三种曲面三角网格在极值度量下的正方形堆积
发布时间：2018-10-11 18:31
【摘要】：正方形堆积是一个古老的经典问题,在图的可视化方面有很好的应用,也有多种不同的计算方法。本文考虑的是三角网格曲面的正方形堆积问题,采用极值长度的算法。极值长度是曲面的一个共形不变量,通过极值长度计算出的曲面度量叫极值度量,可以给出曲面的一种平面参数化。文中用三种曲面的离散化三角网格为例,展示了其上的离散极值度量。文章给出了计算拓扑四边形曲面三角网格和拓扑圆柱曲面三角网格的离散极值度量算法,从而为拓扑四边形曲面三角网格和拓扑圆柱曲面三角网格的每个点附加一个离散极值度量m(v);根据三角网格中点的极值度量以及网格中点与点的连接方式,给出了上述两种曲面三角网格的正方形堆积方法。正方形堆积中的一个正方形对应了原三角网格中的一个点,正方形的边长为对应点的离散极值度量的值,在原三角网格中相邻的两点对应的正方形在正方形堆积中是相邻的。正方形堆积的结果本质上来讲是三角网格的离散极值度量被以欧式度量的方式在欧式空间中可视化的结果。同时文中也给出了拓扑圆环曲面三角网格的离散极值度量的计算算法,并对拓扑圆环曲面三角网格进行了近似的正方形堆积。
[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.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O18
本文编号：2264825
[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.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O18
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