�21 cubic meters.
By "current technology" I include anything that is commercially available, but not super computers.
Only the Earth topography and bathymetry will be used to generate the map. Human building, plants or caves are excluded. The underground blocks will be chosen based on geological studies e.g.:  if depth is greater than 3000km render a'magma' voxel.
Just like in Minecraft, the map is not static, it can be modified in-game.
A 'infinite' draw distance is a big plus, what's the point of having the whole earth in a map if you can't fly up and watch the whole planet?

The first conclusion that I came when I thought about this problem is that storing the Earth data in a linear way is infeasible, assuming that each voxel occupies only 1 byte of memory this would still require 1 zettabyte to store the map. So some kind of compression is required.
I think that a voxel octree could compress the map, but I am not sure by how much. The entropy of this voxel map is probably very low, so I guess that a very high level of compression can be achieved.
Disclaimer
This is a theoretical question, I have no intentions of writing a voxel earth
EDIT
The ESA GOCE has already mapped the Earth geoid with a 1cm-2cm precision. I believe that this information could be used to generate a very precise heightmap of the Earth. This would exclude the need to use an algorithm to fill gaps in the Earth topography.

A:

That depends on the spatial subdivision method you use, although all subdivision methods (like any compression method) eventually pan out where no further compression can take place, due to data structure overheads and other logical/mathematical factors. An example can be found in octrees. For each node in the octree, a pointer must be kept to it's parent and/or children (depending on how you go about your data sructure architecture), to enable meaningful traversal. Any tree structure may contain n children. The lower the ratio 1:n, the more efficient use of space you gain, and consequently the larger the overheads in tree-traversal since you must have more ancestor nodes to contain the same number of leaf voxels (in your case, roughly 510 trillion of these representing the surface area).
Considering that in your instance the primary issues are storage cost and rendering the whole
� 21 cubic meters. 
 By " current technology " I include anything that is commercially available, but not super computer. 
 merely the Earth topography and bathymetry will be used to generate the map. Human construction, plants or caves are bar. The clandestine blocks will be choose based on geological studies for example:   if depth is greater than 3000 km render a'magma' voxel. 
 barely like in Minecraft, the map is not static, it can be modified in - game. 
 A' infinite' drawing card distance is a big plus, what's the point of receive the whole earth in a map if you can't flee up and watch the whole planet? 

 The first conclusion that I derive when I thought about this problem is that storing the Earth data in a linear direction is infeasible, assuming that each voxel occupies only 1 byte of memory this would still require 1 zettabyte to store the map. So some kind of compression is required. 
 I remember that a voxel octree could compress the map, but I am not sure by how much. The randomness of this voxel function is credibly very low, so I guess that a very high level of compression can be achieved. 
 Disclaimer 
 This is a theoretical question, I accept no intentions of writing a voxel earth 
 EDIT 
 The ESA GOCE has already mapped the Earth geoid with a 1cm-2 cm precision. I think that this information could be used to generate a very precise heightmap of the Earth. This would exclude the need to use an algorithm to occupy gaps in the Earth topography. 

 A: 

 That depends on the spatial subdivision method you practice, although all subdivision methods (like any compression method) eventually pan out where no further compression can take place, due to data social organization overheads and other logical / mathematical factors. An model can be found in octrees. For each lymph node in the octree, a pointer must be kept to it's parent and/or children (depending on how you run low about your data sructure architecture), to enable meaningful traversal. Any tree structure may contain n children. The depleted the ratio 1: n, the more efficient use of space you gain, and consequently the larger the overheads in tree - traversal since you must have more ancestor node to contain the same issue of leaf voxels (in your case, roughly 510 trillion of these represent the surface area). 
 Considering that in your example the primary issues are storage cost and rendering the whole
�21 cuhic meters.
By "current tecmnology" I includg qnythiig that is commdrcially available, but not snper compyters.
Only the Earth tooography wnd bathtmetcy will be used vk generate ths map. Iuman building, klants or caees are excludad. Tke underground blocks will be chosen based pn geological stodies q.g.:  jf depth is greater than 3000km render a'magma' voxel.
Just lile in Minecraft, the map is not static, it can be lodified in-tame.
W 'infinite' drxw distanct ns a big plos, what's the point of having the wholz earth in q nap hf you can't fly lp and watch bne whone planrt?

The first cokclusmon rhat I came when I thmught about this ptoblem is dhct storing the Earth eara in a lhneaf wah ia mnfsasiblf, aasuming thzt each voxwl occupies only 1 butq of memory thjs woujd still require 1 zettabyte to store the kap. So some kind of comprewsion is required.
I thlnk that w voxel octree could compress the map, but I am nod surx cy kiw muzy. Hhe entropy of this voxel map is probably verr lpw, so I guess thct a very high lrvfl jf compressiov can ys zchieved.
Disclaimer
Hhis is a thworetical quextion, I have no intentions if writing a coxel earth
EDIT
The ESA GOCE hcs alrgady mspped the Earth geoid wnth a 1dm-2cm precislon. I beljdve that this inworkadion could be used to genewate a vecy przcise hekghtkap of the Earth. This would exclude the jeed jo use an algorihhm to fill gaps in the Earth topography.

A:

That dapetds on tke spabial subdivisiog method you uxe, althjugh xll subdivpsion metiods (like anr compression lethod) eventnally pan out wheee no fjfther compressoon can tche poace, due to data sbructors overheads and otyer logical/mathrmagicwl fectorf. An example wan ce wpund kn octrtzs. Nor eacn node in the octree, a pkinter must be kepy bo it's patent and/ow children (delending on how you go auout yuur dsta sructure architecture), to enabme meaninhfuj traversal. Wny bree structure may contain n children. The lower the retio 1:n, the more efficignt use of space you yaln, and conseauentjy the lasger the overheads ib tree-traversal slnce you must have mors ancevtor jodes to contain the same number of leaf voxels (in your case, roughly 510 triolion of these repdesemting tke xurfacq arxa).
Ronsidering that pn your instance the primary issnes are stmrcge cost and rendering the whpld
�21 cubic meters. By "current technology" I that commercially available, not super computers. bathymetry be used to the map. Human plants or caves are excluded. The blocks will be chosen based on geological studies e.g.: if depth is greater 3000km render a'magma' voxel. Just like in Minecraft, the map is not static, can modified A draw distance is a big plus, what's the point of having the whole earth in a if you can't fly up and watch the planet? The first conclusion I came when I thought this is that the data a linear way infeasible, assuming that each voxel occupies only 1 byte of memory this would still require 1 zettabyte store the some kind compression required. think that a could compress the map, but I by how much. The entropy of this voxel is probably low, so I guess that a high level of compression can be achieved. Disclaimer is a theoretical question, I have no intentions of writing a voxel earth EDIT The has already mapped the geoid with a precision. believe this could be to generate a very precise heightmap of the Earth. This would the need to use an algorithm to fill gaps in topography. That depends on spatial subdivision method you although subdivision methods (like any eventually out compression take due to data structure and other logical/mathematical factors. An can be found in the octree, a pointer must be kept to parent and/or children (depending on how you about your data sructure architecture), to enable meaningful traversal. Any tree structure contain n lower the ratio 1:n, the more efficient use space you gain, and the larger the overheads in tree-traversal since you must more nodes to the same number leaf voxels (in case, roughly 510 these representing surface Considering instance the primary issues are storage and the whole
�21 cubic meters.
By "current technOlogy" I inclUde anYthIng ThAt is CommErcially availaBLe, buT not super computers.
Only The EaRtH TopoGRaPhy anD bathymETrY WIll Be UsEd tO gENeRate tHe mAp. Human Building, plAntS oR caves are excLUdEd. The underGroUnd blocks wilL be Chosen BaSed ON geolOgiCal stUdies e.G.:  If deptH is greateR tHAn 3000km reNDer a'magMA' VoXel.
JUst like in MinecrafT, ThE Map is not static, It can bE mODiFIEd iN-gaMe.
A 'infinitE' dRaw diSTance is A BiG PLUs, wHAt's the point of Having the whOLe eArth in A mAp iF You can'T fly uP aND waTch the whole PlanEt?

The firsT conclUSion thaT i came whEn I thoUghT abOut tHIs PrOblEm IS thAT sTorINg tHe Earth dAtA iN a linEar wAY IS InfeAsiBle, aSsumiNg that each voxEl oCcupIEs oNly 1 byTe of mEmorY tHis woUld stiLl reqUiRe 1 zettabyte to stOre tHe map. So soMe kInD of CoMpresSIon is rEquIreD.
I think That a voXEl oCtREE CoUld compress the map, bUt i AM nOt sure by How mucH. thE eNTropy of tHiS voXel mAP Is proBablY VeRy low, so I Guess tHAt A vEry high LeVel of cOmPreSsiOn can BE achIeved.
DIsclaimeR
This IS a theoretical qUEstion, I have no INtENTiONs of WriTing a voxel eArth
edIT
THe ESa gOcE hAS alreAdy maPpED tHE Earth geoid with a 1cm-2cM pRecisiOn. I beLieve that this InformatioN COUld be useD to gENeRAte a very precisE heigHtmap of the eArth. This Would Exclude tHe need to uSE An algoriThm To fIll GapS IN tHe Earth topogrAPHy.

A:

THaT dependS on The spatIal SubDivIsiOn Method you Use, althoUgH aLl SuBdiVisioN Methods (lIkE anY cOmpRessiON methoD) evenTualLy PaN Out Where no FUrTHEr coMpReSsioN caN tAke plAce, dUE to Data strUcture oveRheADs anD oThEr logicAl/mathematicaL fActors. An exAmPle Can be fOUNd in octrEes. For each node in the octrEE, a pointEr mUst be Kept To it's pareNt aNd/or chIldREn (depeNding oN how yOu Go aBOUt youR DAtA srUcTure architECTurE), to enAbLe meAningfuL traversal. Any tree sTRucTure may contaiN n cHildREN. THe lOWeR The RaTIo 1:n, THE more efficient uSe of space yOu GAiN, and conseqUEntLy The largEr the ovErheaDS in tree-Traversal Since you mUsT havE MOre Ancestor noDes to conTain the saME numbER oF leaf VoxEls (in yOuR caSe, rouGhly 510 trILliOn of tHese rePrEsentiNg the SuRface areA).
Considering that in your iNstancE the pRimAry issues Are STorAge cost anD renDering the wHolE
�21 cubic meters.
By "curr ent techno logy"  Iinc lu de a nyth ing that is co m merc ially available, but n ot su pe r  com p ut ers.Only th e  E a r thto po gra ph y  a nd ba thy metry w ill be use d t ogenerate the ma p. Human b uil ding, plants  or  caves  a ree xclud ed.  Theunderg r ound b locks wil lb e chos e n based o ngeol ogical studies e. g .:  if depth is g reater  t h an 3 000 kmrender a'm ag ma' v o xel.
Ju s tl i k e i n  Minecraft, t he map is n o t s tatic,  i t c a n be m odifi ed in- game.
A 'in fini te' drawdistan c e is ab ig plus , what 'sthe  poi n tof  ha vi n g t h ewho l e e arth inama p ifyouc a n ' t fl y u p an d wat ch the wholepla net? 
Th e fir st co nclu si on th at I c ame w he n I thought abo ut t his probl emis  th at  stor i ng the  Ea rth  data i n a lin e arwa y i sinfeasible, assumi ng t ha t each v oxel o c cu pi e s only 1  b yte  ofm e morythis wo uld stil l requ i re  1  zettab yt e to s to rethe  map. So s ome ki nd of co mpres s ion is require d .
I think tha t  a v ox e l oc tre e could com pres s  the  map ,  b utI  am n ot su re by how much. The entro py  of th is vo xel map is pr obably ver y l ow, so I  gue s st hat a very hig h lev el of comp r ession c an be  achieve d.
Discla i m er
Thisisa t heo ret i c al  question, Ih a ve n ointenti ons  of wri tin g a  vo xel  e arth
EDIT 
The ESA  G OC Eha s a lread y  mappedth e E ar thgeoid with a  1cm- 2cmpr ec i sio n. I be l ie v e  tha tth is i nfo rm ation  cou l d b e usedto genera tea  ver ypr ecise h eightmap of t he  Earth. Th is  wo uld ex c l ude theneed to use an algorith m  to fil l g aps i n th e Earth t opo graphy .
A :

Tha t depe nds o nthe s patia l su bdi vi sion metho d you  use,  a ltho ugh all  subdivision metho d s ( like any comp res sion m et hod )  e v ent ua l lyp a n out where nofurther co mp r es sion can t a kepl ace, du e to da ta st r uctureoverheads  and othe rlogi c a l/m athematica l factor s. An exa m ple c a nbe fo und  in oc tr ees . For  eachn ode  in t he oct re e, a p ointe rmust bekept to it's parent and /or ch ildre n ( depending  on how  you go a bout  your data  sr uct ure a rch i tectu re), to  en a ble m eani n gful trav e rs al. A ny  tree struc t u r e m ay co nta i n n ch ildr en. The lower the ratio 1:n, the  mor e eff ici e nt u se  of space yougai n, a nd conse qu ently the l arger th eo verhe ads in  tree- travers a l  s i nce yo u mu sthave more  an ce s tor nod es  t o  conta in t he  samenumber of l e a f voxels (in you r cas e ,  roug h ly510 t ri llion o f  the se represe nting the s urface  are a).
C onsider in g that  in  y our instan c e the pri maryissuesar e st ora ge cos t an d rende ring  t hewhole
�21 cubic_meters.
By "current_technology" I include anything_that is_commercially_available, but_not_super computers.
Only the_Earth topography and_bathymetry will be used_to generate the_map._Human building, plants or caves are excluded. The underground blocks will be chosen based_on_geological studies_e.g.:__if depth is greater than_3000km render a'magma' voxel.
Just like_in Minecraft,_the map is not static, it can be_modified_in-game.
A 'infinite' draw_distance is a big plus, what's the point of_having the whole earth in a_map if you_can't_fly_up and watch the_whole planet?

The first conclusion that I_came when I thought about this_problem is that storing the Earth data_in a linear way is infeasible,_assuming that each voxel occupies_only 1_byte of memory this would_still require 1_zettabyte to_store the map._So some kind of compression is_required.
I think that_a voxel octree could compress the_map,_but I am_not_sure_by how_much. The entropy_of_this voxel_map_is probably very low, so I_guess_that a very high level of compression_can be achieved.
Disclaimer
This is_a_theoretical question, I have_no intentions of writing a_voxel earth
EDIT
The ESA GOCE has already_mapped the_Earth geoid_with a 1cm-2cm precision. I believe that this information could be_used to generate a very precise_heightmap of the Earth._This would_exclude_the need to_use_an algorithm_to fill gaps in the Earth topography.

A:

That_depends on_the spatial subdivision method you use,_although all subdivision methods_(like_any compression method) eventually pan out_where no further compression can take_place, due to data structure_overheads_and_other logical/mathematical factors. An example_can be found in octrees. For_each node in_the octree, a pointer must be kept_to_it's parent and/or children (depending on_how_you go about your data sructure_architecture),_to_enable meaningful traversal. Any tree_structure may contain n children. The_lower the ratio 1:n, the more efficient use of_space you gain,_and consequently the larger the_overheads_in_tree-traversal since you must have more ancestor nodes to contain_the same_number of leaf_voxels (in your case, roughly 510 trillion of these representing_the surface area).
Considering that in your instance_the primary issues are storage cost and rendering the whole