spo2ida tool

8/20/2019 Spo2ida Tool

1/105

SPO2IDA

Provided courtesy of Dimitrios Vamvatsikos

Last updated January 9, 2012

This spreadsheet represents a guide for impementing !P"2#D$ as an aternative %&mu&T reationship

for use 'ith a (oninear !tatic Procedure such as the ones impemented )y *+, -*.$//0 or $!+*

*ffectivey, !P"2#D$ can repace the +1 coefficient and the ma3imum ao'a)e vaue %c for the strenfactor .ost importanty, it can do so for 4uite compe3 static pushover shapes that are not tacked )y a

such reationship, ao'ing a cose fit to difficut shapes

Implementation

!tep 15

!tep 25

!tep 65

!tep /5

Notes:

1 "ny vaues in )ue shoud )e changed

2

6

Perform static pushover anaysis and copy the )ase shear versus roof drift 7ordispacement8 resuts in ces $5+2 in 'orksheet !P"

Perform eigenvaue anaysis and insert the tota height, tota 'eight and T1 period of thestructure in ces :15:6 of 'orksheet !P"

-it the resuting static pushover curve )y suppying the four corner points re4uested inces L605.66 in 'orksheet !P" $so seect .D"-&to&!D"- transition method 7aka+08

;o to 'orksheet #D$ resuts and input vaues of !a in )ue to get the median


2/105

*# /1&0

gth reduction ny other


3/105

=eight >?0 kips +oorado .ode 6 & si3 story %+ frame

@eight ft 7suppied )y %D @anson8

T1 19 sec ma3

Pushover curve "ther *DPs5 !tory Drift %atios

)ase 7kips8 Aroof 7ft8 Broof Bma3 B1 B2 B6 B/ B>

0000 0 0 000000 0 0 0 0 0

00/1 961*&00? /9*&00? 000000 //*&00? >>*&00? >1*&00? 2*&00? >6*&00?

10201 0006> 0000126 00001> 000011 000016? 000012 00001>/ 00001622091 001? 00002>1 000062 000022/ 000022 000026 000061 00002?

61>1 002 00006 0000/ 0000669 0000/2 000069? 0000/? 0000/0

/22?1 006> 0000>09 0000/ 0000/>/ 0000>? 0000>62 000069 0000>/?

>291 00/6 00006 00000 0000>9 0000?1/ 0000? 000001 0000>

6>1 00>2 0000? 00009 0000/ 0000> 000001 000096 000026

?/6/1 001 00009> 000112 0000?99 0001002 000096 000112> 000092

>061 00?0 000102/ 000129 000091/ 00011/ 00010? 00012 00011

9>?21 00? 00011>2 0001/> 000102 000129 000120> 0001// 000126

10/12 00? 000121 00011 00011/6 0001/6/ 0001669 00011 00016?

11?102 009 0001/1 0001?? 00012> 0001>? 0001/?/ 0001??1 0001>1>

12??92 010> 0001>6 000196 00016?6 0001?22 00010 0001966 0001>6

16/2 0116 0001? 000209 0001/ 0001 0001?/6 000209> 0001?91

1/91?2 0122 0001?9 00022 000106 000201 0001?? 00022>? 0001929

1>92 0161 000192/ 0002/2 0001?1 00021>/ 0002012 0002/1 00020

1?0>>2 01/0 00020>6 0002> 000162 000229 00021/? 0002> 000220

112/2 01/ 000212 0002?/ 00019/? 0002//2 000221 0002?/2 00026//

191962 01>? 000261 000290 000202 0002> 0002/1 0002906 0002/6

20222 01 0002/69 00060? 00021?? 0002?6 0002>> 00060> 000221

216612 01?> 0002> 000626 0002292 0002?/ 0002> 000622? 0002?>9

22/002 016 00029 000669 0002/0? 0006019 000219 000669 00029?

26/92 0192 00022> 0006>> 0002>21 000616 00029>/ 0006>> 000606

2/>62 0201 00029>/ 0006?1 00026 000660? 00060 0006?12 00061?/

2>0?2 0210 000602 0006? 0002?>1 0006/>1 0006226 0006?/ 00066122?2 021 0006211 000/0/ 0002 0006>9> 00066>? 000/06> 0006/>

2??/>2 022? 00066/ 000/20 000291 0006?69 0006/92 000/19? 0006>9

21/2 026 0006/ 000/6 000609 00066 00062 000/6>9 0006?2?

2962 02/> 0006>9? 000/>2 0006211 000/02? 0006?1 000/>21 0006>

609>22 02>6 0006?2 000/ 000662> 000/1?1 00069 000/2 000/00/

620212 022 0006>/ 000// 0006// 000/61> 000/06 000/// 000/1/2

660902 02?1 000696 000>01 0006>>> 000//>9 000/1> 000>00 000/2

6/1>92 020 000/112 000>1? 0006? 000/06 000/299 000>1? 000//1

6>222 02 000/2/ 000>66 0006?> 000/?/? 000//6/ 000>629 000/>>?

629?2 029? 000/69 000>/9 00069 000/91 000/> 000>/91 000/9>

6?62 060 000//9 000>> 000/01> 000>06> 000/?06 000>>6 000/66

6/6>2 061> 000/2 000>1 000/129 000>1?9 000/6? 000>1/ 000/9?1

69>0/2 0626 000/?>> 000>9 000/2// 000>626 000/9?2 000>9? 000>11

/0>?62 0662 000// 0001/ 000/6>9 000>/? 000>10 00016 000>2/

/1/22 06/1 000>016 00060 000//?/ 000>12 000>2/1 000299 000>6

/2?112 06>0 000>1/1 000/ 000/>9 000>?> 000>6? 000/1 000>>2>

/6?02 06> 000>2? 0002 000/?0/ 000>9 000>>1 00026 000>6

///92 06? 000>699 000? 000/19 0000// 000>/> 000?> 000>01

/>912 06? 000>>2? 0009> 000/966 0001 000>??9 0009/ 000>969

/9?2 06> 000>> 000?11 000>0/ 000662 000>91/ 000?10 0000?

/0>2 0696 000>?> 000?2? 000>16 000/? 0000/ 000?2? 00021

/912>2 0/02 000>916 000?/6 000>2? 0002 00016 000?/61 0006>/

>019/2 0/11 0000/2 000?>9 000>696 000?/ 00061? 000?>96 000/96>1262 0/20 0001?1 000??> 000>>0 00090 000/>2 000??>> 00061

>26622 0/2 000299 000?92 000>22 000?0>2 000> 000?91? 000?9


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>//?02 0// 000>>? 0002/ 000>>2 000?6/ 000>> 0002/ 000?0/

>>>692 0/>> 000> 000/0 000>9? 000?// 00099 000/02 000?1/

>02 0/6 0001/ 000> 00002 000?2 000?12> 000>6 000?622

>???2 0/?2 0009/6 000?6 00019? 000???2 000?2>9 000?2> 000?/

>?/6 0/1 000?0?1 0009 000612 000?91 000?69/ 000? 000?>99

>91>6 0/90 000?2 00090> 000/2 0000 000?>2 00090/9 000??6?

0/6 0/9 000?629 000921 000>/1 00020> 000?6 000921 000??>

19>62 0>0? 000?/>? 00096? 000> 0006/9 000??9? 00096?2 00001660222 0>1 000?> 0009>6 000??1 000/96 000?962 0009>6/ 0001>2

/0912 0>2> 000??1> 0009?0 000 0006? 0000 00099> 00029

>106 0>66 000?/6 0009 000?001 000?1 000201 0009>? 000/2

2296 0>/2 000?9?2 001002 000?11 00092> 00066> 0010019 000>?

?296 0>>1 000101 00101 000?26 000909 000/? 001011 000?0>

6?2 0>0 000229 00106/ 000?6/> 0009216 0000/ 00106/2 000/6

9/62 0> 0006> 0010>0 000?/ 00096>? 000?69 0010>0/ 00091

?0/9>1 0>?? 000/? 0010? 000?>?/ 0009> 000?6 0010? 0009122

?1>121 0> 0001> 0010/ 000?6 000969 000900/ 00106 000929

?2/91/ 0>9> 000?// 001100 000??91 0009?/ 00091/2 0011002 0009/12

?6//0 006 000?6 00111 000?9 000992 00092? 00111> 0009>>

?/6??/ 012 0009001 001166 000 00100? 0009/1 0011661 0009?02

?>26>9 021 000916 0011>0 0001 0010212 0009> 0011>06 0009/?

?0191 060 00092>9 0011 00020> 001066 0009?01 0011/ 000999

??>/ 06 00096 00112 00060 0010>11 00096? 00112 001016

??/9? 0/? 0009>1 00119 000/1 0010> 00099?? 00119?9 001021

?1?26 0> 0009/> 00121/ 000>1 00100/ 001011 001216 0010/2?

?/6> 0> 0009??/ 001260 00009 00109>> 00102 001229 0010>?

?9/1/ 0?6 0009902 0012/ 000?11 001110/ 0010/21 0012/>9 001099

006?9 02 0010061 00122 0002/ 00112>2 0010>?6 00121 001029

0>?91 091 00101 0012?? 0009/? 0011/0 0010?21 0012?? 00109>/

101? 0?00 00102 001292 00090? 0011>>2 0010?1 0012922 00110?1

1/1/9 0?0 0010/1? 00160 000922/ 0011?06 001102? 00160?? 0011121??9/ 0?1? 0010>/ 00162/ 00096>/ 0011>1 001116 001626 0011602

21161 0?2 0010?/ 001669 0009/ 001200 00116/ 001669> 0011/1?

2/62 0?6> 001006 0016>> 000921 00121> 0011/9 0016>/9 0011>6

2?>9/ 0?/6 0010962 0016?0 0009?>? 001262/ 0011>2 0016?06 0011/6

602> 0?>2 00110 0016 000992 0012/6 00110 0016>? 0011?>>

6699 0?1 001119 001/01 001002> 001269 001192 001/01 0011?6

69>2 0??0 001161 001/1 00101>/ 0012?9> 001211 001/1 0011992

69/6 0?? 0011// 001/61 00102/ 00129>> 00122?1 001/609 0012109

/22 0?? 0011>?> 001// 0010/1 001611? 0012/2 001//>> 001222/

/>692 0?9 0011?0/ 001/1 0010>/ 00162?> 0012>?? 001/0 00126/>

/???0 00> 001162 001/? 0010? 0016/2 0012?2? 001/?2 0012/??

>00?2 016 001191 001/92 0010?/ 0016>?? 0012?? 001/919 00121>26?> 022 001209 001>0 0010902 0016?2? 001602? 001>0?? 0012?//

>/? 061 001221 001>26 0011019 0016? 00161?? 001>26/ 0012?

>91 0/0 00126/? 001>69 001116? 001/02 001662? 001>692 0016011

>9266 0/ 0012/? 001>>> 00112>/ 001/11 0016/? 001>>/ 00161/6

160? 0>? 00120/ 001>?0 00116 001/66> 001666 001>?06 00162?/

621> 0 0012?66 001> 0011/6 001//9 0016?? 001>> 0016/0/

/9/2 0?> 00122 00101 0011>92 001/69 001696? 00100? 0016>/

>9 06 001299 0011 0011?01 001/?? 001/0 0011> 0016?

6?/ 092 0016119 00161 001109 001/96/ 001/26/ 00161 001616

?00 0901 00162/ 001/ 001191? 001>02 001/66 001/1 00169/9

?11 0910 00166? 0012 0012021 001>22 001/>6 0011? 001/0>

?621> 091 0016>0> 001?? 001212> 001>6?6 001/96 001??> 001/22

?/9 092? 00166/ 00196 001222? 001>>1 001// 00196/ 001/6>

? 02? 0 96 0 016?6 0 01?09 0 012661 0 01>2 0 01/99 0 01?092 0 01//9>


5/105

??6 09/> 001691 001?2> 0012/6> 001>0? 001>1/9 001?2> 001/62

??/> 09>6 001/02 001?/1 0012>69 001>9>6 001>601 001?/0 001/?9

010> 092 001/1/9 001?>? 0012/6 00109 001>/>6 001?>? 001/90?

1/> 09?1 001/2?? 001??2 0012?/? 0012// 001>0> 001??2> 001>0//

210 090 001//0 001? 0012>1 00169 001>?> 001?6 001>12

691/ 09 001/>6> 00106 00129> 001>/2 001>911 001066 001>609

/9>? 099? 001/6 0011 00160 0019 0010> 0011 001>/61

>920 100 001/?92 00162 0016226 001>/ 00121 001621 001>>/?62 101> 001/921 001/> 00166 001?01 00166 001/>6 001>>/

?>// 1026 001>0/9 001>9 0016>6? 001?1? 001>11 001>> 001>?

6> 1062 001>1? 001?2 00169/ 001?6/ 001> 001?1 001>

919 10/1 001>60? 001> 0016>1 001?>02 0010> 001> 001>9?2

990 10>0 001>/6> 0019 001/009 001?/ 0019>6 00192 0010?

90?96 10> 001>>/ 001911 001/1 001?2 001?1 001911/ 0011>

910/ 10? 001>96 00192> 001/626 001?9 001?2/ 00192/ 001291

92/19 10? 001>21 00196 001// 0011> 001?69> 00196? 00169?

96260 10> 001>9> 0019>1 001/6 001612 001?>/2 0019>1 001>06

9/0/2 1096 0010?9 0019/ 001/?9> 001/?/ 001?9 0019/6 00109

9/> 1102 00120? 0019?? 001/9>2 0016 001?6? 0019??> 001?1>

9>? 1111 00166 001991 001>109 001?9 001?9/ 001990? 00121

9/?9 1120 001/> 00200/ 001>2 0019 001162 0020069 00192?

9?210 112 001>96 00201 001>/19 001912 00126 00201? 001?06/

9?902 116? 001?22 002061 001>>9 00192?9 001/6? 002061> 001?1/

9>9/ 11/ 001>1 0020/> 001>?19 0019/6 001>9 0020/>/ 001?2/

992 11>> 0019?9 0020>9 001>9 0019>9? 001?// 0020>92 001?6>2

999?9 116 001?10 0020?6 00101 0019?> 0019? 0020?61 001?/>

900?0 11?2 001?26? 0020? 0011 001991> 00190>1 0020? 001?>/

90162 111 001?6> 002101 00161 00200?/ 001920/ 0021009 001??

9020>/ 1190 001?/9/ 00211> 001/ 0020266 00196> 00211/? 001????

902?/> 119 001?26 002129 0011 0020692 0019>11 00212 001?6

906/69 120? 001??>1 0021/6 001? 0020>>1 0019> 0021/2 001?9990/129 121 001? 0021> 00191 0020?1 00191 0021>> 00109>

90/20 122> 001009 0021?0 001?0 00209 00199?2 0021?0/ 001202

90>>0 1266 00116 0021/ 001?21? 002102 002012> 0021/2 00160

901? 12/2 0012 00219 001?6> 00211> 00202?? 00219 001/1?

906 12>1 00169> 002212 001?>16 00216/1 0020/2 0022119 001>2/

90?>/2 120 001>2/ 00222 001? 0021/9 0020> 00222> 00166

9021 12 001>2 0022/0 001?0 0021>> 0020?62 002269 001?/1

909? 12?? 001?1 0022>6 001?9> 002112 0020/ 0022>6/ 001/

909>?/ 12 00191 0022? 00110/ 002199 002106 0022?6 0019>

9102>0 129> 001906 00221 0012>1 002212 00211 002211 00190>

910919 1606 00191? 00229> 00169 002221 002166 00229/9 00191?/

911>/ 1612 001929 002609 001>/ 0022/66 0021/ 00260? 001929120/ 1619 001969 002619 001> 0022>>1 002101 002619/ 00196?>


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B

0

61*&00?

??*&00>00001>9

00002/

0000621

0000/02

0000/6

0000>/

0000/>

0000?2?

00000

00009

00009?

00010>1

0001162

0001216

000129>

00016?

0001/>?

0001>6

000119

0001? Segment Vb (kips) δroof (ft) ESDOF Parameters

0001?1 7Point C *nd of 000 000 Ay 0?0 ft

00016 *astic !"#"" "#$" fy /000 kips

00019// @ardening %&2#"" '" Ec 1000202> !oftening %&"" '& ah 1000F

000210 %es Pateau "#"" '& ac &66F

00021? Gero !trength 0 161 rp 000F

00022 mf 1?

00026/9 Vma3 9120/6 kips !ay 01906 g

0002/6 init point 19 T 19 sec

0002>12 Hinit 1221?1? kipsft

0002>96 He4 1200 kipsft !ay Derivation "ptions 7.D"- to

0002?/ Hdiff 2 1 !ay I -y=tot 7simpest )ut may

0002?>> !ay 01/> g

00026

000291? 2 ser suppied +0 7from code or ei

000299 !ay I dy K /M2 7+0KT1M2 Kg8

00060 +0 7+0NI1, e

000611 !ay 01906 g

00062/2

0006626 6 %esuts from eastic response spe

0006/0/ se either code spectra or avera

0006/> !ay option 2 !a used5 "#2" g

0006> Aroof "# ft

0006/ !ay 01/? g

0006?29

00061000691 Pro)em5 Oou can either infate dy

00069?2 !ti, in my #D$ vie', they do not n

0 0.2 0.4 0.6 0.8 1 1.2 1.4

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

900.00

1000.00

push

over

ft

Roof displacement (ft)

B a s e

s h

e a r

( k i p s )

Select MDOF to SDOF Scali!

Sa" # F" $ % &si'plest(

)se *0 &+ro' co,e or ei!evalue aal

-esults +ro' respose spectru' aal


7/105

000/16/ methods in genera

000/21

000/29?

000/6?

000//>9

000/>/

000/21

000/?02000/?/

000/>

000/9/

000>02?

000>10

000>19

000>2?

000>6>1

000>/61

000>>0

000>>9

000>?

000>?/

000>26

000>90

000>996

0000?

0001

00026>

00061

00066

000//

000>0/000>2

0001

000?1

000?2>

000??

0006?

0009

00091

000?02

000?02

000?1/?

000?212000?2?

000?6/6

000?/0

000?/?2

000?>6

000?0

000??

000???

000?>6

000?96

00001?

00009

0001?9

0 002>


8/105

00066

000/1?

000/9?

000>??

000>

000?66

0000

000?>00096?

000999

000901

0009126

00091

00092/?

0009609

00096?1

0009/66

0009/9>

0009>>

00092

00092

0009?/2

000906

0009/

000992>

00099

00100/

001010?

00101?

001022

00102900106/9

0010/1

0010/?2

0010>6

00100/

00109

0010?6>

001001

0010?

0010962

0011001

00110?00111/1


9/105

+heck

"k"k

"k

"k

"k

"k

!D"- connection8

ecome inaccurate8

genvaue anaysis8

ua to 1 for !D"-8

ctrum anaysis

e severa timehistories, scaed to same !a7T18

7average from severa records or singe resut from code spectrum8

or !ay # am not sure 'hich one is )est

ecessariy have to correspond to each other


10/105


11/105


12/105

*oof +ispla,ement gi-en Sa res.lts

!a A1F A>0F A/F mean A mean +% )eta A

1 "#"' 011 011 011 011 100 000

2 "#"/ 022 022 022 022 100 000

6 "#"% 066 066 066 066 100 000/ "#&2 0// 0// 0// 0// 100 000

> "#& 0>> 0>> 0>> 0>> 100 000

"#& 0 0 0 0 100 000

? "#2& 0?/ 0? 0?9 0? 099 006

"#2! 01 0 092 0 09? 00?

9 "#2$ 0? 09> 10 09> 09 010

10 "#2 09 09 111 099 09 011

11 "#' 111 161 *rr5>02 166 09/ 01 caution

0.00 0.50 1.00 1.50 2.00 2.50 3.00

0.00

0.10

0.20

0.30

0.40

0.50

0.60

16 /Sa

50 /Sa

roof displacement (ft)

S a ( T 1 )

( g )


13/105

0a1 ID* gi-en Sa res.lts

!a Bma31F Bma3>0F Bma3/F mean B )eta B

"#"' 00020 00020 00020 00020 000

"#"/ 000/1 000/1 000/1 000/1 000

"#"% 0001 0001 0001 0001 000"#&2 0002 0002 0002 0002 000

"#& 00102 00102 00102 00102 000

"#& 00122 00122 00122 00122 000

"#2& 0016? 001/0 001/> 001/0 006

"#2! 001/ 001>? 001?0 001>? 00?

"#2$ 0010 001?/ 00196 001?/ 009

"#2 0016 001?9 00200 001?9 010

"#' 00199 00261 Q($ 00261 01> caution

0.0000 0.0100 0.0200 0.0300 0.0400 0.0500

0.00

0.10

0.20

0.30

0.40

0.50

0.60

16 'aSa

50 'aSa

maximum interstory drift ratio


14/105

#D$ 1 #D$ 1 & Bma3 #D

!a A ind3 B7o'8 B7high8 A7o'8 A7high8 Bma31 !a

"#"" "#"" 1 00000 00000 000 000 "#"""" "#""

"#&% "#$" 2 00129 00161 0?0 0?1 "#"&2% "#&%

"#2& "#$! ? 0016? 00169 0?/ 0?> "#"&'$ "#2"

"#2' "#$% 92 001/> 001/ 0?9 00 "#"&! "#22

"#2 "#' 9 001>1 001>2 02 06 "#"&2 "#2'

"#2$ "#$ 101 001>9 0010 0? 0? "#"&/" "#2!"#2% "#%2 10 001 001 091 092 "#"&/$ "#2/

"#'& "#%/ 111 001?/ 001? 09> 09 "#"&$ "#2$

"#'' "" 11 0012 0016 100 101 "#"&' "#2%

"#' "! 121 001 00190 10/ 10> "#"&% "#'"

"#'$ "% 12 0019> 0019 10 109 "#"&%/ "#'&

"#'% &' 161 00202 00206 116 11/ "#"2"2 "#''

"#!& &$ 16 00209 00210 11? 11 "#"2"% "#'!

"#!' & 1/0 0021/ 0021 121 122 "#"2& "#'

"#! / 1/> 00221 00226 12> 12 "#"222 "#'$

"#!$ '" 1>0 0022 00229 129 160 "#"22% "#'

"#!$ '" 1>0 0022 00229 129 160 "#"22% "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

" ! & '& 1>1 0 0229 0 0261 1 60 1 61 " "2'& " '


15/105

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! '& 1>1 00229 00261 160 161 "#"2'& "#'

"#! 2#$& "#"!/& "#'


16/105

>0 #D$ >0 & Bma3 #D$/

A ind3 B7o'8 B7high8 A7o'8 A7high8 Bma3>0 !a A

"#"" 1 00000 00000 00000 00000 "#"""" "#"" "#""

"#$" 2 00129 00161 099 0?0/ "#"&2% "#&% "#$"

"#$! 0016> 0016? 0?6/ 0?/6/ "#"&'$ "#2" "#$!

"#$ 91 001/6 001/> 0??/ 0??1 "#"&!! "#2& "#$

"#' 9 001>1 001>2 0221 0609 "#"&2 "#22 "#2

"#$ 101 001>9 0010 0>9 0?/ "#"&% "#2' "#$"#%& 10 001 001 0909 091/ "#"&/$ "#2! "#%&

"#%/ 111 001?/ 001? 09>6/ 0921 "#"&$! "#2 "#%

"" 11 0012 0016 099?1 100>9 "#"&2 "#2 "#%%

"! 120 001? 001 10621 10/09 "#"& "#2/ "!

" 12> 0019/ 0019> 10?>9 10/ "#"&% "#2$ "

&' 160 00200 00202 1119 112/ "#"2"& "#2 &2

&$ 16> 0020? 00209 116/ 11?21 "#"2" "#2% &$

& 1/0 0021/ 0021 120?1 121>9 "#"2& "#'" &

/ 1/> 00221 00226 12>09 12>9 "#"222 "#'& /

'" 1>0 0022 00229 129/ 1606/ "#"22% "#'2 '"

'" 1>0 0022 00229 129/ 1606/ "#"22% "#'2 '"

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

& '& 1>1 0 0229 0 0261 1 606/ 1 6121 " "2'& " '2 & '&


17/105

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

'& 1>1 00229 00261 1606/ 16121 "#"2'& "#'2 '&

2#$& "#"!/& "#'2 2#$&


18/105

#D$ / & Bma3

ind3 B7o'8 B7high8 A7o'8 A7high8 Bma3/

1 00000 00000 00000 00000 "#""""2 00129 00161 099 0?0/ "#"&2% 0016> 0016? 0?6/ 0?/6/ "#"&'$91 001/6 001/> 0??/ 0??1 "#"&!!9 001>1 001>2 0221 0609 "#"&2

100 001>? 001>9 0>?1 0>9 "#"&%10> 001> 001 09009 0909 "#"&/$110 001?6 001?/ 09// 09>6/ "#"&$!11> 0010 0012 09/ 099?1 "#"&2120 001? 001 10621 10/09 "#"&12> 0019/ 0019> 10?>9 10/ "#"&%160 00200 00202 1119 112/ "#"2"&16> 0020? 00209 116/ 11?21 "#"2"1/0 0021/ 0021 120?1 121>9 "#"2&1/> 00221 00226 12>09 12>9 "#"2221>0 0022 00229 129/ 1606/ "#"22%1>0 0022 00229 129/ 1606/ "#"22%1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&

1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&

1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 0 0229 0 0261 1 606/ 1 6121 " "2'&


19/105

1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&

1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&

1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&1>1 00229 00261 1606/ 16121 "#"2'&

"#"!/&


20/105

!P"2#D$5 $ periodsVaid for firm soi, >F damping and a periods

!P" data

!ayiedRyied

Stati, PO

Segment E C end

000 000

*astic 100 100

@ardening 109 1

!oftening 10 1?

%es Pateau 000 1?

+oapse 0 1?

F in !$ terms 1F >0F /F

apa,it3 4 $ $ $

* 2#" 2#"& /%

ontrols

@ardening E /@ardening sope &"#""!oftening sope 5 S pro)ems e3ist for very o'

%esidua pateau " S for rI09>0?, TI/sec, acI

-racturing E %

Period T 7sec8 %"Damping 5.0%Pinch 'eight 100%

Interme+iate res.lts 4 gi-en * res.lts 7pease provide the %&vaue in

% E1F E>0F E/F mean E

%peak 10>?1/ 1 "#&/ 01 01 01 01

mend 1/9 2 "#'2 062 062 062 062

mpeak 11> 6 "#!$ 0/? 0/? 0/? 0/?

me4 29 / "#/' 06 06 06 06

mr 1/9 > "#$% 0?9 0?9 0?9 0?9

mr 7'ith mf8 1? "#% 09> 09> 09> 09>

mc 7'ith mf8 1 ? &" 10 109 116 109re4 000 / 11> 122 162 126

( 20 -i3ed 9 !2 12> 16 1>2 16

p 1 10 !$ 12 1/0 1>9 1/1

m 1 11 2#"& 1>9 1? *rr5>02 190

r 0

1F >0F /F

%mc 2/??? 199 1?>

!$!$yied C end

000 0>0 100 1>0 20000

0>0

100

1>0

200

2>0

600

!tatic P" #D$&>0F capa

+.

* 7

S A 8 S A 3


21/105

smc 0?9 0969 119>6


22/105

c and high % 7say &2F and 99F8 !uch points 'ere never reay fitted :ut &2F and 90F are fine

009 the fit is rather )ad #n genera there seems to )e a ot of sensitivity for the o' ac vs high ac There is itte

)ue8 * gi-en 4 res.lts 7pease provide the E&vaue in )ue8

mean +% )eta E E %1F %>0F %/F mean % mean +E )eta %

100 000 "#2" 020 020 020 020 100 000

100 000 "#!" 0/0 0/0 0/0 0/0 100 000

100 000 "#" 00 00 00 00 100 000

100 000 " 11 126 16/ 12/ 09? 00?

100 000 /" 1/ 1?0 206 1?2 09> 01

100 000 2#"" *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

099 006 '#"" *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>0209? 00? !#"" *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

09 010 #"" *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

09 011 /#"" *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

09/ 01 caution $ *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 600 6>0 /00 />0

ity #D$&1F #D$&/F

,tilit36 4000 0>0 100 1>0 200

000

002

00/

00

00

010

012

01/

01

01

020

)eta

+.,tili

b e t a9

*


23/105


24/105

e3panation for that .ust do something ese

2>0 600 6>0 /00 />0

U%

t36 4


25/105


26/105

&/ IDA

Segment % E 3i 2021/0

000 000 000 000

*astic 100 100 100 100

111 10 111 10

121 112 121 112

162 119 162 119

1/2 12> 1/2 12>

1>6 161 1>6 161

16 16? 16 16? FO* * !pine fit

1?/ 1/6 1?/ 1/6 (I 6/

1/ 1/9 1/ 1/9 *P 2nd avg

@ardening 19> 1>> 19> 1>>

20 11 20 11

21 1? 21 1?

22? 1?/ 22? 1?/ T$ $(D %*."V*D 1 D" T@#! T" $LL +$!*!

26? 10 26? 10 0?966

2/ 1 2/ 1 0?966

2/ 1 2/ 1 26/ 0>06

!oftening 2>0 1? 2>0 1? 22 09/6

2>0 1? 2>0 1? 296 10?/?

2>0 1? 2>0 1? 62 111

2>0 1? 2>0 1? 61 12/9

2>0 1? 2>0 1? 699 16/?

2>0 1? 2>0 1? //0 1/0

2>0 1? 2>0 1? /2 1>?6>

2>0 1? 2>0 1? >2? 12>

2>0 1? 2>0 1? >?/ 1?/0

2>0 1? 2>0 1? 26 1299

2>0 1? 2>0 1? ?/ 1906

2>0 1? 2>0 1? ?2? 1961

2>0 1? 2>0 1? ?0 20>//

2>0 1? 2>0 1? 6> 21221

2>0 1? 2>0 1? 90 212

2>0 1? 2>0 1? 9/ 22/?

2>0 1? 2>0 1? 1001 2606?

2>0 1? 2>0 1? 10> 26>?2

2>0 1? 2>0 1? 1110 2/0?0

2>0 1? 2>0 1? 116 2/>66

2>0 1? 2>0 1? 121/ 2/91

2>0 1? 2>0 1? 122 2>6>6

2>0 1? 2>0 1? 160 2>?09

2>0 1? 2>0 1? -or interpoation 16>0 2060

2>0 1? 2>0 1? 169 261>

2>0 1? 2>0 1? i1 1 1/2/ 2>/

2>0 1? 2>0 1? i2 2 1/>> 2??

2>0 1? 2>0 1? % mu 1/1 29>

2>0 1? 2>0 1? 26/ 1? 1>06 2?09

2>0 1? 2>0 1? 22 19/ 1>19 2?20>


27/105

2>0 1? 2>0 1? 1>60 2?2?

2>0 1? 2>0 1? 1>6> 2?612

2>0 1? 2>0 1? 1>6> 2?612

2>0 1? 2>0 1?

2>0 1? *rr5>02 *rr5>02 %mr 2>0 %evised e

2>0 1? *rr5>02 *rr5>02 smend 0> *rr5>02

2>0 1? *rr5>02 *rr5>02 intmend 21? *rr5>02

2>0 1? *rr5>02 *rr5>02 %mi *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 mmi *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 ne'U%mi *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 ne'Ummi *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 FO* * !pine fit

2>0 1? *rr5>02 *rr5>02 (I 6/

2>0 1? *rr5>02 *rr5>02 *P 2nd avg

2>0 1? *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? Q($ *rr5>02 S&& interpoate *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 S&& this is 'here the spine stops *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 SS # @$V* +@$(;*D T@#! *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 SS +".P$%* $(D -# *rr5>02 *rr5>02

2>0 1? *rr5>02 *rr5>02 SS $L!" .$TL$: V*%!#"( *rr5>02 *rr5>02

2>0 1? *rr5>02 1? SS :*+$!* *rr5>02 *rr5>02

+oapse 2>0 6? *rr5>02 6? -or interpoation *rr5>02 *rr5>02

*rr5>02 *rr5>02

i1 Q($ *rr5>02 *rr5>02

i2 Q($ *rr5>02 *rr5>02

% mu *rr5>02 *rr5>02


28/105

Q($ Q($ *rr5>02 *rr5>02

Q($ Q($ *rr5>02 *rr5>02

*rr5>02 *rr5>02

cap% capmu *rr5>02 *rr5>02

Q($ *rr5>02 *rr5>02 *rr5>02


29/105


30/105

+ontro Poygon

% E&091>? &0?662

2?6120? 2021/0

2?6120? 66?969

#n each iteration, the ne' num)er of points is (W I 2K(1&k I 2K7(&18, 'here k

1 10

1st avg dou)e 2nd avg 1st avg dou)e 2nd avg 1st avg dou)e 2nd avg 1st avg

&000/ &000/

0/>16 0/>16 0/>16 &000/ &000/

0?96 0?96 0?96 0/>16 0/>16 0/>16 0/>16 090?6

0?966 0?966 0?96 0?96 0?96 0?96 090?6 1666 1666 1196

0?966 0?966 0?966 090?6 116>6 116>6 1666 1666 20/?2 22?>2

090?6 10216 10216 116>6 116>6 1>6/6 1?0>6 20/?2 2>062 2?612

10216 10216 126>0 166/ 1>6/6 1?6 20/?2 20/?2 2?612 2?612

1122 126>0 1/6/> 1>6/6 1>6/6 2112 22?>2 2>062 2?612 2?612

126>0 126>0 119 1?0>6 1?6 2692 2>062 2>062

166/ 1/6/> 1?90 1?6 1?6 2>02 21?2 2?612

1/6/> 1/6/> 19/?> 201? 2112 2?/2 2?612 2?612

1>2?2 119 20900 2112 2112 2?612 2?612 2?612

119 119 2212 22?>2 2692 2?612 2?612 2?612

1?0>6 1?90 26622 2692 2692

1?90 1?90 2/620 2/?/? 2>02

191 19/?> 2>1?> 2>02 2>02

19/?> 19/?> 2>? 21?2 2?/2

201? 20900 2/>? 2?/2 2?/2

20900 20900 2> 2?02? 2?612

21>/1 2212 2?1?0 2?612 2?612

2212 2212 2?612 2?612 2?612

22?>2 26622 2?612 2?612 2?612

26622 26622

2621 2/620

2/620 2/620

2/?/? 2>1?>

2>1?> 2>1?>

2>>61 2>?

2>? 2>?

21?2 2/>?

2/>? 2/>?

2?1 2>

2> 2>

2?02? 2?1?0

2?1?0 2?1?0

2?2/1 2?612


31/105

2?612 2?612

2?612 2?612

2?612 2?612

timates to avoid 'eird intersections 'hen rp is arge

+ontro Poygon

% E*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

1 10


*rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02










*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02


32/105

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02


33/105


34/105

6 and ( is the num)er of points in the previous iteration

FO* m. !pine fit

/ 6 (I 6/

dou)e 2nd avg 1st avg dou)e org points *P 2nd avg 1st avg dou)e

&091 &091 &091

&000/ &091 &091 &091 &091

&000/ &000/ 090?6 2?612 2?612

1196 1196 2?612 2?612 2?612

1196 2?612 2?612 2?612 0>61691 0>61691 0>61691

2?612 2?612 2?612 2?612 0>61691 0>61691 0>61691

2?612 1? 0>?>21> 019069 0?0?

2?612 19/ 026 0?0? 0?0?

2?612 212 0?/909 0?91>09 0?662

260 066921 0?662 0?662

2>0 091?66 09>62 10/062>

2?2 099962? 10/062> 10/062>

29/ 10?991 1119/9 119?

619 11>901 119? 119?

6// 12669 12?>012 16>16>?

6?2 16161> 16>16>? 16>16>?

/01 1611? 1/2/?? 1/969

/61 1/16? 1/969 1/969

// 1>66?/6 1>909 169?/

/9 10//6? 169?/ 169?/

>66 1?6?1 1?0?>6 1??>>21

>?1 1?/1>? 1??>>21 1??>>21

10 100/2 1/0>6 190>0

>1 1?60> 190>0 190>0

9/ 196?1/ 19?26 20600/

?6 199961 20600/ 20600/

?/ 20>9?6> 209/61 21/22

62 211912? 21/22 21/22

2 21??10> 220>6 2219>6

966 2266?1 2219>6 2219>6

9 2226 261>96 269/66

10/1 26/2>6 269/66 269/66

109? 269/9 2/206/ 2/?122

11>/ 2//>0> 2/?122 2/?122

1216 2/9>60 2>196> 2>?/69

12?2 2>/669> 2>?/69 2>?/69

1666 2>900? 212?02 2>?9>


35/105

169> 26>666 2>?9> 2>?9>

1/>? 2?916 2?00/02 2?/269

1>20 2?2121 2?/269 2?/269

FO* m. !pine fit

/ 6 (I 6/


*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02


36/105

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02


37/105


38/105

1 10 /

2nd avg 1st avg dou)e 2nd avg 1st avg dou)e 2nd avg 1st avg dou)e 2nd avg

&0?662

&0021// &0021// &0021// &0?662

02//? 02//? 02//? &0021// &0021// &0021// &0021//

0//6?/6 0//6?/6 0//6?/6 02//? 02//? 02//? 02//? 019069 1620226 1620226

0//6?/6 0//6?/6 0//6?/6 0//6?/6 019069 09961 09961 1620226 1620226 26090/

0>61691 019069 0?9/66> 0?9/66> 09961 09961 1>0696 1/0>6 26090/ 60699

0?0? 0?9/66> 0?9/66> 1122621 12?>012 1>0696 2100?6/ 26090/ 26090/

0?662 09>62 1122621 1/2??06 1>0696 1>0696 2>60>6 2?00/02 60699

10/062> 1122621 1122621 1?10/? 1/0>6 2100?6/ 2?01>1 60699 60699

119? 12?>012 1/2??06 19?0/9 2100?6/ 2100?6/

16>16>? 1/2??06 1/2??06 22021/ 261>96 2>60>6

1/969 1>909 1?10/? 2/261?6 2>60>6 2>60>6

169?/ 1?10/? 1?10/? 21>>2 2?00/02 2?01>1

1??>>21 1/0>6 19?0/9 2?>2? 2?01>1 2?01>1

190>0 19?0/9 19?0/9

20600/ 209/61 22021/

21/22 22021/ 22021/

2219>6 261>96 2/261?6

269/66 2/261?6 2/261?6

2/?122 2>196> 21>>2

2>?/69 21>>2 21>>2

2>?9> 2?00/02 2?>2?

2?/269 2?>2? 2?>2?


39/105

1 10 /


*rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02




*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02



*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02


40/105


41/105


42/105

6

1st avg dou)e org points

&0?662 &0?662

&0?662 &0?662 &0?662

019069 2021/0 2021/0

2021/0 2021/0 66?969

2?00/02 66?969

66?969 66?969


43/105

6


*rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02


44/105


45/105


46/105

" IDA

Segment % E 3i 21//066

000 000 000 000

*astic 100 100 100 100

10? 10 10? 10

11/ 112 11/ 112

121 11 121 11

12 12/ 12 12/

16 160 16 160

1/6 16 1/6 16 FO* * !pine fit

1>0 1/6 1>0 1/6 (I 6/

1>? 1/9 1>? 1/9 *P 2nd avg

@ardening 1/ 1>> 1/ 1>>

1?1 11 1?1 11

1? 1? 1? 1?

1> 1?6 1> 1?6

196 10 196 10 0>90092

200 1 200 1 0>90092

200 1 200 1 190 0/012

!oftening 201 1? 201 1? 210 0?/22>2

201 1? 201 1? 262 0/0>22

201 1? 201 1? 2>> 096>26

201 1? 201 1? 2?9 102?>>6

201 1? 201 1? 60> 111616

201 1? 201 1? 666 1201906

201 1? 201 1? 61 12/62/

201 1? 201 1? 691 166>?/

201 1? 201 1? /22 1/69>/

201 1? 201 1? />/ 1>12>/

201 1? 201 1? /? 1>260/

201 1? 201 1? >20 1/?>

201 1? 201 1? >>/ 1?122?>

201 1? 201 1? >9 1??2>0>

201 1? 201 1? 26 129>>

201 1? 201 1? > 16/>>

201 1? 201 1? 92 196/1?>

201 1? 201 1? ?2 191?2>

201 1? 201 1? ?> 20210

201 1? 201 1? ?90 20?61

201 1? 201 1? 21 210>6>

201 1? 201 1? >0 21/022

201 1? 201 1? ? 21?192

201 1? 201 1? -or interpoation 906 2200/>

201 1? 201 1? 92 222>1

201 1? 201 1? i1 1 9/? 22/00

201 1? 201 1? i2 2 9> 22?02

201 1? 201 1? % mu 90 222?

201 1? 201 1? 190 1?? 996 229>>>

201 1? 201 1? 210 19> 1002 260>0


47/105

201 1? 201 1? 1009 2611/0

201 1? 201 1? 1012 261/>?

201 1? 201 1? 1012 261/>?

201 1? 201 1?

201 1? *rr5>02 *rr5>02 %mr 201 %evised e

201 1? *rr5>02 *rr5>02 smend 0? *rr5>02

201 1? *rr5>02 *rr5>02 intmend 209 *rr5>02

201 1? *rr5>02 *rr5>02 %mi *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 mmi *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 ne'U%mi *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 ne'Ummi *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 FO* * !pine fit

201 1? *rr5>02 *rr5>02 (I 6/

201 1? *rr5>02 *rr5>02 *P 2nd avg

201 1? *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? Q($ *rr5>02 S&& interpoate *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 S&& this is 'here the spine stops *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

201 1? *rr5>02 1? *rr5>02 *rr5>02

+oapse 201 6? *rr5>02 6? -or interpoation *rr5>02 *rr5>02

*rr5>02 *rr5>02

i1 Q($ *rr5>02 *rr5>02

i2 Q($ *rr5>02 *rr5>02

% mu *rr5>02 *rr5>02


48/105

Q($ Q($ *rr5>02 *rr5>02

Q($ Q($ *rr5>02 *rr5>02

*rr5>02 *rr5>02


Q($ *rr5>02 *rr5>02 *rr5>02


49/105


50/105

+ontro Poygon

% E&0961>12 &090>9>>

261/>? 21//066

261/>? 62>??1

#n each iteration, the ne' num)er of points is (W I 2K(1&k I 2K7(&18

1 10


&011999 &011999

02>??1 02>??1 02>??1 &011999 &011999

0/>2 0/>2 0/>2 02>??1 02>??1 02>??1 02>??1 091>62

0>90092 0>90092 0/>2 0/>2 0/>2 0/>2 091>62 109?296 109?296 1>060>/

0>90092 0>90092 0>90092 091>62 09//16 09//16 109?296 109?296 1?0>96> 1901>

091>62 0?929?2 0?929?2 09//16 09//16 12/9/>/ 1/011/ 1?0>96> 21119 261/>?

0?929?2 0?929?2 0961?6 10?1966 12/9/>/ 1>>6??/ 1?0>96> 1?0>96> 261/>? 261/>?

00?6 0961?6 11096 12/9/>/ 12/9/>/ 10?6?> 1901> 21119 261/>? 261/>?

0961?6 0961?6 162>>6/ 1/011/ 1>>6??/ 20102> 21119 21119

10?1966 11096 1/??9/ 1>>6??/ 1>>6??/ 212/1 221616 261/>?

11096 11096 11?1?/ 10>?> 10?6?> 226> 261/>? 261/>?

12/611/ 162>>6/ 1?/69?> 10?6?> 10?6?> 261/>? 261/>? 261/>?

162>>6/ 162>>6/ 1>09> 1901> 20102> 261/>? 261/>? 261/>?

1/011/ 1/??9/ 19>9>6> 20102> 20102>

1/??9/ 1/??9/ 20/29 2066 212/1

1>/?/6/ 11?1?/ 212/6? 212/1 212/1

11?1?/ 11?1?/ 21??? 221616 226>

10>?> 1?/69?> 226/9 226> 226>

1?/69?> 1?/69?> 22?>6 22921 261/>?

10106> 1>09> 26019 261/>? 261/>?

1>09> 1>09> 261/>? 261/>? 261/>?

1901> 19>9>6> 261/>? 261/>? 261/>?

19>9>6> 19>9>6>

200691> 20/29

20/29 20/29

2066 212/6?

212/6? 212/6?

21>0? 21???

21??? 21???

221616 226/9

226/9 226/9

22>?>1 22?>6

22?>6 22?>6

22921 26019

26019 26019

26026 261/>?


51/105

261/>? 261/>?

261/>? 261/>?

261/>? 261/>?


+ontro Poygon

% E*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

1 10


*rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02












*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02 *rr5>02 *rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02


52/105

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02


53/105


54/105

FO* m. !pine fit

/ 6 (I 6/


&0961>12 &0961>12 &0961>12

&011999 &0961>12 &0961>12 &0961>12 &0961>12

&011999 &011999 091>62 261/>? 261/>?

1>060>/ 1>060>/ 261/>? 261/>? 261/>?

1>060>/ 261/>? 261/>? 261/>? 0>26?2? 0>26?2? 0>26?2?

261/>? 261/>? 261/>? 261/>? 0>26?2? 0>26?2? 0>26?2?

261/>? 1?? 0>?166 019069 0?1/6>1

261/>? 19> 09> 0?1/6>1 0?1/6>1

261/>? 21/ 0?011 00> 09?/0

26/ 0>1// 09?/0 09?/0

2> 09/121 09>1>6 10?29

20 102902> 10?29 10?29

60> 111/? 11>>9 12/02

662 11969 12/02 12/02

60 120909 162099? 1/011?>

690 1610 1/011?> 1/011?>

/22 1/696?1 1/??> 1>>692

/>> 1>1>?> 1>>692 1>>692

/91 1>902? 12>?2 19912

>2? 12?? 19912 19912

> 1?66>9> 1?00 166/

0 102/21 166/ 166/

/ 196> 1901?? 1992

92 196/69 1992 1992

?6? 199?>/9 2021? 209/6?

?/ 20>0 209/6? 209/6?

62 2111?> 21/916 220/6

1 21?>> 220/6 220/6

961 226126/ 22>0?9 2611??1

92 22/92> 2611??1 2611??1

106> 266?2> 261?9 2/11>

10 2662 2/11> 2/11>

11/1 2/6// 2/>??11 2>066>

119> 2/0??6 2>066> 2>066>

12/9 2>2>00> 2>/1?> 2>>1>

1606 2>?6/> 2>>1> 2>>1>

16>? 20??9/ 22?0?2 2>29


55/105

1/10 2/6>1 2>29 2>29

1/6 2601> 2?00/02 2?6>1?>

1>1> 2?1?? 2?6>1?> 2?6>1?>

FO* m. !pine fit

/ 6 (I 6/


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56/105

*rr5>02 *rr5>02 *rr5>02 *rr5>02

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57/105


58/105

1 10 /


&090>9>>

&01/6/> &01/6/> &01/6/> &090>9>>

026??91 026??91 026??91 &01/6/> &01/6/> &01/6/> &01/6/>

0/2/1> 0/2/1> 0/2/1> 026??91 026??91 026??91 026??91 019069 161>6 161>6

0/2/1> 0/2/1> 0/2/1> 0/2/1> 019069 10002 10002 161>6 161>6 2/2221

0>26?2? 019069 0096 0096 10002 10002 1/1?0? 1901?? 2/2221 29?>

0?1/6>1 0096 0096 110/2 162099? 1/1?0? 2120/? 2/2221 2/2221

09?/0 09>1>6 110/2 1/16>2 1/1?0? 1/1?0? 2>161 2?00/02 29?>

10?29 110/2 110/2 1??1?92 1901?? 2120/? 269/9/ 29?> 29?>

12/02 162099? 1/16>2 206192 2120/? 2120/?

1/011?> 1/16>2 1/16>2 2216 261?9 2>161

1>>692 12>?2 1??1?92 2/1/9/ 2>161 2>161

19912 1??1?92 1??1?92 260> 2?00/02 269/9/

166/ 1901?? 206192 2?99/ 269/9/ 269/9/

1992 206192 206192

209/6? 21/916 2216

220/6 2216 2216

2611??1 261?9 2/1/9/

2/11> 2/1/9/ 2/1/9/

2>066> 2>/1?> 260>

2>>1> 260> 260>

2>29 2?00/02 2?99/

2?6>1?> 2?99/ 2?99/


59/105

1 10 /


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60/105


61/105


62/105

6


&090>9>> &090>9>>

&090>9>> &090>9>> &090>9>>

019069 21//066 21//066

21//066 21//066 62>??1

2?00/02 62>??1

62>??1 62>??1


63/105

6


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64/105


65/105


66/105

! IDA

Segment % E 3i 221?0?

000 000 000 000

*astic 100 100 100 100

10> 10 10> 10

110 112 110 112

11> 11 11> 11

119 12/ 119 12/

12/ 160 12/ 160

129 16 129 16 FO* * !pine fit

16/ 1/2 16/ 1/2 (I 6/

169 1/ 169 1/ *P 2nd avg

@ardening 1// 1>/ 1// 1>/

1/ 10 1/ 10

1>6 1? 1>6 1?

1> 1?6 1> 1?6

16 1?9 16 1?9 0/6/629

1 1 1 1 0/6/629

1 1 1 1 11 0/?10?

!oftening 19 1? 19 1? 1?> 0>>9/

19 1? 19 1? 190 0/01

19 1? 19 1? 20> 0?19//

19 1? 19 1? 221 0?9/?

19 1? 19 1? 26 0???9

19 1? 19 1? 2> 0962

19 1? 19 1? 2?/ 1001?

19 1? 19 1? 292 10?1//

19 1? 19 1? 611 116/11

19 1? 19 1? 660 119/1?2

19 1? 19 1? 6>0 12>11?

19 1? 19 1? 69 160/>2

19 1? 19 1? 69 16>?/

19 1? 19 1? /09 1/02

19 1? 19 1? /29 1/>>2?

19 1? 19 1? // 1/99?

19 1? 19 1? /? 1>/1/>>

19 1? 19 1? / 1>022

19 1? 19 1? >0/ 11?1?

19 1? 19 1? >21 1>1126

19 1? 19 1? >6 12/>

19 1? 19 1? >>/ 1?111?9

19 1? 19 1? > 1?6?29

19 1? 19 1? -or interpoation >2 1?0?91

19 1? 19 1? >9/ 1?1

19 1? 19 1? i1 1 0> 1?999>

19 1? 19 1? i2 2 1/ 11>2>

19 1? 19 1? % mu 26 12

19 1? 19 1? 11 1?? 29 16912>

19 1? 19 1? 1?> 19> 6/ 1/9>


67/105

19 1? 19 1? 6? 1>211

19 1? 19 1? 69 1>/?92

19 1? 19 1? 69 1>/?92

19 1? 19 1?

19 1? *rr5>02 *rr5>02 %mr 19 %evised e

19 1? *rr5>02 *rr5>02 smend 162 *rr5>02

19 1? *rr5>02 *rr5>02 intmend 201 *rr5>02

19 1? *rr5>02 *rr5>02 %mi *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 mmi *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 ne'U%mi *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 ne'Ummi *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 FO* * !pine fit

19 1? *rr5>02 *rr5>02 (I 6/

19 1? *rr5>02 *rr5>02 *P 2nd avg

19 1? *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? Q($ *rr5>02 S&& interpoate *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 S&& this is 'here the spine stops *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 *rr5>02 *rr5>02 *rr5>02

19 1? *rr5>02 1? *rr5>02 *rr5>02

+oapse 19 6? *rr5>02 6? -or interpoation *rr5>02 *rr5>02

*rr5>02 *rr5>02

i1 Q($ *rr5>02 *rr5>02

i2 Q($ *rr5>02 *rr5>02

% mu *rr5>02 *rr5>02


68/105

Q($ Q($ *rr5>02 *rr5>02

Q($ Q($ *rr5>02 *rr5>02

*rr5>02 *rr5>02


Q($ *rr5>02 *rr5>02 *rr5>02


69/105


70/105

+ontro Poygon

% E&01902 &09?991

1>/?92 221?0?

1>/?92 616?6/

#n each iteration, the ne' num)er of points is (W I 2K(1&k I 2K7(&18

1 10


&01>0>? &01>0>?

016>9 016>9 016>9 &01>0>? &01>0>?

06>0??6 06>0??6 06>0??6 016>9 016>9 016>9 016>9 0>1?

0/6/629 0/6/629 06>0??6 06>0??6 06>0??6 06>0??6 0>1? 0>2112 0>2112 11669

0/6/629 0/6/629 0/6/629 0>1? 0/999 0/999 0>2112 0>2112 16>6/>2 1>20>>

0>1? 001//2 001//2 0/999 0/999 09??//? 1102?2 16>6/>2 1??9 1>/?92

001//2 001//2 0?>111 061226 09??//? 12211? 16>6/>2 16>6/>2 1>/?92 1>/?92

0?9??? 0?>111 090/66> 09??//? 09??//? 1/6?009 1>20>> 1??9 1>/?92 1>/?92

0?>111 0?>111 10/011> 1102?2 12211? 10/122 1??9 1??9

061226 090/66> 11>/> 12211? 12211? 1?29/>? 1??126> 1>/?92

090/66> 090/66> 1206/ 1662>6 1/6?009 11601/ 1>/?92 1>/?92

09?222> 10/011> 16/? 1/6?009 1/6?009 1>/?92 1>/?92 1>/?92

10/011> 10/011> 1/??? 1>20>> 10/122 1>/?92 1>/?92 1>/?92

1102?2 11>/> 1>26// 10/122 10/122

11>/> 11>/> 16>/> 1?9 1?29/>?

12229> 1206/ 19126 1?29/>? 1?29/>?

1206/ 1206/ 1?>06/ 1??126> 11601/

1662>6 16/? 1?9212/ 11601/ 11601/

16/? 16/? 126/> 166906 1>/?92

1/61? 1/??? 1//6/? 1>/?92 1>/?92

1/??? 1/??? 1>/?92 1>/?92 1>/?92

1>20>> 1>26// 1>/?92 1>/?92 1>/?92

1>26// 1>26//

1>99 16>/>

16>/> 16>/>

1?9 19126

19126 19126

1?2/26> 1?>06/

1?>06/ 1?>06/

1??126> 1?9212/

1?9212/ 1?9212/

10??91 126/>

126/> 126/>

166906 1//6/?

1//6/? 1//6/?

1/9>? 1>/?92


71/105

1>/?92 1>/?92

1>/?92 1>/?92

1>/?92 1>/?92


+ontro Poygon

% E*rr5>02 *rr5>02

*rr5>02 *rr5>02

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1 10


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*rr5>02 *rr5>02


72/105

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02

*rr5>02 *rr5>02


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FO* m. !pine fit

/ 6 (I 6/


&01902 &01902 &01902

&01>0>? &01902 &01902 &01902 &01902

&01>0>? &01>0>? 0>1? 1>/?92 1>/?92

11669 11669 1>/?92 1>/?92 1>/?92

11669 1>/?92 1>/?92 1>/?92 0>1912 0>1912 0>1912

1>/?92 1>/?92 1>/?92 1>/?92 0>1912 0>1912 0>1912

1>/?92 1?? 0>9101 019069 0?191

1>/?92 19> 09? 0?191 0?191

1>/?92 21> 0??? 01//69 090991

26? 022 090991 090991

20 09>>>/ 100116 109229

2> 10/?1/ 109229 109229

611 116>?0> 11?9112 12>92

6/0 1222>19 12>92 12>92

6?0 160?1> 16/6 1/60/

/01 1691 1/60/ 1/60/

/6> 1/99 1>09>1 1>?0>?

/?0 1&

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