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Nested Grids: the c-squares global grid

Nested Grids: the c-squares global grid. Tony Rees CSIRO Marine and Atmospheric Research, Hobart Tony.Rees@csiro.au for: PEMS Workshop on Nested Grids, 21 October 2007 version: final - with update, September 2009. The Big Challenge:.

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Nested Grids: the c-squares global grid

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  1. Nested Grids: the c-squares global grid Tony Rees CSIRO Marine and Atmospheric Research, Hobart Tony.Rees@csiro.au for: PEMS Workshop on Nested Grids, 21 October 2007 version: final - with update, September 2009 Tony Rees – C-squares Oct 2007 1

  2. The Big Challenge: Integrating distributed and heterogeneous spatial data resources to advance science and societal goals Opening the “Data Closet” (With thanks to K. Stocks et al. / SDSC for the image and concept!) Tony Rees – C-squares Oct 2007 2

  3. One solution: rasterised data on a common grid • Grids come in different flavours… • Geodesic, global “equal area” (e.g. triangular, hexagonal, other) • Lat / lon, “equal angle” e.g. 1º x 1º grids, etc. (in unprojected, = “geographic” projection) • Local projected “equal area” grids e.g. 100 km grids, etc. • Typically regional / national scale, do not integrate globally;do not cope well with longitudinal shifts • Areas of interest are sometimes outside the grid (e.g. offshore islands, high seas, etc.) • This project (PEMS) has identified a requirement for a large scale “Grid System 1” lat / lon based grid, meshing with local, projected “System 2” grids for finer scale data • C-squares is an example global scale, lat / lon based grid that may be of interest for this project’s needs for Grid System 1. Tony Rees – C-squares Oct 2007 3

  4. The c-squares global grid • C-squares: acronym for “Concise Spatial Query and Representation System” (or: CSIRO squares ??) • Developed at CMAR in 2001-2, published in scientific literature in 2003* • Cover entire world surface, not just the sea (despite choice of journal for initial publication) • Based on pre-existing, established “WMO square” notation, for global 10º x 10º squares • C-squares notation subdivides WMO squares into a nested grid using alternate base 2, base 5 division, giving the sequence10º x 10º > 5º x 5º > 1º x 1º > 0.5º x 0.5º > 0.1º x 0.1º, etc. * Rees, Tony. 2003. "C-squares", a newspatial indexing system and its applicabilityto the description of oceanographic datasets.Oceanography 16 (1), pp. 11-19. Tony Rees – C-squares Oct 2007 4

  5. 180° W 150° W 120° W 90° W 60° W 30° W 0° 30° E 60° E 90° E 120° E 150° E 180° E 90° N 5117 5017 7517 5317 5417 7817 5217 7217 7117 5517 5717 7717 7317 5817 5617 7417 7617 7017 5316 5816 7116 7816 7716 5116 5716 7416 5216 7516 5516 7316 5616 5016 7216 7616 7016 5416 7615 7515 7815 5315 5715 7215 5215 7115 7415 5415 5615 5115 5515 5815 7015 5015 7715 7315 5814 7614 5614 7114 5714 7314 7714 7414 5214 7214 5314 5414 7014 7814 5114 7514 5514 5014 7013 5813 5413 7713 5113 5513 5013 7113 7513 5613 5213 7213 5713 7813 7313 5313 7413 7613 5412 7212 7012 5712 7612 5312 7712 7312 7812 5612 7512 5212 7412 7112 5112 5512 5812 5012 7411 5711 5411 7011 7511 7611 5511 7111 5011 5611 7211 5111 7311 5211 7811 5811 5311 7711 7610 5710 5410 5610 5810 5510 5210 5010 7510 7810 7710 5310 7010 7210 7110 7310 7410 5110 5109 5409 5309 7409 5209 7509 7109 7009 7609 7209 7809 5809 7709 7309 5709 5009 5609 5509 7108 7008 7708 5508 5308 5608 7608 5008 5408 7508 5108 7808 5808 5208 7208 5708 7408 7308 5007 7407 7307 5407 7807 7607 7507 7707 5107 5607 5507 5707 7207 7007 5807 7107 5307 5207 5406 7406 5706 5506 5306 7806 7006 5006 5206 7306 5606 7106 5106 7506 7706 5806 7206 7606 7205 7605 5205 5005 7305 5705 5505 7405 5805 7505 7805 5405 5305 7005 5605 5105 7705 7105 7204 7404 5604 7504 5204 7304 7804 5304 7104 7004 7604 5504 5704 5004 5404 5804 7704 5104 7803 7803 7803 5703 7803 5303 7803 7803 5003 7803 5403 5803 7803 5103 5203 5603 5503 7803 7202 7702 5702 5202 5602 5102 7102 7302 5402 5002 7002 5802 7602 7802 7502 5302 7402 5502 7501 7401 7301 5201 7801 7201 7001 5701 5001 7601 5601 5101 7701 5801 7101 5301 5501 5401 7800 5600 7000 7300 7100 5500 7200 7700 7400 5800 7500 5000 5100 5300 7600 5400 5200 5700 1400 3600 1700 3400 3800 3100 1100 1000 3000 1600 1500 1800 3200 1300 3500 3700 1200 3300 3201 1401 1001 1301 3001 1601 3301 3601 3401 3501 1501 1801 3701 1201 3801 1101 3101 1701 3402 3002 1402 1102 3102 3502 3802 1802 1002 3302 1302 1502 3202 3602 1702 1602 3702 1202 3603 1503 1803 1703 1103 3203 1203 3503 3103 3803 3703 1603 1003 1303 3003 1403 3403 3303 1804 3104 3604 1004 3504 1504 3404 1204 3804 1404 1104 1704 3204 3304 3004 1304 1604 3704 1705 3205 1105 3005 3105 1505 1405 3405 1805 1005 1605 3505 3605 3705 1305 3305 3805 1205 3106 1106 3206 1806 1406 1506 1206 1006 3006 1606 1306 3606 3506 3406 3706 3306 1706 3806 3307 3807 1307 3107 3707 1607 1007 3607 1407 1707 1207 1507 3507 1107 3407 3207 1807 3007 3208 1708 1808 1408 3608 3308 1208 1308 3708 3108 3808 3508 1108 1508 1008 3008 3408 1608 1809 3209 3409 1709 3109 1509 1109 3509 1409 3309 1009 3009 1309 3709 1609 3809 3609 1209 1510 3210 1010 3710 3310 3010 3410 1610 1810 1410 1210 1310 3610 3510 1110 3810 1710 3110 3111 3411 1511 1011 3011 1811 3511 1111 1711 3211 3611 1611 3311 3711 1211 1311 1411 3811 1812 3212 1212 1412 3412 3512 1312 3812 3712 3112 3312 3012 1612 1112 1012 1712 3612 1512 3513 1313 3213 3613 3113 3413 1713 1213 1113 1013 3313 3013 1413 1613 3813 1813 3713 1513 1314 1414 3514 3614 1714 1014 1114 3414 1814 3714 1514 3114 3814 1214 3214 3314 3014 1614 1715 1615 3415 1815 1215 1315 3215 3515 3315 3815 3615 1515 3115 1015 1415 1115 3015 3715 3116 3716 3216 1616 3016 3316 3416 1216 1516 1016 1116 3516 1816 1316 1416 3816 1716 3616 3317 1617 3217 3117 3717 1517 1117 1717 3417 3517 3617 1017 3017 1217 3817 1417 1317 1817 60° N 30° N 0° 30° S 60° S 90° S WMO 10-degree squares(starting point for c-squares recursive subdivision) NW (7xxx) NE (1xxx) SW (5xxx) SE (3xxx) Tony Rees – C-squares Oct 2007 5

  6. 180° W 150° W 120° W 90° W 60° W 30° W 0° 30° E 60° E 90° E 120° E 150° E 180° E 90° N 5817 7817 7317 7717 7217 5017 5717 7017 7117 5217 5117 5317 7617 5417 5517 5617 7517 7417 5616 7716 7816 7216 7416 7016 5816 5716 5016 5516 5116 7116 7616 5416 7516 5316 5216 7316 5615 7015 5815 7515 5015 7715 5115 7315 7615 5515 5715 5315 7115 5415 7815 7215 5215 7415 5614 7714 5714 5514 7314 5414 7614 5314 5814 5114 5214 7414 7814 5014 7214 7514 7114 7014 5713 5613 7413 7113 7613 5813 5313 5413 7213 5513 7713 7013 5213 7513 7813 7313 5013 5113 7312 7212 5412 5112 5512 5812 7412 5312 5212 5012 7512 7812 7012 7612 7712 5712 7112 5612 7211 7511 7411 5511 5011 5111 5611 7711 7311 5211 7811 5711 7611 7011 5311 5411 5811 7111 7510 7110 5210 5810 5510 5410 5610 7810 5310 5010 7010 7710 5110 5710 7310 7410 7210 7610 5109 5009 7409 7709 7609 7509 7309 7809 7109 5309 5809 5709 7009 5209 5409 5509 5609 7209 7608 7808 5608 5208 7208 5108 5408 7708 7008 5308 7508 7308 7408 5808 7108 5708 5508 5008 5007 5707 5207 7307 5107 7207 7807 5407 7407 5507 7507 5307 5807 7707 7007 5607 7107 7607 7306 5006 5406 7606 7806 5806 7506 5106 5506 7206 5706 7706 5306 7006 7106 5206 5606 7406 7205 7305 5205 7805 5805 7605 5705 7105 7405 5405 5005 5605 7705 5105 5505 7505 5305 7005 7404 7804 5304 5704 5404 7604 5204 5004 7004 5504 7504 7704 5804 7204 7304 5604 5104 7104 7803 7803 7803 7803 5203 5703 5603 5303 5103 7803 5003 7803 5403 7803 7803 7803 5803 5503 7402 5802 5002 5202 5702 7102 7702 5602 7002 7302 7502 7202 5102 5402 5302 7802 7602 5502 7701 7601 5801 7101 7001 7201 5601 5701 5101 5401 5001 5201 5301 7501 7301 7801 5501 7401 7300 5100 7000 5500 5400 5800 7500 5700 5000 7400 5300 7100 7600 7700 5200 7200 7800 5600 1100 3800 3000 3500 1300 1500 1700 3300 1400 1800 3600 1000 3200 3400 1200 3100 1600 3700 3001 1701 1401 3501 1301 1601 3801 1501 3401 1801 3301 1001 3101 3201 1201 3601 1101 3701 1802 1702 3402 1402 1302 3802 3502 3002 3702 1002 3102 1602 1502 1202 3302 3602 1102 3202 1103 1003 1503 1703 3503 3003 3103 3403 3303 3603 1603 3703 1803 1203 1303 3203 3803 1403 3104 3004 1304 1004 1204 1504 1604 1404 1104 3204 3804 3304 3504 3404 3704 1704 3604 1804 1105 1805 3505 1405 1305 1505 3605 1605 3105 3805 3305 3405 3205 3005 3705 1005 1705 1205 1306 3806 3406 1606 3206 3606 1006 1406 1806 3306 3706 3006 1206 3106 1106 3506 1506 1706 1007 3007 1507 1607 3207 3307 3807 3107 1307 1707 3707 1207 3607 1107 3507 1407 3407 1807 1708 3008 1808 1008 3508 3208 3608 3108 1408 3708 3408 1508 1608 1308 1208 1108 3308 3808 3409 1509 1709 1609 3009 3109 3609 3209 1409 3509 3309 1109 1209 1809 1009 1309 3709 3809 3410 3010 1710 3210 1010 1410 3810 1310 3310 1810 3510 1610 3110 1510 1210 3710 3610 1110 1211 3511 3411 1411 1811 3311 1611 1011 3711 1111 3611 1311 3811 3011 3111 3211 1711 1511 3712 1612 1312 3112 1112 3812 3512 3212 1012 1512 3412 1812 1712 1412 1212 3612 3012 3312 1013 1513 1113 3413 1713 3313 3013 3513 1613 1813 3713 1213 3213 1313 3813 3113 1413 3613 1814 1314 1614 3114 1214 3614 1114 1514 1414 3314 3814 3414 1714 3214 1014 3714 3514 3014 3315 3615 1615 1115 3715 3515 3115 1515 1415 1015 3415 1215 3015 1715 1315 1815 3815 3215 3216 3716 3116 1616 3616 3816 1316 1816 3016 1016 1116 3416 1516 3516 1216 1416 1716 3316 1017 1617 3617 1117 3417 1217 3517 1517 1317 3117 3717 3317 1717 3817 3017 1817 1417 3217 60° N 30° N 0° 30° S 60° S 90° S WMO 10-degree squares(starting point for c-squares recursive subdivision) NW (7xxx) NE (1xxx) SW (5xxx) SE (3xxx) * you arehere! Tony Rees – C-squares Oct 2007 6

  7. The c-squares global grid – cont’d • Each grid cell identifier (= c-squares code) “knows” the identity of its parent, grandparent, etc. • Aggregated search can be done by interrogating only the required leading chars. of the code, e.g.: • 10º c-square code (~1000 km): 3414 (= WMO square code) • 5º c-square code (~500 km): 3414:2 • 1º c-square code (~100 km: 3414:227 • 0.5º c-square code (~50 km): 3414:227:3 • 0.1º c-square code (~10 km): 3414:227:383 (etc.) (this is the nested set of squares that includes the point at lat -42.82, lon 147.38, in decimal degrees) • Search for character string “3414” (ten degree square), with wildcard appended, will return any of these nested data items • Same available at other levels of the hierarchy as applicable (i.e., search on any parent code can easily be configured to return all of its children as well, if desired) Tony Rees – C-squares Oct 2007 7

  8. 10-, 5- degree c-squares in the Australian region 3314 Tony Rees – C-squares Oct 2007 8

  9. 10-, 5- degree c-squares in the Australian region 1 2 3314 3 4 Tony Rees – C-squares Oct 2007 9

  10. 100 101 102 103 104 205 206 207 208 209 110 114 215 219 1 2 120 124 225 229 130 134 235 239 140 141 142 143 144 245 246 247 248 249 350 351 352 353 354 455 456 457 458 459 360 364 465 469 4 3 370 374 475 479 380 384 485 489 390 391 392 393 394 495 496 497 498 499 Recursive subdivision principle (in the SE global quadrant)- for 10 -> 1, 1 -> 0.1, 0.1 -> 0.01 degree squares, etc. Tony Rees – C-squares Oct 2007 10

  11. 3314:1003314:133143314:499 Tony Rees – C-squares Oct 2007 11

  12. Points of interest • C-squares notation for 10º squares is identical to that for WMO 10º squares (i.e., no transformation required) • 1º and 0.5º squares are popular data aggregation sizes at regional scales • 0.5º squares are equivalent to 1:100,000 Australian mapsheets (with global, cf. locally applicable, numbering system) • 0.1º squares and finer are useful for data holdings at sub-regional / local scales • No direct support for 2.5º, 2º, or 0.25º squares in this system, or degrees / mins / secs notation (except 30 min, = 0.5 degrees) Tony Rees – C-squares Oct 2007 12

  13. Who uses what? (Google search hits – October 2007…) • “10 degree squares” OR “ten degree squares”: 193 • “5 degree squares” OR “five degree squares”: 563 • “2.5 degree squares” OR “two point five degree squares”: 4 • “2 degree squares” OR “two degree squares”: 135 • “1 degree squares” OR “one degree squares”: 1,660 • “0.5 degree squares” OR “half degree squares” (30 min): 1,060 • “0.25 degree squares” OR “quarter degree squares” (15 min): 17,300 * • “10 minute squares” OR “ten minute squares”: 249 • “0.1 degree squares” OR “tenth degree squares” (6 min): 575 • “5 minute squares” OR “five minute squares”: 47 • “3 minute squares” OR “three minute squares”: 1 • “1 minute squares” OR “one minute squares”: 51 • “0.01 degree squares” OR “hundredth degree squares” (0.6 min): 1 * NB: (1) “quarter degree squares” are a common standard in use in Africa for wildlife surveys, which accounts for many / most of these hits (2) Of the above, c-squares directly supports the resolutions shown in bold + underline, indirectly could support others (by aggregation / approximate matching??) Tony Rees – C-squares Oct 2007 13

  14. D/M/S vs. decimal degrees… • What fine scale grids (e.g. sub 1-degree) are in use locally / internationally – e.g.: • 30 minute = 0.5 degree (~50 km) • 5 minute = 0.0833 degree (~10 km) • 1 minute = 0.0167 degree (~2 km) • 30 second = 0.00833 degree (~1 km) • 9 second = 0.0025 degree (~250m) • 2 second = 0.00055 degree (~50m) • 1 second = 0.000278 degree (~25m) • Is there a requirement / preference to maintain similar (deg / min / sec) resolutions in the selected system? (cf. c-squares is based on decimal degrees and half steps) • Does this preclude (or encourage) the use of c-squares for resolutions e.g. 0.5 degrees and above? Tony Rees – C-squares Oct 2007 14

  15. Use cases for c-squares, of possible interest to this project • Hierarchical spatial search • Example shown: OBIS (Ocean Biogeographic information System), USA • C-squares as spatial metadata, and associated spatial search (also: mapping) • Example shown: MarLIN (Marine Laboratories Information Network), CSIRO, Australia • C-squares as grid cell identifiers, for data storage, rapid access, and mapping of outputs • Example shown: AquaMaps project (Germany + Philippines) • Variable resolution encoding within the same dataset (or data item) • Example shown: CSIRO (CMAR) satellite data index • Using c-squares for Antarctic / Southern Ocean / Polar data • Examples shown: CMAR satellite data index; online polygon fill algorithm (on c-squares website) Tony Rees – C-squares Oct 2007 15

  16. Hierarchical spatial search: OBIS example http://www.iobis.org/ Tony Rees – C-squares Oct 2007 16

  17. OBIS, USA: Hierarchical spatial search (for species with records in selected area) Tony Rees – C-squares Oct 2007 17

  18. OBIS, USA: Hierarchical spatial search (for species with records in selected area) Tony Rees – C-squares Oct 2007 18

  19. C-squares as spatial metadata: MarLIN example http://www.cmar.csiro.au/marlin/ Tony Rees – C-squares Oct 2007 19

  20. C-squares as spatial metadata (list of square IDs = “dataset footprint”) Tony Rees – C-squares Oct 2007 20

  21. C-squares as spatial metadata (list of square IDs = “dataset footprint”) Tony Rees – C-squares Oct 2007 21

  22. C-squares as spatial metadata (list of square IDs = “dataset footprint”) Tony Rees – C-squares Oct 2007 22

  23. C-squares as spatial metadata (list of square IDs = “dataset footprint”) Tony Rees – C-squares Oct 2007 23

  24. C-squares as spatial metadata (list of square IDs = “dataset footprint”) (A) (B) …search for matching square (=tile) ID (A) is much more precise than search by bounding box using “overlapping rectangles” test (B)[far fewer false positives] – presuming tile size is well matched to the data and / or intended query scale (may be an optimization issue here) Tony Rees – C-squares Oct 2007 24

  25. C-squares as grid cell identifiers: AquaMaps example http://www.aquamaps.org/ Tony Rees – C-squares Oct 2007 25

  26. C-squares as grid cell identifiers: example from the AquaMaps project “Half degree cell authority file” (HCAF) – covers the world in 259,200 database rows Tony Rees – C-squares Oct 2007 26

  27. (Looks familiar?) (from PEMS presentation, SSC2007) Tony Rees – C-squares Oct 2007 27

  28. C-squares as grid cell identifiers: example from the AquaMaps project “Half degree cell authority file” (HCAF) – covers the world in 259,200 database rows Tony Rees – C-squares Oct 2007 28

  29. Modelled fish-habitat relationships (SI’s) Digital environmental maps recoded with the SI’s 1.0 Temperature Habitat suitability index map 0.5 Depth Unsuitable Medium 0 Low suitability High suitability 7 8 9 10 11 Salinity Substrate type 1.0 0.5 0 10 20 30 40 50 1.0 0.5 0 28 29 30 31 32 1.0 0.5 0 A B 1/4 Temperature SI map ´ Depth SI map HSI = ´ Salinity SI map ´ Substrate SI map C-squares as grid cell identifiers: example from the AquaMaps project Tony Rees – C-squares Oct 2007 29

  30. C-squares as grid cell identifiers: example from the AquaMaps project Sample map output (produced by the c-squares mapper) NB with multiple maps, can then query individual cells for species richness, etc. etc. Tony Rees – C-squares Oct 2007 30

  31. Variable resolution encoding using c-squares: Satellite Data Index example http://www.marine.csiro.au/remotesensing/csq-chooser.htm Tony Rees – C-squares Oct 2007 31

  32. Variable resolution encoding: example from the CMAR satellite data index Special notation available, e.g. 3414 = ten degree square only (data may be anywhere within it);3414:***:* = all of the 0.5 degree squares within ten degree square 3414. Tony Rees – C-squares Oct 2007 32

  33. Antarctic data – special case or not? • AAD, satellite imagery, oceanographic data – much data from region between Australia and Antarctica, as well as on landmass itself and adjacent waters • Definite integration benefits if on a common grid / spatial query interface, e.g. OBIS example, others… (no fixed boundary in the ocean / natural world) • C-squares covers polar regions as well as rest of world (just have to decide which square to allocate actual pole to!) – uses more squares, but otherwise no intrinsic problem • Example from CMAR satellite data index (uses 0.5 degree squares): Tony Rees – C-squares Oct 2007 33

  34. Tony Rees – C-squares Oct 2007 34

  35. Tony Rees – C-squares Oct 2007 35

  36. Tony Rees – C-squares Oct 2007 36

  37. (what just happened here?) • We clicked on square with bounds(lat) -65 – -70, (lon) 130 – 135 … = c-square 3613:3 (user never sees this, but system generates it for the search) • System searches for unique scenes with prefix “3613:3” in the spatial index, does a join on other table[s] to satisfy any other criteria • Generates list of 473 matching targets in (in this case) <2 seconds • Spatial partitioning used in this system, to optimise search and index rebuild speeds (single table split into 100 smaller ones); “duplicate” single large one retained to quickly retrieve all squares associated with a particular scene (for mapping) fragment of the spatial index… Tony Rees – C-squares Oct 2007 37

  38. Tony Rees – C-squares Oct 2007 38

  39. Tony Rees – C-squares Oct 2007 39

  40. Tony Rees – C-squares Oct 2007 40

  41. Tony Rees – C-squares Oct 2007 41

  42. Polygons encoded to c-squares can include a pole without problem: e.g. on-line polygon-fill algorithm on c-squares web site: http://www.cmar.csiro.au/csquares/converter.htm Tony Rees – C-squares Oct 2007 42

  43. Tony Rees – C-squares Oct 2007 43

  44. Successful filled polygon conversion c-square code: 3606:104|3606:114|3606:124|3606:134|3606:143|3606:144|3606:2**|3606:353|3606:354|3606:363|3606:364|3606:372|3606:373|3606:374|3606:382|3606:383|3606:384|3606:391|3606:392|3606:393|3606:394|3606:4**|3607:1**|3607:205|3607:215|3607:225|3607:235|3607:245|3607:246|3607:3**|3607:455|3607:456|3607:465|3607:466|3607:475|3607:476|3607:477|3607:485|3607:486|3607:487|3607:495|3607:496|3607:497|3607:498|3705:239|3705:248|3705:249|3705:384|3705:392|3705:393|3705:394|3705:457|3705:458|3705:459|3705:466|3705:467|3705:468|3705:469|3705:475|3705:476|3705:477|3705:478|3705:479|3705:485|3705:486|3705:487|3705:488|3705:489|3705:495|3705:496|3705:497|3705:498|3705:499|3706:101|3706:102|3706:103|3706:104|3706:110|3706:111|3706:112|3706:113|3706:114|3706:120|3706:121|3706:122|3706:123|3706:124|3706:130|3706:131|3706:132|3706:133|3706:134|3706:140|3706:141|3706:142|3706:143|3706:144|3706:2**|3706:3**|3706:4**|3707:1**|3707:205|3707:206|3707:207|3707:208|3707:215|3707:216|3707:217|3707:218|3707:219|3707:225|3707:226|3707:227|3707:228|3707:229|3707:235|3707:236|3707:237|3707:238|3707:239|3707:245|3707:246|3707:247|3707:248|3707:249|3707:3**|3707:4**| (etc.) Tony Rees – C-squares Oct 2007 44

  45. Successful filled polygon conversion c-square code: 3606:104|3606:114|3606:124|3606:134|3606:143|3606:144|3606:2**|3606:353|3606:354|3606:363|3606:364|3606:372|3606:373|3606:374|3606:382|3606:383|3606:384|3606:391|3606:392|3606:393|3606:394|3606:4**|3607:1**|3607:205|3607:215|3607:225|3607:235|3607:245|3607:246|3607:3**|3607:455|3607:456|3607:465|3607:466|3607:475|3607:476|3607:477|3607:485|3607:486|3607:487|3607:495|3607:496|3607:497|3607:498|3705:239|3705:248|3705:249|3705:384|3705:392|3705:393|3705:394|3705:457|3705:458|3705:459|3705:466|3705:467|3705:468|3705:469|3705:475|3705:476|3705:477|3705:478|3705:479|3705:485|3705:486|3705:487|3705:488|3705:489|3705:495|3705:496|3705:497|3705:498|3705:499|3706:101|3706:102|3706:103|3706:104|3706:110|3706:111|3706:112|3706:113|3706:114|3706:120|3706:121|3706:122|3706:123|3706:124|3706:130|3706:131|3706:132|3706:133|3706:134|3706:140|3706:141|3706:142|3706:143|3706:144|3706:2**|3706:3**|3706:4**|3707:1**|3707:205|3707:206|3707:207|3707:208|3707:215|3707:216|3707:217|3707:218|3707:219|3707:225|3707:226|3707:227|3707:228|3707:229|3707:235|3707:236|3707:237|3707:238|3707:239|3707:245|3707:246|3707:247|3707:248|3707:249|3707:3**|3707:4**| (etc.) Tony Rees – C-squares Oct 2007 45

  46. Successful filled polygon conversion c-square code: 3606:104|3606:114|3606:124|3606:134|3606:143|3606:144|3606:2**|3606:353|3606:354|3606:363|3606:364|3606:372|3606:373|3606:374|3606:382|3606:383|3606:384|3606:391|3606:392|3606:393|3606:394|3606:4**|3607:1**|3607:205|3607:215|3607:225|3607:235|3607:245|3607:246|3607:3**|3607:455|3607:456|3607:465|3607:466|3607:475|3607:476|3607:477|3607:485|3607:486|3607:487|3607:495|3607:496|3607:497|3607:498|3705:239|3705:248|3705:249|3705:384|3705:392|3705:393|3705:394|3705:457|3705:458|3705:459|3705:466|3705:467|3705:468|3705:469|3705:475|3705:476|3705:477|3705:478|3705:479|3705:485|3705:486|3705:487|3705:488|3705:489|3705:495|3705:496|3705:497|3705:498|3705:499|3706:101|3706:102|3706:103|3706:104|3706:110|3706:111|3706:112|3706:113|3706:114|3706:120|3706:121|3706:122|3706:123|3706:124|3706:130|3706:131|3706:132|3706:133|3706:134|3706:140|3706:141|3706:142|3706:143|3706:144|3706:2**|3706:3**|3706:4**|3707:1**|3707:205|3707:206|3707:207|3707:208|3707:215|3707:216|3707:217|3707:218|3707:219|3707:225|3707:226|3707:227|3707:228|3707:229|3707:235|3707:236|3707:237|3707:238|3707:239|3707:245|3707:246|3707:247|3707:248|3707:249|3707:3**|3707:4**| (etc.) Tony Rees – C-squares Oct 2007 46

  47. Note, (1) C-squares (and the polygon fill algorithm) copes with the polar case with no intrinsic problem • (2) automatic, multi-resolution data compression incorporated into the encoding algorithms on the c-squares web site (can be disabled if desired) • (3) relevant decompression stage incorporated into the c-squares mapper, also can be disabled as required (e.g. for demo purposes i.e. these slides) …Of course, can do much of this (in principle) with any type of grid structure / nomenclature for grid cells, however, c-squares compatible datasets are in general use at sub-national, national, and international scale, e.g.: Tony Rees – C-squares Oct 2007 47

  48. Museum Victoria Bioinformatics search interface (0.5 degree squares, regional) Tony Rees – C-squares Oct 2007 48

  49. AquaMaps, also similar CMAR data (0.5 degree squares, national + global) Tony Rees – C-squares Oct 2007 49

  50. Vertebrate census data, e.g. birds (1 degree squares, national) Tony Rees – C-squares Oct 2007 50

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