º£Æü¤Ï¡¤¡Ö4.2¡¡Ã±°Ì¥³¥¹¥È¡×¤«¤é¤Ç¤¹¡£

¡¡¤µ¤Æ¡¤Ã±°Ì¥³¥¹¥È¾ìC¤Ê¤ó¤Ç¤¹¤¬¡¤²¼¤Î¤è¤¦¤Ê¼°¤Ç¤·¤¿¡£



¤³¤Îñ°Ì¥³¥¹¥È¾ìC¤Ç¤¹¤¬¡¤2¥¹¥Æ¥Ã¥×¤Ç·×»»¤·¤Þ¤¹¡£
¤Þ¤º¡¤¼°(8)¡¦¼°(9)¡¦¼°(10)¤Ë½¾¤Ã¤Æ¥¹¥Ô¡¼¥Éf¤ò·×»»¤·¤Þ¤¹¡£¤³¤Î¤È¤­¤Ë¡¤¾å¤Ë½ñ¤¤¤¿ÀÖÀþ¤Ç¤¯¤¯¤Ã¤¿¼°(4)¤ò»È¤Ã¤Æñ°Ì¥³¥¹¥È¾ìC¤ò·×»»¤·¤Þ¤¹¡£Ã±°Ì¥³¥¹¥È¾ìC¤Ï°ÛÊýÀ­¡ÊÊý¸þ¤Ë¤è¤Ã¤Æ°ã¤¦¡Ë¤¬¤¢¤ë¤Î¤Ç¡¤³Æ¥°¥ê¥Ã¥É¤ò¥ë¡¼¥×¤¹¤ë¤À¤±¤Ç¤Ê¤¯¡¤4¤Ä¤ÎÊý¸þ¤Ë¤Ä¤¤¤Æ¤â¥ë¡¼¥×¤µ¤»¤Þ¤¹¡£¤³¤³¤Ç¤¤¤¦4¤Ä¤ÎÊý¸þ¤È¤ÏÁ°²óÀâÌÀ¤·¤¿¦È=¡Ð0¡¤90¡¤180¡¤270¡Ñ¤ËÂбþ¤·¤Æ¤¤¤Þ¤¹¡£¤Ä¤Þ¤êÅ졦ËÌ¡¦À¾¡¦Æî¤Î4¤Ä¤ÎÊý¸þ¤Ç¤¹¡£


¿Þ4(a)

¾å¤Î¿Þ¤Î¿¿¤óÃæ¤Î¥»¥ëM¤ËÂФ·¤Æ¤Ï¡¤M¤«¤éi¤ÎÊý¸þ¡Ê¤¿¤À¤·¡¤i¢º¡ÐE, N, W, S¡Ñ¡Ë¤Î¥¹¥Ô¡¼¥ÉfM¢ªi¤È¡¤M¤«¤éi¤ÎÊý¸þ¤Ø¤Îñ°Ì¥³¥¹¥È¾ìCM¢ªi¤ò·×»»¤¹¤ëɬÍפ¬¤¢¤ê¤Þ¤¹¡£Êâ¹Ô¤¹¤ë¿Í¤Ï¡¤Continuum Crowd¤Ç¤ÏÁ°Êý¤Î¾ã³²Êª¤òͽ¬¤¹¤ë¤è¤¦¤Ê¥â¥Ç¥ë¤Ë¤Ê¤Ã¤Æ¤¤¤ë¤Î¤Ç¡¤°ÜÆ°¤¹¤ëÊý¸þ¤Ë¤¢¤ë¥°¥ê¥Ã¥É¤Ç¤Î¥¹¥Ô¡¼¥É¤ÈÉÔ²÷Î̤òµá¤á¤Þ¤¹¡£
Î㤨¤Ð¡¤fM¢ªE¤Î¾ì¹ç¤Ï¤Ç¤Ï¡¤E¤Î¥°¥ê¥Ã¥É¤ÎÌ©ÅÙ¦ÑE¤È¡¤ÉÔ²÷ÎÌgE¡¤Ê¿¶Ñ®ÅÙ¤ò¡ÊvE¥Ð¡¼¡Ë¤ò¼°(10)¤ËÂåÆþ¤·¤Þ¤¹¡£



¡¡¤µ¤Æ¤µ¤Æ¡¤¤¢¤ÈưŪ¥Ý¥Æ¥ó¥·¥ã¥ë¾ì¤Î¹½ÃۤˤĤ¤¤Æ¤â¿¨¤ì¤Æ¤¤¤Ê¤¤¤Î¤Ç¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¾ì¤Î¹½ÃۤˤĤ¤¤Æ¤âÀâÌÀ¤·¤Æ¤¤¤­¤Þ¤¹¡£

¡¡Æ°Åª¤Ê¥Ý¥Æ¥ó¥·¥ã¥ë¾ì¤ò¹½ÃÛ¤ë¤Î¤Ï¡¤¥·¥ß¥å¥ì¡¼¥·¥ç¥ó¤ÎÃæ¤ÇºÇ¤âÊ£»¨¤Ç¥¢¥ë¥´¥ê¥º¥à¤Î¥¹¥Æ¥Ã¥×¤ÎÃæ¤Ç»þ´Ö¤¬¤«¤«¤ëÉôʬ¤Ç¤¹¡£
¡¡¥Ý¥Æ¥ó¥·¥ã¥ë¾ì¤ÎÄêµÁ¤Ç¤¹¤¬¡¤°Ê²¼¤Î¼°(5)¤Çɽ¤ï¤µ¤ì¤ë¥¢¥¤¥³¥Ê¡¼¥ëÊýÄø¼°¤È¤·¤ÆÄêµÁ¤·¤Æ¤¤¤Þ¤·¤¿¡£


¡¡¤³¤Î¥¢¥¤¥³¥Ê¡¼¥ëÊýÄø¼°¤È¤·¤ÆÄêµÁ¤µ¤ì¤ë¤¿¤á¤Ë¡¤¤³¤ÎÊýÄø¼°¤òľÀÜŪ¤Ë·×»»¤¹¤ë¤³¤È¤¬¤Ç¤­¤Ê¤¤¤è¤¦¤Ç¤¹¡£ÏÀʸ¤Ç¤Ï¡¤¤³¤Î¼ê¤ÎÊý¼°¤ò²ò¤¯Í­¸ú¤Ê¥Æ¥¯¥Ë¥Ã¥¯¤¬¤¹¤Ç¤Ë³«È¯¤µ¤ì¤Æ¤¤¤ë¤È¸À¤Ã¤Æ¤¤¤Þ¤¹¡£¤½¤ì¤¬¹â®¥Þ¡¼¥Á¥ó¥°Ë¡¡Êfast marching method)¤È¹â®¤Ï¤­½Ð¤·Ë¡¡Êfast sweeping method)¤À¤½¤¦¤Ç¤¹¡£Continuum Crowd¤Ç¤Ï¡¤¹â®¤Ï¤­½Ð¤·Ë¡¤ò»È¤¦¤È¡¤ºÇŬ·ÐÏ©¤¬ÌÌÅݤʥ롼¥È¤Î¾ì¹ç¤ËǽΨ¤¬°­¤¯¤Ê¤Ã¤Æ¤·¤Þ¤¦¤½¤¦¤Ç¤¹¡£¤½¤Î¤¿¤á¡¤¼ÂÁõ¤Ë¤Ï¹â®¥Þ¡¼¥Á¥ó¥°Êý¤òÍѤ¤¤Æ¤¤¤ë¤½¤¦¤Ç¤¹¡£

¡¡¹â®¥Þ¡¼¥Á¥ó¥°Êý¤Î¾ÜºÙ¤Ë¤Ä¤¤¤Æ¤Ï¡¤
TSITSIKLIS, J. N. 1995.
Efficient algorithms for globally optimal trajectories.
IEEE Transactions on Automatic Control 40, 9 (Sept.), 1528–1538.
(PDF¤Ï¤³¤Á¤é¤Ë¤¢¤ë¤è¤¦¤Ç¤¹¡£http://www.mit.edu/~jnt/Papers/J058-95-jnt-traj.pdf)

¤ËºÜ¤Ã¤Æ¤¤¤ë¤½¤¦¤Ç¤¹¤¬¡¤Æñ¤·¤¯¤Æ¤ï¤«¤é¤Ê¤¤¤Î¤Ç¡¤Continuum Crowd¤Ë½ñ¤¤¤Æ¤¢¤ëÀâÌÀ¤ò¤½¤Î¤Þ¤Þ¤·¤Æ¤¤¤­¤Þ¤¹¡£



¤Þ¤º¤Ï¡¤¥´¡¼¥ë¤ò·è¤á¤Þ¤¹¡£
¼¡¤Ë¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¾ì¦Õ¤Ë¥´¡¼¥ë¤ÎÆ⦤ǤÏÃͤò0¤Ë³ä¤êÅö¤Æ¤Þ¤¹¡£
¤½¤Î¼¡¤Ë¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¤¬³ä¤êÅö¤Æ¤é¤ì¤Æ¤¤¤Ê¤¤¥»¥ë¤¬³ÊǼ¤µ¤ì¤ë¡¤¡Ö̤ÃΤΥ»¥ë¤Î¥ê¥¹¥È¡×¤È¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¤¬³ä¤êÅö¤Æ¤é¤ì¤Æ¤¤¤ë¥»¥ë¤¬³ÊǼ¤µ¤ì¤ë¡Ö´ûÃΤΥ»¥ë¤Î¥ê¥¹¥È¡×¡¤¤¢¤È¥Ý¥Æ¥ó¥·¥ã¥ë¤¬³ä¤êÅö¤Æ¤é¤ì¤ë²ÄǽÀ­¤¬¤¢¤ë¥»¥ë¤ò³ÊǼ¤¹¤ë¡Ö´ûÃΤˤʤꤽ¤¦¤Ê¥»¥ë¤Î¥ê¥¹¥È¡×¤Î£³¤Ä¤òÍÑ°Õ¤·¤Þ¤¹¡£
¤¹¤Ç¤Ë¥´¡¼¥ë¤ÎÆ⦤ǤÏ0¤Ë¥Ý¥Æ¥ó¥·¥ã¥ë¤ò³ä¤êÅö¤Æ¤Æ¤¤¤ë¤Î¤Ç¡¤¤³¤ì¤é¤Î¥»¥ë¤Ï´ûÃΤΥ»¥ë¤Î¥ê¥¹¥È¤Ë¥»¥Ã¥È¤·¤Þ¤¹¡£¤½¤Î¾¤Î¥»¥ë¤Ï¥Ý¥Æ¥ó¥·¥ã¥ë¤ÎÃͤò¡ç¤Ë¤·¤Æ̤ÃΤΥ»¥ë¤Î¥ê¥¹¥È¤Ë¥»¥Ã¥È¤·¤Þ¤¹¡£
¡¡¼¡¤Ë¡¤´ûÃΤΥ»¥ë¤ËÎÙÀܤ¹¤ë̤ÃΤΥ»¥ë¤Ï¡¤´ûÃΤˤʤꤽ¤¦¤Ê¥»¥ë¤Î¥ê¥¹¥È¤Ë´Þ¤á¤Þ¤¹¡£¤½¤·¤Æ¡¤¼°(5)¤òÍ­¸Âº¹Ê¬¶á»÷Ë¡¤Ç²ò¤­¤Þ¤¹¡£¤³¤ì¤Ë¤è¤Ã¤Æ¡¤¤³¤ì¤é¤Î°ÌÃ֤ǤΦդò¶á»÷¤·¤Þ¤¹¡£¶á»÷¤Ç²ò¤¤¤¿¥Ý¥Æ¥ó¥·¥ã¥ë¤Î¤¦¤Á¡¤ºÇ¤âÄ㤤¥Ý¥Æ¥ó¥·¥ã¥ë¤ò»ý¤Ä¡Ö´ûÃΤˤʤꤽ¤¦¤Ê¥»¥ë¡×¤ò¤³¤Î¤È¤­¤Ë¡¤¡Ö´ûÃΤΥ»¥ë¡×¤Ë¤·¤Æ¡¤´ûÃΤΥ»¥ë¤Î¥ê¥¹¥È¤ËÄɲä·¤Þ¤¹¡£¤½¤·¤Æ¡¤¤³¤Î¥»¥ë¤Ï´ûÃΤΥ»¥ë¤Ë¤Ê¤Ã¤¿¤Î¤Ç¡¤¤³¤Î¥»¥ë¤ËÎÙÀܤ¹¤ë¥»¥ë¤Ï´ûÃΤˤʤꤽ¤¦¤Ê¥»¥ë¤Î¥ê¥¹¥È¤Ë´Þ¤á¤Þ¤¹¡£¤½¤·¤Æ¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¤òºÆ¶á»÷¤·¤Æ¤¤¤­¤Þ¤¹¡£¤³¤Îºî¶È¤ò·«¤êÊÖ¤·¹Ô¤¤¡¤¤¹¤Ù¤Æ¤Î¥»¥ë¤Î¥Ý¥Æ¥ó¥·¥ã¥ë¤¬ÄêµÁ¤µ¤ì¤ë¤Þ¤Ç¤Î¼Â¹Ô¤·¤Þ¤¹¡£¥´¡¼¥ë¤ÎÆ⦤«¤é³°Â¦¤Ë½ù¡¹¤ËÅÁȤ·¤Æ¤¤¤¯´¶¤¸¤Ë¤Ê¤ê¤Þ¤¹¡£Ê¬¤«¤ê¤Å¤é¤¤¾ì¹ç¤Ï¾å¤Î¿Þ¤ò»²¹Í¤Ë¤·¤Æ¤¯¤À¤µ¤¤¡£¤³¤ó¤Ê´¶¤¸¤Ç¥¢¥¤¥³¥Ê¡¼¥ëÊýÄø¼°¤ò²ò¤¤¤Æ¤¤¤¯¤½¤¦¤Ç¤¹¡£

¡¡¤µ¤Æ¡¤¶ñÂÎŪ¤Ë¸«¤Æ¤¤¤­¤Þ¤·¤ç¤¦¡£¿Þ4(a)¤Ç¤Î¥»¥ëM¤ËÂФ·¤ÆÊýÄø¼°¤ò²ò¤¯¤È²¾Äꤷ¤Þ¤¹¡£
¤Þ¤º¡¤x¼´Êý¸þ¤Èy¼´Êý¸þ¤Î¤½¤ì¤¾¤ì¤Ë±è¤Ã¤ÆÃͤ¬¾®¤µ¤¤¥»¥ë¤òµá¤á¤Þ¤¹¡£¼°¤Ë¤¹¤ë¤È²¼¤Î¤è¤¦¤Ë¤Ê¤ê¤Þ¤¹¡£



¼¡¤Ë¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¤ò¤µ¤«¤Î¤Ü¤ëÊý¸þ¤Ë¡¤°Ê²¼¤Î2¼¡ÊýÄø¼°¦ÕM¤ËÂФ·¤Æ¤è¤êÂ礭¤¤²ò¤òµá¤á¤ë¤³¤È¤Ë¤è¤Ã¤Æ¡¤¼°(5)¤Ç¤¢¤é¤ï¤µ¤ì¤ë¥¢¥¤¥³¥Ê¡¼¥ëÊýÄø¼°¤òÍ­¸Âº¹Ê¬¶á»÷¤·¤Þ¤¹¡£



ÅöÁ³¡¤¦Õmx¤È¦Õmy¤Ï¥Ý¥Æ¥ó¥·¥ã¥ë¤¬ÄêµÁ¤µ¤ì¤Æ¤¤¤ëɬÍפ¬¤¢¤ë¤Î¤Ç¡¤Ãͤ¬Ìµ¸ÂÂç¤Î¾ì¹ç¤Ï¾å¤Î¼°(11¡Ë¤Ï¼Â¹Ô¤Ç¤­¤Þ¤»¤ó¡£¦ÕM¤òµá¤á¤¿¤é¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¤ò¤µ¤«¤Î¤Ü¤ëÊý¸þ¤ÇÎÙÀܤ¹¤ë¥°¥ê¥Ã¥É¤È¤Î¥Ý¥Æ¥ó¥·¥ã¥ë¤Îº¹Ê¬¤ò¼è¤ê¡¤¸ûÇÛ¢à¦Õ¤ò·×»»¤·¤Þ¤¹¡£¤³¤Î¤È¤­¤Ë¡¤¸ûÇÛ¤òÀµµ¬²½¤·¡¤Â®ÅÙv¤òµá¤á¤ë¤¿¤á¤ËŬÀÚ¤ÊÊý¸þ¤Ç¤Î¥¹¥Ô¡¼¥Éf¤ò³Ý¤±¤ë¤È¤¤¤¦ºî¶È¤â¤·¤Æ¤ª¤­¤Þ¤¹¡£¤³¤ì¤Ç¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¤âµá¤Þ¤ê¡¤Â®ÅÙ¤âµá¤Þ¤ê¤Þ¤·¤¿¡£

¡¡
¡¡¤µ¤Æ¡¤¿Í¡¹¤Î°ÌÃ֤ι¹¿·¤Ç¤¹¤¬¡Ä
Continumm Crowd¤Ç¤Ï¡¤Â®ÅÙ¾ì¤òÊä´Ö¤¹¤ë¤³¤È¤Ë¤è¤Ã¤Æ¡¤Ã±½ã¤Ë¿Í¡¹¤Î°ÌÃÖ¤ò¹¹¿·¤·¤Æ¤¤¤ë¤½¤¦¤Ç¤¹¡£¿Í¤Î°ÌÃ֤ϮÅ٤ˤè¤Ã¤ÆÆ°¤«¤·¤Þ¤¹¡£ÏÀʸ¤Ç¤Ï¡¤Â®Å٤ϥª¥¤¥é¡¼ÀÑʬˡ(Euler intergration)¤ò»È¤Ã¤Æ¸úΨŪ¤Ë·×»»¤·¤Æ¤¤¤ë¤È¸À¤Ã¤Æ¤¤¤Þ¤¹¡£¤Þ¤¿¡¤¥ë¥ó¥²¡¦¥¯¥Ã¥¿ÀÑʬˡ¡ÊRunge-Kutta intergration)¤â»î¤·¤Æ¤ß¤¿¤½¤¦¤Ç¤¹¤¬¡¤·àŪ¤ÊÊѲ½¤¬¤Ê¤«¤Ã¤¿¤è¡Á¤È¤â½ñ¤¤¤Æ¤¢¤ê¤Þ¤¹¡£¤Þ¤¡¡¤ËÜÅö¤«¤É¤¦¤«¤Ï¼ÂÁõ¤·¤Æ»î¤·¤Æ¤ß¤¿¤¤¤È²¿¤È¤â¤¤¤¨¤Ê¤½¤¦¤Ç¤¹¤Í¡£

¡¡°Ê¾å¤Ç¡¤Continuum Crowd¤ÎÍýÏÀŪ¤ÊÏäϽª¤ï¤ê¤Ç¤¹¤¬¡¤¼ÂºÝ¤Ë¼ÂÁõ¤·¤Æ¤ß¤ë¤ÈÉÔ¶ñ¹ç¤¬À¸¤¸¤Æ¤·¤Þ¤¦¤½¤¦¤Ç¤¹¡£¤½¤ì¤¬¡Ö4.5¡¡Minimum Distance Enforcement¡×¤Ë½ñ¤¤¤Æ¤¢¤ê¤Þ¤¹¡£

¡¡Continuum Crowd¤ÎÍýÏÀ¤Ç¤Ï¡¤2¿Í¤Î¿Í¤¬¸òº¹¤·¤Ê¤¤¤È¤¤¤¦¤³¤È¤òÊݾڤ·¤Æ¤¤¤Þ¤¹¡£2¿Í¤Î¿Í¤¬¶á¤Å¤¯¤È¤¤¤¦¤³¤È¤Ï¡¤Ì©ÅÙ¤¬¹â¤¯¤Ê¤ë¤È¤¤¤¦¤³¤È¤Ê¤Î¤Ç¡¤¥¹¥Ô¡¼¥É¤Ï¸ß¤¤¤Ë0¤Ë¸þ¤«¤Ã¤Æ¸º¾¯¤·¤Þ¤¹¡£
¡¡¤·¤«¤·¡¤¼ÂºÝ¤Ë¤Ï¥°¥ê¥Ã¥É¤ÎÁƤµ¤ËÂФ·¤Æ¡¤ºÆ¤Ó¥À¥¤¥Ê¥ß¥¯¥¹¤ò²ò¤¯¤À¤±¤Ê¤Î¤Ç¡¤Æ±¤¸¥»¥ëÆâ¤Î£²¿Í¤Î¿Í¡¹¤Ï¤¿¤Þ¡Á¤Ë¸òº¹¤·¤Æ¤·¤Þ¤¦¤è¤¦¤Ç¤¹¡£¤«¤Ê¤êµ©¤Ê¥±¡¼¥¹¤é¤·¤¤¤Ç¤¹¤¬¡¤¤ä¤Ã¤Ñ¤·¸«¤¿ÌÜŪ¤Ë¤Ï¡¤¤¢¤ó¤Þ¤·¤è¤í¤·¤¤¤â¤ó¤¸¤ã¤Ê¤¤¤Ç¤¹¡£¤½¤³¤ÇÏÀʸ¤Ç¤Ï¡¤£²¿Í¤¬¶á¤Å¤­¤¹¤®¤Ê¤¤¤è¤¦¤ËºÇ¾®µ÷Î¥¤ò¼é¤é¤»¤ë¤è¤¦¤Ê½èÍý¤ò¤·¤Æ¤¤¤Þ¤¹¡£ïçÃ͵÷Î¥¤Ê¤¤¤Î¤¹¤Ù¤Æ¤Î¥Ú¥¢¤ËÂФ·¤Æ¥ë¡¼¥×¤µ¤»¡¤ºÇ¾®µ÷Î¥¤¬¼é¤é¤ì¤ë¤è¤¦¤Ë¿Í¤òpush¤·¤Þ¤¹¡£´¶³ÐŪ¤Ë¤ÏBoid¥¢¥ë¥´¥ê¥º¥à¤Î°ú¤­Î¥¤·¥ë¡¼¥ë¤ß¤¿¤¤¤Ê¤â¤ó¤À¤È»×¤¤¤Þ¤¹¡£Ã±½ã¤ËµÕ¥Ù¥¯¥È¥ë¤òºî¤Ã¤ÆºÇ¾®µ÷Î¥°Ê²¼¤À¤Ã¤¿¤éµÕ¥Ù¥¯¥È¥ë¤È­¤·¤Æ²¡¤·½Ð¤¹¤È¤¤¤¦½èÍý¤Ç¤Ï¤Ê¤¤¤Ç¤·¤ç¤¦¤«¡©
¡¡¤Á¤Ê¤ß¤Ë¡¤¤³¤Î½èÃ֤ϱþµÞ½èÃ֤Τ褦¤Ç¡¤¸·Ì©¤Ë¤ÏºÇ¾®µ÷Î¥¤¬Êݤ¿¤ì¤ë¤³¤È¤ÏÊݾڤ·¤Ê¤¤¤È½ñ¤¤¤Æ¤¢¤ê¡¤ºÇ¾®µ÷Î¥¤ò¼é¤é¤»¤ë½èÍý¤Ë¤è¤Ã¤Æ¥¢¡¼¥Æ¥£¥Õ¥¡¥¯¥È¤¬È¯À¸¤·¤Æ¤·¤Þ¤¦¤½¤¦¤Ç¤¹¡£¤¿¤È¤¨¤Ð¡¤Æ°¤¤¤Æ¤¤¤Ê¤¤¿Í¤¬²¡¤µ¤ì¤ÆÆ°¤¤¤Æ¤·¤Þ¤¦¤È¤«¤Ç¤¹¡£YouTube¤Ë¤â¥Ó¥Ç¥ª¤¬¥¢¥Ã¥×¤µ¤ì¤Æ¤¤¤ë¤Î¤Ç³Îǧ¤·¤Æ¤ß¤ë¤È
¿®¹æ¤Ç¿Í¤¬»ß¤Þ¤Ã¤Æ¤¤¤ë½ê¤Ç²¡¤µ¤ì¤Æ¤¤¤¿¤ê¤·¤Þ¤¹¡£



¤Þ¤¡¡¤¤³¤ì¤ò¤­¤Ã¤Á¤ê²ò·è¤·¤è¤¦¤È¤¹¤ë¤È½èÍý¤Ë»þ´Ö¤â¤«¤«¤Þ¤¹¤·¡¤¤·¤ç¤¬¤Ê¤¤¤Î¤Ç¤Ï¤Ê¤¤¤Ç¤·¤ç¤¦¤«¡©
¤Á¤Ê¤ß¤Ë¡¤ºÇ¾®µ÷Î¥¤Î¶¯ÍפÏÀþ·Á¤Î»þ´Ö¤Ë¤Ê¤ë¤½¤¦¤Ç¤¹¡£

5²ó¤ËÅϤäƵ­»ö¤ò½ñ¤­¤Þ¤·¤¿¤¬¡¤¤³¤ì¤Ç°ì±þContinuum Crowd¤ÎÀâÌÀ¤Ï½ª¤ï¤ê¤Ë¤µ¤»¤Æ¤¤¤¿¤À¤­¤Þ¤¹¡£
»þ´Ö¤¬¤¢¤Ã¤¿¤é¼«Ê¬¤Ç¼ÂÁõ¤·¤¿¤¤¤ó¤Ç¤¹¤¬¡¤Ë»¤·¤¯¤Æ¤Ê¤«¤Ê¤«»þ´Ö¤¬¤È¤ì¤Ê¤¤¤ó¤Ç¤¹¤è¤Í¡Á¡£
狼¼ÂÁõ¤·¤Æ¥½¡¼¥¹¥³¡¼¥É¸ø³«¤·¤Æ¤¯¤ì¤ë¿Í¤¤¤Ê¤¤¤Ç¤¹¤«¤Í¡©

º£²ó¤Ï¡¤¡Ö4¡¥¼ÂÁõ¡×¤òÀâÌÀ¤·¤Æ¤¤¤­¤Þ¤¹¡£
¥·¥ß¥å¥ì¡¼¥·¥ç¥ó¤ò¤¹¤ë¤¿¤á¤Ë¤Ï¡¤¡Ö3¡¥»ÙÇÛÊýÄø¼°¡×¤Ç½Ò¤Ù¤¿¥â¥Ç¥ë¤òÎ¥»¶²½¤¹¤ëɬÍפ¬¤¢¤ê¤Þ¤¹¡£
¥·¥ß¥å¥ì¡¼¥¿¡¼¤Ï¡¤°Ê²¼¤Î¤è¤¦¤Ë¤·¤Æ³Æ¥¿¥¤¥à¥¹¥Æ¥Ã¥×¤òÄ̤¸¤Æ¡¤¿Í¤ò¿Ê¤á¤Þ¤¹¡£

³Æ¥¿¥¤¥à¥¹¥Æ¥Ã¥×¤Ë´Ø¤·¤Æ¡§
¡¡¡¡¡¡¡¡¡¦·²¤ì¤òÌ©ÅÙ¾ì¤ØÊÑ´¹¡¡
¡¡¡¡¡¡¡¡³Æ¥°¥ë¡¼¥×¤Ë´Ø¤·¤Æ¡§
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¦Ã±°Ì¥³¥¹¥È¾ìC¤ò¹½ÃÛ
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¦¥Ý¥Æ¥ó¥·¥ã¥ë¾ì¦Õ¤È¤½¤Î¸ûÇÛ¢à¦Õ¤ò¹½ÃÛ
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¦¿Í¡¹¤Î°ÌÃÖ¤ò¹¹¿·
¡¡¡¡¡¡¡¡¡¦¿Í¤È¿Í¤Î´Ö¤ÎºÇ¾®µ÷Î¥¤ò¼é¤é¤»¤ë

¤³¤ì¤é¤Î¾ì¤ò·×»»¤¹¤ë¤¿¤á¤Ë¡¤²¼¤Î¿Þ¤Î¤è¤¦¤Ë¶õ´Ö¤ò¶ÑÅù¥°¥ê¥Ã¥É¤ÇÎ¥»¶²½¤·¡¤³Æ¥°¥ê¥Ã¥É¤´¤È¤ËʪÍýÊÑ¿ô¤ò»ý¤¿¤»¤Þ¤¹¡£




Continuum Crowd¤Ç¤Ï¡¤ÉâÆ°¾®¿ôÅÀ¤Î2¼¡¸µÇÛÎó¤È¤·¤ÆʪÍý¾ì¤òµ­²±¤·¤Æ¤¤¤ë¤è¤¦¤Ç¤¹¡£
¾å¤Î¿Þ¤ÎÀâÌÀ¤Ç¤¹¤¬¡¤¤Þ¤º¥¹¥«¥é¡¼¾ì¤Ï¥°¥ê¥Ã¥É¤ÎÃæ¿´°ÌÃÖ¤ÇÄêµÁ¤µ¤ì¤Þ¤¹¡£¤Á¤ç¤¦¤É¹õ¤¤´Ý¤Ë¤¢¤¿¤ë¤È¤³¤í¤Ç¤¹¡£¤½¤·¤Æ¡¤°ÜÆ°¤¹¤ëÊý¸þ¤Ë¤è¤Ã¤ÆÊѤï¤ë¾ì¤Ï¡¤³Æ¥»¥ë¤¬¦È=¡Ð0¡ë,90¡ë,180¡ë,270¡ë¡Ñ¡¤¤Ä¤Þ¤êÅ졤ËÌ¡¤À¾¡¤Æ¤È¤Ëµ­²±¤·¤Þ¤¹¡£¾å¤Î¿Þ¤À¤È¥ª¥ì¥ó¥¸¤Î´Ý¤Ë¤¢¤¿¤ë¾ì½ê¤Ç¤¹¡£

Íפ¹¤ë¤Ë¡Ä
°ÜÆ°¤¹¤ëÊý¸þ¤¬´Ø·¸¤·¤Ê¤¤¥¹¥«¥é¡¼¾ì¡¤¤³¤³¤Ç¤ÏÉÔ²÷Î̤ÈÌ©ÅÙÎÌ¡¤¥Ý¥Æ¥ó¥·¥ã¥ëÎÌ¡¤¹â¤µ¡¤Ê¿¶Ñ®Å٤ϥ°¥ê¥Ã¥É¤ÎÃæ¿´¤ÇÄêµÁ¤µ¤ì¤ë¤È¤·¤ÆÃÖ¤­¤Þ¤¹¡£
°ÜÆ°¤¹¤ëÊý¤¬´Ø·¸¤¹¤ë¾ì¡¤¤Ä¤Þ¤ê¥¹¥Ô¡¼¥É¤Èñ°Ì¥³¥¹¥È¾ì¡¤¹â¤µ¤Î¸ûÇÛ¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¤Î¸ûÇÛ¡¤Â®Å٤ϡ֤ɤ³¤«¤é¤É¤³¤Ø¤«¡©¡×¤È¤¤¤¦¤³¤È¤¬Ê¬¤«¤ë¤è¤¦¤Ë¡¤¥°¥ê¥Ã¥É¤ÎÀþ¾å¤ÇÄêµÁ¤·¤Þ¤·¤ç¤¦¤Í¡Á¤È¤¤¤¦¤³¤È¤Ç¤¹¡£

¤³¤ì¤Ç¡¤¤¢¤ëÄøÅÙÆ°¤«¤·Êý¤Ï¤Ä¤«¤á¤¿¤È»×¤¦¤Î¤Ç¡¤¤è¤ê¾Ü¤·¤¯¸«¤Æ¤¤¤­¤Þ¤¹¡£
¤Þ¤º¤Ï¡¤Ì©ÅÙ¤ÎÊÑ´¹¤Ç¤¹¡£

¥¹¥Ô¡¼¥É¤ÏÌ©Å٤˰͸¤¹¤ë¤È¤¤¤¦¤³¤È¤òÁ°²ó½Ò¤Ù¤Þ¤·¤¿¡£
¥¹¥Ô¡¼¥É¤òµá¤á¤ë¤¿¤á¤Ë¤Ï¡¤Ì©ÅÙ¤ò»»½Ð¤·¤Ê¤±¤ì¤Ð¤Ê¤ê¤Þ¤»¤ó¡£
¤³¤³¤ÇÃí°ÕÅÀ¤¬£²¤Ä¤¢¤ê¤Þ¤¹¡£¤Þ¤º°ì¤ÄÌܤϡ¤Ì©ÅÙ¾ì¤Ï¿Í¡¹¤Î°ÌÃ֤˴ط¸¤¬¤¢¤ë¤¿¤á¤ËϢ³¤Ç¤Ê¤ì¤Ð¤¤¤±¤Ê¤¤¤È¤¤¤¦¤³¤È¤Ç¤¹¡£¤·¤«¤·¡¤¥°¥ê¥Ã¥É¤Ë¤è¤Ã¤ÆÎ¥»¶Åª¤Ë¤·¤Æ¤¢¤ë¤Î¤Ç¡¤Æ°¤­¤ÏÌ©Å٤ˤè¤Ã¤ÆÉÔϢ³¤¬È¯À¸¤·¤Þ¤¹¡£¥¹¥Ô¡¼¥É¤âƱ¤¸¤Ç¤¹¡£¤â¤¦°ì¤Ä¤Ï¡¤¼«Ê¬¤Î¤¤¤ë¥°¥ê¥Ã¥É¤Ë¤Ï¡¤¼«Ê¬¤Î±Æ¶Á¤¬¤Ç¤Ê¤¤¤è¤¦¤ËÌ©ÅÙ¤ÎïçÃ͡ʦѥС¼¡Ë¤è¤ê¾®¤µ¤¯ÀßÄꤹ¤ëɬÍפ¬¤¢¤ê¡¤ÎÙÀÜ¥°¥ê¥Ã¥É¤Ë¤Ï±Æ¶Á¤òÍ¿¤¨¤ë¤è¤¦¤ËïçÃͰʾå¤ÎÃͤòÍ¿¤¨¤ëɬÍפ¬¤¢¤ë¤³¤È¤Ç¤¹¡£

¤Þ¤º¡¤°ì¤ÄÌܤǤ¹¤¬¡¤ÏÀʸÃæ¤Ç¤Ï¥Ð¥¤¥ê¥Ë¥¢¤ä¥¬¥¦¥·¥¢¥ó¤È¤«¤ò»È¤¨¤Ð²ò·è¤Ç¤­¤ë¤è¡Á¤Ã¤Æ½ñ¤¤¤Æ¤¢¤ê¤Þ¤¹¡£¤Þ¤¡¥Õ¥£¥ë¥¿¥ê¥ó¥°¤ß¤¿¤¤¤Ê¤Î¤ò¤¹¤ì¤Ð¤¤¤¤¤Ã¤Æ¤³¤È¤Ç¤¹¤«¤Í¡©
Æó¤ÄÌܤξò·ï¤Ï¡¤¤Ê¤«¤Ê¤«Ëþ¤¿¤¹¤Î¤¬Æñ¤·¤¤¤é¤·¤¯¡¤ÏÀʸÃæ¤Ç¤Ï¤³¤Î¾ò·ï¤òËþ¤¿¤¹¿·¤·¤¤Ì©ÅÙÊÑ´¹¤¹¤ëµ»½Ñ¤òÄêµÁ¤·¤¿¤È½ñ¤¤¤Æ¤¢¤ê¤Þ¤¹¡£



³Æ¿Í¡¹¤ËÂФ·¤Æ¡¤ºÇ¤â¶á¤¤¥»¥ë¤ÎÃæ¿´¤òµá¤á¤Þ¤¹¡£¤¿¤À¤·¡¤¾ò·ï¤¬°ì¤Ä¤¢¤Ã¤Æ¡¤Ãæ¿´ºÂɸ¤Ï¿Í¤ÎxºÂɸ, yºÂɸ¤ÎξÊý¤È¤â¾®¤µ¤¯¤Ê¤Ã¤Æ¤¤¤Ê¤±¤ì¤Ð¤Ê¤ê¤Þ¤»¤ó¡£¾å¤Î¿Þ¤òÍѤ¤¤ÆÀâÌÀ¤¹¤ë¤È¡¤¿Í¤òÀÖ¤¤´Ý¤È¤·¤Þ¤¹¡£¤¹¤ë¤È¡¤xºÂɸ¡¦yºÂɸ¤È¤â¤Ë¾®¤µ¤¯¤Ê¤Ã¤Æ¤¤¤ëºÇ¤â¶á¤¤¥»¥ë¤ÎÃæ¿´¤ÏA¤È¤¤¤¦¤³¤È¤Ë¤Ê¤ê¤Þ¤¹¡£¡ÊB¤ÏxºÂɸ¤¬Â礭¤¤¤Î¤Ç¤À¤á¤Ç¤¹¡£C¤Ïx,yºÂɸ¤È¤â¤ËÂ礭¤¤¤Î¤Ç¤À¤á¡£D¤ÏyºÂɸ¤¬Â礭¤¤¤«¤é¤À¤á¤Ç¤¹¡£¡ËºÇ¤â¶á¤¤¥»¥ë¤òµá¤á¤¿¤é¡¤¥»¥ëÃæ¿´¤Ë´Ø·¸¤¹¤ë¡¤¿Í¤ÎÁêÂкÂɸ¤ò·×»»¤·¤Þ¤¹¡£¾å¤Î¿Þ¤Ç¸À¤¦¤È­ùx¤È­ùy¤Ë³ºÅö¤·¤Þ¤¹¡£¤½¤·¤¿¤é¿Í¤ÎÌ©Å٤ϰʲ¼¤Î¼°¤Ë¤è¤ê³Æ¥°¥ê¥Ã¥É¤Ë²Ã»»¤µ¤ì¤Þ¤¹¡£



¦Ë¤ÏÌ©Åٻؿô¤Ç¤¹¡£¦Ë¤ÎÃͤˤè¤Ã¤ÆÃͤθº¾¯¤¬·èÄꤵ¤ì¤Þ¤¹¡£ÏÀʸ¤Ë¤è¤ë¤È¡¤¤³¤ÎÌ©ÅÙÊÑ´¹ÊýË¡¤Ï¿Í¤Î°ÌÃ֤˴ط¸¤·¤Æ¤¤¤ë¤Î¤Ç¡¤Ï¢Â³¤Ç¤¢¤ê¡¤¼«Ê¬¤Î¥°¥ê¥Ã¥É¤ËÂФ·¤Æ¤Ï¦Ñ¥Ð¡¼¤è¤ê¾®¤µ¤¤ÃͤòÍ¿¤¨¡¢ÎÙÀÜ¥°¥ê¥Ã¥É¤ËÂФ·¤Æ¤Ï(¦Ñ¥Ð¡¼) = 1/(2^¦Ë)¤Ç¦Ñ¥Ð¡¼°Ê¾å¤òÍ¿¤¨¤ë¤È½ñ¤¤¤Æ¤¢¤ê¤Þ¤¹¡£
¡¡¤É¤³¤«¤é¤É¤¦¤ä¤Ã¤Æ¡¤¤³¤Î¼°¤¬Æ³¤«¤ì¤¿¤«¤Ï¤ï¤«¤ê¤Þ¤»¤ó¤¬¡¤³Î¤«¤Ë¥Æ¥­¥È¡¼¤ÊÃͤòÂåÆþ¤·¤ÆÌ©ÅÙ¤ò·×»»¤¹¤ë¤È¼«Ê¬¤Î¥°¥ê¥Ã¥É¤ÏïçÃͤè¤ê¾®¤µ¤¯¤Ê¤Ã¤Æ¡¤ÎÙÀÜ¥°¥ê¥Ã¥É¤ËÂФ·¤Æ¤ÏïçÃͰʾå¤ÎÃͤˤʤê¤Þ¤¹¡£¤³¤ì¤ÇÀè¤Û¤É½Ò¤Ù¤¿¾ò·ï¤Ï¥¯¥ê¥¢¤Ç¤­¤¿¤Î¤Ç¡¤¾å¼°¤ò»È¤¨¤ÐÌ©ÅÙÊÑ´¹¤¬¤Ç¤­¤Þ¤¹¡£¤¢¤ÈÌ©ÅÙ¤òÊÑ´¹¤¹¤ë¤È¤­¤Ë¼°(7)¤Ë½¾¤Ã¤Æ¡¤Ê¿¶Ñ®Å٤⻻½Ð¤·¤Æ¤ª¤­¤Þ¤¹¡£


¤Þ¤¿¤Þ¤¿¡¤Ä¹¤¯¤Ê¤Ã¤Æ¤·¤Þ¤Ã¤¿¤Î¤Ç¡¤¤Þ¤È¤á¤Æ¤ª¤­¤Þ¤¹¡£

¡¦¥·¥ß¥å¥ì¡¼¥·¥ç¥ó¡¡¢ª¡¡¥°¥ê¥Ã¥É¤Ëʬ¤±¤Æ¹Ô¤¦
¡¦¥°¥ê¥Ã¥É¡¡¢ª¡¡¥¹¥«¥é¡¼¾ì¡§¡¡¥»¥ë¤ÎÃæ¿´¤ÇÄêµÁ
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¥Ù¥¯¥È¥ë¾ì¡§¡¡°ÜÆ°¤¹¤ë¥»¥ë¤È¤Î¶­³¦¾å¤ÇÄêµÁ
¡¦Ì©Å٤εá¤áÊý
¡¡¡¡¡¡­¡¡¡¿Í¤ÎºÂɸ¤ÎξÊý¤ÎÀ®Ê¬¤è¤ê¤âÃͤ¬¾®¤µ¤¤ºÇ¤â¶á¤¤¥»¥ë¤ÎÃæ¿´¤òµá¤á¤ë
¡¡¡¡¡¡­¢¡¡ºÇ¤â¶á¤¤¥»¥ë¤ÎÃæ¿´¤È¤ÎÁêÂкÂɸ¤ò»»½Ð
¡¡¡¡¡¡­£¡¡Ì©ÅÙÊÑ´¹¼°¤ËÁêÂкÂɸ¤òÂåÆþ


¼¡²ó¤Ï¡Ö4.2¡¡Ã±°Ì¥³¥¹¥È¡×¤«¤éÀâÌÀ¤ò»Ï¤á¤Þ¤¹¡£

º£²ó¤Ï¡¤ÏÀʸÃæ¤Î¡Ö3.2¡¡¥¹¥Ô¡¼¥É¡×¤Î½ê¤«¤é»Ï¤á¤Þ¤¹¡£

¡¡Continuum Crowds¤Ç¤Î¥¹¥Ô¡¼¥É¤ÏÌ©Å٤˰͸¤·¤¿ÊÑ¿ô¤Ç¤¹¡£
¡¡¼þ¤ê¤Ë¡¤¤¢¤Þ¤ê¿Í¤¬¤¤¤Ê¤¤¾ì¹ç¤Ç¤¢¤ëÄãÌ©Å٤ξì¹ç¤Ç¤Ï¡¤¥¹¥Ô¡¼¥É¤ÏÃÏ·Á¤Ë¤è¤Ã¤Æ°Í¸¤·¤Þ¤¹¡£Ê¿¤é¤Ê½ê¤Ê¤é¥¹¥Ô¡¼¥É°ìÄê¤Ç¤¹¤¬¡¤ºäÆ»¤Î¤è¤¦¤Ë·¹¼Ð¤¬¤¢¤ë¾ì¹ç¤Ï¡¤¥¹¥Ô¡¼¥É¤Ï·¹¼Ð¤Ë¤è¤Ã¤ÆÊѲ½¤·¤Þ¤¹¡£
¡¡µÕ¤Ë¡¤¼þ¤ê¤Ë¿Í¤À¤é¤±¤Î¹âÌ©Å٤ξì¹ç¤Ï¡¤¶á¤¯¤Î¿Í¡¹¤ÎÆ°¤­¤Ë¤è¤Ã¤Æ¥¹¥Ô¡¼¥É¤Ï»ÙÇÛ¤µ¤ì¤Þ¤¹¡£Îã¤È¤·¤Æ¡¤¿Í¤Îή¤ì¤ËµÕ¤é¤Ã¤ÆÆ°¤³¤¦¤È¤¹¤ë¤È¥¹¥Ô¡¼¥É¤ÏÍÞÀ©¤µ¤ì¤Þ¤¹¤¬¡¤¿Í¤Îή¤ì¤È¤È¤â¤ËÆ°¤¯¤È¤­¤Ï¡¤±Æ¶Á¤µ¤ì¤Þ¤»¤ó¡£Ä«¤Î½Ð¶Ð¥é¥Ã¥·¥å¤Ê¤ó¤«¤ò»×¤¤É⤫¤Ù¤ë¤È¤³¤ì¤ÏǼÆÀ¤Ç¤­¤ë¤ó¤¸¤ã¤Ê¤¤¤Ç¤·¤ç¤¦¤«¡©

¡¡¤µ¤Æ¤µ¤Æ¡¤¤³¤Î¥¹¥Ô¡¼¥É¤Ê¤ó¤Ç¤¹¤¬¡¤Á°½Ò¤·¤¿¤è¤¦¤ËÌ©Å٤˰͸¤¹¤ë¹à¤Ê¤Î¤Ç¡¤¤Þ¤º¤Ï·²¤ì¤ÎÌ©ÅÙ¾ì¦Ñ¤ò¹Í¤¨¤ë¤³¤È¤Ë¤·¤Þ¤¹¡£
¡¡Continuum Crowds¤Ç¤ÏiÈÖÌܤοͤËÂФ·¤Æ¡¤¦Ñi¤Ç¼¨¤µ¤ì¤¿¸Ä¡¹¤ÎÌ©ÅÙ¤ò³Æ¿Í¡¹¤Ë»ý¤¿¤»¤ë¤è¤¦¤Ç¤¹¡£¤½¤·¤Æ¡¤¤³¤Î¸Ä¡¹¤Î¿Í¡¹¤Ë¤â¤¿¤»¤ëÌ©ÅÙ¤ÎÃͤǤ¹¤¬¡¤¾ì¡ÊField¡Ë¤È¤·¤Æ¹Í¤¨¤Þ¤¹¡£¤³¤Î¾ì¤Ï¡¤¤¢¤ë¿Íi¤Î°ÌÃ֤ǺÇÂçÃͤˤʤꡤ¤½¤³¤«¤éÊü¼Í¾õ¤Ë¸º¾¯¤·¤Þ¤¹¡£Íפ¹¤ë¤Ë¿Í¤Î°ÌÃÖ¤òÃæ¿´¤È¤·¤Æ³°Â¦¤Ë¸þ¤«¤Ã¤Æ¸º¾¯¤·¤Æ¤¤¤¯¤è¤¦¤Ê±ß¤È¹Í¤¨¤ë¤È¤¤¤¤¤È»×¤¤¤Þ¤¹¡£



¤³¤³¤ÇÃí°Õ¤·¤Æ¤Û¤·¤¤¤Î¤Ï¡¤È¾·Âr¤Î¥Ð¥¦¥ó¥Ç¥£¥ó¥°¥Ç¥£¥¹¥¯Æâ¤Ç¤Ï¡¤ïçÃ͡ʦѥС¼¡Ë¤è¤ê¾®¤µ¤¯¤Ê¤é¤Ê¤¤¤è¤¦¤ËÀßÄꤷ¡¤µÕ¤ËȾ·Âr¤è¤ê¤â³°Â¦¤Ç¤ÏïçÃͤè¤êÂ礭¤¯¤Ê¤é¤Ê¤¤¤è¤¦¤ËÀßÄꤹ¤ë¤³¤È¤Ç¤¹¡£
¡¡¤³¤Î¤è¤¦¤Ë¡¤³Æ¿Í¡¹¤ÎÌ©Å٦ѣ餬·è¤Þ¤ì¤Ð¡¤¿Í¤Î·²¤ì¤ÎÌ©ÅÙ¾ì¤Ï³Æ¿Í¡¹¤ÎÌ©Å٤ιç·×¤Ë¤Ê¤ê¤Þ¤¹¡£¤Þ¤¿¡¤·²¤ì¤ÎÌ©ÅÙ¾ì¤ò·×»»¤¹¤ë¤È¤­¤Ë¡¤Æ±»þ¤ËÊ¿¶Ñ®ÅÙ(v¥Ð¡¼¡Ë¤â·×»»¤·¤Þ¤¹¡£Ê¿¶Ñ®ÅÙ¡Êv¥Ð¡¼¡Ë¤Ï³Æ¿Í¡¹¤ÎÌ©Å٤˳ƿ͡¹¤Î®ÅÙ¤ò¤«¤±¤¿¤â¤Î¤Ç¡¤·²¤ìÁ´ÂΤΥ¹¥Ô¡¼¥É¤È·²¤ì¤Îή¤ì¤ÎÊý¸þ¤ò¼¨¤·¤Þ¤¹¡£Ì©ÅÙ¾ì¤ÈÊ¿¶Ñ®ÅÙ¤òµá¤á¤ë¼°¤Ï¼°(7)¤Ë¤Ê¤ê¤Þ¤¹¡£

¤Á¤ç¤Ã¤È¸«¤Å¤é¤«¤Ã¤¿¤Î¤Ç¡¤Ê¿¶Ñ®Å٤μ°¤ÏÊÑ·Á¤µ¤»¤Æ¤¤¤Þ¤¹¡£°ì±þÂç¾æÉפÀ¤È»×¤¤¤Þ¤¹¤¬¡¤(xi¥É¥Ã¥È)¤ÏiÈÖÌܤοͤήÅ٤ΰì²óÈùʬ¤Ë¤Ê¤ë¤Î¤Ç¡¤iÈÖÌܤοͤήÅÙ¤ò¤¢¤é¤ï¤·¤Æ¤¤¤Þ¤¹¡£¤Ç¡¤Ì©ÅÙ¾ì¤Î¼°¤Î¥·¥°¥Þ¤âÊ¿¶Ñ®Å٤Υ·¥°¥Þ¤Î¤Û¤¦¤â¤¹¤Ù¤Æ¤Î¥°¥ë¡¼¥×Æâ¤Î¤¹¤Ù¤Æ¤Î¿Í¤Î¿ô¤À¤±ÁíϤò¤È¤ê¤Þ¤¹¡£¡Ö¥°¥ë¡¼¥×¤Ã¤Æ²¿¡©¡×¤Ã¤Æ»×¤Ã¤¿Êý¤ÏÁ°²ó¤ÎContinuum Crowds¤Ë´Ø¤¹¤ëµ­»ö¤ò»²¾È¤·¤Æ¤¯¤À¤µ¤¤¡£


¡¡¤³¤ì¤Ç¡¤Ì©Å٤˴ؤ¹¤ëµ­½Ò¤¬¤Ç¤­¤ë¤è¤¦¤Ë¤Ê¤Ã¤¿¤Î¤Ç¡¤ËÜÂê¤Ç¤¢¤ë¥¹¥Ô¡¼¥É¤ÎÏ䬤Ǥ­¤Þ¤¹¡£
Á°½Ò¤·¤¿¤Î¤è¤¦¤Ë¡¤¥¹¥Ô¡¼¥É¤È¤¤¤¦¤Î¤ÏÌ©Å٤˰͸¤·¤Þ¤¹¡£¶Ë¤á¤ÆÄãÌ©Å٤Υ¨¥ê¥¢¤Ç¤Ï¡¤¥¹¥Ô¡¼¥Éf¤ÏÃÏ·Á¾å¤Î¥¹¥Ô¡¼¥ÉfT¤ËÅù¤·¤¤¤È¤¤¤¦¤Õ¤¦¤Ë¡¤Continuum Crowds¤Ç¤ÏÄêµÁ¤·¤Æ¤¤¤Þ¤¹¡£¤³¤³¤ÇÁÛÄꤷ¤Æ¤¤¤ëÃÏ·Á¤ÏºÇ¾®·¹¼ÐSmin¤ÈºÇÂç·¹¼ÐSmaxÆâ¤Î¾õÂÖ¤ËÀ©¸Â¤µ¤ì¤Æ¤¤¤Æ¡¤¥¹¥Ô¡¼¥ÉÊÑ¿ô¤Ï·¹¼Ð¤ÈµÕ´Ø·¸¤Ë¤Ê¤ë¤È½ñ¤¤¤Æ¤¢¤ê¤Þ¤¹¡£Íפ¹¤ë¤Ë·¹¼Ð¤¬Â礭¤¤¤È¤­¤Ï¡¤¥¹¥Ô¡¼¥É¤¬¾®¤µ¤¯¤Ê¤ê¡¤·¹¼Ð¤¬¾®¤µ¤¤¤È¤­¤Ï¥¹¥Ô¡¼¥É¤¬Â礭¤¯¤Ê¤ë¤È¤¤¤¦¤³¤È¤Ê¤Î¤Ç¡¤ºäÆ»¤ò¤Î¤Ü¤ë¾ì¹ç¤ò»×¤¤É⤫¤Ù¤ì¤Ð¤è¤¤¤Î¤Ç¤¹¤«¤Í¡©
¡¡
¾å¤Î¼°¤Ç¡¤¢àh(x)¡¦n¦È¤ÏÊý¸þ¦È¤Ç¤Î¹â¤µ¾ìh¤Î·¹¼Ð¤Ç¤¹¡£ÏÀʸÃæ¤Ç¤Ï¹â¤µ¾ìh¤ÎÍ¿¤¨Êý¤Ë´Ø¤·¤Æ¤Ïµ­½Ò¤µ¤ì¤Æ¤¤¤Ê¤¤¤è¤¦¤Ê¤Î¤Ç¡¤¹â¤µ¾ì¤Ï¤ª¤½¤é¤¯¥æ¡¼¥¶¡¼¤¬ÃÏ·Á¤Î¹â¤µ¤«¤é¾¡¼ê¤Ë·è¤á¤Æ¤¤¤¤¤â¤Î¤À¤È»×¤¤¤Þ¤¹¡£
¡¡¼¡¤Ë¡¤¹âÌ©Å٤ξì¹ç¤Ç¤¹¤¬¡¤Àè¤Û¤É¤â½Ò¤Ù¤¿¤è¤¦¤ËÄ̶Хé¥Ã¥·¥å¤Î¤è¤¦¤Ê¿Í¤Îή¤ì¤Ë¿È¤òǤ¤»¤ë¾õÂ֤ˤʤë¤Î¤Ç¡¤·²¤ì¤ÎÊ¿¶ÑÌ©ÅÙ(v¥Ð¡¼¡Ë¤òÍѤ¤¤¿¼°(9)¤Î·Á¤Ë¤Ê¤ê¤Þ¤¹¡£


¡¡¼°(9)¤Ç¤Î(rn¦È¡Ë¤È¤¤¤¦¥«¥Ã¥³Æâ¤Ç­¤µ¤ì¤Æ¤¤¤ë¥ª¥Õ¥»¥Ã¥È¤Ï¤¢¤ë¥¨¥ê¥¢¤«¤é¿Í¤¬Æ°¤³¤¦¤È¤¹¤ë¤È¤³¤í¤ËÂФ·¤ÆÊ¿¶Ñ®ÅÙ¤òɾ²Á¤¹¤ë¤¿¤á¤ËÀ¸¤¸¤ë¤è¤¦¤Ç¤¹¡£¤³¤ì¤¬¹âÌ©Å٤ξì¹ç¤Ç¤¹¡£
¡¡¤³¤³¤Þ¤Ç¤Ç¡¤ÄãÌ©Å٤ȹâÌ©Å٤ˤĤ¤¤Æ¤Ï¿¨¤ì¤Þ¤·¤¿¤¬¡¤¡Ö¤¸¤ã¡¤´Ö¤Ç¤¢¤ëÃæÌ©Å٤Ϥɤ¦¤¹¤ë¤Î¤µ¡©¡×¤È»×¤¦¤Î¤Ç¤¹¤¬¡¤ÏÀʸ¤Ç¤ÏÀþ·ÁÊä´Ö¤òÍѤ¤¤Æ»»½Ð¤¹¤ë¤È¸À¤Ã¤Æ¤¤¤Þ¤¹¡£ÃæÌ©Å٤μ°¤Ï¼°(10)¤Ë¤Ê¤ê¤Þ¤¹¡£


ÃæÌ©Å٤μ°¤Ë¤Ä¤¤¤Æ¤â½Ð¤¿¤Î¤Ç¡¤¥¹¥Ô¡¼¥É¤Ë¤Ä¤¤¤Æ¤Î¤ª¤µ¤é¤¤¤ò¤·¤Æ¤ª¤­¤Þ¤¹¡£



¡¦¥¹¥Ô¡¼¥É¡¡¢ª¡¡Ì©Å٤˰͸¤¹¤ë
¡¦Ì©ÅÙ¡¡¢ª¡¡³Æ¿Í¡¹¤ËÌ©ÅÙ¤ò»ý¤¿¤»¡¤¤½¤ÎÌ©ÅÙ¤òÁíϤ·¤Æ·²¤ì¤ÎÌ©Å٤Ȥ¹¤ë

­¡ÄãÌ©ÅÙ¡¡¢ª¡¡ÃÏ·Á¤Ë¤è¤Ã¤Æ·è¤Þ¤ë¡Ê¡áÃÏ·Á¤Î·¹¼Ð¤Ë¤è¤Ã¤Æ¤­¤Þ¤ë¡Ë
­¢¹âÌ©ÅÙ¡¡¢ª¡¡¿Í¤Îή¤ì¤Ë¤è¤Ã¤Æ·è¤Þ¤ë¡Ê¡á·²¤ì¤ÎÊ¿¶Ñ®Å٤˴ط¸¤¹¤ë¡Ë
­£ÃæÌ©ÅÙ¡¡¢ª¡¡Àþ·ÁÊä´Ö¤Çµá¤á¤ë¡£


¼¡²ó¤Ï¡¤3.3¤ÏÀâÌÀ¤»¤º¤Ë¡¤¡Ö4.¡¡¼ÂÁõ¡×¤ò¿¨¤ì¤Þ¤¹¡£

Á°²ó¤Ë°ú¤­Â³¤­¡¤Continuum Crowd¤Î¤ªÏá£
º£²ó¤Ï¡¤¡Ö3¡¥The Governing Equation¡×¤«¤é¸«¤Æ¤¤¤­¤Þ¤¹¡£

3Àá¤Î»ÙÇÛÊýÄø¼°¤Ç¤¹¤¬¡¤»ÙÇÛÊýÄø¼°¤Ï·²½¸¤ò´Ñ»¡¤·¡¤¤½¤³¤«¤é4¤Ä¤Î²¾Àâ¤òΩ¤Æ¤Æ½Ð¤·¤Æ¤¤¤ë¤½¤¦¤Ç¤¹¡£

²¾Àâ1¡§¡¡³Æ¿Í¡¹¤ÏÃÏÍýŪ¤Ê¥´¡¼¥ëG¤Ëé¤êÃ夳¤¦¤È¤¹¤ë¡£
²¾Àâ2¡§¡¡¿Í¡¹¤Ï²Äǽ¤Ê¸Â¤êºÇÂ祹¥Ô¡¼¥É¤Ç°ÜÆ°¤¹¤ë¡£¤³¤ì¤ÏºÇÂ祹¥Ô¡¼¥É¾ìf¤È¤·¤Æɽ¸½¤µ¤ì¤Þ¤¹¡£f¤Ï°ÌÃÖx¤ÇÊý¸þ¦È¤Ë°ÜÆ°¤¹¤ë¿Í¤¬»ý¤Ä®Å٥٥¯¥È¥ë¤Ç¤¹¡£
²¾Àâ3¡§¡¡ÉÔ²÷¾ìg¤¬Â¸ºß¤·¡¤¡Ê¤¹¤Ù¤Æ¤¬Æ±¤¸¤È¤·¤Æ¡Ë¡¤¤â¤·g(x') > g(x)¤Ê¤é¤Ð¡¤x'¤è¤ê¤âx¤ò¿Í¤Ï¹¥¤ß¤Þ¤¹¡£
²¾Àâ4¡§¡¡°ÌÃÖx¤Ë¤¤¤ë¿Í¤Ï¡¤¼°¡Ê2¡Ë¤òºÇ¾®¤¹¤ë·ÐÏ©P¤òÁªÂò¤¹¤ë¡£¡Ê¤¿¤À¤·¡¤¥¹¥Ô¡¼¥É¾ìf¡¤ÉÔ²÷¾ìg¡¤¥´¡¼¥ë¤ÏÊѲ½¤·¤Ê¤¤¤³¤È¤òÁÛÄê¡Ë

¡¡¤¤¤¤²Ã¸º¤ÊÀâÌÀ¤ò¤·¤Æ¤ª¤¯¤È¡¤²¾Àâ1¤Ï¡Ö¤É¤³¤«½Ð¤«¤±¤ë»þ¤Ë¤Ï¡¤¤¢¤ëÄøÅÙÌÜŪÃÏ·è¤á¤ë¤Ç¤·¤ç¡©¡×¤Ã¤Æ¤³¤È¤Ç¤¹¡£¤¿¤È¤¨¤Ð¡¤¡Ö¤³¤Î¾ì½ê·ù¤À¤«¤é¡¤¶õ¤¤¤Æ¤ë¾ì½ê¹Ô¤³¤¦¡×¤È¤«¡Ä¤½¤ó¤Ê´¶¤¸¤Ç¤¹¡£
¡¡²¾Àâ2¤Ï¡¤²Äǽ¤Ê¸Â¤êºÇÂ祹¥Ô¡¼¥É¤ÇÆ°¤¯¤È²¾Äꤹ¤ë¤È¤¤¤¦¤³¤È¤ò·è¤á¤Æ¤ª¤­¡¤¥¹¥Ô¡¼¥É¤Ïºä¤Î·¹¼Ð¤ä¿Í¤Îή¤ì¤Ë¤è¤Ã¤ÆÊѤï¤ë¤È¤¤¤¦¤³¤È¤¬¸À¤¤¤¿¤¤¤è¤¦¤Ç¤¹¡£¤¿¤È¤¨¤Ð¡¤µÞ¤Ê²¼¤êºä¤Î¾ì¹ç¤Ï¡¤¥¹¥Ô¡¼¥É¤¬Â®¤¯¤Ê¤ê¡¤¿Í¤Îή¤ì¤ËµÕ¤é¤Ã¤Æ°ÜÆ°¤¹¤ë¤È¡¤¤¢¤Þ¤êÁ᤯¿Ê¤á¤Ê¤¤¤È¤¤¤¦¤³¤È¤À¤½¤¦¤Ç¤¹¡£¤½¤Î¤è¤¦¤Ê·¹¼Ð¤ä¿Í¤Îή¤ì¤Ê¤É¤Î¥¹¥Ô¡¼¥É¤ËÍ×°ø¤òÍ¿¤¨¤ë¤â¤Î¤ò¥¹¥Ô¡¼¥É¾ìf¤È¤·¤Æɽ¸½¤·¤Æ¤¤¤Þ¤¹¡£
¡¡²¾Àâ3¤Ï¡¤¡ÖÉÔ²÷¤Ê½ê¤ÏÊ⤫¤ó¤Ç¤·¤ç¡©¡×¤È¤¤¤¦¤³¤È¤Ç¤¹¡£¤¿¤È¤¨¤Ð¡¤Á𸶤ÎÃæ¤ÇƧ¤ß¸Ç¤á¤é¤ì¤¿¤±¤â¤ÎÆ»¤È¡¤»¨Áð¤ÎÃæ¤òÊ⤯¤È¤·¤¿¤é¡¤¤±¤â¤ÎÆ»¤ÎÊý¤òÁªÂò¤¹¤ë¤ó¤¸¤ã¤Ê¤¤¡©¤È¤¤¤¦¤è¤¦¤Ê¤³¤È¤òÏÀʸ¤Ç¤Ï¤¤¤Ã¤Æ¤¤¤Þ¤¹¡£³Î¤«¤Ë¡¤¼«Ê¬¤À¤Ã¤¿¤é¡¤¤¯¤µ¤ä¤Ö¤è¤ê郎´û¤ËÊ⤤¤¿Æ»¤ÎÊý¤òÁªÂò¤¹¤ë¤È»×¤¤¤Þ¤¹¤Í¡£
¡¡²¾Àâ4¤Î¼°¡Ê2¡Ë¤Ï¡¤¤Þ¤¢¤½¤Î¤Þ¤Þ¤Ç¡Ö·ÐÏ©¤ÎŤµ¡Ü»þ´Ö¡ÜÉÔ²÷¡×¤¬¾®¤µ¤¯¤Ê¤ë¤è¤¦¤Ê·ÐÏ©ÁªÂò¤¹¤ë¤È¤¤¤¦¤³¤È¤Ç¤¹¡£¼°¡Ê2¡Ë¤Ï´Êñ¤Êɽµ­¤Ë¤¹¤ë¤È¼°¡Ê4¡Ë¤Ë¤Ê¤ë¤è¡ª¤È¤¤¤¦¤³¤È¤ò¸À¤Ã¤Æ¤¤¤Æ¡¤Á°²ó¤Ë½Ð¤Æ¤­¤¿Ã±°Ì¥³¥¹¥È¾ìC¤Ï¤³¤Î¼°¡Ê4¡Ë¤ÎÃæ¤Ë½Ð¤Æ¤­¤Þ¤¹¡£


¡Ö¤ó¤¸¤ã¡¤¼°¡Ê4¡Ë¤òºÇ¾®¤Ë¤¹¤ëñ°Ì¥³¥¹¥È¾ìC¤Ï¤É¤¦¤ä¤Ã¤Æ·è¤á¤ë¤ó¤¸¤ã¤¤¡ª¡×
¤È¤¤¤¦Ïäˤʤë¤ï¤±¤Ç¤¹¤¬¡¤¤³¤³¤ÇºÇŬ·ÐÏ©¤ò·èÄꤹ¤ë¤¿¤á¤Ë¥Ý¥Æ¥ó¥·¥ã¥ë´Ø¿ô¦Õ¤òƳÆþ¤·¤Þ¤¹¡£
¥´¡¼¥ë¤Ç¤Ï¦Õ=0¤È¤Ê¤ê¡¤¤½¤ì°Ê³°¤Î¾ì½ê¤Ç¤Ï¼°(5)¤Î¥¢¥¤¥³¥Ê¡¼¥ëÊýÄø¼°¤òËþ¤¿¤·¤Þ¤¹¡£
¤½¤ì¤Ç¡¤¼°¡Ê5¡Ë¤Ï¡ÖËÜÅö¤ËÀ®¤êΩ¤Ä¤Î¤«¤è¡©¡×¤È»×¤¦¤ï¤±¤Ç¤¹¤¬¡¤ÊÑʬˡ¤ÎÄêÍý¤Ë¤è¤Ã¤Æ¡¤¤Á¤ã¤ó¤ÈÀ®¤êΩ¤Ä¤Î¤¬Êݾ㤵¤ì¤Æ¤¤¤ë¤è¤¦¤Ç¤¹¡£
¤Á¤Ê¤ß¤Ë¡¤»²¹Íʸ¸¥¤Ï
KIMMEL, R., AND SETHIAN, J. A. 2001. Optimal Algorithms for Shape from Shading and Path Planning. Journal of Mathematical Imaging and Vision 14, 237–244.
¤Ë¤Ê¤Ã¤Æ¤¤¤Þ¤¹¡£

¤Ç¡¤Ã±°Ì¥³¥¹¥È¾ìC¤Ï¥¹¥Ô¡¼¥É¾ìf¤ÈÉÔ²÷¾ìg¤¬·è¤Þ¤ì¤Ðµá¤Þ¤ê¤Þ¤¹¡£ÉÔ²÷¾ìg¤Ë¤Ä¤¤¤Æ¤Ï¡¤ÏÀʸÃæ¤Ç¾Ü¤·¤¤ÀâÌÀ¤¬¤Ê¤¤¤Î¤Ç¡¤¤ª¤½¤é¤¯¤³¤ì¤Ï¥æ¡¼¥¶¡¼¤¬Ç¤°Õ¤Ë·è¤á¤Æ¤¤¤¤¤â¤Î¤À¤È»×¤¤¤Þ¤¹¡£¤è¤Ã¤Æ¡¤¤¢¤È¤Ï¥¹¥Ô¡¼¥É¾ìf¤¬·è¤Þ¤ì¤Ð¡¤Ã±°Ì¥³¥¹¥È¾ìC¤¬µá¤Þ¤ê¤Þ¤¹¡£¤Þ¤¿¡¤¥¹¥Ô¡¼¥É¾ìf¤¬µá¤Þ¤ì¤Ð®ÅÙ¤¬µá¤Þ¤ë¤Î¤Ç¡¤¿Í¤òÆ°¤«¤¹Êý¸þ¤â·è¤á¤é¤ì¤½¤¦¤Ç¤¹¡£¤½¤ó¤Ê¤ï¤±¤Ç¡¤Â®ÅÙ¤òµá¤á¤ë¼°¤¬¼°(6)¤ËºÜ¤Ã¤Æ¤¤¤Þ¤¹¡£


¡Ä¤Á¤ç¤Ã¤ÈŤ¯¤Ê¤ê¤½¤¦¤Ê¤Î¤Ç¡¤¼¡²ó¤Ï¥¹¥Ô¡¼¥É¤Ë¤Ä¤¤¤Æ¤Î¤ªÏ䫤é»Ï¤á¤ë¤³¤È¤Ë¤·¤Þ¤¹¡£

Continuum Crowds¤ÎÏÀʸ¤ò¸«¤¿¤Î¤Ç¡¤¼ÂÁõ¤·¤è¤¦¤È»×¤Ã¤¿¤Î¤Ç¤¹¤¬¡¤¤Ê¤«¤Ê¤«ÁȤà»þ´Ö¤¬¤Ê¤¯¤Æ¤ª¤¶¤Ê¤ê¤Ë¤Ê¤Ã¤Æ¤¤¤Þ¤¹¡£
ÏÀʸ¤ò¸«¤¿¤Î¤â¤À¤¤¤ÖÁ°¤Ê¤Î¤Ç¡¤¼ÂÁõ¤¹¤ëºÝ¤Ë˺¤ì¤Ê¤¤¤è¤¦¤Ë¤È¤ê¤¢¤¨¤ºÏÀʸ¤ÎÆâÍƤò¤Þ¤È¤á¤Æ¤ª¤³¤¦¤«¤È»×¤¤¤Þ¤¹¡£
°Ê²¼¤Ï¼«Ê¬¤Ê¤ê¤ÎÍý²ò¤Ê¤Î¤Ç¡Ä
´Ö°ã¤Ã¤Æ¤¤¤ë¤³¤È¤¬¤¢¤ë¤«¤â¤·¤ì¤Ê¤¤¤Î¤Ç¡¤±­Æݤߤˤµ¤ì¤Ê¤¤¤è¤¦¤Ëµ¤¤ò¤Ä¤±¤Æ¤¯¤À¤µ¤¤¡£

Continuum Crowds¤ÏήÂÎÎϳØŪ¤Ë¿Í¤Îή¤ì¤ò¥·¥ß¥å¥ì¡¼¥·¥ç¥ó¤·¤è¤¦¤È¤¤¤¦ÏÀʸ¡£
¿Í¤¬¤¿¤É¤êÃ夯ÌÜŪÃϤò·è¤á¤Æ¤ª¤­¤Þ¤¹¡£¤³¤ì¤Ï¤É¤³¤Ç¤â¤¤¤¤¤è¤¦¤Ç¤¹¡£
¤Ç¡¤ÌÜŪ¤Î¥Ý¥Æ¥ó¥·¥ã¥ëÎ̤ò0¤È¤·¤Æ¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¤¬ºÇ¾¯¤È¤Ê¤ëÊý¸þ¤Ë¿Í¤òÆ°¤«¤¹¤ß¤¿¤¤¤Ç¤¹¡£
¥·¥ß¥å¥ì¡¼¥·¥ç¥ó¼«ÂΤÏ2¼¡¸µ¤Î¥°¥ê¥Ã¥É¤Ë¶èÀڤäƹԤ¤¤Þ¤¹¡£

¥·¥ß¥å¥ì¡¼¥·¥ç¥ó¤Î¤ä¤êÊý¤Ç¤¹¤¬¡¤4Àá¤ÎImplementation¤Ë¼¡¤Îµ¿»÷¥³¡¼¥É¤¬ºÜ¤Ã¤Æ¤¤¤ë¤Î¤Ç¡¤¤½¤³¤«¤éÀâÌÀ¤·¤Þ¤¹¡£

For each timestep:
¡¡¡¡¡¡¡¡¡¦Convert the crowd to a density field.
¡¡¡¡¡¡¡¡For each group:
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¦Construct the unit cost field C.
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¦Construct the potential ¦Õ and it's gradient ¢¦¦Õ.
¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¦Update the people's locations.
¡¡¡¡¡¡¡¡¡¦Enforce the minimum distance between people.

¡¡¤Þ¤º¡¤³Æ¥¿¥¤¥à¥¹¥Æ¥Ã¥×¤Ë´Ø¤·¤Æ¥ë¡¼¥×¤µ¤»¡¤¿Í¤Î·²¤ì¤òÌ©ÅÙ¾ì¤ØÊÑ´¹¤·¤Þ¤¹¡£
¡¡¼¡¤Ë¡¤³Æ¥°¥ë¡¼¥×¤Ë´Ø¤·¤Æ¥ë¡¼¥×¤µ¤»¤Þ¤¹¡£¤³¤Î¥°¥ë¡¼¥×¤È¤¤¤¦¤Î¤Ï3.1Àá¤Ç½ñ¤¤¤Æ¤¢¤ë¡Ö·²½°¤ò¥°¥ë¡¼¥×¤Ëʬ¤±¤ë¡×¤È¤¤¤¦¤È¤³¤í¤Î¥°¥ë¡¼¥×¤Ë¤¢¤¿¤ê¤Þ¤¹¡£¤Ê¤¼¡¤¥°¥ë¡¼¥×¤Ëʬ¤±¤ë¤«¤È¤¤¤¦¤³¤È¤Ç¤¹¤¬¡¤ÏÀʸÃæ¤Î¼°(5)¤Î¥¢¥¤¥³¥Ê¡¼¥ëÊýÄø¼°¤ò²ò¤¯¤È¤³¤í¤¬¡¤¥·¥ß¥å¥ì¡¼¥·¥ç¥ó¤ÎÃæ¤ÇºÇ¤â½Å¤¿¤¤¤Î¤Ç¡¤¤³¤ÎÉé²Ù¤ò¸º¤é¤¹¤¿¤á¤Ëʬ¤±¤ë¤è¤¦¤Ç¤¹¡£
¡¡¼¡¤Ë¡¤¡Öñ°Ì¥³¥¹¥È¾ìC¤ò¹½ÃÛ¤¹¤ë¡×¤È¤¤¤¦½èÍý¤Ç¤¹¤¬¡Ä
¤Þ¤º¡¤¥°¥ê¥Ã¥É¤ò¹½ÃÛ¤·¡¤³Æ¥°¥ê¥Ã¥É¤ËʪÍýÎ̤ò»ý¤¿¤»¤Æ¤ª¤­¤Þ¤¹¡£¶ñÂÎŪ¤Ë¤Ï¡¤ÏÀʸÃæ¤ÎFigure 4(a)¤Ë¼¨¤µ¤ì¤Æ¤¤¤ë¡ÖÉÔ²÷ÎÌ¡¦¥Ý¥Æ¥ó¥·¥ã¥ëÎÌ¡¦Ì©ÅÙÎÌ¡¦¹â¤µÎÌ¡¦Ê¿¶Ñ®Å١פò¥°¥ê¥Ã¥É¥»¥ë¤ÎÃæ¿´¤ËÄêµÁ¤·¤Æ¤ª¤­¡¤¤¢¤ë¥°¥ê¥Ã¥É¡ÊM¡Ë¤«¤éË̤Υ°¥ê¥Ã¥É¡ÊN)¡¤Æî¤Î¥°¥ê¥Ã¥É¡ÊS)¡¤Åì¤Î¥°¥ê¥Ã¥É¡ÊE)¡¤À¾¤Î¥°¥ê¥Ã¥É¡ÊN)¤Ë°ÜÆ°¤¹¤ëºÝ¤Î¥¹¥Ô¡¼¥ÉÎÌ¡Êf)¤È¥³¥¹¥ÈÎÌ(C)¤ò·×»»¤·¤Æ»»½Ð¤·¤Þ¤¹¡£
¡¡¥³¥¹¥È¾ì¤ò¹½ÃÛ¤·¤¿¤é¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¾ì¦Õ¤È¤½¤Î¸ûÇۤǤ¢¤ë¢¦¦Õ¤ò·×»»¤·¤Þ¤¹¡£¤³¤Î½èÍý¤¬½ª¤ï¤ë¤È¡¤¥´¡¼¥ë¤ËÅþÃ夹¤ë¤¿¤á¤Ë¡¤¥Ý¥Æ¥ó¥·¥ã¥ë¤òºÇ¾®¤Ë¤¹¤ë¤¿¤á¤Ë¤Ï¤É¤Î·ÐÏ©¤òÁªÂò¤¹¤ì¤ÐÎɤ¤¤«¤È¤¤¤¦¤Î¤¬Ê¬¤«¤ë¤Î¤Ç¡¤·×»»¤·¤¿·ë²Ì¤«¤é¥Ý¥Æ¥ó¥·¥ã¥ë¤òºÇ¾®¤Ë¤¹¤ë·ÐÏ©¤òÁªÂò¤·¤Æ¡¤¿Í¤òÆ°¤«¤·¤Þ¤¹¡£
¡¡ºÇ¸å¤Ë¡¤¤¢¤ë¾ò·ï¤Î¾ì¹ç¡¤¿Í¤È¿Í¤¬¤Ö¤Ä¤«¤ê¤ä¤¹¤¯¤Ê¤Ã¤Æ¤·¤Þ¤¦¤È¤¤¤¦¤³¤È¤¬¤¢¤ë¤Î¤Ç¡¤¿Í¤È¿Í¤¬¤Ö¤Ä¤«¤ë¤Î¤òÈò¤±¤ë¤¿¤á¤Ë¡¤¿Í¤È¿Í¤Î´Ö¤ÎºÇ¾®µ÷Î¥¤ò¼é¤ë¤è¤¦¤Ë¡¤¶á¤¹¤®¤¿¾ì¹ç¤Ï°ú¤­Î¥¤¹½èÍý¤ò¤·¤Þ¤¹¡£

°Ê¾å¤¬¥·¥ß¥å¥ì¡¼¥·¥ç¥ó¤Î³µÍפǤ¹¡£
¥·¥ß¥å¥ì¡¼¥·¥ç¥ó¤Î¾ÜºÙ¤Ë¤Ä¤¤¤Æ¤Ï¡¤¼¡¤Îµ­»ö¤«¤éÀâÌÀ¤¹¤ëͽÄê¡£