mesh of topological quadrilateral surface and triangular mesh of topological cylindrical surface is presented. Thus, a discrete extremal metric m (v); is added to each point of the triangular mesh of the topological quadrilateral surface and the triangular mesh of the topological cylindrical surface according to the extreme value metric of the point in the triangular mesh and the connection between the point in the mesh and the point in the mesh. A square packing method for the above two triangular mesh surfaces is presented. A square in the square packing corresponds to a point in the original triangular grid, the side length of the square is the value of the discrete extremum measure of the corresponding point, and the square corresponding to the two adjacent points in the original triangular grid is adjacent in the square packing. The result of square packing is essentially the result that the discrete extremum metric of triangular mesh is visualized in Euclidean space by Euclidean metric. At the same time, the algorithm of calculating the discrete extreme value of the triangular mesh of the topological ring surface is given, and the approximate square packing of the triangular mesh of the topological ring surface is carried out.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O18

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本文編號：2264825