projective articulated dynamics

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  • 8/8/2019 Projective Articulated Dynamics

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    +a,AWV, +AWNwA,# #vW5

    AO,5W5hiti?|i_ |L

    Ai U@_i4U 6@U*|)

    M)

    aL? *iL

    W? @h|@* 6***4i?|Lu |i +i^hi4i?|t uLh |i #i}hii

    @t|ih Lu 5Ui?Ui ? iU@?U@* ,?}?iih?}

    BiLh}@ W?t|||i Lu AiU?L*L})@hU Sc bbb

    LT)h}| Ubbb M) aL? *iL

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    Aw, 6 A,A5

    wW5A 6 6WBN+,5

    k`w,#B,,A5

    5N+v

    OA,+ WA+#NAW

    5Uhit 22 +i*@|i_ Lh! e Vi*LU|) At|t Se UUi*ih@|L? At|t fD 6LhUi hi?Uit .S LLh_?@|i Ah@?tuLh4@|L?t 2f. L4i?|4 hi?U 22H 5T@|@* W?ih|@ 2

    b k?i|U ,?ih}) @?_ Lih 2Df 544@h) 2D

    OA,+ 2 kW,AW5 2.

    2 Vi*LU|) k?i4@|Ut 2.22 UUi*ih@|L? k?i4@|Ut 2 544@h) e

    OA,+ ,"NAW5 6 AW D

    6hii L_) #@}h@4 D2 aL?| ALh^i S i|L?,*ih ,^@|L?t .e h|U*@|i_ W?ih|@ W_i@ bD +iUhti h|U*@|i_ W?ih|@t eS +iUhti *}Lh|4 ee. "it|L?t e.

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    OA,+ e B+OWw VW,` 6 w+ #vW5 eb

    e *@?@h At|t eb

    e2 At| __|L? D2e2 __|L? Lu |L hL|@|L?t De22 __|L? Lu @ hL|@|L? | @ |h@?t*@|L? DD

    e *@?@h hi?Uit DSee hi?U __|L? Sf

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    eD Vi*LU|) k?i4@|Ut SDeS UUi*ih@|L? k?i4@|Ut S.e. ,^@|L?t Lu L|L? SHeH ,@4T*it Lu *@?@h aL?|t .f

    eH +iL*|i aL?| .2eH2 ht4@|U aL?| .eeH +iL*|i @?_ ht4@|U aL?| .DeHe *@?i aL?| ..

    eb "it|L?t .H

    OA,+ D w+ +a,AWV, B,,A+v Hf

    D OL4L}i?iLt LLh_?@|it H

    D L?|t ? OL4L}i?iLt LLh_?@|it HD2 w?it ? OL4L}i?iLt LLh_?@|it HeD L?| @?_ w?i *}iMh@ H.

    D2 L?U @TT?}t @?_ #@*|) bfD2 L?Ut @?_ *}iMh@U @TT?}t bfD22 L?Ut @?_ BiL4i|hU@* @TT?}t bD2 #@*|) @?_ #iUL4TLt|L?t be

    D *|ih?@|i OL4L}i?iLt LLh_?@|it b.D Ah@?tuLh4@|L? AL *|ih?@|i LLh_?@|it b.D2 L?|t ? *|ih?@|i LLh_?@|it bHD w?it ? *|ih?@|i LLh_?@|it ff

    De W?ih|@ @TT?}t @?_ #iUL4TLt|L? fDD ,|i?tL? |L # 5T@|@* "@?||it f.DS "it|L?t fb

    OA,+ S 5N5,5 f

    S @tU _iUL4TLt|L? f

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    S2 #iUL4TLt|L?t @?_ ti_LW?ihtit .S2 hi?U #iUL4TLt|L? bS22 At| #iUL4TLt|L? b

    S2 *@?@h W?ihThi|@|L? 2fS L4TL?i?| hLiU|L?t 22

    S hLiU|L? 544@h) 2S2 aL?| 5T@Ui W?ih|@t 2

    Se W?ih|@ _iUL4TLt|L? 2DSD hLiU|i k?i4@|Ut 2bSS hLiU|i #)?@4Ut S. hLiU|i h|U*@|i_ ,^@|L?t Lu L|L? SH hLiU|i i|L?,*ih ,^@|L?t Lu L|L? eSb *@?@h ,@4T*i D

    OA,+ . +AWNwA,# W,+AW5 e

    . 6hii 6*L@|?} @? e. h|U*@|i_ W?ih|@ *}Lh|4 ee

    .2 h|U*@|i_ W?ih|@ ,@4T*i eS

    . h|U*@|i_ OLh3L?|@* @? Lu *|T*i +}_ L_it Df

    .e L?t|h@?i_ @? DD.e h|U*@|i_ LM*|) *}Lh|4 D.

    .D ,@4T*i Lu h|U*@|i_ LM*|) Db

    .S @? 5T*||?} S2

    .. "it|L?t SeOA,+ H Aw 5AWw Awj E5A SH

    H L?t|@?|t @?_ 6?U|L?t SbH ,*i4i?|@h) N?| ViU|Lht SbH2 +L|@|L? @|hUit SbH ViU|Lh hLtt hL_U| .fHe 5T@|@* hLtt hL_U| .f

    H2 LLh_?@|i 5)t|i4t .H2 LLh_?@|i L?t|hU|Lh .2

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    H 5Uhi L?t|hU|Lh ..H2 At| 6?U|L? .HH hi?U 6?U|L? .bHe 5T@|@* W?ih|@ 6?U|L? HfHD 5T@|@* LM*|) 6?U|L? H

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    HS |ih L?t|hU|Lh T|L?t H2H. i4Mih 6?U|L?t @?_ Tih@|Lht HeHH 5Uhi W?uLh4@|L? 6?U|L?t Hb

    He ,@4T*i 54*@|L? bHe 5LhUi L_i uLh ,@4T*i b

    HD 544@h) b.

    OA,+ b A+,,5 # w5 bb

    b 5|@U!i_ 6Lh4 @?_ +}_ L_) Ahiit 2ffb _@Ui?U) @|h 2ffb2 5|@U!i_ 6Lh4 2f2

    b2 #hiU| 5L*|L? 2fb 5|@U!i_ 6Lh4 @?_ L?|@U|t i|ii? L_it 2

    b L?|@U| @|h 22b2 5|@U!i_ 6Lh4 2

    be ihi Lu L?t|h@?i_ ,^@|L?t 2Dbe Ti? wLLT UUi*ih@|L?t 2Sbe2 L?|@U| 6LhUit 2Sbe *Lti_ wLLT 5L*|L? 2H

    bD L?t|h@?i_ hLiU|i #)?@4Ut *}Lh|4 2bbS *@?@h L?t|h@?i_ ,@4T*i 22fb. 544@h) 22e

    OA,+ f wN5W # +,+k5 22S

    f L?|hM|L?t 22Sf2 6|hi Lh! 22H

    f2 Bhi@|ih #@*|) @?_ 5)44i|h) 22Hf22 L?ih}i?Ui ? @?t 22Hf2 Vt@*3@|L? Lu h|U*@|i_ W?ih|@t 22bf2e 5TiU@* @tit 2f

    WwWB+Ov 22

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    wW5A 6 6WBN+,5

    Ai i*U@* i*_ Lu *?i@h i*LU|) uLh @?) TL?| L? @ h}_ ML_) @t @hit*| Lu }i?ih@* 4L|L? Ai ?i| i*LU|) O @| @?) TL?| UL?tt|t Lu|L T@h|tc O |i *?i@h i*LU|) T@h@**i* |L |i tUhi @tc @?_ O2 |i|@?}i?|@* i*LU|) |@| hiThiti?|t |i hL|@|L?@* 4L|L? Lu |i ML_)@ML| |i tUhi @t H

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    ef wLU@* ULLh_?@|i t)t|i4 ti_ ? T*@?@h i@4T*it .

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    SD Ai hi*@|i L?| @UUi*ih@|L? t |i _gihi?Ui Lu |i |L @MtL*|i@UUi*ih@|L?t @?_ 3 @*L?} L?| Ai) @hi ML| ThLiU|i_ uhL4|i tT@|@* ^@?||it t?} |i TihUttL? tMtT@Ui A

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    H ,@4T*i Lu ULLh_?@|i _i?|L? L? @ LL! L?| 5|@h|?} uhL4 |i_iu@*| ULLh_?@|i t)t|i4 ft ~ @ |h@?t*@|L? @*L?} 5 Lu c @ hL|@|L?@*L?} + Lu c @ hL|@|L? @*L?} % Lu @?_ @ |h@?t*@|L? @*L?} 5 Lu _i?i |i |T ULLh_?@|i t)t|i4 %+5 .e

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    +a,AWV, +AWNwA,# #vW5

    TThLi_G

    #h O@hi) wT!?c @h4@?

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