BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY...

32

Transcript of BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY...

Page 1: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

���������������� ����������� ������� �� �!�"�# $�&% '����(�*)�% ',+-/.(�10324�'��657��89�!'����� ��

:<;(=>;(?/@BADCFE�CGIH#J!KLH�MBN�O�N�P,QSRUT6V/P,WFH#QXP,Y-H9Q-KLZ/[�\B]_^LP,`FP�abV�YSc�def;gCihjClknm�Eio�@pfa(qsrLN>QXO�qtY�KuH,vxw�P,Q-ynP!Zg[�YXP,zsKkn;9{�@}|~����u��m!m�E� P,zsq�vjH9Q-a(q�Pu[�aFO�Y�qsY��(Y-N�H�v G/N�RXT(a(H#ztH9�#KLZFw�P#O�P9c�N>aFP!Z ���:<@}����;(m!h ������CF�LEi�M�N�aFO�O�N>z�P�N>Q"w�H9zsK!Y-N�RXT(a(q�R"[�aFO�Y-qtY-�(Y�NLZgGIQ-H�KLZF�f�

AD��=7o���;(�9o

��H�rLN>a4R�ztH9Y-T4R7H9y�`iH�O�qsY�NuynP�Y�N>Q-q�P,z�O�T�P�rLN�WFN>N>a4N> !Y-N>aFO�qtrLN>zsKD�FO�N�c¡Y�HnQ�N>qsa!vjH9QSR7NuY�TgN�O�Y�Q-�FR7¢Y��(Q-N�O�H�v�P,�gY�H9y�H9W(qsztN�O�P,aFcuY�TgN"P,qtQ�vjQXP�yDN�O/H,v1P,qsQXR7QSP�vjY>d�[�Y�q�O�£�N>ztzs¢}J�a(H�£Ba�Y-TFP,Y�Pf£�H�rLN>auR7zsH9Y-TR7H9y�`iH�O�qsY�N¥¤�`(zsK(¦BTFP#OIY-T(NBR>P�`FP,WgqtztqsY�KfH�v(§FY�Y-qta(�"Y�HBv¨P,qsQ�zsK¥R7H9y�`(ztN> "�9N�H9yDN>Y-Q�qsN�O7d/©�qtY�Y-qta(�BTgN>Q�NyDN�P�aFOªY-TFP,Y«P3`gztKDq�OBc!N7vjH9Q-yDN�cDP�aFc¡P�`(`(zsqtN�c&Y-HDP�¬9­�O��(Q�v¨P9R7N¥qsa¡O��FRXT¡Pu£BP>KDY-TFP,YBqsYBq�O®qsaR7H9a�YXP#R7Y N>rLN>Q-K!£BT(N�Q�N®£BqsY�T�Y�T(N"O��(Q�v¨P#R7NLd ¯fH�£�N>rLN>Q>Z�qtY�q�O�a(H9Y°P,zs£BP>K(O�`iH�O�O�qtW(zsNfY-H�§FY�P±£®H�rLN>aR7ztH#Y�T²R�H9yD`FHLO�qtY-N&`(zsK�Y-HbT(qt�#T(ztK4R��(Q�rLN�c³O��(Q�v¨P9R7N�O�db[�a²O���RUT²R�P9O�N�O�qtY�q�O�a(N�R7N�O�O-P,Q-K�Y-HbR7�(Y`(qtN�R7N�O7Z�H9Q«¤Xc(P�Q�YXO�Z´¦fH#�(Y H,vFY-T(N"R7zsH9Y�T�qta�H9QXc�N>Q�Y�HµP9R>R7H#yD`(zsq�O�T¥Y-T(Nª§FY-Y�qsa(�(d�[¶auY-T(q�O/`FP�`iN�Q>ZL£®N`(Q�N�O�N>a�YBc(P�Q�YBqsaFO�N>Q-Y�qsH9a6P,zs�9H9Q-qtY-T(ynO c!N>rLN>zsH9`FN�c3vjH#QB�FO�N¥qsanP�£®H�rLN>anR�ztH9Y-TnR7H#yD`FHLO�qsY�N ��� ­O�KgO�Y-N>ybd/��NB§FQSO�YBc�N7§Fa(NBH#�(Q®yDH�c�N>z�O�H�v�c(P,Q-YXO�Z!Y�TgN>aDc�N�O�R7Q-qtWFNBT(H�£·P,`g`(Q�H#`(Q�q�P,Y�N�ztKuqta�O�N>Q-Y�N�cc(P,Q-YXO"R>P,a6O��(`(`(Q-N�O�OBP�a(H9ynP�ztqsN�Oªqsa¸Y-T(N±Q-N�O��(zsY�qsa(��¬9­<R7H#yD`FHLO�qsY�N±`gztKnP�aFcDT(H�£$Y-H&H#`(Y�qsyDqt¹>NY�T(N«O�T�P,`FNfH�v�c(P�Q�YSO7d��4N�§Fa�P,ztzsK�`(Q-N�O�N�a!Y O�N>rLN>QSP,z(N> gP,y�`(ztN�O�H�v/T(H�£º`iH�O�O�qtW(zsN±P�a(H9ynP�ztqsN�O�R>P�aWFN�Q�N�yDH�rLN�c�W!K�qtaFO�N>Q�Y-qta(��c(P�Q�YSO7d

»±N>K!£�H9QSc(O7¼ � H#yD`(�(Y-N>Q�¢ � q�c�N�c¸½"N>H9y�N>Y�Q-q�R"­fN�O�qs�9a/Z � zsH9Y-T¡]¡H�c�N>ztqsa(�(ZF­±P�Q�YSO

Page 2: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

¾�¿ ÀÂÁ ÃÅÄ Æ ÇÈÀ¾®ÃÉ¿

Ê rLN>Q®Y-T(N±`FP#O�YBY�£®H�c�N�R>P9c�N�O7ZgP9c!r#P,a�R7N�cnR7H9y�`iH�O�qsY�N"ynP,Y-N>Q�q�P,z�O�TFP>rLN±WFN>N�aDqtaFR�Q�N�P#O�qtag�9ztK��FO�N�cqtaºP�qtQXR�QXP�vjY�P,a�cËH9Y-T(N>QurLN>Tgq�R7zsN�O�qsaË`gz�P9R�N¸H�v�P,zs�(yDqsa!�(yÌP�aFc�c��(QXP�zt�(yDqsa·Í�Î�Ï�d � yDH#a(�¡Y-T(NynP,Ð�H#Q R7H#yD`FHLO�qsY�N�`(Q�H�c!��R7Y�qsH9auvjH9Q�yÑO7Z9£�H,rLN�a�R7ztH#Y�T�R7H#yD`FHLO�qsY�N�O�TFP>rLNBWiN�N>auN> �Y�N>aFO�qtrLN>zsK±�FO�N�cvjH9QBQ-N>qta�vjH9QXR�qta(��O�Y-Q��FR�Y��(QSP,z�N�ztN>yDN�a!YSO�qtanP�qtQSR7QXP>vjY>ZLWFN�R>P,��O�N¥H,v�Y�T(N�qtQ Q�N>yÑP,Q�J#P�W(ztN«O�Y-Q�N>a(�#Y�T(¢jY�H#¢£®N�qt�9T�Y®QSP,Y-qtHLO"P,a�c¸T(qs�9Tn`(ztq�P,W(qsztqsY�Ku£BTgN>anY�T(N>KÑP,Q�N�c!N�vjH9Q�y�N�c&qta�Y�HÒR7H9y�`(ztN> �R��(Q�rLN�c�O�TFP�`iN�O7d�fH#Q�ynP�ztztK�Z�Y�TgN�O�N6R7H#yD`(ztN� 4R7H9yD`FH�O�qtY-N�OuP,Q-N6R7Q�N�P�Y�N�clW�K�§FY-Y�qtag�bQ�N�O�qta(¢jqtyD`gQ�N>�#aFP,Y-N�c�£®H�rLN>aO�TgN>N>YXODH#a!Y-HPlyDH9z�c�dÂ\®K˧FY-Y�qsa(�(Z±£�NbyDN�P,aY-TFP,Y6Y�T(N4`(zsK�H,v�£�H�rLN>a·R7ztH#Y�TÓR7H9y�`iH�O�qsY�N�Oq�O�c!N7vjH#Q�yDN�c4P,a�cËP�`(`(zsqtN�c�Y-HbY�T(N�yDH9z�c�O��FRUT³Y�TFP�YuqtY�q�O�qsa²R7H9a�YXP#R7Y�N�rLN>Q�K�£BT(N>Q-N&£BqsY�TlY-T(NO��gQ�v¨P9R�NLZ(£BqtY-T(H9�(YB��P,`FO"H9QB£BQ�qsa(J�ztN�O�dG®T(N�c!N�O�qt�9a�P�aFc�ynP�a!��v¨P9R7Y-�(Q�N�H�vF¬�¢�­ºR7H9y�`iH�O�qsY�N `FP,Q-YXO/R7�gQ�Q�N�a!Y-ztK"qta�rLH9ztrLN�ynP�a!KB`(Q-H9W(zsN>ynO

P,a�c&qta(N�ÔnR7qsN>aFR7qsN>O�d/©(H9Q ynP�a!K�`FP,Q-YXO�H,v�Y-T(Nf`gQ�H�R7N�O-O7Z�c!N�O�qt�#aDP��(Y�H#ynP,Y-qtH9a�Y�HLH#z�O�P,Q�N«O�R�P,QXR�NfH#Qa(H#a(N> �q�O�Y-N>a�Y>d�G®T(q�O±q�O"N�O�`FN�R7q�P,zsztKnY�Q-�(N3vjH#Q¥Y�T(N�Õ�¢�­�`FP,Y-Y�N>Q-a(¢jynP,J�qta(��`(Q�H�R7N�O�O7dDÖL`FN�R�q�§×R>P�ztzsKLZH9a�R7N�Y-T(Nu¬�¢�­*`(zsKnH9�(Y-ztqtagN�O®TFP>rLN�WFN>N>aØc!N>Y-N>Q�yDqsa(N�cuW!KnY-Q�q�P�z�P,aFc¡N�Q�Q�H#Q>ZFY�T(NÒR7H9Q-Q�N�O�`FH9aFc!qsa(�Õ,¢¨­Ù¤�Ú×P,Y-Y�N>a(N�c(¦D`FP,Y-Y�N>Q-aFO±y&�FO�Y±WFNDR�Q�N�P�Y�N�c�dÒ[¶abQ-N�O�`FH#aFO�NDY-HnY�T(q�Ofa(N>N�c×ZI£�NuTFP>rLN�c!N7§FagN�cY�TgN±Q�N�ÛL�(qsQ�N>yDN�aLYXO/H,v�P�WgQ�HLP#c(R7zsH9Y�T6R7H#yD`FHLO�qtY�N�O ��� ­ÜO�KgO�Y-N>y4ÍÝÕ�Ï�Z�c!N>rLN>zsH9`FN�cuynP,`g`(qta(��P�zt�9H#¢Q�qsY�T(yÑO�vjH#QBc!N�vjH9Q�y�qta(��P�Ú×P�YB£®H�rLN>a�O�T(N>N�Y®qta�Y�HÒPuR7H9y�`(ztN> Ò¬,¢¨­<O�TFP�`iNÞÍݬ9Ï�ZgP,aFcDN> �`(zsH9Q�N�c3Y-T(NynP�Y�T(N>yÑP,Y�q�R>P,z�R7H9aFO�Y�Q-�FR7YXO®agN>N�c!N�cDY-H�R7H9Q-Q�N�R7Y�Y�T(N�P�a(H9ynP�ztH#�FO®N7ß×N�R7YSO®`(Q�H�c!��R7N�cnc!�(Q-qta(�uY-T(NynP�`(`(qtag�u`(Q�H�R7N�O�O>Íáà9ϨdG®T(N®vjH9Q-yDqtag�BH,v1P±¬,¢¨­R7H#yD`(ztN� ¥O�TFP�`FNBqta�Y�H«P�Ú×P,YxÕ,¢¨­â£�H,rLN�a�`�P,Y�Y-N>Q�auq�OIagH9Y c!N�§Fa(N�c�W�K�P

H9agN>¢}Y-H9¢jH9a(N"ynP�`(`(qtag�(d�G®TgN®§FaFP,zgynP,`(`gqta(�"q�O�PBvj�(aFR7Y-qtH9auH�v/Y-T(N®a��(yDN>Q-H9�FO/qtagqtY�q�P,zgR7H9a�c!qtY-qtH9a�OH,v�Y-T(N±`(Q-H�R7N�O-O®£BT(q�RXT&§FQSO�YBR�Q�N�P�Y�N�c&Y-T(N«¬,¢¨­ãc�N7vjH9Q-yDN�c�O�TFP�`iN�Z(qtaFR7zs�Fc!qsa(�¥H9Q�qsN>a�YXP,Y-qtH#aDH,v�Y-T(NÚ×P�YDO�T(N>N>Y�Z�qta(qsY�q�P�zBR7H#a!YSP9R7Yu`FH#qta�YXO7Z�P,a�cËY�TgNˤSO�£�N>N>`(qsa(�L¦bc!qsQ�N�R�Y�qtH#a/Z�q�däNLdtZ�Y-T(N6c!qtQ-N�R7Y-qtH9a³H,vP,`g`(ztq�R>P,Y-qtH9abH#aFR7Nuqsa(qtY-q�P,z�R7H#a!YSP9R7Y¥q�O"ynP9c!N�d�ÖLqtaFR�NuY�T(Nu�#N>H9yDN�Y�Q�q�R±ynP,`(`gqta(�Dq�Ofa(H#Y��ga(q�ÛL�(NLZqtYuq�O�qtyD`FH�O�O�qsW(ztN�Y�H³c!N>Y�N�Q�yDqsa(N&Y-T(N6R7H9Q-Q�N�R�Y�Õ,¢¨­È`FP�Y�Y�N�Q�a�Y-TFP,Y�ynP�`FO�qsa!Y-H4P�O�`iN�R7q�§×Rn¬�¢�­O�T�P,`FN�£BqsY�T(H#�(Yf�gaFc!N>QSO�YXP�aFc!qsa(�&Y-T(N±§FY�Y-qta(��`(Q-H�R7N�O�OBqtYSO�N>zåv-d [�a¸H#QXc!N�QBY�H�P9R>R7�gQXP,Y-N>ztK�`(Q�H�c!��R7NY�TgN¥Õ,¢¨­ã`FP�Y�Y-N>Q�a/ZgP¡¤�vjH#Q�£BP�QXc(¦�O�qsy&�gz�P,Y-qtH#auy&�FO�Y®WFN±`FN>Q�vjH9Q�y�N�c�ZL£BT(q�RXTDyDH�c�N>z�O�Y�TgN�R�H9Q�Q-N�R7Yc!N7vjH#Q�ynP�Y�qsH9aD`(Q-H9`FN>Q-Y�qtN�OªH,v�Y�TgNµÚiP,YB£®H�rLN>aÑO�T(N>N�Y>Z(P#O®£®N>zsz/P#O®Y�T(N±`gQ�H�R7N�O-O�H�v c�N7vjH9Q-yDqta(�¥Y-T(NO�TgN>N>YBqta�Y�H�PuR�H9yD`(zsN> �¬,¢¨­*O�T�P,`FNLd� �(Q�Q-N>a�Y�ztK�Z�c!N�O�qt�#a(N>QSOµ`gQ�N�O-O�Ú×P,Y�O�T(N>N>YSOµH#a!Y-HnPDyDH9z�c¡P�aFc�O�JLN>YXRXT¡H#�(Y¥Y�T(N�P�`(`(Q-H, �qtyÑP,Y�N

O�T�P,`FN�O¸H�v�Y�T(N³Õ,¢¨­Ù`FP�Y�Y-N>Q�aFO�dæ­f�(Q-qta(�ºY�T(q�OÑ`gQ�H�R7N�O-O7Z¥Y�T(N³Õ,¢¨­Ù`(zsqtN�O�P,Q�Nçc!N7vjH9Q-yDN�cºP,aFc¤XcgP,Q�Y-N�c(¦DqtabH#QXc!N�Q±Y�HDvjH9QSR7NuY�TgN>yæY�HD§FY±Y-HDY�T(N�¬�¢�­ÂO��gQ�v¨P9R�NLd�G®TgNuqtaFO�N>Q�Y-qtH9abH�vu¤Sc(P,Q-YXO�¦Dq�O

Õ

Page 3: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

R7Q-�FR7q�P�z!vjH9Q�P>rLH9q�c!qtag��P�a(H9yÑP,ztH#�FO�N>rLN>a�YXO�O��FRXTDP#Oª�LP�`FO®P�aFc&£BQ-qta(J�ztN�O�Z9`FP�Q�Y�q�R7�(z�P,Q�zsK�£BT(N�a&Y-T(N`(zsKbq�Of§FY�Y-N�cbY�H6P¸T(qs�9T(zsKbR7�gQ�rLN�c4O��(Q�v¨P9R7N�dDG®T(N>Q-N�P,Q-NnR7�(Q-Q�N>a�Y�zsK¸agH¡Y�N�RUT(agH9ztH#�9qsN�O±H9Q¥Y�HLH#z�OY�H�P#O�O�q�O�Y"qta�Y�T(N�P,�gY�H9yÑP,Y�q�R�qsaFO�N�Q�Y�qsH9anH,vxc(P�Q�YXOBc��(Q�qsa(�uY�T(N�c!N�O�qt�#a6O�YXP��9NLd [�anY�Tgq�Oª`�P,`FN>Q>Z(£�NP9cgc!Q�N�O-O�Y-T(N¥`(Q�H#W(ztN�ynOªQ-N>z�P�Y�N�c&Y-HDcgP,Q�Y"qta�O�N>Q-Y�qtH#a6P,aFcD`(Q-N�O�N>a�YBH9�gQ±O�H9zt�gY�qtH#aFOBY�HuY�TgN>ybd��N�WFO�Y-N>Q>èéO/�fN>£³[¶a�Y�N�Q�aFP�Y�qtH#aFP,z�­"q�R7Y-qtH9a�P,Q�Kµc!N7§Fa(N�O�P"c(P,Q-Y�P#O®êfë�ì¨ítì�îXïFð-ñµì¨ê7òFð�ó�í�ô9õxö�÷9øùñ�ú9ë�ð-ñ

ð�ë�òFð-î>í�ê9øsøåû�í�ôDü ìjì�í�ô9õbõ�êLó7ý&ð�ô�ìþë�ì�÷4ìþïFðÑî>ú!ó�ÿ,ð�ë¸÷�öDì�ïFð��X÷�ñLû,d6[�aFO�N�Q�Y�qsa(�bcgP,Q�YSO�q�O�P¡`iH#`(�(z�P,QY�N�RUT(agq�ÛL�(NDqta²Y-T(ND§FN>z�clH�v¥�LP�Q�yDN>a�Y�c!N�O�qt�#aÜÍ��,ϨZ®P�aFc�q�O��FO�N�cçvjH#Q�§FY�Y-qta(�³Pb`(qtN�R�NDH,v�R�ztH9Y-TaFP�Y��(QSP,ztzsKºP,Q�H#�(aFc�`(Q-H9Y-Q��Fc!qsa(�²O��(Q�v¨P#R7N¡Q-N>�9qsH9aFO�d$G®TgN¡qta�Y�Q-H�c!�FR7Y-qtH#a�H,vÒc(P�Q�YSO3qsa��LP�Q�yDN�a!Yc!N�O�qt�#a/Z,TgH,£�N>rLN>Q�Z7TFP#OIWFN>N>a¥WFP#O�N�c±ynP�qta(zsKBH9a�qtyD`(Q-H�r!qsa(� Y�T(N�§�Y�H�v(Y-T(N �LP,Q-yDN>a�Y>Z�W!K"Q�N�c��FR7qtag�Y�TgNBO�Y-QXP�qtaFO�P�Q�H#�(aFcuT(qt�#T(ztK�c!N7vjH#Q�yDN�c�P�Q�N�P#O7d � auqtyD`FH#Q�YXP�a!Y�c�q�ß×N>Q�N�aFR7N®WFN>Y�£�N>N>a¥Y�T(q�O�Y�K!`FN�H,vc(P�Q�Y�qsa(��P,a�c¸Y�TgN¥c(P,Q-Y�qsa(�&£�N¥P,Q-N�R7H9aFO�q�c!N�Q�qtag�uq�OªY-TFP,YBqsYBq�O a(H9Y"N�O�O�N>a�Y�q�P�z�Y-TFP,YBY-T(N±Q�N�O��(zsY�qtag��LP�Q�yDN�a!Y�`FP,Y-Y�N>Q-aFO�£BqsY�T6c(P�Q�YXO"O�TgH9�(z�c�§�YfN> gP9R�Y�ztK�H9a�Y�H�PuO��gQ�v¨P9R�NLd[�a¡Y�TgNµvjH#ztzsH,£Bqsa(�(Z(£�N±§FQXO�Y±c!N�§Fa(N�y�H�c!N>z�OªvjH#Q±cgP,Q�YSO7ZFY�H#�9N>Y-T(N>QB£BqtY-TbPuyDH�c!N>z�vjH#Qf£�H�rLN>a(¢

R7zsH9Y�Tg¢�R7H#yD`FHLO�qtY�N¥ynP�Y�N>Q-q�P�z�O7dB�4N�Y-T(N>abc�N�O�R7Q-qtWFNucgP,Q�Y«qtaFO�N>Q�Y-qtH9aØP,zs�9H9Q-qtY-T(ynO7Z(£BTgq�RXTbP,Q-NuP�`(¢`(zsqtN�c�Y-H�Q-N>�9qsH9aFO qtau£BT(q�RUT�N> gR7N�O-O�qtrLN�O�T(N�P,Q°c!N7vjH#Q�ynP�Y�qtH#auq�O�`(Q-N�c!q�R�Y�N�c�d/�4N�vjH�R��FO�H9aDH�rLN>Q-z�P,`Q�N�yDH�r9P�z/P�zt�9H#Q�qsY�T(ynO�Z!£BT(q�RUT6P�ztztH�£·�FOBY�H�P,�(Y-H9ynP�Y�q�R�P,ztzsKDc�N>Y�N>Q-yDqtagNfY-T(N�O�TFP�`iNuH�v�P�c(P,Q-YfY-HWFN¥qtaFO�N>Q�Y-N�c�d ©�qsaFP,zsztKLZL£®N¥`(Q-N�O�N�a!Y"O�N>rLN>QXP�z�N> gP,y�`(ztN�O�H�v�c(P,Q-YBqtaFO�N>Q�Y-qtH#a/d

Ä ���ܾ�¿ ¾�À¾®ÃÉ¿ �

[�aDY�Tgq�OBO�N�R7Y�qsH9a/Z�£®N¥c!N�§Fa(N¥H9�(QBy�H�c!N>z(vjH9QB£�H,rLN�anR7ztH#Y�TnR�H9yD`FHLO�qtY-N�O7ZgP,aFcDyDH�c!N�z�OxvjH#Q"c(P,Q-YXO�d

� ��� ��������� ��� �� ����� "!#�$&%(')�*,+- . /*G®T(N �(aFc�N>Q�zsK!qsa(�®yDH�c�N>z>vjH9Q�£®H�rLN>a«R7ztH#Y�T�R7H9y�`iH�O�qsY�N�O×R7H9aFO�q�O�YXO�H,vgY�TgNxvjH#ztzsH,£Bqsa(�"P9O-O��(y�`(Y�qsH9aFO�Í à�Ï�¼

0 G®T(N�R7zsH9Y-T¡R�H9aFO�q�O�YSO�H�v�rLN�Q�Y�q�R>P,z1P,aFcnT(H9Q-qt¹>H#a!YSP,z/qsa(N> �Y�N>aFO�qtW(zsNfY-T(Q�N�P9c(O�d

0 G®T(N�Q�N�q�O�agHbO�zsqt`(`�P,�9NÑP,YuP6R7Q�H�O�O�qta(�6H,v«P¡rLN>Q-Y�q�R�P,z�Y�T(Q-N�P9c�132�êLó�ò54¥P,a�clP¸T(H#Q�qs¹>H9a�YXP�zY-T(Q�N�P#c6172ªðtö�ì84B£BT(N�a¸Y-T(N�R7ztH#Y�Tnq�OBc�N7vjH9Q-yDN�c�d

0 � Y�TgQ�N�P#c¸O�N>�9y�N>a!Y�WFN>Y�£®N>N>aÑP9c,Ð-P#R7N>a�Y"R7Q�H�O�O�qsa(�LOBq�OBO�Y�QSP,qt�#T!Y�d

� ztY-T(H9�g�9T<Y�T(N�O�N²P#O�O��gyD`(Y�qsH9aFObP�Q�N²O�qtyD`gztNLZ±Y-T(N>K·`(Q�H�r�q�c!N²P��#HLH�c*P�`(`(Q�H� �qtynP�Y�qsH9aÜY-HyDH�O�YuP#c!r#P,aFR�N�cl£®H�rLN>a²R7zsH9Y-T�R�H9yD`FHLO�qtY-N�O�O��FRUTºP#O�§FWFN>Q��#z�P9O-O:9�N>`FH, �KLZB»±N>r�z�P�Q�9�N>`FH, �KLZ�P,aFc

¬

Page 4: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

(b)

warp

weft

(a)

mesh point

©�qs�9�(Q-N�Î9¼;1�P<4Bw�z�P,qtan£�N�P>rLN±`(ztKÑP,aFc61}W"4®Y-T(N¥Y�H9`FH#ztH9�#KnH,v qsa(qtY-q�P,z×yDN�O�TD`FH9qta�YXO

�9QSP,`(TgqtY�N=9>N>`FH� !K�d&ÖL`FN�R7qå§×R>P,zsztKLZF£BqtY-T�Y-T(N�§FQSO�Y�P9O-O��(yD`gY�qtH#a/Z�Y-T(N�c!N7vjH#Q�ynP�Y�qtH#abq�OfzsqtyDqsY�N�cDY-H¤XO�T(N�P�QX¦�c�N7vjH9Q-ynP,Y-qtH9a?>ÞY-T(q�O P#O�O��gyD`(Y�qsH9auTFP#OªWFN>N>a�c!N>y�H9aFO�Y�QXP�Y�N�c�N� !`FN>Q-qtyDN>a�YXP�ztzsK�ÍA@�Ï�d�V�qsJLN>¢£Bq�O�NLZLP#O®P±Q�N�O��(ztY�H,v/Y-T(N«O�N�R7H#aFc�P,aFcuY�T(qsQXcuP#O�O��gyD`(Y�qsH9aFO�Z�R7ztH#Y�T�R>P�a&WFN"Y�Q�N�P,Y�N�c&P#OªP¥c!q�O�R7Q-N>Y�NyDN�O�T¥H,v�¤�`(qsa(¢�§F !N�c(¦fyDN�O�T�`FH9qsa!YSO�Y�T�P,Y R>P�a�Q-H9YXP�Y�N"P�Q�H9�gaFc3N�P9RXT�yDN�O�TuP� !q�O7d�G®T(N�O�N"P9O�O��(yD`(¢Y�qsH9aFO"P,Q-N�P,z�O�H�Q�N�P#O�H9a�P,W(zsNLZ�WFN�R>P��FO�N�Y�T(NÒP9R7Y-�FP,z�£®H�rLN>anynP�Y�N>Q-q�P,z�O®�FO�N�cÑvjH9QµR7H9yD`FH�O�qtY-N�OBP,Q-N�FO��FP,zsztK¡N�y&WFN�c(c�N�c¸qsalPnO�Y-q�RXJ!KnQ-N�O�qsabynP,Y-Q�qt 6P�aFc�Y�TgN�c!q�O�YXP,a�R7NuWFN>Y�£®N>N>a4P#c,Ð-P9R�N>a!Y¥Y-T(Q�N�P#cR7Q-HLO�O�qta(��O�q�O®rLN>Q�K�O�yÑP,ztz¨d[�a¡P#c(c!qsY�qtH#a/ZF£®N¥qtyD`gztq�R�qtY�ztK�ynP,JLN±Y-T(N±vjH9zsztH�£Bqta(��P,�g !qsztq�P�Q�K�P9O-O��(yD`gY�qtH#aFOB£BqtY�TgH9�(Y"ztH�O�OBH,v

�9N�a(N>QXP�ztqsY�K�d¡©�qsQXO�Y>Z�Y�TgNDqta(qsY�q�P,z�O�TFP�`FN¸H�v±Y-T(ND£�H,rLN�alR7zsH9Y-Tlq�O�P9O�O��(yDN�c4Y�HbWFNDQ�N�R7YXP�a(�9�(z�P,Q�dÖLN�R�H9aFc�ZFY�TgN>Q�N¥q�O®agHD`(T�K(O�q�R>P�z�c!q�ß×N>Q-N>aFR7N±WFN>Y�£�N>N>an£®N7vjYSOfP�aFc¸£°P,Q-`FO7d"©�qsaFP,zsztKLZ�Y�T(N�£®N�P>r�qta(�H,v�H#�(Q�R7ztH#Y�Tbq�O"�9qtrLN�a¡W�KbP�¤-`(z�P�qtab£®N�P�rLN�Z´¦�P9O¥O�T(H�£Ba4qtaØ©�qt�#�(Q�NnÎB1¨PC4Sdu[�abPD`(z�P�qtab£�N�P>rLNLZ£®N�vjYXOuP,a�c磰P,Q-`FOuP,Q-N¡P�ztY-N>Q�aFP�Y�N>zsK�qsa!Y-N>Q�zsN�P>rLN�c¡WFH9Y-T�rLN>Q-Y�q�R�P,ztzsK4P,aFclT(H#Q�qs¹>H9a�YXP�ztztK�d�[�a²H9�gQyDH�c!N�z�Z!Y-T(N�qsa!Y-N>QXO�N�R7Y-qtH9aD1}H9Q"Y�TgNuR7Q-HLO�O�qta(�E4®H�v°P3£�N7vjY"P,aFcbPu£BP�Q�`/Z×O�TgH,£Ba6qtaØ©�qt�#�(Q�N�Î�1}WF4SZq�O«R>P,zsztN�cbPl¤�y�N�O�Tb`FH9qsa!Y�d´¦nG/H9`FH9zsH9�9q�R>P,zsztKLZ/N�P#RUTby�N�O�T6`iH#qta�Y¥q�O±ztqsa(JLN�c¸£BqsY�T¡vjH#�(Q�P9c,Ð-P#R7N>a�YyDN�O�TD`FH9qsa!YSO®Y�TFP�Y±P�Q�N¥N�ÛL�(q�c!q�O�YSP,a�YBP,YBY-T(N¥H9�(YSO�N>Y�d G®T(N�N�a!Y-qtQ�N«Õ,¢¨­ã£�H�rLN>anR7zsH9Y�T6R7H#yD`FHLO�qtY�NqtanqsYXO®qtagqtY�q�P,z1O�YXP�Y�N¥q�O®Y-T(N>Q-N7vjH9Q-N�Q-N>`(Q-N�O�N>a�Y�N�c&W!KÑP�ztqtagJLN�c&a(N>Y�£�H9Q�J�H,v�yDN�O�T�`iH#qta�YXO�d½"qtrLN>aØPDO�N>Y"H,v�qsa(qtY-q�P,z�R�H9aFc!qsY�qsH9aFO±P�aFc¡Y�TgNuP,WFH�rLN�P9O-O��(y�`(Y�qsH9aFO�ZiN>rLN�Q�KnÕ�¢�­�yDN�O�T¸`FH#qta�Y

R>P�a$WFNbynP�`(`FN�c�Y�HlY-T(N4R7H#Q�Q�N�O�`FH9aFc�qta(� ¬,¢¨­ `FH9qsa!YnH#aY�T(N4O��(Q�v¨P#R7N$¤-�9N>H#yDN>Y-Q�q�R�P,ztzsKLZ´¦²Íä¬>Ïqta³H9QXc�N>QuY�H4O�qty��(z�P�Y�NuY�TgND`(Q�H�R�N�O�O�H�vf§FY-Y�qsa(�4PbO�qsa(�9zsNnR7H9y�`iH�O�qsY�N�`(ztK4H9a�Y�H4P¡yDH#z�c�dØG®T(NynP�`(`(qtag�&`(Q-H�R7N�O-Ofq�O"P9R7Y-�FP,zsztK6PDO�N>Q�qsN�O�H�v°O��(Q�v¨P9R7NG9�O��(Q�v¨P9R7Nuqsa!Y-N>QXO�N�R7Y-qtH9a6R>P�z�R7�gz�P,Y-qtH#aFO�ÍIHLZKJ�Ï�d

à

Page 5: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

i,j

Pi-1,j

Pi,j-1

r1

r2

P

weft

γ

warp

©�qs�9�(Q-N�Õ�¼®G®TgQ�N�P#c¸P�a(�9zsNMLØP,Y"PuyDN�O�T�`iH#qta�Y�NPORQ S

©(H9Q-ynP,zsztKLZ�Y�H¥ynP�`DP±yDN�O�Tu`FH9qta�Y�1TNKOUQ SV4XZL£®N"a(N>N�c�Y�£�H¥a(N>qt�#T!WFH#Q�qtag��yDN�O�T�`FH9qsa!YSOW1XNPOUYCZ3Q SªP,aFcNKOUQ S[YCZ\4 Y-TFP,Y"TFP>rLN¥P,zsQ�N�P#c!KDWFN>N>anynP�`(`FN�cDY�HuY-T(N�O��(Q�v¨P9R7NLZFP#OfO�T(H�£Ba¡qsa¡©�qt�9�gQ�N�Õ!d\®N�R>P��FO�NDH�v¥Y�TgNDqta(N� !Y-N>aFO�qsW(qtzsqtY�KbP#O�O��(yD`(Y-qtH9a1Z�Y�T(NnynP�`(`FN�c�`FH9qsa!YuH�v]NPORQ Suq�Ouc�N7§Fa(N�c³P9O

Y�TgN�qta�Y�N�QXO�N�R7Y�qsH9anWFN>Y�£®N>N>anY-T(N��#qtrLN>aØO��(Q�v¨P9R7NÒP,aFc¡Y�£®H�O�`gT(N>Q�N�Of£BT(HLO�NuQXP#c!qtq�P�Q�N�^_Z±P�aFc6^_`�d©(H9Q�Y�T(NfvjH#ztzsH,£Bqsa(�uc�q�O�R��FO�O�qtH9a1Z!£®Nµc!N7§Fa(NµP&ì�ïgóUð-êLñuêLô9õ9øsða1bLK4xP9O®Y�TgN¥P,a(�#ztN±WFN>Y�£�N>N>a�Y�T(N±zsqta(NO�N��9yDN>a�YXO NKOUQ S3NPORYEZ[Q S�P,a�c NKOUQ S3NKOUQ S[YCZ,d6[�a(qtY-q�P,zsztKLZ/Y-T(NnO�TgN�P,QÒP,a(�#ztNDq�O�P9O-O��(y�N�c�Y�H6WFN�c�d�ÕbP�YN>rLN>Q-K&y�N�O�TD`FH#qta�Y>d

��� ���*��Ve�gfih��5 .*­±P�Q�YXO P�Q�NBqta�O�N>Q-Y�N�c¥qta�Pf�#qtrLN>a�`(ztK�H,v×£®H�rLN>aÒR7ztH#Y�T�R7H#yD`FHLO�qsY�N�O/qtauH#QXc!N�Q�Y�H¥P>rLH#q�cuP,agH9ynP�ztH9��ON>rLN>a�YXO×O��FRXTuP#OI��P,`FO�P,aFc¥£BQ�qtagJ!zsN�O7d�¯fN>Q-N�£®N°c!N7§FagNªY�£�H±c!qåß×N>Q�N>a�Y�y�H�c!N>z�OivjH#Q�cgP,Q�YSO7¼ ë�ì�ítì¨îUïFð-ññLêLóXìþë°P,aFc4ì�ó�í�ýuý&ð-ñ�ñLêLóUì�ë�d�qtY-TbO�Y-qtYSRUT(N�c¡c(P�Q�YXO�Z�N> gR7N�O-O�qtrLN«ynP,Y-N>Q�q�P,z�OBP�Q�NuQ-N>yDH�rLN�cDP�aFc¡Y�T(N�N�c!�#N�O±P,Q-NuO�Y�qtYSRUTgN�c¸Y-H

`(Q-H�c!�FR7N«P¥c(P,Q-Y�qtag��N�c!�9NLZ�P9O O�T(H�£BaDqsa�©�qt�#�(Q�N"¬�d��qtY-TuY�Q�qsyDyDN�c¥c(P,Q-YXO7ZLN> gR7N�O-O�qsrLN®ynP�Y�N>Q-q�P,z�OP,Q-NDO�qtyD`gztK¡Q-N>yDH�rLN�cD£BqtY-T(H9�gYuO�Y-qtYSRUT(qsa(�(d�GIQ-qtyDy�N>c6c(P,Q-YXO�P�Q�Nuvj�(Q�Y-T(N>Q�R7z�P9O�O�q�§FN�c qsa!Y-H¸Y�£�HY�K!`FN�O�P9R>R�H9QXc�qta(�6Y�HbY�TgNnO�TFP�`FN¸H�v±Y-T(N�Y�Q�qsyDyDN�cnynP,Y-N>Q�q�P,z�O7d6[¨v°Y�T(NÑO�TFP�`iNnq�O��9qsrLN>alW�KlP�aP,Q-W(qtY-QXP�Q�K¡`FH#ztK��9H9a1Z�Y�TgNuY�Q�qsyDyDN�c�c(P,Q-Y�q�O±R>P�ztztN�cbPÑòg÷9øåû�õL÷Lô(ê9ø î�úÞìjdu[}v-Z�H9a4Y�TgNuH9Y�TgN>Q¥TFP,aFc×ZY�TgN±O�TFP,`FN¥q�O��9qsrLN>auW�K�P�ztqsa(N�P�Qªzsqta(N"O�N>�9y�N>a!Y�Z9qtY q�OªR�P,ztzsN�c�P&øåí�ôið-êLó«î>úÞìjd ©�qs�9�(Q-NfàÒO�T(H�£"OªY�£�H`FH9zsK!�#H9aFP�z�R7�gYXOBP,a�c¡PuztqtagN�P,Q°R7�(Y>d�fH9Y-NBY�TFP�Y�H9�gQ��(aFc!N�Q�ztK�qtag�fqsa(N> �Y�N>aFO�qtW(qsztqsY�K«P9O-O��(y�`(Y�qsH9auq�O/JLN>`(Y�r#P,zsq�c��(aFc�N>Q�Y�TgN®qta�O�N>Q-Y�qtH#a

H,v°c(P�Q�YSOM1}£BT(N�Y�T(N>Q"Y�TgN>K6P,Q�NÒO�Y-qtYXRXT(N�cnH9Q"Y�Q-qtyDyDN�c,4Xd�G®T(Nuc�q�O�YSP,aFR�NuP,a�c¡Y�H9`FH#ztH9�#KbWFN>Y�£®N>N>aP9c�Ð-P9R7N>a�YByDN�O�TD`FH9qsa!YSO7Z(T(H�£®N�rLN>Q>Z�ynP>KuWiNÒP�ß×N�R7Y-N�cDW!K�Y�T(N¥qta�O�N>Q-Y�qtH#aDH,vªP&c(P�Q�Y�d

Page 6: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

(darting triangles)

darting edges

stitched darts

©�qt�#�(Q�N�¬!¼BÖLY-qtYXRXT(N�c�c(P,Q-YXOj1}WFN7vjH9Q-N�P,aFc6P�vjY�N�QBqtaFO�N>Q�Y-qtH9a�O:4

a linear cut

polygonal cuts

©�qs�9�(Q-N¥à(¼ G/Q�qty�yDN�cuc(P�Q�YXOj1}WFN7vjH#Q�N�P,a�c¡P�vjY-N>QBqta�O�N>Q-Y�qtH#aFO:4

@

Page 7: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

ÖLY�qsYXRXT(N�cDP�aFc¸Y-Q�qsyDyDN�c&c(P�Q�YSOfP�Q�N±vj�(Q�Y-T(N>Q"c!N�O�R7Q-qtWFN�cDqtanY�TgNµvjH#ztzsH,£Bqsa(�uO�N�R7Y-qtH9a�O7d

k×o�@þo��,��m�|�kn;(�>o�=ÖLY-qtYXRXT(N�c�c(P,Q-YXO"P,Q�N�c!N�§Fa(N�cDW�KDY�T(N±vjH#ztztH�£Bqsa(��P9O-O��(yD`gY�qtH#aFO7¼

0 G®T(N�O�TFP,`FN�H�v�P�O�Y�qsYXRXT(N�cDcgP,Q�YBq�OBP,a6q�O�H�O�R7N�ztN�O®Y-Q�q�P�a(�9zsNLZ(R�P,ztzsN�cDP6ñLêLóUì¨í�ô9õDì¨ó7í�êLô#õ9øtðXd

0 G®£�H¡H,v"Y-T(N�rLN>Q�Y-q�R7N�O"H,v«Pnc(P,Q-Y�qsa(�¡Y-Q�q�P�a(�9zsNDy��FO�Y±WFN�ztH�R>P�Y�N�c4H9alY-T(N&WFH#QXc!N>Q�H,v"Y-T(NR7zsH9Y-T/d

0 �fHuY�£�H�c(P,Q-YXOBynP>K&H�rLN>Q-z�P,`1d

G®T(NBP�WFH,rLN°P9O-O��(yD`gY�qtH#aFO/�9�FP�QXP,a�Y�N�N®Y�T�P,Y�Y-T(N Y�£�H±O�q�c!N�OIH�v×PfcgP,Q�Y-qta(�«Y�Q�q�P,a(�#ztN £BqtzszLN> gP9R7Y-ztKynP�YXRXTl�(`²Y�HbvjH9Q-y P�O�qta(�#ztN6c(P�Q�Y�qsa(�4N�c!�9N�d�G®T(q�O�q�O�qsyD`FH9Q�YSP,a�Y>Z�O�qsaFR7NnP4c!q�O�Y�H#Q�Y�qsH9aºynP>KQ�N�O��(zsY±q�v°Y�T(NuY�£®H6O�q�c!N�O±H�v"Pnc(P,Q-Y�qsa(�nY�Q�q�P,a(�#ztN�c!Hna(H9Y¥ynP�YXRXT/Z�£BT(q�RUTbqsabY��(Q-a�yÑP�K6r!qsH9z�P,Y�NH9�gQ�qtagN> !Y-N>aFO�qtW(qsztqtY�K�P9O-O��(yD`gY�qtH#a vjH#Q�Y-T(Q�N�P#c(O7d � ztY-T(H9�g�9T4Y�T(N�P9O-O��(yD`gY�qtH#a�Y-TFP,Y¥Y-T(NDO�TFP,`FNy��FO�Y�WiN6P�aËq�O�H�O�R7N>zsN�O�Y�Q-q�P�a(�9zsNDq�OuP�`(`FP,Q-N>a�Y�ztK³Q�N�O�Y�Q�q�R7Y�qsrLNLZ/qtYu`(Q-H�r!q�c!N�O�P¡�#HLH�c˧FQXO�Y�¢jH9QSc!N>QP,`g`(Q�H� �qtynP�Y�qtH#aDY�H�P,aØP,Q-W(qtY-QXP,Q-KDY�Q-q�P�a(�9�(z�P,Q"O�Y�qtYSRUTgN�cnc(P,Q-Y>d� O�Y�qsYXRXT(N�cDcgP,Q�Y"q�O®qsaFO�N�Q�Y�N�c&qtanY�TgNµvjH#ztzsH,£Bqsa(��O�Y-N>`FO�¼

Î9d±ÖL`FN�R�q�vjKnY�T(Q-N>NuyDN�O�T¡`FH9qsa!YSO±Y�TFP�Y�R�H9Q�Q-N�O�`FH#aFc Y-HnY�T(NurLN>Q-Y�q�R7N�OBH,v°Pnc(P,Q-Y�qtag�¸Y-Q�q�P,a(�#ztNLdG®£�HuH,v�Y�T(N>yÂy��FO�Y WFN±H9anY-T(N¥WiH#QXc!N�QBH,v�Y�T(N±H#Q�qs�9qta�P,z�Q-N�R7YSP,a(�#�(z�P�QB£®H�rLN>anR7zsH9Y-T/Z�P,aFcY-T(NnY�£�Hbqta�Y�N>Q-qtH#QuN�c!�9N�O�H,v¥Y-T(NnY�Q�q�P,a(�#ztNl1�R�P,ztzsN�cìþïFð�ë�í�ñ!ðbð-ñ>õ!ð�ë74�y&��O�Y�WFNnN�ÛL�FP,zBqsazsN>a(�9Y-T/d

Õ!d±Ö�R�P,aDY-T(N±O�q�c!N"N�c!�#N�OªH�v/Y-T(N¥c(P�Q�Y�qsa(�¥Y�Q-q�P,ag�9ztN�Z!P�aFcDR7Q-N�P,Y-Nfy�N�O�Tu`FH9qsa!YSO®R>P�ztzsN�c¡ñLêLóXì¨í�ô9õý&ð�ëXïÒò(÷Lí�ô�ìþë�ztH�R>P�Y�N�cnP�YfY-T(N±qta�Y�N�QXO�N�R7Y�qsH9aFO WiN�Y�£�N>N>aDY-T(N�O�q�c!N¥N�c!�9N�OBP,aFcDY�TgN�Y-T(Q�N�P9c(O�d

¬!d�m O�YSP,W(zsq�O�TDa(N>£ºY�H9`FH#ztH9�#q�R>P�z/P�aFcDc!q�O�YXP�aFR7N±Q-N>z�P�Y�qsH9aFO�T(qt`FO�WFN>Y�£®N�N>auY�T(N«yDN�O�Tu`FH#qta�YXOªH#aH#Q±P#c,Ð-P9R7N�a!YBY-HuY�T(N�c(P�Q�Y�qsa(��N�c!�9N�O7d

G®T(N�O�NnO�Y-N>`FOuP,Q-NDQ�N�`iN�P,Y�N�c vjH9Q�N�P9RXT²O�Y-qtYSRUT(N�c�c(P�Q�Y�db©�qt�#�(Q�Nn�bO�T(H�£"OuP,a³N> (P�yD`(zsNuH,vµPO�Y-qtYSRUT(N�c¡c(P�Q�Y¥qtaFO�N>Q�Y-N�c¸qsabH9a(N�O�q�c!NuH,v°PD�9qsrLN>a¡Q-N�R7YSP,a(�#�(z�P�Q¥R7ztH#Y�T/d�[�a4©�qt�#�(Q�N��61¨PC4XZ×yDN�O�T`FH9qsa!YSO®z�P,WFN>zsN�c�vjQ�H9yÉαY�H�ÎoH�P�Q�N�P�ß×N�R7Y-N�c&W�K&Y-T(N"qtaFO�N>Q�Y-qtH9a�H,v�Y�T(N¥cgP,Q�Y�d®ÖL`FN�R7qå§×R>P,zsztKLZ#yDN�O�T`FH9qsa!YSO&c!N�a(H9Y-N�cËW�KlW(z�P9RXJ²O�H#ztq�c²R7qsQXR7zsN�Oqp�Õ�ZI��ZIJ!ZsÎ_r�ZtÎ>Õ�ZtÎs�!ZtÎtH<ubQ�N�`(Q�N�O�N>a�YuY�T(N6c(P�Q�Y�qsa(�4yDN�O�T`FH9qsa!YSO7d � yDH#a(�±Y-T(N>ybZ�yDN�O�Tu`iH#qta�YXO;pt�!ZvJ!ZsÎ_r!ZsÎ>Õ�ZtÎ_�Eu¥P,Q-N±R7Q-N�P,Y-N�cuc!�(Q-qta(�¥Y-T(N±cgP,Q�Y qsaFO�N>Q-Y�qsH9a/d

H

Page 8: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

17

(a) (b)

32

4

1

5 5 6

9887

111010

12 12 13

14 15 15 16

1717

7 9

31

4

5

6

8

2

10

11

12

13

14

15

16

©�qs�9�(Q-N��!¼ [�aFO�N�Q�Y�qsH9auH�v�P�O�Y�qsYXRXT(N�c�cgP,Q�Yw1[1¨PC4�P�ß×N�R7Y-N�cuyDN�O�T�`FH9qta�YXO P�aFcx1}W"4�agN>£²yDN�O�Tu`FH#qta�YY�H#`FH9ztH#�9K.4

�fH#Y�NnY�TFP�Y>Z N> gR7N>`(Y¥vjH9Q�Y�T(NnyDN�O�T�`FH#qta�Y&z�P,WFN>ztN�clÕ!Z®£�NDTFP>rLNnN> gP9R7Y-ztK4Y�£�Hb`FP,qsQXO�vjH#Q&N�P#RUTc(P�Q�Y�qsa(��y�N�O�T�`FH9qta�Y>d ]¡N�O�T�`iH#qta�YXO�c!N>a(H#Y�N�c&W�Ku£BT(qsY�N¥R7qsQXR7zsN�OepLÎ#Z´¬!Zäà(Zv@!ZyH�ZIz�ZtÎ9Î#ZtÎ�¬!ZtÎ�à(ZsÎ_@{u�P,Q-NP9c�Ð-P9R7N>a�YBY�HuY-T(N�c(P,Q-Y�qsa(�&N�c!�9N�O®Y-TFP,Y"P�Q�N�P�ß×N�R�Y�N�cDW�KDY�T(N¥qsaFO�N>Q-Y�qsH9aDH�v Y�T(N�c(P�Q�Y�d G®T(N¥yDN�O�T`FH9qsa!Y�z�P,WFN>zsN�c�Õ�P,a�cÑY-T(N"`FP,qsQ®H,v�y�N�O�T�`FH9qta�YXO z�P�WiN�ztN�cnÎoH�P�Q�N¥R7H#qtaFR�q�c!N>a�Y�H#aDY�T(N«rLN>Q�Y-q�R7N�O�H,vY�TgNuc(P�Q�Y�qsa(��Y�Q�q�P,a(�#ztNLd � vjY-N>Q"c(P�Q�Y"qtaFO�N>Q�Y-qtH9a1ZiY-T(N¥Y�H9`FH#ztH9�#q�R>P�z P,a�cbc!q�O�YXP,a�R7N�Q-N>z�P�Y�qtH#aFO®y��FO�YWFN±yDH�c!qå§FN�c�d�©(H9Q®N� (P�yD`(ztN�Z9P>vjY�N>Q�Y�T(N"qtaFO�N>Q�Y-qtH#aDH,v�Y-T(N¥c(P�Q�Y>Z�Y�T(N"yDN�O�T&`FH#qta�Y®z�P�WFN>ztN�cuà�T�P9OPfa(N�£�a(N>qs�9T�WFH9Q�qsa(�±yDN�O�T�`FH#qta�Y�z�P�WiN�ztN�c]�!Z�P,aFcuY�TgN"c!q�O�YXP,a�R7N®WFN>Y�£®N�N>auY�T(N�yãq�O�O�TgH9Q�Y-N>Q�Y-TFP,aY�TgN�H9Q-qt�#qtaFP�z c!q�O�YXP�aFR7N�WFN>Y�£�N>N>abP#c,Ð-P9R�N>a!YµR7Q�H�O�O�qsa(�LO�d¥G®T(N�RXTFP,a(�#N�qsabyDN�O�Tn`FH9qsa!Y«Y�H9`FH#ztH9�#KP�vjY-N>Q"O�Y-qtYSRUT(N�cDc(P,Q-YfqsaFO�N�Q�Y�qsH9anq�O®qsztzs�FO�Y-QXP,Y-N�c&qsa¡©�qt�9�gQ�N]�B1}WF4SdG®T(N�P9c!r#P,a�YXP��9N�H,v�O�Y�qsYXRXT(N�c6c(P,Q-YXO�q�OfY�T�P,Y¥Y�T(N�K¡Q�N�yDH�rLN�`gT(N>a(H#yDN>aFP�O��FRXT³P9O±�LP�`FO¥P,aFc

H�rLN>Q�z�P,`FO�1�O�N>N�©�qt�#�(Q�NjJ<4Xd G®T(N�qtQ"c!q�O�P9c�r9P�a!YSP,�#N�q�O®Y�TFP�YBY�T(N�KnP,Q-N±ztN�O-O®N7ß×N�R7Y-qtrLNBvjH9QBQ�N�yDH�r!qsa(�P,agH9ynP�ztH9��O®N>rLN>a�YXOªY-TFP,a6Y�Q-qtyDyDN�cuc(P,Q-YXOj1�O�N�N�©�qt�9�gQ�N�O±Îs@&P�aFc�ÎsJC4Xd

|®��@~}$}Ëm�|lkn;(�>o�=� O yDN>a�Y�qtH#a(N�c�N�P�Q�zsqtN>Q�ZÞ£�N¥c!N7§�a(N±Y�£®H�Y�K�`FN�OªH�v�Y�Q-qtyDyDN�c�c(P�Q�YXO�¼ª`FH#ztK��9H9a�P,z�R7�(YSO®P�aFcDztqtagN�P,QR7�(YSO7dGIQ-qtyDy�N�cc(P,Q-YXO$1þvjH#Q�WFH9Y-T*`FH9zsK!�#H9aFP�znP,a�c zsqta(N�P,Q4R7�(YSO:4nTFP>rLN²Y�£®H·P#c!r#P,a�YXP,�#N�O�H�rLN>Q

J

Page 9: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

O�Y-qtYSRUT(N�c�c(P�Q�YXO�¼�qsY�q�O�agH9Y�a(N�R7N�O�O-P,Q-K�Y�H«ynP,YSRUT��(`uY�T(Q-N�P9cgO�P,zsH9a(��c(P�Q�Y�qsa(�¥N�c!�#N�O7ZLP�aFcuY�T(N>Q-N®q�Oa(HuQ-N�O�Y-Q�q�R�Y�qtH#aDP#O®Y�Hu£BT(N�Q�N±Y-Q�qty�yDN>cucgP,Q�YSO®ynP>KuWFN±qtaFO�N>Q�Y-N�cDP�aFcD£BTFP,Y"O�TFP,`FN¥Y�T(N�KDO�T(H9�(z�cWFNLZ(P#OªzsH9a(��P#OªY�TgN>K�P,Q-N±N>qtY-T(N>Q `FH9zsK!�#H9aFO®H#QBztqtagN"O�N>�#yDN>a�YXO7d Ê a&Y-T(N±H9Y-T(N>Q�TFP,aFc×Z!Y�TgN>K&T�P�rLNY�TgN�c!q�O-P9c!r#P,a�YXP��9NDY-TFP,Y¥Y-T(N>Q�Nuq�O±PD`FHLO�O�qtW(qsztqsY�K6H,v°�LP,`�O�P,a�c H�rLN>Q-z�P,`�OfqtabY-T(N�§FY�Y-qta(�nQ-N�O��(zsY>ZP9OB£Bqtzsz�WFN�c!q�O-R7�FO-O�N�cnz�P,Y-N>Q>d

e"Cih����FCFE�;(hW�]�/o�=w�H9zsK!�#H9aFP�z�R��(YXOBP�Q�N�c!N7§FagN�cDW!KDY-T(N±vjH9zsztH�£Bqta(��P#O�O��(yD`(Y-qtH9a�O7¼

0 G®T(N�O�TFP,`FN�H�v�Pu`iH#ztK��9H#aFP,z�R7�(YBq�OBP,a6P,Q-W(qtY-QXP,Q-qtzsKnO�TFP�`FN�c¸`FH9zsK!�#H9a6£BqtY�TgH9�(Y"T(H9zsN�O7d

0 G®T(N«rLN>Q�Y-q�R7N�O�H�v�Y-T(N±`FH9zsK!�#H9a¡yÑP�KuWFN±zsH�R>P,Y-N�cnP,a�K!£BTgN>Q�N±qsaDY�TgN±H9Q-qt�9qsaFP,z/Q-N�R7YSP,a(�#�(z�P�Q£�H,rLN�anR7ztH#Y�T/d

0 �fHuY�£�Hu`iH#ztK��9H#aFP,z�R7�(YSO�ynP>KuH�rLN>Q-z�P,`1d� `iH#ztK��9H#aFP,z�R7�(YBq�O®qtaFO�N>Q�Y-N�cDqtanY�T(N±vjH#ztztH�£Bqsa(��O�Y-N>`FO7¼

Î9d±ÖL`FN�R�q�vjK�P,ztz/Y-T(N¥rLN>Q�Y-q�R7N�OxH�v�Pu`iH#ztK��9H#a¡qta6R7zsH�RUJ�£Bq�O�N±H9QSc!N>Q�d

Õ!d±Ö�R�P,a4Y�T(N�`FH9ztK��9H#aFP,z°P,Q-N�P¡P�aFclO�N�Y�N�rLN>Q�K6yDN�O�T6`FH9qta�Y�qsaFO�q�c!NuY�TgN&`FH9zsK!�#H9alY-H Ê p±G±d�fH#Y�N"Y�TFP�Y®qsa(qtY-q�P,zsztK¥N>rLN>Q-K�yDN�O�T�`iH#qta�Y q�O O�N>Y�Y�HÒ[���Z9£BT(q�RXT�qtyD`(zsqtN�O/Y�T�P,Y Y�T(N«ynP,`(`gqta(�R>P�z�R7�gz�P,Y-qtH#a¡O�T(H9�gz�cDWFN�`FN>Q�vjH#Q�yDN�cDP,YBY-T(N¥yDN�O�T�`iH#qta�Y>d

¬!d�m O�YSP,W(zsq�O�T�a(N>£�Y�H9`FH#ztH9�#q�R>P�z±P�aFcc!q�O�YXP�aFR7NnQ�N�z�P,Y-qtH#aFO�T(qs`FOuWiN�Y�£�N>N>a²Y�TgN¸y�N�O�T²`FH9qsa!YSOzsH�R>P,Y-N�cnP,ztH#a(��Y�T(N¥WFH9QSc!N>Q"H,v Y-T(N¥`iH#ztK��9H#a/d

G®T(N�O�NDO�Y�N>`FO¥P�Q�NuQ�N�`iN�P,Y�N�cØvjH#Q�N�P9RXTb`iH#ztK��9H#aFP,z°R7�(Y>dÒ©�qt�#�(Q�N�@D`(Q�N�O�N>a�YXO±P�a�N> gP,y�`(ztN�H,vY�TgNuqtaFO�N>Q�Y-qtH9a6H,v�P&`FH9ztK��9H#aFP,z�R7�gY>d�ÖL`FN�R7qå§×R>P�ztztK�ZiY-T(N�yDN�O�T¡`FH#qta�YXO¥c!N>a(H#Y�N�c¡W�KnW(z�P#RUJ6O�H9ztq�cR7qsQXR7zsN�O�P,Q-N±Q�N�yDH�rLN�c�W!KuY-T(N±qsaFO�N>Q-Y�qsH9aDH�v�Y�T(N±`FH#ztK��9H9a�P,z�R7�(Y�d�G®T(N«yDN�O�T�`FH9qsa!YSO®c!N>agH9Y�N�cÑW�K£BT(qsY�N�R7qtQSR7ztN�O"z�P,WFN>zsN�c¸vjQ�H#y ÎuY-HlÎ_�6P,Q-NnP�ß×N�R7Y-N�cbW!KbY-T(N&qsaFO�N�Q�Y�qsH9a4H,v°Y�T(N�`FH9ztK��9H#aFP,z"R��(Y>dG®T(N>qsQ�Y-H9`FH9zsH9�9q�R>P,z"P�aFc²c!q�O�YXP�aFR7NnQ�N>z�P,Y-qtH9a�O�T(qs`FO�£BqsY�TlY-T(Nna(N>qt�#T!WFH#Q�qtag�¡yDN�O�Tl`FH9qsa!YSO�y��FO�YWFNuyDH�c!qå§FN�c¡P�`(`(Q-H9`(Q-q�P,Y-N>ztK�d¥©�H#Q±N> gP,yD`gztNLZ(Y-T(NuyDN�O�T¸`FH#qta�Y±z�P�WiN�ztN�c6J&H#Q�qs�9qta�P,ztzsKnTFP9OfvjH9�gQa(N>qs�9T�WFH9QXO�Z(W(�(Y«P�vjY-N>QBY�T(N¥qsaFO�N>Q-Y�qsH9anH,v�Y�T(N¥`FH9zsK!�#H9aFP�z�R��(Y>Z(Y-T(Q�N>N¥H�v�Y-T(N>yæP�Q�N¥Q�N>y�H,rLN�c�d

�®@jE�m!;(�B�]�/o�=V�qta(N�P,Q«R7�(YXOBP�Q�N�c!N7§�a(N�cDW!K�Y�T(N±vjH9zsztH�£Bqtag��P9O�O��(yD`(Y-qtH#aFO7¼

z

Page 10: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

15

2

3

5

6

7

8

9

11

10

1312

14

4

1

©�qs�9�(Q-Nj@!¼ � anN> gP,yD`(zsNfH�v�Y-T(N¥qtaFO�N>Q�Y-qtH#a¸H�v�P�`FH9zsK!�#H9aFP�z R7�(Y

0 G®T(N�O�TFP,`FN�H�v�PuztqtagN�P,Q°R7�(YBq�OBP�O�Y-QXP�qt�9T�YBztqsa(N¥O�N>�9yDN�a!Y�d

0 G®T(N¥N>a�cÑrLN�Q�Y�q�R7N�O H,vxP3zsqta(N�P�QBR7�gYBynP>K&WFN¥ztH�R>P�Y�N�cnP�a!K�£BT(N>Q-N�qsanY�T(N¥H9Q-qt�#qtaFP�z/Q�N�R7YSP,a(¢�#�(z�P�Qf£�H,rLN�anR7ztH#Y�T/d

0 G®£�H&H#QByDH9Q-N±ztqsa(N�P,Q"R��(YXO®ynP>K�a(H9YBH�rLN>Q-z�P�`¸£BqsY�TnN�P#RUTnH9Y-T(N>Q�d

� ztqtagN�P,Q°R7�(YBq�O®qsaFO�N�Q�Y�N�cÑqsanY�T(N±vjH9zsztH�£Bqtag��O�Y�N�`FO7¼

Î9d±ÖL`FN�R�q�vjK�Y�T(N¥Y�£®HuN>a�c¸`FH9qsa!YSO®H,v�PuO�Y�QXP�qt�#T!Y"ztqsa(N¥O�N��9yDN>a�Y>d

Õ!d±Ö�R�P,anY�T(N¥zsqta(NLd

¬!d�m O�YSP,W(zsq�O�T�a(N�£*Y�H#`FH9ztH#�9q�R>P,z°P,aFc4c!q�O�YXP�aFR7N�Q�N>z�P,Y�qsH9aFO�T(qt`�OµWFN>Y�£�N>N>abN>rLN>Q-KnyDN�O�Tb`FH#qta�YH#a¡H9Q"P#c,Ð-P9R�N>a!YBY-H&Y-T(N¥ztqsa(NLd

G®T(N�O�NBO�Y-N>`FO�P,Q-N®Q�N�`iN�P,Y�N�cµvjH9Q�N�P#RUT¥ztqsa(N�P�Q�R7�gY>d � O/qta¥Y�T(N�`FH9ztK��9H#aFP,z�R7�(Y>Z�Y�TgN®qta�Y�N�QXO�N�R7Y�qsH9aR>P�z�R7�(z�P,Y-qtH9a�q�O®`FN>Q�vjH#Q�yDN�c&WFN>Y�£®N>N>a�Y�T(N¥R��(YBztqsa(N¥P,a�cÑY-T(N¥Y�T(Q-N�P9cgO�qsaDY�T(N�O�N�R7H9a�c¸O�Y�N>`1d G®T(Nqty�`iH#Q�YSP,a�Y"c!q�ß×N>Q-N>aFR7N¥WFN>Y�£®N>N�abPuztqtagN�P,Q«R7�(Y«P,aFcbPu`FH9zsK!�#H9aFP�z R7�(Y"q�OBY�TFP�Y±a(HDy�N�O�Tn`FH9qsa!YSOP,Q-NBQ�N>y�H,rLN�c±c!�(Q-qta(�¥P"ztqtagN�P,Q�R7�(Y�Z9N> gR7N>`(Y�£BT(N>a�Pfy�N�O�T¥`FH9qsa!Y�zsqtN�O/H9auY-T(N"R7�(Y�ztqsa(NLd�©�qs�9�(Q-NaHqtzszt�FO�Y�QSP,Y�N�OBP,a¡N� (P�yD`(ztN"H,vxY�T(N¥qta�O�N>Q-Y�qtH#anH,v�Puztqsa(N�P,Q"R��(Y �a�&d�[�anY�T(q�O�N> gP,y�`(ztNLZLH#a(N¥H,v Y-T(NN>aFc4`iH#qta�YXO�H�v±Y-T(NDztqsa(N�P�QuR7�(Y�1T�q4«q�O�zsH�R>P,Y-N�clH9a²P�a²N�c!�9NnH�v"Y�T(NnQ�N�R7YXP�a(�9�(z�P,QÒR7ztH#Y�T/Z�W(�gYP,a4N>aFcb`FH9qsa!Y¥a(N>N�c a(H#Y�P,zt£°P>K(O±WFN&H#a²P,a4N�c!�#NLd�GIH#`FH9ztH#�9q�R>P,z°P,aFclc�q�O�YSP,aFR�NuQ�N>z�P,Y�qsH9aFO�T(qt`�OWFN>Y�£®N>N�a¸y�N�O�T6`iH#qta�YXO"c!N>a(H#Y�N�c¡W�KD£BT(qsY�NÒR7qtQSR7ztN�O®y��FO�YBWiNuy�H�c!q�§FN�c�dfÖL`FN�R7qå§×R>P�ztztK�Z(q�v Y-T(N>Q�Nq�O�P,a6qta�Y�N>QSO�N�R7Y-qtH#a&WFN>Y�£®N�N>aDY�TgN±ztqsa(N�P,Q°R7�(Y°P,aFcnY�T(N±N�c!�9N¥WFN>Y�£®N>N�aDY�£®HuP#c,Ð-P9R�N>a!Y"R�Q�HLO-O�qsa(�LO�Z

Î_r

Page 11: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

B

A

©�qt�#�(Q�N)H�¼ � anN> (P�yD`(zsNfH�v Y�T(N¥qsaFO�N>Q-Y�qsH9anH,vxP3zsqta(N�P,QBR��(Y

Y�TgN�zsqta(J�q�OBc!q�O�R7H#a(a(N�R7Y-N�cnP,aFc¡Y-T(N�c!q�O�YXP�aFR7N¥q�O"RUT�P,a(�#N�c¸Y-H&Y-T(N�c!q�O�YXP,a�R7N±vjQ�H9yæY-T(N�R7Q�H�O�O�qsa(�Y�H�Y�TgN�qsa!Y-N>QXO�N�R7Y-qtH9a1d

Á��(�ÅÆ ¾�Á���� �*¿ À�� �Ì¿ Ä �ØÀÂÁ ��À���� ¾���� Ã�� Ä��ÌÁ À

¾�¿ ����Á À¾®ÃÉ¿

¯fN>Q-NB£®NB§FQXO�Y®q�c!N>a�Y�q�vjK¥Y-T(NfY�K�`FN�O�H,v�P,agH9ynP�ztH9��OxN�rLN>a!YSO�Y�T�P,Y®yÑP�K¥H�R>R��(Q>ZgP,aFc&Y-T(N>a�c!N�O-R7Q�qsWiNT(H�£ÜY-Hu`(Q�N>rLN�a!Y�Y�T(N>y�W!K�qtaFO�N>Q�Y-qta(��cgP,Q�YSO7d

�g�w&%(he��&�w*����� ��e �*ÖLN>rLN�QXP,z°P,a(H#ynP,zsH9�FO�N�rLN>a!YSO�ynP>KbH�R>R��(Q&£BTgN>a²ynP,`(`gqta(�ØP yDN�O�Tl`FH9qsa!YuqsaºP¡�9qtrLN�al`(ztK³H,v£®H�rLN>aÑR7ztH#Y�TnR7H#yD`FHLO�qtY�N�OªWFN>Y�£®N>N�aDÕ�¢�­�P,aFcn¬,¢¨­<O�`FP#R7N�O¥Íáà9Ï�d G®TgNf§FQXO�Y"O�N>YBH�v�N>rLN>a�YXO H�R>R7�(QSO£BT(N>auY-T(NBO�T(N�P�Q�ztqsyDqtYSOiWFN>Y�£®N>N�a�Y-T(Q�N�P9c(O�P�Q�NBN> gR7N>N�c!N�c¥c!�(Q-qta(�±Y-T(NBc�N7vjH9Q-ynP,Y-qtH9a1d�G®TgNBztqty�qtYXOqta�Y�N�Q�ynO�H�v�Y�T(N"Y�TgQ�N�P#c&P�a(�9zsN±WFN>Y�£®N>N>a�T(H#Q�qt¹�H9a�YXP,z×P�aFc&rLN>Q-Y�q�R�P,z�Y�T(Q-N�P9c(O�Z(R>P�ztzsN�c�Y�T(NÒøå÷�î:�#í�ô9õêLô9õ9øsð)1}H#QD¤}Ð-P�yDyDqtag�L¦�P,a(�#ztNG4SZ/P,Q-N&`(Q-N�c!N>Y-N>Q�y�qta(N�cuvjH9Q¥N�P9RXT¡yÑP,Y�N�Q�q�P�z�Y-TFP,Y«q�Of�FO�N�c¡vjH9Q±Y-T(N§FY-Y�qtag�l`(Q�H�R�N�O�ObÍ�z,Ϩd<[¶aH#Y�T(N�QD£®H#QXc(O�ZfP#ODztH9ag�²P9ODY�TgN¡Y�TgQ�N�P#cP,a(�#ztN4P,YnY-T(N¡yDN�O�T�`FH#qta�YO�YSP>K(OBWFN>Y�£®N>N>a6P�R7N>Q-YXP,qsanyDqta(qsyu�(y�1bL<��OI�E4�P,aFc¡ynP� !qsyu�(y�1bL<�����=4®r#P,zs�(NLZ(Y-T(N¥`(ztKDWFN>T�P�rLN�OP9R�R7N>`(YSP,W(zsKLd Ê a�R7NBY�T(NBY-T(Q�N�P9c�P,a(�#ztNB�9HLN�OªWFN>KLH9a�c�Y�T(N"ztqsyDqtYSO7Z>Y�TgNB`(ztK�ynP>K±WFN>�9qsa&Y-H�WFN>T�P�rLNqta6P�a¡�(aFP#R>R7N>`gYXP,WgztN±ynP�a(a(N>Q�d

Î9Î

Page 12: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

©(H9Q�N� (P�yD`(ztN�Z�q�v"Y-T(NDP�a(�9zsND�9HLN�O�WiN�ztH�£�L<��Ov�(Z±¤�£BQ-qta(J�ztqsa(�L¦nH�R>R7�(QSO�P�aFclN>rLN>a�Y��FP�ztztKnY-T(NR7H#yD`FHLO�qsY�NnynP>KlWFN¡Y-H9Q-a·P,`FP�Q�Y>dÜÖLqsyDqtz�P,Q�N>rLN>a�YXO�ynP>KlTFP�`(`FN>a£BT(N>aºY�T(NØP,a(�#ztN6N> (R�N>N�c(OL<�����Ld [�a�N>qtY-T(N>Q R>P#O�NLZ�N> gR7N�O�O�qtrLN°O�T(N�P�QBc!N�vjH9Q�yÑP,Y�qsH9auqsaFc!q�R�P,Y�N�OªP¥`FHLO�O�qtW(zsN±P�a(H9yÑP,ztH#�FOªN�rLN>a!Y�dÊ abY�T(N�H9Y-T(N>Q±TFP�aFc�Z/Y�TgN>Q�NÒP,Q�N�O�qtY-�FP,Y-qtH9a�Ofqta6£BT(q�RXT¡Y-T(N�R7H9y�`iH�O�qsY�NuR�P,a(a(H#Y±WFN�§FY�Y-N�c¸Y-H6PO��gQ�v¨P9R�N�WFN�R>P��FO�N¥H,vxqtYXOBztH�R�P,z/T(qs�9TbR�H9aFR>P>r�qtY�K�H9Q«R7H9a�rLN> �qtY�KLd�G®Tgq�OB`(Q�H�c!��R7N�O"P3`(TgN>a(H9y�N>a(H9aR>P�ztztN�c�¤�W(Q-q�c!�#qta(��¦�1�¤�rLH#q�c(¦<4®H#Qu¤�W(Q-N�P,J#P,�#NLd´¦Ê W!r�qtH#�FO�zsKLZ,Y-T(NBP�a(H9yÑP,ztH#�FO�N>rLN�a!YSO/O�YXP�Y�N�cuP�WFH,rLN°P,Q-N®�(aFc�N�O�qsQXP,WgztNBP�aFcuO�TgH9�(z�c�WiN"P>rLH#q�c!N�c

q�v1`FHLO�O�qtW(zsNLd [�aD�9N�a(N>QXP�z�Z�Y�T(N¥c�q�ÔÑR7�(ztY�K�H,v�`(Q-N�c!q�R�Y�qtag��P�aFcD`(Q�N�rLN>a!Y-qta(�µP,a(H#ynP,zsH9�FO N>rLN>a�YXO�qta(¢R7Q-N�P9O�N�Oªqsa&`(Q-H9`FH9Q-Y�qsH9anY�H�Y�T(N«R7H9y�`(ztN> �qtY�K±H�v�Y�T(N«�9qtrLN�aD¬�¢�­ÜO��(Q�v¨P#R7N¥O�TFP,`FN±Y-H�WFNf§FY-Y�N�c�ZLY-T(NR7H#yD`(ztN� !qsY�KuH�v Y�TgN�yÑP,Y�N�Q�q�P�z�`(Q-H9`FN>Q-Y�qtN�O�H�v Y�T(N��9qsrLN>a6Õ,¢¨­ã`(zsK¸H�v £®H�rLN>a6R7zsH9Y-T¡R�H9yD`FHLO�qtY-N�O7ZP,a�c&Y�T(NµR7H9yD`gztN> �qtY�K¥H,v�Y-T(Nfqsa(qtY-q�P�z�R�H9aFc!qsY�qsH9aFO�vjH9Q®Y-T(Nf§FY-Y�qsa(�(d ¯fN�Q�NB£®N«ztqty�qtY�H9�(Q°P,Y�Y-N>a�Y�qtH#aY�H�Y�T(NÒP,a(H#ynP,zsH9�FOfN�rLN>a!YSOBR>P,��O�N�c¡W�KnN> (R�N�O�O�qtrLN¥O�T(N�P,Qµc!N7vjH9Q-ynP,Y-qtH#a/d"[¶a6Y�T(q�Of£BP>KLZF`(Q-N�c!q�R�Y�¢qtag�nP,a(H#ynP,zsH9�FO±N>rLN�a!YSO�WFN�R7H#yDN�O®Q-N>z�P�Y�qtrLN�ztKnO�Y�QXP�qt�#T!Y�vjH9Q�£°P,QSc�Z�O�qta�R7NuH9a(zsK¡Y-T(NuY�T(Q-N�P9cbP�a(�9zsNztqsyDqtYSP,Y-qtH9a�OxQ-N�ÛL�(qtQ-N¥R7H9a�O�q�c�N>QXP�Y�qtH#a/d­±P,Q-Y�qsaFO�N>Q-Y�qsH9a/Z�£BT(q�RXT�q�O�Y-T(NDR�N>a!Y-QXP�zxvjH�R��FO�H�v"Y�T(q�O�`FP�`iN�Q>Z�`gQ�H�r!q�c!N�O±H9agNnP,`(`gQ�HLP#RUT²Y-H

`(Q-N>rLN>a�Y�qtag�DP�a(H9ynP�ztH#�FO±N>rLN>a�YXO±R>P��FO�N�c W�K¡N> gR7N�O-O�qsrLN�O�T(N�P�Quc!N7vjH#Q�ynP�Y�qsH9a/d�G®T(q�O±yDN�Y�T(H�c¡q�OÛL�(qtY-N&N7ß×N�R�Y�qtrLNu£BTgN>alY�TgNDynP,Y-N>Q�q�P,z��gaFc!N>Q-�9HLN�O�yDqsa(qty�P,z�O�TgN�P,Q�c!N�vjH9Q�yÑP,Y�qsH9a4H9Q�£BT(N>alY-T(NO��gQ�v¨P9R�Nbq�O&T(qs�9T(zsKR7�gQ�rLN�c�d � c(c�qtY�qsH9aFP�zfy�N>Y�T(H�cgO3vjH9Qn`(Q-N>rLN>a�Y�qtag�4P,a(H#ynP,zsH9�FODN>rLN>a�YXO�P,Q-N`(Q-N�O�N>a�Y�N�c&qta³Í à#Ï�dG®T(N>Q-NBP,Q-NBY�£®H"`(Q�H#W(ztN>yÑOIQ-N>z�P�Y�N�c±Y�Hµc(P,Q-Y�qtaFO�N>Q�Y-qtH#a/¼�1�Îo41£BT(N>Q�N°c(P,Q-YXO�O�T(H9�gz�c�WFNBqtaFO�N>Q�Y-N�c�Z

P,a�c�1¨ÕC4 £BTFP�Y"O�TFP�`FN�O�Y-T(N>K�O�T(H#�(z�cDWFNLd [�c!N�P�z/c(P�Q�YBqsaFO�N>Q-Y�qsH9aD£�H9�(z�cÑ`gQ�N>rLN>a�Y�P,zsz/P,agH9ynP�ztH9��ON>rLN>a�YXO�Z!�FO�qta(�uY-T(N�O�qsyD`(ztN�O�Y�¢¨O�T�P,`FN�cnc(P,Q-YXO�d

� !a ��, �fih��5 .* �a!w&�j���¢¡) �£��w*5 ��� � /�G®T(N"O�H9zt�gY�qtH#auY�H±Y-T(NB`(Q-H9W(zsN>y<H,v1c(P,Q-Y�ztH�R�P,Y�qsH9auWFN�R7H#yDN�O/Y�QSP9R7YSP,W(zsN®q�v×£�N®ztqsyDqtY×H9�(QxP,Y�Y-N>a�Y�qtH#aY�H�P,agH9ynP�ztH9��O�N>rLN�a!YSO®R>P��FO�N�cnW!K�N> (R�N�O�O�qtrLN«O�T(N�P�Q±c�N7vjH9Q-ynP,Y-qtH9a1dª�qsY�TnY�T(q�O®ztqsyDqtYSP,Y�qsH9a/ZLY-T(N`(Q-H9W(zsN>y R>P�a$agH,£ÉWFN�Q-N>`(T(QSP9O�N�c$P#OÑH#a(N4H,vuq�c!N>a�Y�qåvjK!qsa(��Y-T(N4Q�N>�#qtH9a·qta£BTgq�RXTN> (R�N�O�O�qtrLNO�TgN�P,QÒc!N7vjH9Q-ynP,Y-qtH#a�N> �q�O�YXO�dn[¶a4N�O-O�N>aFR�NLZ�c(P,Q-YXOuO�TgH9�(z�c�WFNDqtaFO�N>Q�Y-N�cb£BT(N>Q�N�N> gR7N�O-O�qtrLN�O�T(N�P�Qc!N7vjH#Q�ynP�Y�qsH9a�q�O�ztqsJLN>ztK«Y�H±H�R>R��(Q>ZL�(aFc�N>Q��9qsrLN>a�qsa(qtY-q�P�z(R7H#aFc!qsY�qtH#aFO7d���NBTgN>Q�N�P>vjY�N>Q�Q�N�vjN>Q�Y�HµO��FRXTP¸Q-N>�9qsH9a²P#O�P³î>ó7ítì¨í�îXê9ø�óUðjõLí�÷Lô�d � Q-qtY�q�R>P,z�Q�N>�#qtH9a�O�P,Q-NnR7z�P9O�O�q�§FN�c qsa!Y-H¡Y�£®HnY�K!`FN�O�¼B1�Ît4uøå÷<2 ð�óî>ó�ítì�í�îXê9ø×óXðjõLí�÷LôÞë�ZLqta�£BT(q�RXT�Y�T(N"Y�T(Q-N�P9c�P,a(�#ztN"H,v�N>rLN>Q-K�yDN�O�Tu`FH9qsa!Y�q�O�ztN�O-O�Y�TFP�aBL<��Ov�uP,a�cx1�Õ<4ú>òLòiðUó&î>ó�ítì¨í�îXê9ø óUðjõLí�÷LôLë�Z�qta4£BT(q�RUTbY-T(NDY�TgQ�N�P#c�P�a(�9zsNDH,v°N>rLN>Q�K6yDN�O�Tb`iH#qta�Y�q�Oµ�#Q�N�P�Y�N>Q¥Y-TFP,a

Î>Õ

Page 13: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

L<�����Ld[�a�H9QSc!N>QDY-Hlq�c�N>a!Y-q�vjKlY-T(N¡N� !q�O�Y�N�aFR7NnH,vÒPlR7Q-qtY-q�R>P�zBQ�N>�#qtH9a1Z®£®N4O�YXP,Q-YDW�KË�#N>a(N>QSP,Y-qta(�²P�a

qtagqtY�q�P,z®§FY-Y�qsa(�(Z®�#qtrLN>aºP�`(`(Q�H#`(Q�q�P,Y-Nbqta(qsY�q�P�z"R7H9a�c!qtY-qtH9a�O¡Íä¬,Ï�d G®T(N>a�£�NbR>P�a�N>qsY�T(N�Qu`(ztH#Y&Y-T(Nc!q�O�Y�Q-qtW(�gY�qtH#a�H�v±Y-T(Q�N�P9clP�a(�9zsN�O�WFN>Y�£®N�N>a�Y-T(N�£®N7vjYÒP,aFc�Y-T(ND£°P,Q�`çP,Y�N�P9RXTlyDN�O�Tb`iH#qta�Y>Z�H#QO�T�P9c!NBN�P#RUT�yDN�O�T�`FH9qsa!Y P«R7H9zsH9Q�P9O�O�H�R7q�P�Y�N�cu£BqtY-T�Y-T(NBY�T(Q-N�P9cuP�a(�9zsNLd��TgN>auY�T(N�Y�T(Q-N�P9cuP�a(�9zsNP,YµP3yDN�O�Tn`FH9qta�Y±N> gR7N>N�c(O®Y�T(N�yDqtagqtyu�(y�zsH�RUJ�qta(��P,ag�9ztN�1bL<��OI�{4SZi£�N�ynP�Q�JDY-T(N�y�N�O�Tn`FH9qsa!Y�ZH9Q«O�T�P9c!N�qtY"P�O��(qsYXP,WgztN�R7H9zsH9Q�ZFO��FRXT6P9OfQ-N�c�d®ÖLqsyDqtz�P,Q�zsKLZL£BT(N>anY�TgN�Y�TgQ�N�P#c¸P�a(�9zsN�N> gR7N>N�c(OªY-T(NynP� !qsy&�(y�ztH�RXJ!qsa(��P,a(�#ztNB1~L<�/�-�G4XZF£®N�ynP,Q-JDY�TgN�yDN�O�TD`FH9qsa!Y�ZiH#Q¥O�TFP#c!NuqtY"P�O��(qsYXP,WgztN�R7H9zsH9Q�ZO���RUT²P#O�W(zt�gNLd Ê Y�T(N�Q�£Bq�O�ND£®NÑO�J�qt`lY-T(NDyDN�O�T�`FH#qta�Y>Z�H9Q�O�TFP9c�NDqtYÒP,a(H#Y�T(N>Q�R�H9ztH#Q>Z O��FRUTçP9O�9Q-N>N>a/d Ê vµR7H9�gQXO�N�Zª£�N¡R�P,aºR7H9a�Y�qsa!�gH9�FO�ztK²R7H#ztH#QuN>rLN>Q�Kby�N�O�Tl`FH#qta�Y&W�K�qsa!Y-N>Q�`FH#z�P,Y-qta(�bY�£�HN> �Y�Q-N>yDN«R7H9zsH9QXO®vjH9Q"Y�TgN�ztH�RXJ�qta(��P�a(�9zsN�O7dB©�qtaFP�ztztK�Z!W�K¸Y-QXP#R7qta(��Y�TgN�yÑP,Q�JLN�c&yDN�O�T¸`FH#qta�YXO7Z(£�NR>P�a¸q�c!N>a�Y�qåvjKDR7Q-qtY-q�R>P�ziQ-N>�9qsH9aFO�d

� !ah/ ¤fih��5 .*g�a!w&�j���¥¡) �£5�w*5 /�5 . /�Ê aFR7N R�Q�qtY-q�R>P�z9Q-N>�9qsH9aFO�TFP>rLN�WFN>N�a�q�c!N>a�Y�qå§FN�c�Z�Y�T(N Y�K!`FN�H�vFcgP,Q�YSOIY-TFP,Y/WFN�O�YI§�Y/qta�Y�H®N�P9RXT�R�Q�qtY-q�R>P�zQ�N��9qtH#a¥y&�FO�Y�WFNBc�N>Y�N>Q-yDqtagN�c�d×[¨v�PBR7Q-qtY�q�R>P,z#Q�N>�#qtH#a�q�O�R�H9yD`(zsN>Y�N�ztK®qsaFO�q�c!N�Y-T(N �9qtrLN�a�Q-N�R7YSP,a(�#�(z�P�Q`(zsKLZ!Y-Q�qty�yDN>cucgP,Q�YSOfP�Q�N±Y-T(N¥H9a(zsKnRXT(H9q�R7NLd�[}v-Z!H9a6Y�T(N«H9Y�TgN>QBTFP,a�c�ZFPuR7Q�qsY�q�R>P,zFQ�N��9qtH#anY�H9��RUT(N�OY�TgN¸WFH#�(aFc(P�Q�K²H,v¥Y-T(Nn`(ztK�Z�N>qtY-T(N>QuO�Y�qsYXRXT(N�c�H#Q&Y-Q�qty�y&N�cbcgP,Q�YSO3yÑP�K4WFN6P,`(`(zsq�R>P�W(ztN�dlG®T(q�OQ�N�O�Y�Q-q�R7Y-qtH#abQ�N�O��(ztYSO�vjQ�H#y_Y�T(N�P9O-O��(yD`gY�qtH#aFO±�FO�N�c qsabH9�(Q¥yDH�c!N�z�OfH�v"O�Y-qtYSRUT(N�cbP,aFcbY�Q-qtyDyDN�cc(P�Q�YXO�d�fN> �Y>Z9Y-T(N"O�T�P,`FNfH�v/N�P#RUT�cgP,Q�Y y��FO�Y�WFN"c!N>Y-N>Q�yDqsa(N�c�d1G®T(NBH9`(Y-qtynP�z(O�TFP,`FN±q�O�Y�TgN"O�qty�`(ztN�O�Y

H9agN�Y-TFP,Y6Q�N>yDH�rLN�OuP�ztz�R7Q-qtY�q�R>P,z"Q�N��9qtH#aFO¸£BqsY�TY-T(NlO�qtyD`gztN�O�YDO�TFP,`FNLd � agH9Y�TgN>QnH9`(Y-qtynP�ztqtY�KR7Q-qtY�N�Q�qtH#a&yÑP�KuqsaFR7zs�Fc!N±Y-T(N±N�P#O�N±H�v�qsaFO�N>Q-Y�qsa(�uc(P�Q�YSO7d�[¶a�Y��gqtY�qsrLN>ztK�Z,Y-T(N±ztN�O�OªQSP,�#�9N�cnY�T(N¥O�TFP,`FNq�O�Z,Y-T(N WFN>Y�Y-N>Q�qsY/ynP>KfWFNLd�[�Y/q�O�c!q�ÔÑR7�(zsY�Y�H«c!N>Y-N>Q�y�qta(N�Y�T(N�H9`(Y-qtynP�zLO�TFP,`FNLZ9WFN�R�P,�FO�N®Y�TgN®O�TFP,`FNH,v«Y�TgNnR7Q�qsY�q�R>P,z�Q-N>�9qsH9al`gQ�H�r!q�c!N�O¥ztqtY-Y�zsN&qsaFO�qs�9T�Y�qsa!Y-H¡Y-T(NDH9`gY�qtyÑP,z�O�TFP�`FN¸H�v±Y-T(Nnc(P�Q�Y�Y�HbWFNqta�O�N>Q-Y�N�c�d�p±O���P,ztzsKLZLP¥c(P�Q�Y®£BTgHLO�N«O�T�P,`FN±q�O O�ynP,zsztN>Q�Y�TFP�a&Y-T(N«R7Q�qsY�q�R�P,z�Q�N>�#qtH9a�q�O O��!ÔnR�qtN>a�Y>d�[�aH9QSc!N>Q Y�H¥§FaFc&Y-T(N"H9`(Y-qtynP�zFO�TFP�`FNLZ!£�NfN>y�`(ztH�K�P¥O�Y�QSP,Y-N>�9K�WFP9O�N�c&H#anP±Q�N>z�P, gP,Y�qsH9a�Y�N�RXT(a(q�ÛÞ�gNLd[�a�H#Y�T(N�Q�£®H#QXc(O�Z�£®N�O�YSP,Q�Yu£BqsY�T³Pbc(P,Q-Y�H�v«P¡R7N>Q-YXP�qta³O�TFP�`iNnY-TFP,Y�qtaFR7zs�Fc!N�O¥Pn`FP,Q-YB1}H#Q�Y-T(N£BT(H#ztNG4BH�v�Y�T(N�R7Q-qtY-q�R>P�z/Q�N>�#qtH9a1d¥G®T(N>a/Z�£�NuO��FR>R7N�O-O�qsrLN>ztKDy�H�c!q�vjKnY�TgNuO�T�P,`FNDO�HnY�TFP�Y±qtabN�P#RUTO�Y-N>`n£®N�R>P�a¡c�N�R7Q�N�P9O�N¥Y-T(N�R7Q�qsY�q�R�P,z�Q-N>�9qsH9an�(a�Y�qsz�a(H#a(N�q�O®ztN7vjY�d� alqsyD`FH9Q�YSP,a�Y�R7H9yD`FH#a(N>a�Y�H�v"H9�(QuQ-N>z�P� (P�Y�qsH9alY-N�RUTga(q�ÛL�(Nuq�O�P¸�#HLH�cËqtagqtY�q�P,z�c(P�Q�YuO�`FN�R7qt¢

§×R>P�Y�qsH9a/dn[}vB£�NDO�YXP�Q�Y�£BqsY�T³P,a²P�Q�W(qsY�QSP,Q�K�¢¨O�TFP�`iN�cç`FH#ztK��9H9a�P,z"R7�(Y�Z/�LP,`�OuP,aFc�H�rLN>Q-z�P�`FO±ynP>K

Î>¬

Page 14: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

overlap

"polygonal cut"

X Y

Z

gap

©�qs�9�(Q-NjJ!¼ � a�N> (P�yD`(zsNBH,v�Y�T(N±qsaFO�N�Q�Y�qsH9aDH�v P¥`FH9ztK��9H#aFP,z�R7�(Y�¼e1¨PC4�§FY-Y�qtag�uN> (P�yD`(zsNBqtaD£BT(q�RUTPu�LP,`ØP,aFc6P,anH�rLN>Q�z�P,`nH�R>R7�gQ>ZFP,a�c¦1}W"4 Y�T(N¥`(z�P,a(N�c!N>rLN�ztH9`gyDN>a�Y�`FP,Y-Y�N>Q-a

H�R>R7�gQ"P,YBY�TgN�O-P,yDN«Y�qty�NLZLP9OBO�T(H�£Ba¡qsan©�qt�#�(Q�N]J�d®ÖLqtyDqsz�P�Q�ztK�Z9q�v�£�N¥O�YSP,Q�Y"£BqtY-TnP,aØP,Q-W(qtY-QXP,Q-K!¢O�T�P,`FN�c¡O�Y�qsYXRXT(N�c�c(P,Q-Y>ZFPuO�H#zt�(Y-qtH#a¸Y-HuY�T(N¥ynP�`(`(qsa(�uR>P�z�R7�gz�P,Y-qtH#aFOªynP>Kua(H#Y"P,zs£BP>K(O®WFNfvjH#�(aFcÍݬ�Ï�d Ê anY�T(N«H9Y�TgN>QfT�P,aFc�Z(qåv�£®N�O�YSP,Q-Yf£BqsY�TnPuztqsa(N�P,Q°R7�(YBqsaFO�N>Q-Y�N�c�qta�Y�H�PuR7Q-qtY�q�R>P,z×Q�N>�#qtH#a/Z!Y-T(NQ�N�O��(zsY±H,v°Y�T(N�§FY-Y�qsa(�nynP>K¸`gQ�H�c!�FR�NuN>qtY-T(N>Q¥PD�LP�`�H#Q�P,a4H,rLN�Q�z�P�`/Z�W(�gY±a(H9Y¥WFH9Y-T/d�G®T(q�O¥R>P�aWFN&N� !`(z�P,qsa(N�c¡W�KbY�T(Nuv¨P9R7Y¥Y-TFP,Y�P¸zsH�£®N>Q¥R�Q�qtY-q�R>P�z�Q�N��9qtH#a�q�O¥R>P,�FO�N�cbW!K4PnO��gQ�`(zs�FO�H�vB£®H�rLN>aR7zsH9Y�T6ynP,Y-N>Q�q�P,z¨ZÞ£BTgqtztNÒP,a6�(`(`FN>Q«R7Q�qsY�q�R�P,z/Q�N��9qtH#a¡q�OBR>P,�FO�N�c¡W�KnP&O�T(H9Q-YXP��9NuH,v�qsY>dBG®T(q�O�q�OfP�aqty�`iH#Q�YSP,a�Yª`gQ�H9`FN>Q-Y�KuY�TFP�Y®q�O �FO�N�vj�(z(vjH9QBc�N>Y�N>Q-yDqtagqta(�"Y�T(N«H9`(Y-qtynP�zFO�TFP�`FNfvjH9Q°P�c(P�Q�Y>d [�Y�ynP>KWFN±vjH9Q�yÑP,ztzsKDO�YXP�Y�N�cnP9O®vjH9zsztH�£"O7¼

e¥��C,§ m��>oX��¨ª©töÑê�øåí�ôið-êLónî>úLì�í�ëní�ôÞë�ðUóUì�ð-ñlí�ô!ì¨÷lêbøå÷<2ªð�ó6î>ó7ítì¨í�îXê9øBóXðjõLí�÷LôC«¥ì�ïFðfüxì}ì¨í�ô9õ²óUð-ë�úÞø´ìýuêLû3ò×ó-÷�ñLú!î7ðÒêLôl÷Lÿ,ð�óXøåê7òK¬�©tö�ê¡øåí�ôFð-êLó&î>úLì¥í�ë�í�ôÞë�ðUóUì�ð-ñ�í�ô�ì�÷bêLô²ú>òLòiðUó&î>ó�ítì¨í�îXê9ø óUðjõLí�÷Lô<«"ìþïFðü ìjì�í�ô#õ¡óXð�ë�úÞøéìBýuêLûfò×ó�÷�ñLú�î7ð¥ê�õ�ê7òK¬

\®K�YSP,J�qta(�ÒP9c!r#P,a�YXP��9N±H�v/Y-T(q�O�`(Q-H9`FN>Q�Y�KLZL£�NfTFP>rLN"c!N�rLN>ztH#`iN�cuP,anP�zt�9H#Q�qsY�T(y*vjH#Q®c�N>Y�N>Q-yDqtag¢qtag�¸Y-T(NuH9`gY�qtyÑP,z O�TFP,`FNuvjH9Q�P¡c(P�Q�Y¥£BT(N>a4H9agztK¡zsH�£®N>Q¥R�Q�qtY-q�R>P�z�Q-N>�9qsH9aFO±N> �q�O�Y>d � O�O�T(H�£Ba�qsa©�qs�9�(Q-Njz!ZFPuztqsa(N�P,Q°R7�(Y�q�O®qta�O�N>Q-Y�N�c&qsa!Y-HuN�P9RXTDzsH,£�N>QBR�Q�qtY-q�R>P�zFQ�N>�#qtH9anqsa¸Y-T(Nf§FQSO�Y«O�YSP,�9N¥H�v�Y-T(NP,zs�9H#Q�qtY-T(ybd«[¶Y«O�TgH9�(z�c¡WiNuagH9Y�N�c¡Y�TFP�Y±Y�T(q�O±P,zs�9H#Q�qtY-T(y_c�HLN�Ofa(H#Y¥R7H�rLN>Q"Y�T(NÒR>P9O�Nuqtab£BT(q�RUTØPztqsa(N�P�Q�R��(Y¥q�O±qtaFO�N>Q�Y-N�cbqta�Y�H6P,a4�(`(`FN>QÒR7Q�qsY�q�R�P,z�Q-N>�9qsH9a/d � O�O�YXP,Y-N�cbqta³e���C.§ m!�>oX��¨FZ�P¸��P,`ynP>K�H�R>R7�(Q±£BTgN>abPuztqsa(N�P,Q"R��(Yfq�O�qsaFO�N�Q�Y�N�cÑqsa!Y-HDP�a¡�(`g`iN�Q±R7Q-qtY-q�R>P�z/Q�N>�#qtH9a1dB[�a¡Y�Tgq�O"R>P9O�NLZ�P�ztzY�T�P,YBq�O®agN>N�c!N�c�q�OªY-H&`gQ�N>`FP�Q�N¥P�a(H9Y-T(N>Q"`(ztK�P,a�cÑ`�P,YXRXTn�(`nY�T(N«�LP,`6£BqtY-TDqtY�d ]¡H9Q�Nµc!N>YXP�qtz�O®H,v

Î7à

Page 15: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

Y�TgN�P�zt�#H9Q�qsY�T(yØZ!N�O�`iN�R7q�P�ztztK�H9anY-T(N¥Q�N>yDH�r#P,z×H,v�H�rLN>Q�z�P,`FO�Z!£Bqtzsz/WFN��#qtrLN>a�qtanY�T(N¥a(N� !Y"O�N�R7Y�qsH9a/d\®N7vjH9Q-NB`(Q�H�R�N>N�c!qsa(�¥Y�H¥Y�T(N«c!N�O-R7Q�qs`(Y�qsH9auH�v/H�rLN>Q�z�P,`(`gqta(�±Q-N>yDH�r#P,zgP,zs�9H9Q-qtY-T(ynO7Z#qtY�O�T(H#�(z�cuWFN

Q�N�ynP,Q-JLN�c¸Y-TFP,Y±§FaFc�qta(�nY�TgNuWiN�O�Y¥qta(qsY�q�P,z�zsqta(N�P�Q±R��(Y¥q�O±O�Y�qtzsz P,a4H9`FN>a4`(Q-H9W(zsN>ybd � O¥O�N>N>abqsaH9�gQªqsa(qtY-q�P�z!N> �`FN>Q�qsyDN>a�YXO�Z>T(H�£®N>rLN>Q�ZLP±�9HLH�cDO�H9zs�(Y�qsH9a�q�O�H#W(YXP�qta(N�cu£BT(N>a�Y�TgNBqta(qsY�q�P�z!zsqta(N�P,Q R7�gY�9HLN�OfY�T(Q-H9�(�#TbP�R7Q�qsY�q�R>P,z×Q�N>�#qtH9aØP,aFcnQ�N�P#RUTgN�OBO�zsqt�9T�Y�zsK&qsa!Y-HuY�T(NÒO��(Q-Q�H#�(aFc!qsa(�&agH9Q�yÑP,z/Q�N��9qtH#a£BT(N>Q-NnY�T(NnO�T(N�P�Q�c!N7vjH9Q-ynP,Y-qtH#alq�O�£BqsY�T(qsaËY-T(NnP�ztztH�£°P,W(zsNDztqsyDqtYSO7d�ÖLN�Nn©�qt�#�(Q�N�ODÎoHl1}W"4�P,aFcÎ_z�1�c.4�vjH9Q"N> (P�yD`(zsN�O�H,v H#�(QBN> �`iN�Q�qty�N>a!YSP,z×R7�(YBqsaFO�N�Q�Y�qsH9aFO�d

Ã�­���Á�®��¥¯�¯ ¾�¿ � Á���� Ã�­��¥® �¥® � ÃÅÁ ¾�À�° � �

� OfN� !`(z�P,qsa(N�c¸qsabY�T(Nu`gQ�N>r�qtH#�FO±O�N�R7Y�qsH9a/Z�H�rLN>Q-z�P�`FO�yÑP�KnH�R>R��(Q±qtabY-T(N�§FY-Y�qtag�¸Q-N�O��gztY"£BT(N>a³Pztqsa(N�P�Q R7�(Y q�O�qtaFO�N>Q�Y-N�c�qta�Y�H�P±ztH�£®N�Q R7Q�qsY�q�R>P,z�Q�N>�#qtH#a/d [�auQ�N>��P,QXc�Y�H±§FY�Y-qta(��P¥Õ,¢¨­$`(zsK�H�v/£®H�rLN>aR7zsH9Y�T R7H9y�`iH�O�qsY�N�O�Y-H²P Q-N�P,z«¬,¢¨­_O��gQ�v¨P9R�NLZ®yDqsa(H9QuH�rLN>Q-z�P,`�OuP,Q�N¡vjQ-N�ÛL�(N>a�Y�ztK4H9W�O�N>Q-rLN�c²P,aFcP9R�R7N>`(YSP,W(zsNLdu]bP,Ð�H#Q±H�rLN>Q�z�P,`FO�Z�T(H�£®N>rLN�Q>Z/R>P��FO�N�O�N�Q�qtH#�FOf`(Q-H9W(zsN>ynO�Z/O�qsaFR7NuY�TgN>K¡ynP>K6RXTFP,a(�#NY�TgNnO��(Q�v¨P9R7N�`(Q�H�§FztN±1�R>P�ztzsN�c Y-T(Nn[�]bV�H9Q�©�ôÞë�í�ñ!ð)² ÷9øåñD³xí�ôið[4µP,aFc²P�ztY�N�Q�Y-T(ND�(agq�vjH9Q-yDqtY�K6H,vO�Y-Q��FR�Y��(QSP,z�Q-N>qta�vjH9QXR�N>yDN>a�YXO�d Ê �(Q®�#HLP,z/q�OªY-T(N>Q�N�vjH9Q�N"Y�H�Q�N>y�H,rLNByÑP,Ð�H9Q H�rLN>Q�z�P,`FO P�aFc&§FaFc&Y-T(NH9`gY�qtyÑP,z/O�TFP,`FN¥vjH9Q"P�c(P,Q-YfY-TFP,YBq�O�Y-HuWiN�qtaFO�N>Q�Y-N�c&qsa!Y-H�P3zsH,£�N>QBR�Q�qtY-q�R>P�z�Q-N>�9qsH9a/d� O�O�T(H�£Bauqta�©�qs�9�(Q-N;z!Z#H9�(Q�vj�gaFc(P,y�N>a!YSP,zgP,zs�9H9Q-qtY-T(yÜvjH9Q�Q-N>yDH�r!qsa(�BH�rLN>Q�z�P,`FO/qta�R7zt�Fc�N�OIY�£�H

ynP,Ð�H#Q¥O�Y-N>`FO�¼)1�Îo4B§Fa�c!qta(��H,rLN�Q�z�P�`FO±P�aFc´1¨ÕC4"�(`×c(P�Y�qtag�¡Y�TgN�O�TFP�`iN�H,v�Y�T(N�c(P�Q�Y>dÒG®T(N&H#Y�T(N�QY�£®HnO�Y�N>`�OfqtaØ©�qt�#�(Q�N�z�Z®¤XO�N>ztN�R�Y±P�abH,rLN�Q�z�P�`(`(qsa(�DyDN�O�Tn`iH#qta�YfvjQ�H#yÅY-T(N Ê rLN>Q�z�P,`(`(qsa(��w�H9qsa!YV�q�O�Y�1 Ê w V�4XZ´¦6P,aFc·¤�Q�N�yDH�rLN�Y�TgNuyDN�O�Tb`FH#qta�Y>Z´¦D£Bqsztz�WFNnc!N�O�R7Q-qtWFN�cbP,zsH9a(�6£BqtY-T�Y-T(NDO�N�R7H#aFcynP,Ð�H#QBO�Y�N>`/d

µ�+7�w�¶+7�w·�¸��; ��?��h�'j*G®T(N&§�QXO�YuyÑP,Ð�H9Q�O�Y-N>`lY-H,£°P,QSclc!N>Y-N>Q�yDqsa(qtag�DY�T(N�H9`(Y-qtynP�z®O�TFP,`FNnH,v«P6c(P,Q-YuY�H6WiNnqsaFO�N>Q-Y�N�cqta�Y�H6PnztH�£®N>Q�R7Q-qtY-q�R>P�z�Q-N>�9qsH9alq�OµY-H¸§Fa�c�H�rLN>Q�z�P,`FO�d � O-O��(yDqsa(�DY-TFP,Y�WiH#Y�T²Y�TgNDÕ�¢�­ P�aFc�Y-T(N¬,¢¨­Üc!N�vjH9Q�y�N�c3£�H�rLN>a�R7ztH#Y�T�R7H9y�`iH�O�qsY�N�O P,Q-N¥P,`g`(Q�H� �qtynP�Y�N�c�W�K�P�R7H#ztzsN�R7Y�qsH9auH�v�Y�Q�q�P,a(�#ztN�O�Z�P9OO�TgH,£Ba4qta4©�qt�9�gQ�NnÎ_r�Z/H,rLN�Q�z�P�`FOfqsabY�T(N�§FY-Y�qsa(�nQ�N�O��(ztY±yÑP�K�WiNuvjH9�gaFc £BqsY�T4PD`FH9qsa!Y-¢}Y-Q�q�P�a(�9zsNztH�R�P,Y�qsH9a4P�zt�9H#Q�qsY�T(yÉqtab¬�¢�­ÂO�`�P9R7NLd�Ö�`iN�R7q�§×R�P,ztzsKLZ(N>rLN>Q-KDyDN�O�T¡`FH9qsa!Y«q�OBY�N�O�Y�N�c¸vjH#Q±qtaFR�zt�FO�qtH9aqta³N�P9RXT�Y-Q�q�P,a(�#ztNDqsa²¬,¢¨­æO�`FP#R7NLd � alH�rLN>Q�z�P,`4q�O¥q�c!N>a�Y�qå§FN�c¡qåv"Y�T(ND`gQ�H9Ð�N�R�Y�qtH#a�H�v±Y-T(N�yDN�O�T`FH9qsa!YM¹ùwBè�H9a�Y�HDY-T(Nu`(z�P,a(N�vjH#Q�yDN�cnW!KnY-T(Q�N>Nuy�N�O�Tn`FH9qsa!YSO7Z � Z×\±Z�P�aFc � Z×q�OfzsH�R>P,Y-N�c¡qtaFO�q�c!NY�Q-q�P�a(�9zsN � \ � Z(P9O"O�TgH,£Ba6qta6©�qs�9�(Q-NuÎ9Î#d

Î_�

Page 16: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

OPL empty

start

?

read woven cloth

composites

no

yesstop

Select an overlapping

mesh point from OPL

Safe to remove Remove the mesh pointyes

Update OPL and the dart shape

no

write

and find overlaps

Insert a linear cut,perform mapping,

?

©�qs�9�(Q-NBz�¼ � zt�#H9Q-qtY�TgyÅvjH9Quc�N>Y�N>Q-yDqtagqta(��Y�T(N�O�T�P,`FNnH,v"P6c(P,Q-Y�Y-H¡WFNDqta�O�N>Q-Y�N�cbqta�Y�H6P¸zsH�£®N>QR7Q-qtY�q�R>P,z×Q�N>�#qtH#a

©�qt�#�(Q�N�Î_r�¼®G/Q�q�P,a(�#�(z�P�Qfy�N�O�TnP�`(`(Q-H, �qtyÑP,Y�qsH9a&vjH#Q�§�aFc!qtag�uH,rLN�Q�z�P�`FO

G®T(q�OuO�qtyD`gztN�P,zt�#H9Q-qtY�Tgy £®H#Q�JgO�£®N>zszBP9OuztH#a(�4P9OuY�TgN¡c�q�O�YSP,aFR�NDWFN>Y�£®N>N>açP9c,Ð-P#R7N>a�YuyDN�O�T`FH9qsa!YSOÑq�ODO���ÔnR7qsN>a�Y�ztKºO�ynP,zsz±P�aFcâY-T(NbY�TgQ�N�P#c$O�N>�9yDN�a!Y�WFN>Y�£®N>N>aºY�T(N�y R>P�a$WFN4Q�N>��P,QXc�N�cP9O�PbO�Y-QXP�qt�9T�Y�ztqtagNLZ P9O�£�N¸T�P�rLN6P#O�O��gyDN�c vjH#Q&H#�(Qu£®H�rLN>aºR7zsH9Y�T³yDH�c!N>z¨dl[�a²Y�N>Q-ynO�H�v±Y-T(NR7H#yD`(�(YSP,Y�qsH9aFP�z(R�H9yD`(zsN> �qtY�KLZ7qåvF£®NBT�P�rLN�ºg»w¼&yDN�O�T�`FH9qsa!YSOIvjH9Q�Y�T(NB£�H,rLN�auR7zsH9Y�TÒR7H9y�`iH�O�qsY�NLZ£®N�a(N>N�c¦½]1�1Tº�¼P4 ` 4BY�qsyDN±Y�HD§Fa�cbP,ztz�Y�TgNuH,rLN�Q�z�P�`FO7d«[�abH9QXc�N>Q±Y�H�qtyD`(Q-H�rLN±Y�T(NuN�ÔnR7qsN>aFR7K�H,v§FaFc�qta(�6H,rLN�Q�z�P�`FO7Z/£�N&ynP>K6�FO�N�P¸T(qsN>QXP�QXRXT(q�R�P,z c(P�YXP6O�Y�Q-�FR7Y-�(Q�NuvjH9Q�JLN>N>`(qsa(�DY�QSP9RXJbH,v°yDN�O�T`FH9qsa!YSO>Í à#Ï�d�G®T(q�O¥c(P�YXPbO�Y-Q��FR�Y��(Q-NDO�T(H9�(z�c `gQ�H�r!q�c!N�Y�T(N�R7H9y�`(�(YXP�Y�qsH9aFP�z O�`FN>N�c�¢}�(`³a(N>N�c!N�c Y-HynP�JLNf`(Q-H�R7N�O-O�qtag�&H�v T(qt�#T6c!N>aFO�qtY�KDyDN�O�T(N�O�`(QSP9R7Y-q�R>P�z�d

Î_@

Page 17: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

A B

C

P

©�qs�9�(Q-N�Î#Î9¼ � `iH#qta�Y�¢jY�Q-q�P,ag�9ztN6qtaFR�zt�FO�qtH9a²Y-N�O�Y�Zª£BT(N�Q�NnY�T(Nn`(Q-H9Ð�N�R7Y-qtH#aËH�v¥yDN�O�Tl`FH9qsa!Y�wãq�OztH�R�P,Y�N�cÑqsaFO�q�c!N¥Y�Q-q�P,ag�9ztN � \ �

(c)(a) (b)

©�qs�9�(Q-NfÎ�Õ!¼�1�PC4 � Y�K�`(q�R�P,zLH�rLN>Q�z�P,`(`gqta(�"O�qtY���P,Y�qsH9a/Z¾1}WF4×a(H9ag¢�O-P�vjNBQ�N�yDH�r9P�z�Z�P,aFcB1¨Ro4�H#a(NBR�H9Q�Q-N�R7YO�H#zt�(Y-qtH#a¡Y�HuH�rLN>Q-z�P�`¸Q-N>yDH�r#P,z

¿i')�jhÀ "+7�a·� F!w Á�a!wh�') �e�±hÂfih��5 Ê aFR7N�H,rLN�Q�z�P�`FO±P�Q�N�vjH9�gaFc�Z/£®N�TFP>rLN�Y�HnQ-N>yDH�rLN±Y�TgN>y_P�aFc¡�(`×c(P,Y-N&Y-T(N�O�T�P,`FN&H�v�Y�T(N�c(P�Q�Y�dMBN>yDH�r!qsa(�¡H�rLN>Q-z�P�`FO�ynP>K�qsa(qtY-q�P�ztztK³O�N�N>y P,aºN�P9O�K²ynP,Y-Y�N>Q�d²¯fH�£®N>rLN>Q�Z�£®N6R>P�a(a(H9Y�O�qsyD`(zsKQ�N�yDH�rLN±P�ztz/Y�TgN�H�rLN>Q�z�P,`(`gqta(�uyDN�O�TD`FH9qsa!YSO7dfÖ��(`(`FHLO�NLZivjH9Q"qta�O�YXP�aFR7NLZ(£�N¥TFP>rLN�P�O�qsY��FP�Y�qsH9a¡qsa£BT(q�RUT¥H�rLN>Q�z�P,`FO�H�R�R7�(Q>Z#P9O�O�T(H�£Ba�qsa�©�qt�#�(Q�N«Î>Õj1�PC4Sd�[}vg£®NBO�qtyD`gztKBQ�N�yDH�rLN�P�ztzLY�TgN®H�rLN>Q�z�P,`(`gqta(�yDN�O�T¡`FH9qsa!YSO7Z�Y�T(NuQ-N�O��(zsY±qta³©�qs�9�(Q-NnÎ>Õ¦1jWF4Bq�Oµ`gQ�H�c!�FR�N�c�Z�P,aFc³PÑagN>£*��P,`4q�O±H9`FN>a(N�c�d�G®T(NQ�N�yDH�r9P�z�H,v«P�a²H,rLN�Q�z�P�`(`(qsa(�nyDN�O�Tb`FH#qta�Y�q�O�R>P,zsztN�c�ë�ê�ö�ð«q�v"qtY�c!HLN�O�a(H9Y�H9`FN>a²P¡��P,`l£BT(H�O�NO�qs¹>N�q�O±z�P�Q��9N�Q�Y-TFP,a³Y�T(N�c!q�O�YXP�aFR7N�WiN�Y�£�N>N>a³P9c,Ð-P#R7N>a�Y¥yDN�O�Tb`FH#qta�YXO7dn[�a4H9Y-T(N>Q¥£®H#QXc(O�Z�q�v"P�aH�rLN>Q�z�P,`(`gqta(��yDN�O�T�`FH9qsa!YBzsqtN�O H9anY�T(N¥WFH9QSc!N>QBH�v�Y-T(N�P9R7Y-�FP,z�O�TFP,`FN¥H,v Y-T(N±ynP�Y�N>Q-q�P�z�ZLY�T(N�aDqtYSOQ�N�yDH�r9P�z/q�Ou¤XO-P�vjNLdé¦D©�qt�#�(Q�N�Î>Õx1¨Ro4°O�T(H�£"OfH#a(NuH,v�Y�TgN�r#P,zsq�c¸£°P>K(OBH,v�Q�N�yDH�r!qsa(��Y-T(NuH�rLN>Q�z�P,`FOqta4Y�Tgq�O±N> gP,yD`(zsNLZFW!KØP,`(`(zsK!qsa(�6P¡O�N�ÛÞ�gN>aFR7NuH�v"O�P>vjN&Q-N>yDH�r#P,z�O7d��fH9Y-NuY�TFP�Y�Y-T(N>Q�N�P�Q�N�ynP,a�Kr#P,zsq�cnP,aFO�£®N>QSO7d

ÎoH

Page 18: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

G®T(N�c!qåß�N�Q�N>aFR�N�O�WFN>Y�£�N>N>a¡r#P�ztq�cbP�aFO�£�N>QXO"Q�N�O��(ztYBvjQ�H#yÅY�TgN�c!q�ß×N>Q-N>a!Y«O�N�ÛÞ�(N�aFR7N�OBqtab£BT(q�RUTyDN�O�T¡`FH9qsa!YSO±ynP>K¸WFN�O�N>zsN�R7Y-N�c¸qsa�Y-T(N�RUTgN�RUJ�qtag�&H�vBH�rLN>Q�z�P,`FO�du[�Y±q�O"Y�T(N>Q-N7vjH9Q-Nua(N�R7N�O�O�P�Q�KbY-HQ�N�O�H9Q-Y�Y-HbP¡`FP�Q�Y�q�R7�(z�P,Q¥H9`(Y-qtyDqs¹>qtag�nO�Y-QXP,Y-N>�9K³c!�(Q-qta(�6H�rLN>Q�z�P,`4Q�N>yDH�r#P,z¨dnG®T(NDH#`(Y�qsyDqt¹�P�Y�qsH9aR7Q-qtY�N�Q�q�P¥Y�TFP�Yf£�N±�FO�N�qta�R7zt�Fc�N±Y�T(N±vjH#ztztH�£Bqsa(��P,zsY�N>Q-aFP,Y-qtrLN�O�¼

Î9d"]¡qsa(qtyDqs¹>NBY�TgN�O�T(N�P�Q"c!N7vjH9Q-ynP,Y-qtH#a¸qsaDY�TgN�Q-N�O��gztY�qsa(�u£®H�rLN>a6R7zsH9Y-T

Õ!d"]¡qsa(qtyDqs¹>NBY�TgN�QSP,�#�9N�c!agN�O�OBH,v Y-T(N�c(P,Q-Y�qsa(�uN�c!�#N

¬!d"[�aFR7Q-N�P9O�N¥Y�T(N�O�K�yDyDN�Y�Q-KuP�ztH9ag�&Y-T(N�R7�(Y

[�Y�ynP>K¥a(H9Y WFNB`FHLO�O�qtW(zsNfY-H±qty�`(ztN>y�N>a�Y/P�aDP�zt�9H#Q�qsY�T(y�Y�TFP�Y®O-P,Y-q�O¶§�N�O P,ztzgH,v×Y�T(N"P�WFH,rLN"H9`gY�qt¢yDqs¹>qta(��R7Q-qtY-N>Q�q�P�O�qsy&�gztYXP�a(N>H#�FO�zsKLd�©(H9QBY-T(q�OBQ�N�P9O�H#a/Z(£®N¥TFP>rLN¥qty�`(ztN>y�N>aLY-N�c&O�N>rLN>QSP,z/c�q�ß×N>Q�N�a!YP,zs�9H#Q�qtY-T(ynO±Y�H4R�H9Q�Q-N�R7Y-ztK¡Q-N>yDH�rLNuH�rLN>Q�z�P,`FO�dn©(H9QuN>rLN>Q-K¡yDN�Y�T(H�c�Z�£®N�ynP,qsa!YSP,qsalP6R7H9yDy�H9ac(P�YXP±O�Y�Q���R7Y��(Q-N"R>P,zsztN�c¥P�a6÷Lÿ,ð�óXøåê7òLò×í�ô9õfòg÷Lí�ô!ì/øåí�ë�ì"1 Ê w V�4XZ9£BTgq�RXT�q�O�Pfzsq�O�Y�H,v×yDN�O�T¥`FH9qta�YXO�Y�TFP�YP,Q-N±vjH9�(aFc¡Y-HuH�rLN>Q�z�P,`6P3`�P,Q�Y"H,v�Y�TgN�£�H�rLN>a6R7ztH#Y�TD§FY�Y-N�cDY�H�P&O��(Q�v¨P#R7N¥yDH9z�c�d G®T(N±vjH9zsztH�£Bqtag�q�OBPuztq�O�Y�H,v Y-T(N¥yDN>Y�TgH�c(OBP,aFcnRXTFP,QSP9R7Y-N>Q�q�O�Y-q�R>O Y�TFP�Yf£�N�T�P�rLN«qtyD`(zsN>y�N>a!Y-N>c×¼

0 k1m{ÃK��m�Eio�@j;(h :<mÞo���C/|�ÄG®T(N�§FQXO�Y�yDN�O�Tb`FH9qta�Y�qsalY�TgN&H�rLN>Q-z�P,`g`(qta(�n`FH9qsa!Y�ztq�O�Y¥q�O�O�N>zsN�R7Y�N�cbP,aFc�Y-N�O�Y-N�c�Y-Hbc!N>¢Y-N>Q�yDqsa(N"£BT(N>Y�TgN>QfqsY"R>P,a6WFNuO�P>vjN>ztKnQ-N>yDH�rLN�c�d�[¨vxO�HgZiY-T(N�y�N�O�Tn`FH9qsa!YBq�O�Q-N>yDH�rLN�c�P,aFcY-T(N6O�TFP�`iN6H,v«Y�T(N6c(P�Q�YuY-H9�9N�Y�T(N>Q�£BqtY-T²Y�T(N Ê w V$q�O��(`×c(P,Y-N�c�dºG®T(q�OuR>P�a²WiNnqsyD`(ztN�¢yDN�a!Y-N�c&£BqtY-TbPD©�[�© Ê 1�©�qtQXO�Y�¢¨[�ab©�qsQXO�Y-¢ Ê �(YV4®H#Q¥V/[�© Ê 1¨V/P9O�Y�¢¨[¶a4©�qtQXO�Y�¢ Ê �(Y�4°O�Y-QXP,Y-N>�9K�dG®T(q�O�y�N>Y�T(H�cnq�OBN�P9O�K¡Y-H&qsyD`(ztN�y&N>a�Y>Z�P�aFc¡qtY"q�OB�FO���P,ztzsKn�9�FP�QXP,a�Y�N�N�c¡Y�TFP�Y±R�Q�qtY-N>Q�qsH9aØÕH�v"Y�T(N�H9`(Y-qtyDqs¹�P,Y-qtH#a4R>P,a4WFNnO�P�Y�q�O�§FN�c�Z�WFN�R>P,��O�N�H,v"Y�TgNDO�Y�Q���R7Y��(Q-N�cbyDN>Y�TgH�c �FO�N�c�Y-HR7Q-N�P,Y-N�Y-T(N Ê w V�Zi£BTgq�RXTbO���R>R7N�O-O�qtrLN�ztK�`(Q�H�R7N�O�O�N�OfH9a(NuQ-H�£ãH�v yDN�O�Tn`iH#qta�YXO±P�Y¥P&Y-qtyDNLd¯fH�£�N>rLN>Q>Z(qsYfq�Ofa(H#Y���O��FP�ztztKn�#�FP,QSP,a�Y�N>N�c¡Y-TFP,Y¥H#`(Y�qsyDqt¹�P�Y�qsH9a6R7Q�qsY�N>Q-q�PnÎuP,a�cb¬¸R�P,abWFNO-P,Y�q�O¶§FN�c�d

0$Å ;gE�|�C.} :<mLo���C/|�Ä�qsY�TDY-T(q�O�yDN>Y-T(H�c�ZL£®N«QXP,a�c!H9yDzsK�O�N>zsN�R7Y�P�y�N�O�T�`FH9qta�YªvjQ-H9yÂY�T(N Ê w V�P�aFc&Y�N�O�Y®qsY®Y-Hc!N�Y�N>Q-yDqta(N £BT(N�Y�T(N>Q�qtY R>P�a&WFN"O-P�vjN>zsK�Q�N�yDH�rLN�c�d Ê a�P>rLN>QXP��9NLZ#Y�T(q�Oxy�N>Y�T(H�c¥�9�FP�QXP�a!Y-N>N�OY-TFP,Y±H#`(Y�qsyDqt¹�P,Y�qsH9a6R7Q-qtY�N�Q�qtH#ab¬DR�P,abWFN�O�P�Y�q�O�§FN�c�Z×W(�(Y±a(H#Y±a(N�R�N�O�O-P,Q�qsztK6R7Q-qtY�N�Q�q�PDÎÒP,aFcÕ�d

0 �]�/oDkn@j=7o�;(E��Lm¡e¥��@jCi��@�oX�º:ãmLo���C/|�Ä�qsY�T�Y-T(q�OuyDN>Y-T(H�c�Z Y�T(N Ê wªVÜq�O&O�H9Q�Y-N�cP9R�R7H9QSc!qta(�4Y�H4Y�TgNbc!q�O�YXP�aFR7NnvjQ�H9y Y-T(NbR7�gY

Î_J

Page 19: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

qsaFO�N>Q-Y�N�c×d&G®TgN&yDN�O�Tb`FH9qsa!Y�R7zsHLO�N�O�Y±Y-H¡Y�TgNDR7�gY±q�Of§FQSO�YuO�N>ztN�R7Y�N�c6P,aFc4Y�N�O�Y�N�c¸vjH#QuO�P>vjNQ-N>yDH�r#P,z�d G®T(q�ODyDN>Y-T(H�c�9�FP�QXP,a�Y�N�N�ODY�TFP�Y¡H9`gY�qty�qt¹�P�Y�qtH#aR7Q-qtY-N>Q�q�PlÕ²P,aFcܬºR>P,a·WFNO-P,Y�q�O¶§FN�c�Z(W(�(YBa(H#YfagN�R7N�O-O�P,Q-qtzsKDR7Q-qtY-N>Q�qsH9abÎ#d

0 |�����m�;(|ADE��ihjm¡e¥��@jCi��@�oX�º:ãmLo���C/|�Ä�qsY�TlY-T(q�O¥yDN>Y�TgH�c�Z/Y�T(N Ê w Vq�O¥O�H#Q�Y�N�cËP#R>R7H#QXc!qsa(�¡Y-H¡Y�TgNDr#P,zt�gN�O�H�v"Y�T(Q-N�P9c²P,ag�9ztN�O1~LP4SdbG®T(NDy�N�O�Tb`FH9qsa!Yu£BTgHLO�NÑR7HLO5L²q�O¥z�P,Q-�9N�O�Y�q�Oµ§FQSO�YuO�N>ztN�R7Y�N�c4P,a�cçY-N�O�Y-N�c¡vjH9Q�O�P>vjNQ-N>yDH�r#P,z�d�G®T(q�O�yDN�Y�T(H�cD�9��P,QXP�a!Y-N>N�OfY-TFP,Y"H9`gY�qty�qt¹�P�Y�qtH#a6R7Q�qsY�N>Q-qtH9aØÎuR>P,a6WFNuO�P�Y�q�O¶§FN�c×ZW(�gYBa(H9Y"a(N�R7N�O�O�P�Q�qsztK�R7Q�qsY�N>Q-q�P�Õ�P,a�c¡¬!d

G®T(NnRXT(H9q�R7N�H,v«yDN>Y�TgH�clc!N>`FN>aFcgO�H9a²£BTFP�YuH9`(Y-qtyDqs¹�P,Y-qtH#alR7Q-qtY-N>Q�qsH9a4q�O�R�H9aFO�q�c!N>Q-N�c�yDH�O�Yqty�`iH#Q�YSP,a�YªvjH9QBY-T(N�R7�(Q-Q�N>a�Y�R7H9a!§��9�(QSP,Y�qsH9a/d°©�H#QBqtaFO�YXP�aFR7NLZ�q�v�R7Q-qtY�N�Q�qtH#abαq�O�R7H9a�O�q�c�N>Q�N�cDyDH�O�Yqty�`iH#Q�YSP,a�Y>ZLY�T(N"Y�TgQ�N�P#c¸P�a(�9zsN±`(Q-qtH9Q-qtY�K�y�N>Y�T(H�cuq�O Y�T(N«WiN�O�YBRXT(H#q�R7NLd�[}v�R7Q-qtY�N�Q�qtH#aDÕ¥q�O�R7H9aFO�q�c!¢N>Q-N�c¸yDH�O�YBqsyD`FH9Q�YSP,a�Y>Z(Y-T(NuR7�gY±c!q�O�YSP,aFR7N�`(Q�qsH9Q-qtY�KDyDN>Y-T(H�cDH9Q±Y-T(N�O�N�ÛL�(N>a�Y�q�P,z/yDN�Y�T(H�cnynP>KWFN¥Y�T(N¥WFN�O�Y«RXT(H9q�R7NLd[�a¡Y�TgN�agN> !Y"O�N�R7Y-qtH9a1Z(£®N¥`(Q�N�O�N>a�Y±O�N>rLN>QSP,zi§�Y�Y�qsa(��N> (P�yD`(zsN�Oªqsa¸£BTgq�RXT¸H#a(N�H#Qfy�H9Q�Nµc(P,Q-YXO

P,Q-N®qsaFO�N>Q-Y�N�c×d�w�P,Q�Y-q�R7�gz�P,Q�P�Y�Y-N>a!Y-qtH#a�q�O/`FP�q�c�Y-Hf£BT�P,Y�J�qtaFc±H�vFyDN>Y-T(H�c(OivjH9Q�Q�N>yDH�r�qta(��H�rLN>Q�z�P,`FOP,Q-N��FO�N�c¡P�aFc¸£BT�P,Y±J�qtaFcDH�v H9`(Y-qtyDqs¹>qtag�uR7Q-qtY�N�Q�q�P�P,Q-NuO�H#�(�9T�Y±£BT(N�abc(P�Q�YXO"P,Q-N�qsaFO�N>Q-Y�N�cDqsa!Y-HztH�£�N>QBR7Q-qtY-q�R>P�z�Q�N��9qtH#aFO7d

�ÇÆÈ�¥� ¯Á®É�(�

¯fN>Q-N&£�NDc�N�O�R7Q-qtWFN�O�N>rLN>QSP,z N> gP,yD`gztN�OBH,v"§FY�Y-qta(�6PbÕ�¢�­ `gztKbH,v"£�H�rLN>alR�ztH9Y-T²R7H#yD`FHLO�qsY�N�O±Y-HO��gQ�v¨P9R�N�O®yDH�c!N>zsN�c&W�Kn�±p±M"\fÖ�1��fH#a(¢�p"a(q�vjH#Q�yæM"P,Y-qtH9a�P,z�\®¢�ÖL`(ztqsa(NG4xO��(Q�v¨P9R7N�O¥ÍåÎ_r9ϨZ!qtan£BT(q�RUTc(P�Q�Y"qtaFO�N>Q�Y-qtH9a�TFP9OBWFN>N>abP�`(`(zsqtN�c�dG®T(N�§�QXO�Y"N> gP,yD`gztN"q�OBP�§FY�Y-qta(��Y�H�P,a6H9W(Ð�N�R7YB£BqsY�T6P�R7H9a�rLN> nR7H#Q�a(N�Q>d�©�qt�#�(Q�N�Î>¬�O�TgH,£"O«P

§FY-Y�qtag�¸H�v"PD£®H�rLN>a4R�ztH9Y-T4R7H9y�`iH�O�qsY�Nu`(zsK¡H9a�Y�H6P�a�H#W(Ð�N�R7Y¥£BqtY-T4P¸R�H9a�rLN> ¡Q-H9�(aFc�N�c�R�H9Q�agN>Q>dG®T(N"qta(qsY�q�P,zFR7H#aFc!qsY�qtH#aFOxvjH#Q Y�T(NB§FY�Y-qta(�ÒP,Q-N±O�`iN�R7q�§FN�c3W�K�Y-T(Q�N>N"`FP�QXP,y�N>Y�N>QSO7¼�P�O�YXP�Q�Y�qsa(��`FH#qta�Y1TN�Ê:4SZ P¡WFP9O�Nn`FP,Y-T�1jH9QÒP¡�9�(q�c!N>ztqsa(NG4SZ�P,a�cËPbO�£®N>N�`(qta(�Øc!qtQ-N�R7Y-qtH9a1dbG®T(N�O�NnP,Q-NnO�`FN�R7qå§FN�c�qsaWFH9Y-T�Õ�¢�­�P,aFc²¬,¢¨­æO�`FP#R7N�O�d¡G®T(NÑO�YXP�Q�Y-qta(�6`iH#qta�Y�qsalY�T(q�O±N> (P�yD`(zsNuq�O�H#alY�TgN�ËÂP� !q�O7Z�P,aFcY�TgNuWFP9O�N&`FP�Y�T4q�O¥O�`FN�R�q�§FN�c¡qsa4O��FRXT4PD£BP>K¡Y-TFP,Y¥qsY�q�O±P,zsqt�#a(N�c¡£BqtY-T�Y-T(N�R7�(Q-rLN�H#a�Y-T(NqÌlË`(z�P,a(NLZ×P,a�c¡Y�T(NÒO�£®N�N>`(qtag�Dc!qsQ�N�R�Y�qtH#anq�OBqta¡Y-T(N�`FH�O�qtY-qtrLN¶Í c!qsQ�N�R�Y�qtH#a/d � O"R>P,abWFNuO�N>N>anvjQ�H9yY�TgNuQ�N�O��(ztY�ZiY-T(NuY�T(Q-N�P9cbP�a(�9zsN�OfWFN�R7H#yDN¥rLN>Q�K6O�ynP,zsz�P,Q�H#�(aFcbY�T(N�R�H9Q�agN>Qfy�HLO�Y«c!q�O�YXP�a!Y"vjQ�H9y

Î_z

Page 20: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

sweeping direction

Ps

X Y

Z

base path

©�qt�9�gQ�N�Î>¬�¼®©�qsY�Y-qta(��Y�H�P,a¡H#W(Ð�N�R7YB£BqsY�T6PuR7H9a�rLN> �R7H9Q-a(N>Q

Y�TgNuO�YSP,Q-Y�qtag�D`FH9qta�Y>d"©�qs�9�(Q-NDÎ�à61�P<4BO�T(H�£"OfY�T(N�`(z�P�a(Nuc�N>rLN>ztH#`(yDN>a�Y®`�P,Y�Y-N>Q�aØR7H9Q-Q�N�O�`FH9aFc!qsa(�Y�H�Y�T(N�§FY-Y�qsa(�(d¥©�qs�9�(Q-NDÎ�à¦1jWF4°O�T(H�£"O±Y�T(N�c�q�O�Y-Q�qsW(�(Y�qsH9a6H,v�Y�T(Q-N�P9cbP�a(�9zsN�O7Z×`(Q�H9Ð�N�R7Y�N�c6P,WFH�rLNY�TgN�P9O�O�H�R7q�P�Y�N�cb`(z�P,a(N�c!N�rLN>ztH#`(yDN>a�Y>d"[�Y±q�O"R7zsN�P,QfvjQ-H9y ©�qt�#�(Q�NnÎ�à¦1jWF4BY-TFP,Y±Y-T(N>Q-N�P,Q�N�O�H9yDNyDN�O�T¡`FH9qsa!YSOf£BT(H�O�NuY�TgQ�N�P#c�P�a(�9zsNuq�O"P,zty�HLO�Y"¹>N>Q-H(Z/P�aFc¡Y�T��FOf£�N�R>P,aga(H9Y¥P>rLH#q�cbP,agH9ynP�ztH9��ON>rLN>a�YXO�O��FRXT6P9OB£BQ�qsa(J!zsN�OªqsanY�T(N�R7Q-qtY�q�R>P,z×Q�N>�#qtH#a/d[�aY�T(q�O&N> gP,yD`(zsNLZ�O�H9y�N¡Y�TgQ�N�P#c$P�a(�9zsN�O&qtaY-T(N4R7Q-qtY�q�R>P,z"Q�N��9qtH#aWFN�R7H9y�N¡ztN�O�O&Y-TFP,aY-T(N

P,zsztH�£BP�W(ztNuy�qta(qsyu�(y#1bL<��OI�E4XZ�P,aFcbY�TgN>Q�N7vjH#Q�NuqsY�q�O±R7z�P9O�O�q�§FN�c�P#O�PDzsH,£�N>Q¥R7Q-qtY-q�R>P�z�Q-N>�9qsH9a/d�[�aH9QSc!N>Q¥Y�H6qta�Y��(qsY�qsrLN>ztKDq�c!N>a�Y�qåvjK¸Y-T(N�R7Q�qsY�q�R�P,z�Q-N>�9qsH9a/Z�£®N�O�T�P9c!NDN�P9RXT�yDN�O�Tb`FH9qsa!Y�P¡c�q�ß×N>Q�N�a!YR7H#ztH9QÑP9R>R7H#QXc!qsa(�4Y�HlqsYXOuY�T(Q-N�P9cP�a(�9zsNbr9P�zt�(N�dÜ©�qs�9�(Q-N�O¸Îs��1�P<4�P,a�c¤1}WF4�O�T(H�£æY�T(N6Q�N�O��(ztYSOR7H#Q�Q�N�O�`FH9aFc�qta(�lY-H²©�qs�9�(Q-N�ODÎ>¬lP�aFcÜÎ7àÎ1�PC4SZ®Q�N�O�`FN�R7Y-qtrLN>zsKLd�[�aº©�qs�9�(Q-NlÎ_��ZBY�T(N6r9P�Q�q�P,W(zsN6ÏP,Y-YXP#RUT(N�c¡Y�HnY�T(N�R�H9ztH#Q±WFP�Q�Q-N>`(Q-N�O�N>a�YXO"Y�T(NuY-T(Q�N�P#cbP,a(�#ztN�L�Z/P,aFcbY�TgNuztH�£®N>Q«R7Q-qtY�q�R>P,z�Q�N��9qtH#aq�O«R7H9zsH9Q�N�c¸Q�N�c�d¥[�abP9cgc!qtY-qtH9a1Z�Y�T(N�Q�N�c¡zsqta(N�O�qsab©�qs�9�(Q-N�O�Î_�±1�PC4�P,aFc$1}WF4�Q�N�`(Q�N�O�N>a�YfY-T(NuWFP9O�N`FP�Y�T¸vjH#QBY�T(N±§FY-Y�qsa(�(d�fH9Y-N Y�TFP�Y/Y�T(Q-H9�(�#T(H9�(Y�Y�T(N N> gP,yD`gztN�O(£®N�TFP>rLN P9O-O�qt�#a(N�c�R7H9zsH9QXO/P#O1vjH#ztzsH,£"O�¼/Q�N�cfq�O/P9O-O�qt�#a(N�c

£BT(N>a$LªÐ�rbc!N>�#Q�N>N�O7Z��9Q-N>N>alq�O�P#O�O�qs�9a(N�cç£BTgN>a$L�Ð�z=r�c�N>�9Q-N>N�O7Z�W(zt�gNDq�OuP#O�O�qs�9a(N�cç£BTgN>aLxÐ<ÎsJGr¥c!N>�#Q�N>N�O7Z�P,aFc�P,a�qta�Y�N�Q�`FH9z�P,Y�N�cuR7H9zsH9Q q�O P9O-O�qs�9a(N�cuqtauT��(N«O�`FP#R7N�ÍåÎ9Î7Ï�vjH9Q qta�Y�N>Q-yDN�c!q�P,Y-Nr#P,zs�(N�O�H�v�L�d¡�qtY-T�Y-T(q�O¥Q��(zsNLZ�PnyDN�O�T4`FH9qsa!Y�YXP,JLN�O�H9açP¡Q�N�c(c�q�O�T³R7H#ztH9Q�£BT(N>aÑL²WFN�R7H#yDN�O

ÕGr

Page 21: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

S

base path

sweeping direction

P

= 0.0

(b)(a)

I

π/2

I

J

γ

©�qs�9�(Q-NDÎ7àg¼)1�P<4"w�z�P,agNuc!N>rLN�ztH9`gyDN>a�Y®`FP�Y�Y�N�Q�ab�9N�a(N>QXP�Y�N�c¸vjQ-H9y P3§FY�Y-qta(��vjH9Q¥PDO��(Q�v¨P#R7Nu£BqtY-TPbR7H#a!rLN> 4R�H9Q�agN>Q>Z�P,aFcÉ1}W"4¥Y�T(Nnc�q�O�Y-Q�qsW(�(Y�qsH9alH�v"Y�T(Q-N�P9c²P�a(�9zsN�O�P�YuyDN�O�T4`FH9qsa!YSO�`(Q�H9Ð�N�R7Y�N�cP,WFH�rLN¥Y�T(N¥`(z�P,a(N�c!N�rLN>ztH#`(yDN>a�Y

ztH�£�N>Q±Y�T�P,a²P�`(`(Q�H� �qtynP�Y�N>zsK6¬Gr¡c�N>�9Q-N>N�O7Z/£BT(q�RUT4P�ztzsH,£"O±�FO¥Y�Hnr�q�O���P,ztzsK¡qsa!Y-N>Q�`(Q-N>Y±Y-T(N&`FH#qta�YP9O®zsK!qsa(��qsanP�ztH�£�N>QBR7Q-qtY-q�R>P�ziQ-N>�9qsH9a/d � ztY�TgH9�(�#T¸£�N¥R>P�a¡O�T(q�vjY�Y�T(N�R7H#ztH#QBc!q�O�Y�Q-qtW(�gY�qtH#a&vjH9Q®§�a(NY��ga(qta(�gZ!Y-T(N�P,WFH�rLN±Q��(zsN±q�O Q�N�P#O�H#aFP,W(zsNLZFO�qsaFR7N"yDHLO�YBR7H#yDyDN>QSR7qsP,z!v¨P�W(Q�q�R>O�¤-ztH�RXJ(¦�H#Q�¤jÐ-P,yn¦uP�YP,ag�9ztN�O�zsN�O�O®Y-TFP,a6¬G��c!N>�#Q�N>N�O¥ÍAz,ϨdG®T(N¥qtyD`FH#Q�YXP�a!Y®vjN�P,Y��gQ�N¥H,v Y-T(q�O®N� (P�yD`(ztN"q�O®Y-TFP,Y"Y�TgN�R�Q�qtY-q�R>P�z�Q-N>�9qsH9anTFP9O"P�O�K�yDyDN>Y-Q�qsR>P,z

O�T�P,`FNLdÂ[�YDq�ODY�TgN>Q�N7vjH#Q�N6`iH�O�O�qtW(zsN�Y-HËqsaFO�N�Q�YDN>qsY�T(N�QnP²O�Y�qsYXRXT(N�cºc(P,Q-Y¸H#Q6Pç`FH#ztK��9H9a�P,zuR��(Y>d©�qs�9�(Q-N&Îs@�1¨PC4�q�O®Y-T(N¥Q�N�O��(ztYBH�v�§FY�Y-qta(��Pu£®H�rLN>anR7zsH9Y-T¡R�H9yD`FHLO�qtY-N�`gztKD£BqsY�T6P&O�Y�qsYXRXT(N�cDc(P�Q�Y�ZP,a�c©�qt�#�(Q�N³Î_@É1}WF4�q�O�Y�T(NØÕ,¢¨­ `(z�P,a(NØc!N>rLN>zsH9`(y�N>a!Y�d[�YDO�T(H9�gz�c�WFNba(H9Y-N�c�Y�T�P,YnPlO�ynP,zsz`(Q-H9`FH9Q-Y�qtH#a�H�vBY-T(N�R7Q�qsY�q�R>P,z/Q-N>�9qsH9a³O�Y�qsztz�TFP9O±Q-N�c(c!q�O�TbR�H9ztH#QXO¥P�vjY-N>Q±qsaFO�N>Q-Y�qsH9abH,v�Y-T(N�O�Y-qtYXRXT(N�cc(P�Q�Y>d� ztY-N>Q�a�P,Y�qsrLN>ztK�Z(£®N�R>P�a�qsaFO�N>Q-Y¥PD`FH9ztK��9H#aFP,z�R7�gY>du[�abY�Tgq�O¥R>P9O�NLZ�£�N�P,`(`(zsKbY�T(N�P�zt�#H9Q�qsY�T(y

H9�gY�ztqsa(N�cuqta�©�qs�9�(Q-Naz�d®ÖL`FN�R7qå§×R>P,zsztKLZ�£®NB§FQSO�Y qtaFO�N>Q�Y�P±ztqsa(N�P�Q®R��(Y qtaFO�Y�N�P#c3H�v�P�`FH#ztK��9H9a�P,z/R��(Y>ZP9O¥O�T(H�£Babqta4©�qs�9�(Q-NDÎoH±1jWF4XZ/P�aFc¡H9WgYXP,qsa�Y-T(N�§�Y�Y�qsa(�DQ-N�O��(zsY¥O�TgH,£Babqsa4©�qt�#�(Q�N�ÎoH±1�P<4Xd�[�Yfq�Oqta�Y�N�Q�N�O�Y�qtag�&Y-TFP,Y±£BqsY�TbY-T(NuqtaFO�N>Q�Y-qtH#a¡H,v°PDztqsa(N�P�Q±R7�gY>Z�Y-T(N�`FP�Q�Y¥H,v�Y-T(N�R7Q�qsY�q�R>P,z/Q-N>�9qsH9ab£BqtY-TQ�N�c(c!q�O�T6R7H9zsH9QXO®r#P�a(q�O�T(N�O7d

� O�`(Q-N�c!q�R�Y�N�c�W�K³e���C.§ m!�>oX�(¨iZ P�a�H�rLN>Q-z�P,`³q�O�H9W�O�N>Q-rLN�c�qta²Y-T(ND§FY�Y-qta(�bQ-N�O��(zsY�qsa�©�qt�9¢�(Q-NDÎoHn1�PC4Sd"\®KnP,`(`gztK�qta(��Y�T(N�H�rLN>Q�z�P,`(`(qsa(��Q�N>yDH�r#P,z1P,zs�9H9Q-qtY-T(yæWFP9O�N�c¡H9abY-T(N�R7�(Y«c!q�O�YXP,a�R7N`(Q-qtH9Q-qtY�K�yDN>Y�TgH�c�ZL£®N±H#W(YXP�qtab©�qt�9�gQ�NuÎsJ!d�pfa(ztqsJLNBY�T(N±§FY-Y�qsa(��Q-N�O��(zsYB£BT(N>anPuO�Y�qsYXRXT(N�cDc(P�Q�YBq�Oqta�O�N>Q-Y�N�c�Z1©�qt�#�(Q�NnÎsJ¦1�P<4«c!HLN�O±a(H9Y�R7H#a!YSP,qsalPnR7Q-qtY�q�R>P,z�Q�N��9qtH#a/d�©�qt�#�(Q�NnÎsJ61}WF4"q�O±Y-T(N�R7H9Q-Q�N>¢

Õ!Î

Page 22: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

©�qs�9�(Q-N�Îs�!¼�©�qtY-Y�qtag��Q-N�O��gztYXO�£BqsY�TnR7H#ztH#QXOªW�P9O�N�c&H9anY�TgQ�N�P#cDP,a(�#ztN±r#P�zt�(N�OV>F1¨PC4 ¬�¢�­$§FY-Y�qsa(��P,aFc1}W"4�Õ,¢¨­ã`(z�P,a(NÒc!N>rLN>zsH9`(yDN�aLYª`�P,Y�Y-N>Q�a

Õ9Õ

Page 23: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

©�qs�9�(Q-NlÎ_@�¼ËÖLY-qtYSRUT(N�cËcgP,Q�Y�qtaFO�N>Q�Y-qtH9a1¼´1¨PC4�¬�¢�­È§�Y�Y�qsa(�²P�aFc¤1}WF43Õ,¢¨­ `(z�P,a(NØc!N>rLN>zsH9`(y�N>a!Y`FP�Y�Y�N�Q�an£BqtY-TbPuO�Y-qtYSRUT(N�cDc(P,Q-Y

Õ9¬

Page 24: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

©�qs�9�(Q-N�ÎtHL¼ V�qtagN�P,Q�R7�(Y qsaFO�N>Q-Y�qsH9a/¼�1�PC4x¬,¢¨­â§FY-Y�qtag��P�aFcx1jWF4�Õ,¢¨­ `gz�P,agN±c!N�rLN>ztH#`(yDN>a�Y/`FP,Y-Y�N>Q-a£BqtY-T6P3zsqta(N�P�QBR7�gY

Õ,à

Page 25: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

©�qs�9�(Q-NnÎ_J!¼ � `FH9ztK��9H#aFP,z°R7�(Y±H#W(YXP�qta(N�c¡W!KØP,`(`(zsK!qsa(�DY-T(NuH�rLN>Q�z�P,`¡Q-N>yDH�r#P,z�P,zs�9H9Q-qtY-T(yb¼j1�P<4¬,¢¨­ §�Y�Y�qsa(��P,a�c¦1}W"4BÕ�¢�­<`(z�P�a(N�c!N>rLN>zsH9`(yDN�a!Y�`�P,Y�Y-N>Q�an£BqsY�TbP�`FH#ztK��9H9a�P,z�R7�(Y

ÕG�

Page 26: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

O�`FH#aFc!qtag�¥Õ,¢¨­Ë`(z�P,a(N°c!N>rLN>zsH9`(y�N>a!Yg`FP,Y-Y�N>Q-a/d�G®T(N yDqsa(H9Q/H�rLN>Q-z�P�`±Q�N>yÑP,qtagqta(��qta�©�qt�#�(Q�N"ÎsJM1�P<4c!HLN�OBa(H#Y±R>P��FO�N�O�N>Q�qsH9�FO®`(Q-H9W(zsN>ynO�Z(P9OBztH#a(��P9O®Y�TgN>Q�N¥q�O®agH&��P,`/dG®T(N�O�N�R7H9aFc¡N� (P�yD`(ztN¥q�O±P&§FY�Y-qta(�DY-HnP,a4H9W(Ð�N�R7Yf£BqsY�T4PnR7H#aFR>P>rLNuR7H#Q�a(N�Q>d¥©�qs�9�(Q-NnÎ_z61�P<4

O�TgH,£"OBY�TgNu¬,¢¨­ §�Y�Y�qsa(��Q�N�O��(ztYB£BqsY�T6R7H9zsH9QSO�WFP#O�N�cnH9a6Y�T(N�Y�T(Q-N�P9cnP,ag�9ztN�O7Z×P,aFc6©�qt�#�(Q�N�Î_z�1�Rt4O�TgH,£"O�Y�T(N°Õ,¢¨­�`(z�P�a(N�c!N>rLN>zsH9`(yDN�a!Y�d�pfagztqtJLN�Y�T(N�`(Q�N>r�qtH#�FO/N> (P�yD`(zsNLZ7Y-T(N Q�N�O��(ztYSOIqsaFc!q�R�P,Y�N Y-T(NN> �q�O�Y�N>aFR�N®H,vIP,a��(`(`FN>Q�R7Q-qtY�q�R>P,z�Q�N��9qtH#a&£BqsY�T�W(zt�gN"R7H9zsH9QXO�d���N"R�P,a�Q�N>yDH�rLN Y�TgNf�(`g`iN�Q®R�Q�qtY-q�R>P�zQ�N��9qtH#a¡W�KDqta�O�N>Q-Y�qtag�DPuztqsa(N�P,Q"R��(Y>ZFP#O±O�T(H�£Ba6qtab©�qt�9�gQ�N�Î_zx1¨c,4XZFP�YfY-T(NuR�HLO�Y"H,vx`(Q�H�c!��R7qta(�ÑP�LP�`nqta�Y�T(N¥¬�¢�­$§FY-Y�qsa(��Q-N�O��(zsY>Z�P9O�O�T(H�£BanqtaÑ©�qt�#�(Q�N�Î_zB1jWF4Xd�e���C.§ m!�>oX�ɨ�P�z�O�H�`(Q�N�c!q�R7YSO�Y�T(q�OWFN>TFP>r�qtH9Q�d±��N�Y�T(N�Q�N7vjH#Q�N�agN>N�c¸Y�£�HDH9Q±y�H9Q�NÒO�N>`�P,QXP�Y�Nu`(zsKDvjQXP,�#yDN>a�YXO®Y-H¡R�H9yD`(zsN>Y�N�ztK�R7H�rLN>QY�TgN�O��(Q�v¨P#R7NLZ(�#qtrLN>aDY-T(N�O�P�yDN±qtagqtY�q�P,z1R7H9aFc�qtY�qsH9aFO®vjH9QBY-T(N±§FQXO�Yf`gztKLd

G®T(N�z�P9O�YBN> (P�yD`(zsN±q�OBP�§FY�Y-qta(�uY-HDP�O�TgHLN>¢}zsqtJLN¥H9W(Ð�N�R7Y>d ©�qs�9�(Q-N�OBÕGr±1�PC4°P,a�c¦1}W"4�O�T(H�£ÜY-T(N§FY-Y�qtag�fQ-N�O��(zsY�P�aFc�Y�TgNBÕ,¢¨­�`(z�P,a(N°c!N>rLN>zsH9`(yDN�a!YF`FP�Y�Y�N�Q�a/Z9Q-N�O�`FN�R�Y�qtrLN�ztKLd×G®£®H±q�O�H#z�P,Y-N�c�R�Q�qtY-q�R>P�zQ�N��9qtH#aFO�P,Q�N°R7ztN�P,Q�zsKfr�q�O�qtW(zsNLd�ÖLqta�R7N a(N>qtY-T(N>Q×H,v×Y�T(N�R7Q-qtY-q�R>P�z9Q�N��9qtH#aFO�q�O/O�K�yDyDN>Y-Q�q�R�P,z¨ZXqtY�q�O/N�P9O�qtN>QY�H�P�`(`(ztKuY-Q�qsyDyDN�c¥c(P�Q�YXO Y�H¥Y�TgNfN> gP,y�`(ztNLd1©�qtQSO�Y>Z#Y�£�H¥ztqtagN�P,Q�R7�(YSO P,Q�N"qta�O�N>Q-Y�N�c�Z�P9O®O�T(H�£Ba&qsa©�qs�9�(Q-N�Õ�ÎB1�P<4XZ×P,aFcnY�T(N¥§FY�Y-qta(��Q�N�O��(zsY"R7H9Q-Q�N�O�`iH#aFc!qsa(�DY�H�qtYBq�OfO�T(H�£Babqta6©�qs�9�(Q-N�Õ#Õx1�P<4Xd � OqtanY-T(N±`(Q-N>r!qsH9�FO®N� (P�yD`(ztN�Z9£®N¥TFP>rLN±H�rLN>Q-z�P,`�O7d��4N¥Y�N�O�Y�N�c�Y�T(Q-N>N¥yDN>Y�TgH�c(OxvjH#QBQ�N>yDH�r�qta(�¥Y-T(NH�rLN>Q�z�P,`FO�¼W1-Îo4�Y�T(N�O�N�ÛÞ�gN>a!Y-q�P�z�yDN>Y-T(H�c61�©�qs�9�(Q-NuÕ�Îq1jWF4ªvjH#QfY-T(N±§FaFP�z�O�TFP,`FNuH,vxY�T(N�c(P�Q�Y«P,aFc©�qs�9�(Q-N±Õ#Õq1}W"4IvjH#Q Y�T(NB§FY�Y-qta(�¥Q-N�O��(zsY�4SZ,1¨ÕC4�Y�T(N«R7�(Y c�q�O�YSP,aFR�Nf`(Q-qtH#Q�qtY�K�yDN>Y�TgH�c�1¨©�qt�#�(Q�N"Õ�ÎM1�Rt4vjH9Q�Y�TgNª§FaFP�z(O�TFP,`FNBH�vFY�T(N�c(P�Q�Y P�aFc�©�qt�9�gQ�NBÕ#Õ�1¨Ro4FvjH9Q�Y�T(N §FY�Y-qta(�"Q�N�O��(ztYV4XZ�P�aFcB1�¬<4�Y-T(N®Y-T(Q�N�P#cP,ag�9ztN¥`(Q-qtH#Q�qtY�KDy�N>Y�T(H�c±1�©�qs�9�(Q-N�Õ�Îq1¨c,4 vjH9QBY�TgN�§FaFP�z�O�TFP�`FN�H,vxY�T(N�c(P�Q�Y«P,aFc6©�qt�#�(Q�N�Õ9Õ�1�c.4vjH9Q«Y�T(N�§FY-Y�qsa(�DQ�N�O��(zsY�4Xd«[�a¡Y�N�Q�ynOBH,v�Y�TgQ�N�P#cbP,a(�#ztNur#P,zs�(N�O7Z×yDN>Y�TgH�c¦1�¬<4B`(Q-H�c!�FR7N�O"Y�T(NuWFN�O�YQ�N�O��(zsY>d�[�a�Y�N>Q-ynO�H,v×QXP��9�#N�c!a(N�O-O7ZLyDN>Y-T(H�c(O�1�Ît4�P,aFcB1¨ÕC4/`gQ�H�c!�FR�NBWiN�Y�Y�N�Q�Q-N�O��(zsYXO�Y-TFP,auy�N>Y�T(H�c1�¬<4Xdn[�a4Y�N>Q-ynOfH,v�O�K�yDyDN>Y-Q�KD£BqsY�T4Q�N�O�`FN�R7Y¥Y�H6Y�T(N�ztqsa(N�P,Q�R7�gYXO7Z/yDN�Y�T(H�c$1�Õ<4f`gQ�H�c!�FR�N�O�Y-T(NWFN�O�Y"Q�N�O��(zsY>d

ÕG@

Page 27: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

©�qs�9�(Q-N�Îsz!¼6©�qtY-Y�qsa(�LOuY�H4P�a�H9W(Ð�N�R7Yu£BqtY-TP4R7H9aFR�P�rLNÑR7H9Q-a(N>Q>¼61¨PC4Ò¬,¢¨­È§FY�Y-qta(�bQ-N�O��gztYu£BqtY-Ta(HØc(P,Q-YXO7Z�1}WF4«¬�¢�­�§�Y�Y�qsa(�nQ�N�O��(ztY«£BqtY�T³P¸zsqta(N�P,Q¥R7�gY>Z�1�Ro4«Õ�¢�­ `gz�P,agNDc!N�rLN>ztH#`(yDN>a�YB`FP,Y-Y�N>Q-aR7H#Q�Q�N�O�`FH9aFc�qta(��Y�H±1�P<4XZFP,a�c¦1�c.4�Õ,¢¨­ã`(z�P,a(N�c!N>rLN�ztH9`gyDN>a�Yª`�P,Y�Y-N>Q�a6R7H#Q�Q-N�O�`FH9a�c!qta(��Y�H±1}W"4

ÕCH

Page 28: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

©�qs�9�(Q-NnÕGr�¼x1�P<4 � §�Y�Y�qsa(�bY�HØPbO�T(HLN�¢}zsqtJLN�H9W(Ð�N�R7Y�£BqtY-T²R7H9zsH9QSO�WFP9O�N�clH9alY-T(NDY�TgQ�N�P#cËP�a(�9zsNr#P,zs�(N�OBP,Y"N�P#RUTnyDN�O�TD`FH9qsa!Y�Z(P,a�c¦1}W"4®Y-T(N�Õ,¢¨­ã`(z�P,a(N�c!N>rLN�ztH9`gyDN>a�Y

ÕGJ

Page 29: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

©�qs�9�(Q-N�Õ!Î9¼¥Õ�¢�­�`(z�P,a(N�c!N�rLN>ztH#`(yDN>a�Y®`FP�Y�Y-N>Q�aFO±£BqsY�TbY�Q-qtyDy�N�cDc(P�Q�YXO�¼)1�P<4fqsaFO�N�Q�Y�qsH9abH�v®Y�£�Hztqsa(N�P�Q±R7�gYXO7Z�1}W"4®`FH9zsK!�#H9aFP�z�R7�(YXOBH9WgYXP,qsa(N�c¡W�KnY�T(NÒO�N�ÛL�(N>a�Y�q�P,z/yDN>Y-T(H�c�Z�1�Ro4�`FH9zsK!�#H9aFP�z R7�(YSOH9WgYXP,qsa(N�cDW�KDY�T(N�R7�gY"c!q�O�YXP,a�R7N¥`(Q�qsH9Q�qsY�K&yDN�Y�T(H�c�ZgP,aFcl1�c,4 `FH#ztK��9H9a�P,z�R7�(YXO®H#W(YXP�qta(N�c¸W�K&Y-T(NY�TgQ�N�P#c¸P�a(�9zsN�`(Q-qtH#Q�qtY�K�yDN>Y-T(H�c

ÕGz

Page 30: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

©�qs�9�(Q-N¡Õ#Õ!¼b¬�¢�­ §FY�Y-qta(�4Q�N�O��(zsYXOu£BqtY�T²Y-Q�qty�yDN�cbc(P�Q�YXO�¼Ñ1�P<4�qsaFO�N�Q�Y�qsH9a²H,vµY�£�H�zsqta(N�P,QuR��(YXO�Z1}W"4 `iH#ztK��9H#aFP,z�R7�(YSO®H9W(YSP,qtagN�c¸W�K&Y-T(N�O�N�ÛL�(N>a�Y�q�P,z×yDN>Y�TgH�c�ZF1¨Ro4 `FH9ztK��9H#aFP,z�R7�(YSO®H9W(YSP,qsa(N�c¸W�KY�TgN¥R7�(Y°c!q�O�YXP,a�R7N±`(Q-qtH9Q-qtY�KuyDN>Y-T(H�c�Z�P,a�cx1�c,4 `FH#ztK��9H9a�P,z�R7�(YSOªH#W(YXP�qta(N�c�W!K�Y�T(N«Y�T(Q-N�P9cDP�a(�9zsN`(Q-qtH9Q-qtY�K�yDN>Y�TgH�c

¬Gr

Page 31: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

Ç_ÃÅ¿ Ç�®Æ �n¾®ÃÅ¿ �

�4NªT�P�rLN�R7H#aFO�q�c!N>Q-N�c±Y�T(N�`(Q�H#W(ztN>yÓH,v×O��(`(`(Q-N�O�O�qta(�«P,a(H#ynP,zsH9�FO/N>rLN>a�YXOF£BT(qtzsN�§FY�Y-qta(�«PfÕ�¢�­�`gztKH,vx£®H�rLN>anR7zsH9Y-T¡R�H9yD`FHLO�qtY-N�OªY-HDP�¬,¢¨­*R7�gQ�rLN�cDO��(Q�v¨P#R7NLd��4N¥TFP>rLN�`gQ�N�O�N>a!Y-N�cDO�N>rLN>QXP�z�yDH�c�N>z�OvjH9Qµc(P,Q-YXO±P�aFcbO�T(H�£BabT(H�£<Y�TgN�`(Q-H9W(zsN>yÉR>P,a6WiN�O�H9zsrLN�cDW!Knqta�O�N>Q-Y�qtag�Dc(P�Q�YSO7d±�4N�TFP>rLN�P,z�O�HO�YSP,Y-N�c¡Y�T(Nu`gQ�H9WgztN>ynOBH,v�`FHLO�qtY-qtH9agqta(�nY�TgN�c(P,Q-YXO¥P,aFc¡TgH,£�Y�Hnc�N>Y�N>Q-yDqtagN�P�abH9`(Y-qtynP�z�O�TFP,`FNvjH9Q�Y�T(N�c(P�Q�YXO¥qta³P9R>R�H9QXcgP,aFR7N�£BqtY�T³O�N�rLN>QXP�z�H9`(Y-qtyDqs¹�P,Y-qtH#a4R7Q�qsY�N>Q-q�P!d Ê �(QÒO�H9zs�(Y�qsH9alY-HnY�T(N�O�N`(Q-H9W(zsN>ynO�qta�rLH9zsrLN�O�§FQSO�YDq�c!N>a�Y�q�vjK�qtag�4R7Q�qsY�q�R�P,zBQ�N��9qtH#aFOD£BT(N>Q-N¡N> gR7N�O-O�qtrLN6c!N�vjH9Q�yÑP,Y�qsH9aºynP>KH�R>R7�gQ>ZBY�T(N�aqtaFO�N>Q�Y-qta(�³P$¤�zsqta(N�P,Q�R7�(YX¦4qta�Y�H4N�P9RXTR7Q-qtY-q�R>P�zBQ�N>�#qtH9a1ZfP�aFc�§FaFP,zsztK²Y�QSP>rLN>QXO�qta(�H�rLN>Q�z�P,`(`gqta(�nyDN�O�Tb`FH9qta�YXO�P,zsH9a(�6Y�T(N�ztqsa(N�P,Q�R7�gY>dDG®Tgq�O�P�zt�#H9Q�qsY�T(y_q�O¥R7�(Q�Q-N>a�Y�ztK6ztqsyDqtY-N�c¸Y-HY�TgNu¤�ztH�£�N>QX¦±R�Q�qtY-q�R>P�zLQ�N>�#qtH#aFO�H,v×Y-T(N®§FY�Y-qta(�gZLP,a�c3£�N®a(N>N�cuP9c(c!qsY�qsH9aFP�z(`(ztK±vjQSP,�9y�N>a!YSOIY-H¥R7H�rLN>QY�TgNDO��(Q�v¨P#R7NDR�H9yD`(zsN>Y�N�ztKD£BT(N�a$¤-�(`(`FN>QX¦6R7Q�qsY�q�R>P,z�Q�N>�#qtH#aFO¥P,Q�N�`(Q�N�c�q�R7Y-N�c�d Ê �(Q¥`(Q-N>ztqsyDqtaFP�Q�KR7H#yD`(�(Y-N>Q"O�qsy&�(z�P,Y-qtH9a�O®�9qtrLN�N>aFR7H#�(QXP��9qsa(�DQ�N�O��(zsYXOfY-TFP,Y¥O��(`(`FH9Q-Y¥H9�(Q±y�H�c!N>z�OªvjH#Q¥c(P�Q�YXO«P,aFcH9�gQ±P�zt�9H#Q�qsY�T(ynO�vjH9Q"H�rLN>Q�z�P,`DQ-N>yDH�r#P,z�d

Aq�]ÒxÓ6Ô¥���®~±kxÕn~«:ã~wÓx|Ök

G®T(q�O�Q-N�O�N�P,QXRXTl£°P9OuR7H#aFc!�FR7Y-N�clP�YuY�T(N6MBN>aFO�O�N>z�P�N>Qu­"N�O�qs�9aºM�N�O�N�P�QXRXT � N>a�Y�N>Q�1�M"­±M � 4XZP,a�c�£BP#O«§�aFP,aFR�q�P,zsztK4O��(`(`FH9Q-Y�N�c�W�K¡Y-T(N�Mf­±M � [�aFc!�FO�Y�Q�q�P,z � O-O�H�R7q�P,Y�N�O�w�Q-H9�9QSP,ybd�]bP9O-P,J�q� H#a(HD£BP#O¥O�`FH9aFO�H9Q-N�c W�KnY�T(N Ê rLN>QSO�N�P#OµÖÞRUT(H#z�P�QXO�Tgqt`4w�Q�H#�9QXP�yÅH�v"[�\B]Ù^LP�`FP,a³V�YXc×d¥w�P,H#ztH­fN>a�Y�q×£BP#OBO�`FH9aFO�H9Q-N�c¸W�K&Y-T(N¥­fN�`FP,Q-Y�yDN>a�Y H,vx[�aFc!�FO�Y�Q�q�P,z?mxag�9qtagN>N>Q�qsa(��H�v�Y-T(N¥pfagqtrLN>QSO�qtY�K�H,vw�P�Q�ynP�ZL[�YXP,zsKLd�G®T�P,a(JgO P,Q�N«c!�(N"Y�H�­fQ�dL\±dLw�dG×�P,a���N�O�Y H,v�\®HLN�qta(��­fN7vjN�aFO�N�ØãÖ�`FP9R7N±½"Q-H9�(`vjH9QB`gQ�H�r!q�c!qtag�u�FO®£BqtY-T¡O�H9yDN«H,v�Y�T(N¥Q�N�vjN>Q�N>a�R7N�OªQ-N>z�P�Y�N�c�Y�H�Y�T(Nuøù÷,î7�#í�ô9õ6êLô9õ9øtð�ë"H�v R7H#yD`FHLO�qtY�NynP�Y�N>Q-q�P,z�O7d � a�K�H#`(qta(qsH9aFO�Z�§FaFc!qsa(�LO�Z®P�aFc²R7H9a�R7zt�FO�qtH#aFO�N> �`(Q�N�O-O�N�c4qtalY-T(q�O¥`(�(W(zsq�R>P�Y�qtH#a²P,Q-NY�TgHLO�N�H,v�Y�T(N�P��(Y�T(H#QXO�Z�P�aFc¡c!H�a(H#YBa(N�R7N�O-O�P�Q�qtzsK&Q-N7ÚFN�R�YBY�T(N¥r�qtN>£"O®H�v P�a!KDH�v Y�TgN�O�`FH9aFO�H9QXO�d

Á�ÙjÚ<ÙjÛeÙMÜlÝ�ÙMÞ

ÍåÎ7Ï�\±d � d9¯fH�O�J�qtaÒP,aFc � d � d�\BP,JLN>Q�ZFß ÷Lýfòg÷,ë�ítì�ð/²4ê9ì�ð�ó7í�ê9øäë�ö�÷LóÀà«í�ó-î>ó�ê�ö�ì5áFì¨ó�ú!î7ì¨ú�óUð�ë�Z � [ �«� Z[�aFR9dsZ(�fN>£·� H9Q-J�Zg�f�uZ�ÎszGJ=@!d

¬!Î

Page 32: BADCFE Cdavid/Papers/darts.pdf · £®N qt 9T Y®QSP,Y-qtHLO"P,a c¸T(qs 9Tn`(ztq P,W(qsztqsY Ku£BTgN>anY T(N>KÑP,Q N c!N vjH9Q y Nc&qta Y HÒR7H9y `(ztN> R (Q rLNc O TFP`iN O7d

ÍäÕ,Ï�]ld � H9a(HgZ/­�dKmBd×\®Q�N>N�a/Z�P�aFcb]ld×^(di�4H9¹>a�KLZ ¤ � � H#yD`(�(Y-N>Q�¢ � q�c�N�cn\®Q�HLP#c(R7zsH9Y�T � H9yD¢`FHLO�qtY�NÑV/P�KLH#�(Y�­fN�O�qt�#a�ÖLKgO�Y�N�ybZ´¦&`g`/d�Õ#Õ9¬,¢¨ÕG�=r!Z®qsa¤â±ð-÷Lý&ðXì¨ó�í�î�² ÷�ñ!ðXøåí�ô9õuö�÷Ló¶ã°ó�÷�ñLú�î7ìä±ð-ê9øùíyå�ê9ì�í�÷Lô!ZFw�d´M¥d!�qsz�O�H#a/ZF]ld´^(d���H#¹>a�KLZ(P�aFc¡]ldé^(d(w�QXP�Y�Y"N�c(O7ZF�"H9Q�Y-T(¢¨¯fH9zsz�P,a�c�1-Î_z=z9¬C4

Íä¬,Ï�]ld � H#a(H(Z�­�d�mBd \®Q�N>N�a/Z P,aFcº]ld ^(d���H#¹>a�KLZ±¤X©�qsY�Y-qta(�4Pb��H�rLN>a � ztH9Y-T]¡H�c!N�zBY�H³P� �(Q-rLN�c�ÖL�(Q�v¨P9R7NL¼¥]bP�`(`(qsa(� � zt�#H9Q�qsY�T(yÑO7Z´¦lß ÷Lýfò×úLì�ð�ó�à«í�ñ!ð-ñBæuð�ë�í´õLô�Z�× H9z¨d/ÕG@�Z��"H(d�àgZÎ_z=z,àgZ/ÕCH\J,¢¨ÕGz9Õ�d

Íáà9Ï�]ld � H9a(HgZ�¤ � H9yD`(�gY�N>Q-¢ � q�c!N�c˽"N>H#yDN>Y-Q�q�R�­fN�O�qt�#açvjH#Q�©(H9Q�y�qta(�n�4H,rLN�a � ztH#Y�T � H9yD¢`FHLO�qtY�N�O7Z´¦�wxT1d´­�d�Y-T(N�O�q�O7Z×­fN>`�P,Q�Y-yDN>a�YBH,v � H9y�`(�(Y�N�Q�Ö�R�qtN>aFR�NLZFM�N�aFO�O�N>z�P�N>Q±w�H9ztK�Y�N�RUT(agq�R[�aFO�Y-qtY-�(Y�NLZ×Î_z=z,à(d

Í��,Ï�©®dFV�d×»udF¯fN>q�O�N>KLZ�¤ �Çç �FP�a!Y-qtYSP,Y�qsrLN¥]¡N>Y-T(H�c!H9zsH9�#K¸vjH9Q¥½"N>a(N>QSP,Y-qta(�nÖL`FN�R7qå§×R>P,zsztK�©�qtY-Y�N�c½«P,Q-yDN>a�YBw�P�Y�Y�N�Q�aFO�Z´¦�wxT1d´­�d�Y�T(N�O�q�O�ZFpfa(qtrLN�QXO�qsY�KuH,vx]¡qta(a(N�O�H9YSP!ZF]b��Z×Î_z=J,à(d

Í�@,Ï�M¥d{mBdLMBH9WFN>Q-YXO�H9a/Zg¯�d!ÖFd�¯±O�qt�(NLZèm�d���d!ÖLq�RUJ#P�vj��O7Z�P,aFcD½�d(ÖFd9�ud9� N>T1ZI¤S©�qtWFN>QxM�N�P�Q�QSP,a(�#N>¢yDN>a�YXOBc��(Q�qsa(�DY�TgNu]¡H�c!N>zsqta(��H,v � H#a!Y-qta��(H9�FO«©�qtWFN>Q � H9yD`FH�O�qtY-N�Oeé6[Xd�©�z�P,Y � ztH#Y�TbY�HÑP¯fN>y�q�O�`gT(N>Q�N�Z´¦Mã°÷9øåû9ý&ð�ó)ß ÷Lýfòg÷,ë�ítì�ð�ë�Z{× H9z¨d(Õ�Z��fHgd(¬�Z�ÎszGJ!Î#Zi`g`/d/Î>Õ=@,¢-Î>¬!Î#d

ÍIH>Ï�]ld�^(d�w�QXP�Y�YÒP,aFc � d�­�dª½"N>q�O�H�£¥Zf¤7Ö��(Q�v¨P#R7NG99Ö��(Q�v¨P#R7Nn[�a!Y-N>QXO�N�R7Y-qtH9a4w�Q-H9W(zsN>ynO�¦Dqsa�ê�ïFð²4ê9ì�ïFð�ýuê9ì¨í�îUë6÷�ö)á×ú�ótö�êLî7ð�ë�Z�N�c�d�W!K4^(d � d�½fQ-N>�9H#Q�KLZ � z�P,Q-N>aFc!H#a²w�Q�N�O-O7Z Ê  ÞvjH#QXc�ZBÎszGJ=@!Z`(`/d/Î#ÎoH�¢�Î�àLÕ!d

Í�J,Ï�M¥d�mBd�\BP,Q-a(T(qsztz�Z×N�c�dtZ�â±ð-÷Lý&ðXì¨ó7ûqã°ó�÷�î7ð�ëXë�í�ô#õ�ö�÷Ló¶æÒð�ë�í´õLô²êLô(ñ�²4êLôgúSö�êLî7ì¨ú�ó7í�ô9õ#Z®Ö�[ � ]lZw�T(qtz�P9c!N�zt`(T(q�P!Zgw � Z/ÎszGz9Õ�d

Í�z,Ï�]bP,Y-N>Q�q�P,z"Ö�R7qtN�aFR7N � H#Q�`FH9QSP,Y�qsH9a/Z�¤��4H,rLN�a�©FP�W(Q�q�RDM�N�qta!vjH#QXR7N�c � H9yD`FHLO�qtY-N�O�vjH9Q � �gY�H9¢yDH#Y�qtrLN � `(`gztq�R�P,Y�qsH9aFO�Z´¦�GIN�RXT(a(q�R>P,z1M�N�`iH#Q�Y«]�Ö � GB©�M*Î_@=rG�<9tJ!Îsr9Õ(Z�^LP,a��FP�Q�KLZ/ÎszGJG@�d

Í�Îsr,Ïu½�d(©FP,Q-qta/Z�ß ú!ó�ÿ,ð�ëµêLô(ñÖáiú!ótö�êLî7ð�ë�ö�÷LóMß ÷Lýfò×úÞì�ð�ó&à«í�ñ!ð-ñ�â±ð-÷Lý&ðXì¨ó7í�îWæuð�ë�í´õ�ô!ZFG®T(qtQScBm c!qt¢Y�qsH9a/Z � R>P9c!N�yDq�R"w�Q�N�O-OB[¶a�R9dtZFÖ�P,aØ­fqtN>�#H(Z ��� Z×Î_z=z9Õ!d

Í�Î#Î7Ï�­�dB©�d M�H#�9N>QSO7Zaã°ó�÷�î7ð-ñLú!ó-ê9ø/ë®øsð�ý&ð�ô!ì�ëuö�÷Ló¦ß ÷Lýfò×úLì�ðUó¦â"ó�ê7ò(ïgí�îUë�d ]bR�½fQSP>£B¢�¯fqsztz¨Z®[�aFR9dsZ�fN>£·� H9Q-J�Zg�f�uZ�ÎszGJ=�!d

¬9Õ