Etree: A Database-Oriented Method for
Generating Large Octree Meshes
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Tiankai Tu David R. O’Hallaron Julio C. Lopez´ £
Computer Science Department, [email protected] ¤
Computer Science Department and Electrical and Computer Engineering Department, [email protected] ¥ Electrical and Computer Engineering Department, [email protected] Carnegie Mellon University, Pittsburgh, PA, U.S.A.
ABSTRACT
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THE ETREE METHOD 3WC3§ ©AP - ¨§ H - )*L) C39X' ,"'$)* (© )* F ¦¨§ 7 © !"¢!")"*'L)*0v§7R©A E)< ).,=©A 7Q!"(*' ¡ C© 'VOQ!"(© !>'A.!"I) C & § & §)= +0B)*@ 4. THE ETREE LIBRARY § )"- ^)*0RC)**F - ^* )"*C(§¨' ,d3(*!" ¢ ]= e© !"- §).WH §RC)*& )" = @)*0 §R7' ©A8 (O F .(*8 * +C3§ ©AP - I)" k§ + C©A'j ; Y)0 °* ' © C;© )" CC +§ ^' © 8(.O°§ )"- !*§½ © &E9 & §Y!"(© )"ZF ² ' ^W¨'A'V9X ' © C;© )"ih)"!(*& & © ! 05C ² i FG¦¨§>'A© 8 (O¢©A Y © ,=©A ; _© ¢§ 70B)"' ' );WH©A!& )= 9 e© !"- §);WH K§ ) C K)*0H!* 3(© !+7& §<- M9 - ' ?S1*4K¤£254113#ZE ).Wb0?-'eC)= © ! C(§ & ) ² © !§ LD& § )= SF § 3£* 254(£2¨ M Z# I) C * © !* `dO L)Y) C( 8 *=2:¨¦\*;Ad25\* #ek& C3§ 9 © jC)" M- C +© +§ @ *& @W¨OQ* j© <© 9XC)*E' !")*9 © &«0?)v(;,d © !I§j) C@*- )"&I© C;' ' OS C ¤£" ©V§ &7#] C L§ L©Vv© L8 -©A'VD* R M)* 7)"+ © `Fg¦¨§ ©" * £?=*#=LC3§ ©AP - J§J 6- @) Cg8'A* C©A! C)"& )* © © )* )*0D§ 7) C3(* I> E)*_§ )" 3(© )" ¥§¦\254113# (*8 * D©A ]U M- C- !")"& O>) § O © C 8© !k& )= 'A ZFK¦¨§ K - 'Vj© 0?)L M)*© !I RCC © !k) C3(* H)"> ©A `F - =8 *'A*C; R) C"Fv3] ;# § ©" £(1K M 7C- © ,d'VO C)"& )* g*' '§ 8©A! ) C( b§.¨,=© )"'AL§ 9\)*9 C)" M(© =- ©A'h)R© ' ' !d'bC)* ©V© )" j] © M;F e© ' ' O # ¢*4 M $#& § 9: C©¢ C© 0B)*&I© )*> - C(§ © 7§ 254 4.1 The etree API ² ²M³ § IC;*k8 ¦¨§ D i © g© ©V; I8 O ¼v©V] ' * G§ L' & 9: )= H'A© )* § © Y* I§D)= LC) )*( © 9 C;.!")©A¤; 7© =)@§ C'f . g. 3©A,"; E0B)"&¨§ L8*'A C; k) Cv* I M)* /* Initialization and cleanup */ Application etree_t *etree_open(const char *path, int flag, ...); Etree API int etree_close(etree_t *ep); n g /* Octant-level operations */ o r n l i e i t a o a c e t a e r c int etree_insert(etree_t *ep, location_t loc, const void *value); n t u g n o i a i c l A v L L o a int etree_search(etree_t *ep, location_t loc, location_t *hitloc, void *value); a b n int etree_update(etree_t *ep, location_t loc, const void *value); int etree_delete(etree_t *ep, location_t loc); B-Tree int etree_append(etree_t *ep, location_t loc, void *value); Etree library /* Octree-level operations */ typedefint decom_t(location_t loc, const void *value, void *childvalue[8]); int etree_construct(etree_t *ep, location_t rootloc, const void *rootvalue, decom_t *autodecom); Figure 4: Etree architecture. int etree_balance(etree_t *ep,decom_t *baldecom); int etree_sprout(etree_t *ep, location_t loc, const char *childvalue[8]); int etree_initcursor(etree_t *ep, location_t loc); ?255" A;*25\*¯ £A1* & C;*¯8 ¢¡ int etree_getcursor(etree_t *ep, location_t *loc, void *value); ³ C;.; ª* C'A)* ; * R©V0K©VYWb/¡)*9 )" ; int etree_advcursor(etree_t *ep); © .O ' "F £2:*2 ¦XA13*1> &134*25\ ¦¨§ ¡3ª ).,=©f ¢ ¤£ C)"& ' v ¨)*0e)* (© )* ¨)K&I* © - 'AL) C(* Figure 5: Etree API. M)*; I)"Y © `F* )g]*& ' "#= ;C(§ © !K0B)*L*k) C9 (* )I©A © ! < 3W«) C(* ;F¦¥GC3§¢) C(* © " ; +8 O+*<*8 M(*CK ( aO ¨§ © © # µ )*0H§k) C3(* @)7§ )*)"C)= Y© ^)( K)+ © M© 9 WH§ © C(§RW¨ WH© ' '%] 'f© 7© >¦ C© )" F F !"-© §ª§+) C(* k0B)"& * O* C M)* k§R §.+§ *& ' 0f9X' );W¨3 C) ;FH¦¨§j - 'VD©A DE- ©AP=-j`dOR* M9 £25411¦:A13*1 &134M*25\*(©¦¨§ © <© +§ ©A M© C© ,d ¤£ © !"& L0B)*v;*C(§>) C(* ;#WH§© C3§>© L- -' ' OY0?3; 7) ² 0?;.-<)*0U§<3 & §)= ZF M" ¡)*0@ - §9 · ;¸ * h§j ¤£(25\** £¤ 1 F7 )*6]*& ' "# e© !"- § );WH © ! §7W¨)*`=' )d* )/§ > 'A© C;.© )" #L§ >3 ¶*¶ *;¶ *" § );W_W¨HC)*& -¨§g' ) C;© )" *'C)= 0?)¨) C9 ' ©A8 (O - ) ) C9:' ,d'G)" (.© )" U ©VC'VO F (* %6@© e©A!*- F¥D)*© C§.v§ - 3 C)*K© +§ )*3] & ' "#Z§ K0?- C© )" ' ) C;© )**'C)= g© K§ !"- ¨© e0?)*J© ' ' - M(© )* - )* *- )"&I© C;' ' OYCC)"& ' ©A § g§ £*2543£2g M Y© )"'VOZ U' ) C;.©A)*'eC)= j© M- MDU8 © .Ok M©A!F e© !"- F6¦¨§G)* 'VO© -Z0B)"&§ G* ' ©AC© )"@©A e 0?- C© )"7§ H§ j3'A© 8 (O7- H)I & © § );Wª)E ) C vR) C( ;F e‘sleft-lower corner (2, 3) e© !"- @' ©A M H§ v C©¢ C 0B- C3©A)* F binary form (010, 011) interleave the bits to 4.2 Linear Octree obtain Morton code ² k)*( ¨)@&I* k*k) C )@U (*8 * M-C-*# Wb 010 011 · ¸ - I§ IW¨'A'V9:`= );WHª ?S1*4Y¤£2541(1RC(§ ©AP=- F ¦¨§ © & §)= R* © !* DU- ©fP -v`dOI)E*C(§7' ;06) C( ;Fb¦¨§ 00 11 01 `dOR C)= 8)§7§ K' ) C;© )" * >§ ©A¤U)*0J§ K) C9 (* ;F7T IC;*/§/- k> (*8 * k M- C- I - C(§^* append the level of e K¦ C© )" F )@© 3]k§j`dO F § [G9\ 001101_11 § C(= ©A!* ; <`dO - © !7Y,*©A= )*0¨§@W¨'A' µ ·V¶*¸ µ `= );WH ))"^C)= F ))"^C)= k&I K d9 © & © )"'H )"© )/ )* 9X © & © )"'H C;*'A;F¦¨§ Figure 6: Interleaving bits and appending level to &I* © !C;R8DC)"& -; IP - © C(` 'VO 8 O © ' ;;,=© !@§ obtain the locational code. 8 ©V J)*0§g8 © .O@ (© )* b)0§ gC) )( © . b)0 d9X © & ©A)*'Z )*© =;F ¦%)j© )"'A.D- J0f)"&§ H (*© ' G)0S§ g8 ©V9:© ' ;;, © ! * >'A,d'h © ! #W¨@ K*Q8 M(*C3 .( XO ¦¨§ D`dOI ) C©A; kWH© §Y*I) C( g© gC)"& -; b0?)*' 9 µ ² E§LC;78j- Y)I" L*R) C(* ;F § © © ' );WH F8 e©V MjWb C)"& -@§ )*)*/C)= )*0¨§E' 0B9 C)* © M b)0Z§ ®ªC) )*( © ¨)*0$* ) C3(* ! b' 0B9:' );W¨ ' );W¨DC)*L)*0e§j) C(* ;Fv3] ;#=Wb* k§j' ,d' ! 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M(*© !*§=0B)*W¨( «WgOc)©© & ' & § © 0?- C© )"«© )Q© 3(Y§ )"-!"§¢*' 'g§ k) C(* E© § k- =8'f C ² ©V©f' ' O #=§v;,=© !d.©A)*7) CvC)" ©A M H)0%§ L) )*L) C9 ) CH KC3§C3`j§©VG© !"§=8)* h)j & © JWH§ § (* ;Fe¦¨§ g ' ©V© ! ; © C;.¨© 6©A=,d)*`d; j) C©A ¨WH§ 0?- § E C)"& )" ©V© )"© EC .O F T/I0BE)>§ © ² )L )HWH©V§§J) );F 0L C)"& )" ©V© )"© e; Z#© !"§ * )"*C(§° Q" !©"¡©" * £B=*F ¦¨§ )*- !"§C)* C -'A'VO C(§ © 'A /) C3(* Kk*' ' ) C; _ ' © `"; Q)R§E) )* © & ' "#!*'A)*8'U8'A* C©A!§ >aW¨)&I a)*Q (WH8 *C(` F - © !D)( © .Oj© 9:C)*G )"© Fh¦¨§© e ) C -G© %§ e©V M;#I&U-' © 'A_©V(© )* /§)*- !*§§ )"&I©A&IO C)*=© =- E©AI § 9 MJ)*( ;FhT¡§ ,d3J§H ' ©V©A! 8I ; <)> )" *!d. § I© & *C3@)0LR© =O<) C(=;F © C;K & © g§ v*7) C( ) v)*L R) ¦ C)" Z# ;C3§I© !"§=8)*9 © !j)* (© )*IWH© ' '© C- G§ 8> C)"& )* ; Z#b§ W¨>`= );W«0B)*kC(©A_§.I© I© C)* MD)06 ;C(§ © !U§ (*8 * "F 7' ;0L)= §.UC;^8I 0?' 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' );WH© !E&I9 (* ! g ©A!*§=8)* g)E & © LWH§ §g§ 9\)*9 C)*9 3;F 8!"© ©A!R)0¨ ) C © !7;C3§<8 ' ) C(`S#$'A'G(O M(*© @©A K,=© )"'A; S#6* /©V0H )#h 0B)*& © !+> C)*& )*9 ¶ ' & Lj 3D)E8 F¨¼D )"R;* © !EE W) C(=;# ©V© )"$F@® - ©A!Y*C(§ ©V(© )*$#%Y' © M)*0¨W8)"- O W¨< 3& © >§ + )" ©V© )"ª)0@§Q) C3(* ! R' 0B9:' );W¨ ) C(= b©A b!"(; S#=WH§ © C3§I© ¨- ; I* b§D© -G)§ C) L'A© ,d )E§j'A30B9:' ).Wb C)* 3D)0h§ jC)* (*© 9 3] H©V(.© )"$F © !D8 ' ) C3`Fh¦ - )" b§b )* © © )*E© ¤ © 3#"§ §g(O · ¸ ' & © © b 3¨)@8H§ L © ¤v)0$§D) C3(* H © ,=©A ; v)j§H§ )*(*'%C)" MD)*06 ;.C3§© !I © !*§ 8) D© R§ 8 OI§ © ¤)*0%§ j &I*' ' ML) C(=L© R§j )*&I*© $F e© !*9 .(*8 * b0B)*68)"- Oj8 *'A*C© !v© e&@- C(§jC3§;* 3e§ - §);WH @§ C)" U)0H§ 8 ' ) C(`=©A!Q(O^.0B § >C* Q)*0!"' )*8*'v8*'A C© !8C*- >§> -&U8I)0 © ,=© !E© 0?)*&I.© )"7)0e§ ) C3(* H8' )" !*© !E)@§ 8)"- O/) C3(* U© @0? ' @§*/§I -&U8K)0L§ ' 0B9:' );W¨D8 ' ) C(`Y)0e§ )"&I©AY § );WH7© 2 e© !*- F ) C(= H© R§ ©V )"&I© $F e, 1 g, 1 qr.r.n w"x;~%n t;t+q |BqZw" |Ke |B~%wd}?~%%u T/ MK M- O * >©V b, 2 d, 1 f, 1 § j'A.©A)* §©A Q8XW¨+ 8)*- OY) C(* ?2X1343" © !"§=8)* e© § G *& b8' ) C3`.0BJ© ' 8*'V9 *C© !K© g 0?)& ; ZFJ¦=© CL§ 9\)*9 C)" M(© =¨©A g9 a, 2 c, 2 0?)C; _'A) C*' 'VO© ©A R§ © 8 ' ) C(`#b§ 37R)" 'VO^§ )" © 8'AR C.© )" 0?) § R© *'g ©A!*§=8)* )*0*#b* M; :" § );WHY©A8 e© !"- §*'V06 g'A!" * L'A.!" \" * ) aWH© C* L'A!*@ *F \d C;* )D) CC-;FG[bC*- § M Figure 13: Content of the blocking array. ¿v);Wb,d;# C © ) C)* ©V© )"I© & )" U)" § g8' ) C3`@ ©A¤D;P - ©V 6§.b*C(§ 8 ' ) C(`+&I* )RR - 8 U) );#e§=- ) C( @&U- Mj8 0f §U8 ' ) C(`=©A!R.(O+©A j© © ©A'A© ¤ Z#%WbUC;Q )"' ,d ² ^ C * I)*0§©A I -87) ) 8'A) C(` F )*§ § 9:)9 C)" M(*© vWH©V§ © >§ 8 ' ) C(`YWH©V§ )*-vP - O=9 W¨)( #6) C( U&U- M8I7C(§ © 'A )0H )"& ) C(=§ © !^§ Q (*8 * "F¨¦¨§+* )"ª© Y§ R*' ' § +© 0B)*9 © @XWH©ACR U'A!*7* *FQ¿v);Wb,d;#6 © CR^) CR© U &I© )*7!d.( © !k) C(* D©A+ ,=© C© ©VaO 8 ' ) C(` § *'V9 © a)"© C)"& )* ©V©A)*>)*0h§j )*&I*© $#©Vv© H© & )" © 8 ' ;* O78>C)*( ; >© +§8 ' ) C3`=© !k.(;O F e© ©A!k Internal octants Internal octants in the same block not affected by the as b decomposition b b b Decompose octant b (1) (2) (3) b Figure 14: Three scenarios for internal neighbors A tiny octant on of a boundary octant. the boundary of another block 0?)¨) C( ¨)j§;,dL ©A *'© !"§=8)*J§.b).,d3'f § 6!*©A)*@C),"; 8 O ! % =;# e § );WH© e©A!*- =F Figure 16: Scenario (1): internal neighbors not af- fected by the decomposition of the boundary oc- tant. Impossible for an octant to overlap the region covered by b’s parent ) C(= 6§ *'V0S* 6'A!*L* ! h© '© !"§=8)*;FJ¦=© Cb§ 9\)9 C)* M(©A b©A G M© 'A'&I© =(© ; S# )K C)"& )* © © )* )*0 ! © 'g © !*§ 8) E© E ; ; SF !"*© $#J§ I'A9 © )" § © R8XW¨Y§ v Wª8)*- Ok) C(= H I§ ©V b b :" © '$© !"§=8)* H© H C.© ) F Internal octant Internal octant not in the same affected by the Figure 15: Scenario (3) is impossible to occur. block as b decomposition Decompose octant b v);WW¨C;> § );W°§jC)*C3 D)*06§ j' ) C;'h8*'A C9 © !Q C3§& "FQT/k ).,d"#J8 O/© - C3©A)*)"^§ k=- &U83 b )*0v©V(© )")*0 8)*- O/8*'A C© ! #¨§.E§ R C)"&E9 )" ©V© )" )*0L* O+8)*- OQ) C(= @WH©A' 'J )@C*- I 9 C)*& )" ©V© )" I)0j©V k© *'H © !*§ 8) F¦¨§.Y© #¨§ A tiny octant on M*C=R8 ' ) C(` R<*'VWgO /¨© ¦ © (*C© )* R83aW¨" the boundary of ©31- 8 O/) C(= @)"^§ k8)"- © E8XW¨_8' ) C3`= 3*4 another block ² * QWH© ' 'b,d )" !d.k© )Y§ 8 ' ) C(` F <§U0?)*' 9 ' );WH©A!U ) )*0a# W¨v)" 'VOIC)* ©A 3g )*9\© , ©A'C;* gWH§ U8)*- OY) C(* j ) v C)*& )" - © ! 7©V(9 Figure 17: Scenario (2): internal neighbors not af- © )"7)0h8)"- Ok8'f C© !F fected by the decomposition of the boundary oc- tant. )L§j8 jC;* § ML©V(© )">)068)"- .Ok8*'V9 *C© ! #e§ E'A.©A)* §©A 8XW¨^R8)"- O<) C(* ¦¨§ R©A -C© ,dRC; >© k M(© !"§ 0?)Wg( )< ).,d"F[b9 M; UWH©V§/©V © =3*'J ©A!*§=8)* K©A ©V§K C.© ) )* :" C;- v C.©A) © b§v)"'VO )" © 8 ' v'f.© )" §© R89 :" F aWb>§ 8)*- OY) C(* j R§©Vv© 'e ©A!*§9 ¤ M. e© !"- §).WH 6§.b©V0S C© ) § )*'A 60?)*G§ g8 * ¡ 8)* J0?)¨©V(© )* #dWbDC; - g§ H & D.!"-& J0B)* C; "#d§ ¨ C)*& )" ©V© )"E)0 GWH© ' ' -'VG© U0B)"- GC(§ © 'A § U8* UC;* E)7 §);W©§j§E© 'J© !"§=8)* K ) ) C(= L)*06P=- *'$ ©A¤) ! 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OR* H§ v& §R © ¤j© C3;* F ¦ # # # # , # ; ; ¶ ´ ¦ # ,=# =# ,=# # # ¨ ¦¨§ ©V( S#d'A' §b] © & h.¨ 0?)& ; )"@D&I*C(§ © .´ µ WH©V§¢)* 'VO [¨)*0D § O ©AC*'g& & )O F/¦¨§R8 - lS µ [LFg¦¨§=- # Figure 21: Summary of San Fernando meshes. *' ' ) C;.; 8 O^§ 7>'A© 8 (O_© k)* 'VO § JJ& §)= © %H0B;* © 8 ' ¨ )*' -© )")D!* 3(b'A.!" ¦¨§ k& §^!* (.© )"_ ) C U©A E © ,d^8 O §Y&I.9 ) Cj& § H)"Y& & )*O=9:' © & © I&IC3§© F µ ©A*'e& )= 'e ,d' )* ; 78 OR¿v)"'A *!*© M(*' * +¦=," · ¶*¸ ®jO ¦ *® © !")ª¦ (/¼D © ,d ©VXO FºT/ *&E9 ' ; /§R&I3©f'g& )= '¨* M)* §k -'V © 5.3 How does the running time vary with the *2X134(\" @ .(*8 * "#WH§©AC(§7W¨WH© ' 'e0?v)I* D§ physical memory size? ´ µ d*2:¨©(13FG¦¨§¨ © ¤g)*0§¨&I3©f' (8 g©A , [DF T/H.g )G)* 'VO@©A M; U© U§ blSCJ)*0S& & )*O © ¤ )"¢§ 7- © !<©A& >)0)"- Y& 3§ )= Z#¨8 -Y'A )^© 9 ²²² T/bC)" - C3; U'A'=§ b] © & e)" Di ¾v¿D¤g&I9 M; I© R & © © !K§L- © !K© & L)*0e3D'A.; ¤"¶ ² C(§ © gWH©V§I¼v'V( ¦»g¦ C)*=)*' 'A3H* © `U- © ! )" 3(© )" U 'A© C;.© )"9: C© C C)"& -(.©A)*$FET ¥$© =-] F F ,=F¨¦¨§ + §=O © C;'v& & )O^0?)*Y§ >] ©V9 0B)*& *¢] © & © & ©A'A.Y) §7)"+ C3©A8 ;*´<µ ´"´"¶<µ & (* !* U0f)"& [ ) [DFG[b0B)*7*C(§ © k§v ,=©A)*- ¨ C© )"$ W¨v!"(; § D& § bWH©V§ ] © & ;#ZW¨ ;P - =©A'A'VO< C;*/XW¨) F >¾ [ ' ) § > & +'A© 8 (O (& #L©5F *FA#v[G9\+8 - lSY* - §Y§ )" (.© ! MO M& ! g8 - lSHC;*C(§ *F 8 ' ) C(`=©A!^(O_ © ¤"#H] C §. § © E© & YWb>,".©A § D*& )*- J)*0$ § O © C;*'& & )OE;,**© 'A*8'AL))" (.©A! 5.2 Is the etree method feasible? MO M&7F ¦%)D* MW¨h§©A %P - M© )"Z#*Wbb!* (.; & § $)*0 ©VlS9 [b ©A g§ D)(*'S- © !© & "# W¨ & * - I§v© & D ©A¤ * 7& ;* - ; 7§ j© & P=-©V; 7)k!* 3( 0?)>§ Q0?)"' ' );WH© !)* (© )" +)*0@)"-7& §!* 3()*; § &7F7 )*g§©A H] © & gWbjC)" !"- ; k§j § O © C;*' M. :" \d £*2543£25# ©" £(13# 254M* ¢4 # 134 K* .*´µ & & )Oj)j8 [L#=* 3 ] ; § g © ¤H)*0§H[G9\ §¦ *( **13F¦¨§ 8 ME§7)" (.© )" k.7!"(*' ´Uµ 8 - lSg© Y§vj'A© 8 (OI) [¡* § v ©A¤j)*0%§ ¡)* (© )* #7©5F "F #73]C'A- © !½* ' ©AC© )" 9X C©¢ C ¤@µ " 8 ' ) C(`=©A!U.(Ok) [DF e© !"- § );WH ¨§ L'A* ; C)*& -(.© )"$#© 7§ jC) )" © ! C)" M-C;#8 *'A*C Wg' 'hC' ) C3`R© & H)I!"(@& § D)0b ©VlS v © ¤ F * 7(* M0B)*& M C© 8; >© + C© )" F¦¨§ U)* 9 'V§)"- !*§k§ v& * -& ¨v C©¢ CL)@§ © ¨ 9 (.©A)* G*CC)"- 60?)G§b© & ¨] C- © ! ' © 8(.OUC)= g) © C- 'A.L* ' ©AC© )"Z#§OI § );W¡§ L - 'VH)0e!" (.©A! ;,=© !d.¨* j ;C(§K§G3"F*"v-Oj© h@ 'A© C;.© )"9 H )" 9\©A,=©A*'5#.;' 9\Wb)*'A @) Cb& §Z#* 3, © !v hL!*) )= C©¢ CE)" (.© )"/ Q*CC)"- 0B)*j§ K© & K;P -© © ©AC© )"^)0LWH§§ 3K§ I& §)= © K0B;* © 8 ' k© )P -O§ <&I©A'A + (8* ©A*' '§ < M 7)0 & g)0e- © !K©A& * Y& & )*OEP=-©V& ;F § K& §>!* (.)*;F¡ e© 'A;,d@© j' )R< 'A© C;.© )"9 C©¢ CE)" (.© )"/ Q*CC)"- 0B)*j§ K© & K;P -© µ § ¥6' & ®j[ © ¤ ¦¨© & ¦¨§ - ³ )/C)*& - Y§ >&I M 'A;,d7'A© )* § © ¡8XW¨ :µ ³ [ 'A& )= F ;¶ "¶ F F ¦ ,=# "*¶ ´¨ ¶ ¶ ¦ * , # F * e© !"- §).WH h§b- © !L©A& J0?)J§¨& §@!"(9 ´*"´ ´" *¨ . ¦ # # # F , # © )"I ) C FJ¦¨§ H - 'V bL ; E© E0B)"-b!*)*- # ; ; *¶"¶ d´ ´ d ¦ # ,=# # # F # )"U0?)K;*C(§ & §ZF ¥J*C(§ !)"- < = §U- © ! © & v0?) @!"© ,d7& §YWH©V§> ©VlS=L §=O © C;'$& & )O !*-(.©A)*$FGT¡©V§ © >;*C(§7!)"- 7§ - © !U© & © Figure 22: Etree-based mesh generator running C)* .´Rµ [ªC;* *F T/C;Q @§.D§ time and throughput. )&I*' © ¤; 7) § ,U 0B)*&I*CU© & )," D ' © !"§ 'VO ' § * v§ § - Mg)*8 ,*© )"k© ¨§.¨§ L)*(*'- © !© & L) .*´ µ ´"´*¶ § O © C;*'b& & )*O ©A¤R© C* U0f)"& [) !" 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J©A *'C*C(§ © !K& C(§*© & )" §L)* (© !@ MO M& 10 1000 10000 ) C3§©A,dj©V L 30?)*&I C*F B-tree buffer size(KB) SF10 SF5 SF2 SF1 Figure 25: Octree construction time vs. B-tree buffer size (log-log scale) 100% 80% 5.5 What is the impact of local balancing? ² @§ L] © & hW¨ ] ; @§L*& )"- G)0S§ g § O M9 e m i t 60% © C;*'Z& & )Ok* I§ j[J9: 8 - lSH © ¤* Y,*© ; k§ g n i n 8 ' ) C(`=©A!K(O © ¤"F7 e© !"- §);WH b§ HlSC3¨)*0Z' ) C;' n u R ¡ 9X] © E© U§ Y&I] © &U-&¯8' ) C3`=© !<9 40% 8'A* C©A!F¢¦¨§ (OR © ¤' 'A);Wb; 7© R§ jj'A© 8 (O FG¦¨§ ¢ 9X] © g© H§ 20% © & g)K8 *'A*C I) C"FJ¦¨§v (9: )*©A G ' )*; )* § ¢ 9a.] ©A #Z©5F "F #¢ ¤£ #$C) )" )I§ UC* UWH§ 0% ' ) C;*' 8*'A C© !j© G © *8' ; E* U!"' )*8*' 8*'A C© !j© 6 9 0 2 6 8 0 2 6 8 0 2 6 8 0 2 6 8 8 1 5 2 8 1 5 2 8 1 5 2 8 1 5 2 8 5 2 1 8 5 2 1 8 5 2 1 8 5 2 1 ² 0?)& ; ZF /*' 'G§E0?)"- KC;* #GR © !* ©¢ C; @; - C© )* Memory size (MB) © I] C-© )*I© & H© g*C(§ © ,"; 8=OU8 ' © !§ L8 ' ) C(` © ! construct balance transform (O7* R )"© ! 'A) C*'h8'A* C©A!FH¦¨§ ; 9:- R05C)* ´ ; *´ ;¶d (*!" 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