A virtual globe-based vector data model: quaternary quadrangle vector tile model

Figures & data

Figure 1. Recursive subdivision of the QQM hemisphere.

Figure 2. (a) Conceptual model for QQVTM and (b) Logical model of QQVTM. Note: Rectangles represent entity sets and ovals represent attributes. Diamonds with lines connecting to entity sets represent containing or constitution relationships between two entity sets (e.g. a tile contains n vertices and n arcs constitute a boundary). The numbers on the lines indicate three kinds of quantitative relationships: (1) 1:1 indicates a one-to-one relationship, (2) 1:n indicates a one-to-many relationship, and (3) m:n indicates a many-to-many relationship. To implement a relationship between two objects, the key of one attribute table is included in the other attribute table. The associated keys are linked using lines.

Figure 3. Vector data in QQVTM.

Figure 4. Geometry-based mapping of vector data. (a) Simply mapping the vertices contained in the vector data. (b) The resolution of the vector tile is lower than the resolution of the underlying terrain data. (c) The resolution of the vector tile is higher than the resolution of the underlying terrain data. (d) The vector geometry conforms closely to the terrain surface since they have the same resolution.

Figure 5. Elimination of visual cracks.

Figure 6. Vector pyramid (r > s > t and k < m < n).

Figure 7. The Weiler–Atherton clipping algorithm can clip all polygons, including concave polygons and polygons containing holes. The boundary of the clipping result of a polygon (abcdhHIga) constitutes a partial polygon boundary (ab, cd, and hHIg) and a partial tile boundary (bc, dh, and ga).

Figure 8. Tile-based reconstruction of vector data. P0, P1, … P6 are the original vertices of the 2D vector data. Q0, Q1, … Q13 are the intersections of the 2D vector data and the terrain grids. (a) Vertices are stored in tiles. (b) The link relationships of vector tiles are recorded in temporary tables using the PreTile and NextTile items of the intersections.

Figure 9. Storing order of polygon boundaries. Note: The dashed area is the interior of the polygon, which is always on the right of the forward direction when traversing a vertex list.

Figure 10. Renderings of organized global vector, terrain, and image data based on QQVTM.

Table 1. Performance of building QQM vector pyramids.

	Line			Polygon
		Vertex increasing			Vertex increasing
Levels	Time (ms)	Number	Percentage	Time (ms)	Number	Percentage
0	262	2214	2.84	75,313	188,006	208.11
1	453	4318	5.55	263,078	216,986	240.19
2	766	8704	11.18	1,032,984	314,978	348.66
3	1125	17,448	22.41	4,128,625	668,558	740.05
4	1922	35,028	45.00	16,445,219	2,005,781	2220.26

Table 2. Efficiency of the tile-based reconstruction algorithm.

Levels	0	1	2	3	4
Time (ms)	569	1109	2016	4406	11,953

Table 3. Frame rates of quaternary quadrangle vector tile rendering in 30 seconds.

Distance (km)	4000			100
Frame rate	Min	Max	Average	Min	Max	Average
Terrain	41	44	42.6	41	44	42.567
Lines	39	46	41.6	41	44	42.633
Polygons	42	44	42.7	41	44	42.6

Figure 11. Frame rates while flying 4000 km and 100 km above Earth's surface.

Table 4. Data size comparison between terrain pyramids and vertex number comparison between vector pyramids.

		Vertex number
Levels	Resolution (m)	QQM	LLG	DQG	QQM/LLG (%)	QQM/DQG (%)
0	104,245	263,179	276,884	270,937	95.05	97.14
1	52,123	294,311	312,474	294,067	94.19	100.08
2	26,061	353,216	383,969	344,542	91.99	102.52
3	13,031	466,254	526,547	446,904	88.55	104.33
4	6515	691,893	813,244	652,744	85.08	106.00
5	3258	1,145,236	1,389,004	1,065,875	82.45	107.45
6	1629	2,053,978	2,544,637	1,893,221	80.72	108.49
7	814	3,874,091	4,858,509	3,550,610	79.74	109.11
8	407	7,516,503	9,488,208	6,867,040	79.22	109.46
9	204	14,801,592	18,748,168	13,500,942	78.95	109.63
10	102	29,371,442	37,268,072	26,770,257	78.81	109.71

LLG, latitude–longitude grids.

Table 5. Vertex number comparison between two vector pyramids at low and high latitudes.

	Low latitudes			High latitudes
Levels	QQM	LLG	QQM/LLG (%)	QQM	LLG	QQM/LLG (%)
0	170,451	170,536	99.95	92,728	106,348	87.19
1	191,764	192,001	99.88	102,547	120,473	85.12
2	234,693	235,134	99.81	118,523	148,835	79.63
3	320,519	321,378	99.73	145,735	205,169	71.03
4	492,242	494,534	99.54	199,651	318,710	62.64
5	837,561	842,542	99.41	307,675	546,462	56.30
6	1,529,793	1,541,235	99.26	524,185	1,003,402	52.24
7	2,915,547	2,939,979	99.17	958,544	1,918,530	49.96
8	5,688,400	5,739,437	99.11	1,828,103	3,748,771	48.77
9	11,233,883	11,337,470	99.09	3,567,709	7,410,698	48.14
10	22,324,719	22,533,943	99.07	7,046,723	14,734,129	47.83

LLG, latitude–longitude grids.