THE PARTITION OF MULTI-RESOLUTION LOD BASED ON QTM

The partition hierarch of Quaternary Triangular Mesh (QTM) determine the accuracy of spatial analysis and application based on QTM. In order to resolve the problem that the partition hierarch of QTM is limited by the level of the computer hardware, the new method that MultiResolution LOD (Level of Details) based on QTM will be discussed in this paper. This method can make the resolution of the cells varying with the viewpoint position by partitioning the cells of QTM, selecting the particular area according to the viewpoint; dealing with the cracks caused by different subdivisions, it satisfies the request of unlimited partition in part. About the first author: Hou Miaole, Female, 1974, Associate Professor of BUCEA who Get the PHD degree in 2005.7 at CUMTB. Main research topics are Spherical surface digital topology and 3D Rebuilding. Email: houmiaole@bucea.edu.cn


INTRODUCTION
The Quaternary Triangular Mesh (QTM) is an array of discrete grids.In the partition of QTM, an octahedron is used as a basis.
It can simulate the surface of the Earth when it is recursively partitioned to a certain degree.QTM is efficient to deal with the global data because of its advantages of multi-resolution and hierarchy.In recent years, Scholars both at home and abroad made progress in the partition of the QTM.Dutton [1996] brought out a theory that a spherical triangle can be subdivided by the latitudes/longitudes.When a triangle is subdivided, the latitudes/longitudes pairs of any two of its three vertices are averaged to yield edge midpoint locations.Zhao Xuesheng[2001] introduced the recursive refining approach, to determine spatial relation between two spherical objects is approached by recursive refine based on QTM hierarchical partition.Zhang Shengmao[2008] analyzed the triangles which are subdivided based on QTM, the research indicated that along with the increase of the partition hierarchy, the area and change of the triangle become more stable.Sun Wenbin[2009] provided the connotation of "near-equal grid" on spherical surface, then done research on the partition method and character analysis of Near-Equal grid on spherical facet.Bai Jianjun[2011] analyzed the existent partition method of spherical surface and provided a hierarchical tessellation meshes of WGS-84 ellipsoidal surface based on QTM, and also calculated the area and side length of the multi-resolution meshes on different levels.According to the existing literature, the researches on the partition hierarchy based on QTM are mostly based on the whole sphere.However, along with the increase of the partition hierarchy, the number of triangle grids that are subdivided base on QTM is increased four times (the correspondence between the number of triangle grids and the partition hierarchy of QTM is shown in Figure 1).Though the advanced computer hardware devices contribute to improve the speed of rend of the triangle grids, the level of the computer hardware devices is limited while the data volume is limitless.
As a result, the gap between the data volume and the level of the computer hardware devices is huge.Therefore, the speed of the real-time rend of the triangle grids is not satisfactory just by Figure 2 the correspondence between the partition hierarchy and the number of the blocks

Thinning Area
In the progress of partitioning the QTM, it is not necessary to subdivide the whole model, but only to subdivide the block which is near form the viewpoint.The block which is the nearest form the viewpoint is the thinning area.The partition hierarchy of QTM is supposed as k, according to the block strategy, the number of the block (B) is 2*4 (k-2) , and B={B ， Alone with the continuous movement of the viewpoint, the thinning area will be changing, the triangle grids in the thinning area will be changing as well.Whenever the viewpoint is changing, he relationship between the blocks and the viewpoint needed to judge, then the triangle grids in the thinning area will be also updated.

Deal With The Cracks
The QTM grids which are different resolutions will be adjoining by the time of the partition of Multi-Resolution LOD.
Computer use discrete plane to express the information of hook face, so that the sharing edge or vertex of the QTM grids which are different resolutions will not be in the same plane.If the problem is not processed, the cracks will be produced in the process of visualization.As shown in Figure 4: the resolutions of the QTM grids A and the QTM grids B,C,D are different, the cracks will be produced in the rending if we don't take steps.The cracks caused by different subdivisions are eliminated by the way of the vertex extension in his method, it don't change the partition method of the grids.At the same time, this method realizes seamless expressing of the model based on QTM on the base of hierarchical nesting.Based on the advantages above, the vertex extension method of eliminating the cracks that caused by different subdivisions is adopted in this article.

Algorithm Flow
In this paper, the QTM model is firstly partitioned into sever blocks on the base of the partition hierarchy and the latitudes/longitudes of the triangle grids; the distance between the blocks and the viewpoint are compared.The block which is the nearest from the viewpoint is selected as the thinning area, and the triangle grids in the thinning area will be subdivided.
Finally, the cracks caused by different subdivisions will be dealt with.The algorithm flow chart is shown in Figure 5.

Experimental Effect
In this paper, the QTM model is subdivided as seven times, and the number of the triangle grids is 32768.Then we partition the model into several blocks on the base of the latitudes/longitudes of the triangle grids.The number of blocks is 512 based on the block strategy.When the position of the viewpoint is changing, we only judge the distance between the blocks and the viewpoint, and select the block which is the nearest from the viewpoint as the thinning area.
In this article, the partition hierarchy of the thinning area is increased three times on the base of the original partition hierarchy, which means that the partition hierarchy of the thinning area is nine times.If the whole globe model is subdivided, the number of the triangle grids which need rending is 524,288.However, we can realize the effect that the partition hierarchy partition hierarchy is nine, while the number of the triangle grids which need rending is only 36,800 in this paper.In a word, the number of the triangle grids that need rending is decreased on condition that

InternationalFigure 1
Figure 1 Correspondence between the number of triangle grids and the partition hierarchy

Figure 4
Figure 4 the cracks caused by different subdivisions

Figure 5
Figure 5 the algorithm flow chart

International
Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXVIII-4/W25, 2011 ISPRS Guilin 2011 Workshop, 20-21 October 2011, Guilin, China increases the partition hierarchy of the thinning area by this method.The experiment effect is shown as follow.

Figure 6
Figure 6 the partition hierarchy of QTM is six