nds坐标获取瓦片编号

Eiffel Tower 2.2945° 48.858222° 27374451 582901293 0x1a1b373 0x22be5e2d

nds使用的是WGS84坐标系统(the World Geodetic System dating from 1984)，就是平常我们说的经纬度。当我们说一个具体的位置的时候，就说这个问题位置的经度是多少，纬度是多少，这样就可以唯一的定位到一个精确的点。

nds使用EGM96(the Earth Gravitational Model from 1996)来表示高度信息。EGM96描述的高度信息很好的近似海拔高度，它比WGS84中的高度信息更准确。

规定经度使用32位int编码,可表示范围是[-180,180],纬度使用31位int编码，可表示范围是[-90,90]

例: 艾菲尔铁塔的计算如下(Eiffel Tower 2.2945° 48.858222°)

lon = 2.2945
lon_to_int32 = pow(2, 31) * 2.2945 / 180
= 2147483648 * 2.2945 / 180
= 27374451.279644444444444444444444
= 27374451 (使用向下取整法floor)
= 0x1a1b373 (十六进制)
= ‭0001101000011011001101110011‬ (二进制)

lat = 48.858222
lat_to_int32 = pow(2, 30) * 48.858222 / 90
= 1073741824 * 48.858222 / 90
= 582901293.41863253333333333333333
= 582901293 (使用向下取整法floor)
= 0x22be5e2d (十六进制)
= ‭00100010101111100101111000101101‬ (二进制)

使用莫顿码(morton code)进行编码
x = x31x30...x1x0
y = y30...y1y0
c = x31y30x30...y1x1y0x0 总长度为63(32+31)位

x = 0x1a1b373 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1
y = 0x22be5e2d 1 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 0 1
c = 0x809cea967ad1da7 100000001001110011101010100101100111101011010001110110100111

x = 0x1a1b373                    1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1
y = 0x22be5e2d        1 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 0 1 
c = 0x809cea967ad1da7 100000001001110011101010100101100111101011010001110110100111

规整为63位 000100000001001110011101010100101100111101011010001110110100111

故该点在Level10的Tile Number为
Level10 = c.left(2n+1) = c.left(2*10+1) = c.left(21) = 0 0010 0000 0010 0111 0011
= 0x‭20273‬
= ‭131699‬

故该点在Level13的Tile Number为
Level13 = c.left(2n+1) = c.left(2*13+1) = c.left(27) = 000 1000 0000 1001 1100 1110 1010
= 0x‭‭809CEA‬
= ‭8428778‬

 1 struct NDSPoint {
 2     double   dLon;
 3     double   dLat;
 4     int32_t  nLon;
 5     int32_t  nLat;
 6     uint64_t Morton;
 7 
 8     NDSPoint(double lon, double lat) : dLon(lon), dLat(lat), nLon(0), nLat(0), Morton(0) {
 9         nLon   = ToNdsLon(dLon);
10         nLat   = ToNdsLat(dLat);
11         Morton = ToMortonCode(nLon, nLat);
12 
13         printf("xy:[%10.6lf,%10.6lf], nds:[%12d,%12d] Morton:[%24lu]\n", dLon, dLat, nLon, nLat, Morton);
14          15          16     }
17 
18     int32_t ToNdsLon(double lon) {
19         bool positive = true;
20         if (lon < 0) {
21             positive = false;
22         }
23         auto t = pow(2, 31) * lon / 180.0;
24         return positive ? std::floor(t) : std::ceil(t);
25     }
26 
27     int32_t ToNdsLat(double lat) {
28         bool positive = true;
29         if (lat < 0) {
30             positive = false;
31             lat += 180.0;
32         }
33         auto t = pow(2, 30) * lat / 90.0;
34         return positive ? std::floor(t) : std::ceil(t);
35     }
36 
37     uint64_t ToMortonCode(int32_t iLon, int32_t iLat) {
38         uint64_t MortonCode = 0;
39         for (int i = 0; i < 32; i++) {
40             uint64_t uiTmp64 = 0;
41             uiTmp64          = (iLon >> i) & 0x1;
42             uiTmp64 |= ((iLat >> i) & 0x1) << 1;
43             MortonCode |= (uiTmp64 << 2 * i);
44         }
45 
46         return MortonCode;
47     }
48 };