Article View: fj.sci.math
Article #14109Re: 2 curves between 2 point
From: Hiroshi Matsuoka
Date: Fri, 26 Mar 1993 06:53
Date: Fri, 26 Mar 1993 06:53
79 lines
4618 bytes
4618 bytes
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In article <MURATA.93Mar26122610@is19e1s08.jaist-east.ac.jp> murata@jaist-east.ac.jp (Hiroshi Murata) writes:
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|$B$=$l$>$l$N6J@~$ON>$H$J$j$NJ*BN(J($B6J@~$+E@(J)$B$H$N5wN%$r$G$-$k$@$1(J
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^^^^^^^^^^^^^
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S1$B$HJRJ}$NE@$H$N5wN%$H(JS2$B$HJLJ}$NE@$N5wN%$J$s$G$7$g$&$+!#(J
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$B$$$1$J$$$s$G$O$J$$$+$H9M$($F!$(J
$B#1$D$N6KC<$J6J@~$H$7$FD>@~$H!$$=$NBP6K$H$7$F1_$r;W$$$D$-$^$7$?!#(J
S1,S2$B$H$bD>@~$N>l9g!$(J
S1$B$O(J[0 1/3]$B$rDL$j(J,S2$B$O(J[0 -1/3]$B$rDL$j!$(JS1//S2$B$G!$$+$D!$(J[0 1][0 -1]$B$N(J
$B@~J,$HJB9T$K$O$J$i$J$$(J
S1 : y = kx + 1/3
S2 : y = kx - 1/3
[0 1]$B"*(JS1, S2$B"*(JS2, S2$B"*(J[0 -1]$B$N5wN%$OEy$7$/(J 2/{3*sqrt(k^2+1)}
S1,S2$B$H$b1_$N>l9g!$(J
S1$B$OH>7B(JR1(R1>=2/3)$B$G(J[0 (R1+1/3)]$B$KCf?4$r;}$A(J([0 1/3]$B$rDL$k(J)$B!$(J
S2$B$OH>7B(JR2(R2>=2/3)$B$G(J[0 -(R2+1/3)]$B$KCf?4$r;}$A(J([0 -1/3]$B$rDL$k(J)$B!$(J
S1: x^2 + {y - (R1+1/3)}^2 = R1^2 (R1 >= 2/3)
S1: x^2 + {y + (R2+1/3)}^2 = R2^2 (R2 >= 2/3)
$B!J$J$*!$(J^2 $B$O<+>h$rI=$7$^$9!K(J
S1$B$,(J[0 1/3] $B$rDL$j!$(J[0 1][0 -1]$B$K?bD>$JD>@~(J y = 1/3 $B$N>l9g!$(JS2$B$O(J
[0 -1/3]$B$rDL$j(J[0 1][0 -1]$B$K?bD>$JD>@~$G;E@Z$i$l$k2<H>J?LL!JD>@~$r4^$`!K(J
y<= -1/3 $B$HH>7B(J2/3$B$G(J[0 -1]$B$rCf?4$H$9$k1_$N1_<~$N30B&NN0h!J1_<~>e$r4^$`!K(J
x^2 + (y+1)^2 >= (2/3)^2 $B$N=E$J$kHO0O$rDL$k6J@~$J$iG$0U!#(J
S1$B$,(J y>= 1/3 $B$H(J x^2 + (y-1)^2 >= (2/3)^2 $B$N=E$J$kNN0h$rDL$kG$0U6J@~$J$i!$(J
S2$B$O(J y=< -1/3 $B$H(J x^2 + (y+1)^2 >= (2/3)^2 $B$N=E$J$kNN0h$rDL$kG$0U6J@~!#(J
$B>e$N#3Nc$N(J[0 1]$B"*(JS1, S2$B"*(JS2, S2$B"*(J[0 -1]$B$N5wN%$O!$>o$K(J
[0 1]$B"*(JS1 $B$O(J[0 1]$B"*(J[0 1/3] = 2/3
S1$B"*(JS2 $B$O(J[0 1/3]$B"*(J[0 -1/3] = 2/3
S2$B"*(J[0 -1] $B$O(J[0 -1/3]$B"*(J[0 -1] = 2/3
$B$H$J$j$^$9!#(J
$BB>$K$b(J
S1$B$H(JS2$B$,F1$87A$r$7$?3+6J@~!JESCf$G%k!<%W$r:n$C$?$j!$L58B1s$GJD$8$?$j(J
$B$7$J$$6J@~$H$G$b2r<a$7$F!K$G!$$+$D!$=E$J$i$J$$$GJB9T$G!$(J[0 1][0 -1]
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$B#S#2$H$9$k$H!$L58B1sE@$GA26a$7$F$$$-5wN%$O#0$K$J$C$F$7$^$$$^$9!#(J
$B=>$C$F$I$l$@$1$:$i$=$&$,#S#1$H#S#2$N5wN%$O#0$H$J$j!$M?$($i$l$?#2E@(J
$B$H$N5wN%$r:GBg$K$9$k$H(JS1$B$O(J[0 +0]$B$rDL$j(JS2$B$O(J[0 -0]$B$rDL$k$J$s$F$3$H$K(J
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$B$3$s$J2r$b$"$j$G$9$+!)(J
|($B9M;!(J)
|N=1 $B$J$i!$(JS1 $B$O(J $BD>@~(J y=0 $B$G$9$h$M!%(J
$BH>7B#1$G(J[0 1]$B$rCf?4$H$9$k1_$N30B&NN0h!J1_<~$r4^$`!K$H(J[0 -1]$B$r(J
$BCf?4$H$9$k1_$N30B&NN0h!J1_<~$r4^$`!K$N6&DLNN0h$rDL$k6J@~$J$i(J
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[ x^2 + (y-1)^2 >= 1 ] and [ x^2 + (y+1)^2 >= 1 ]
|N=3$B$J$i!$BP>N@-$+$i(J S2 $B$OD>@~(J y=0 $B$G!$(JS1 $B$H(J S3 $B$O(J $B>e2<H?E>$NF1$87A$G!$(J
|$B$9$3$77W;;$9$k$H$?$7$+(J $BJ|J*@~(J $B$K$J$j$^$7$?!%(J
S2$B$,(J y=0 $B$J$i(J
S1$B$O(J y>=0.5$B$H(J x^2+(y-1)^2 >= 0.5^2 $B$N6&DLNN0h$NG$0U$N6J@~$G!$(J
S3$B$O(J y=-<0.5$B$H(J x^2+(y+1)^2 >= 0.5^2 $B$N6&DLNN0h$NG$0U$N6J@~!#(J
--
_/ _/ Hiroshi Matsuoka@Canon Inc., R & D Headquaters,
_/ _/_/ _/ _/_/ Imaging Research Center,
_/ _/ _/ _/ _/ _/ Imaging Research Division 1st,
_/_/_/ _/_/_/ _/_/_/ _/_/_/ Imaging Research Department 15th
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<1993Mar26.065338.27108@cau1.crc.canon.co.jp>Path:
arc1-ca.pugleaf.net!sparky!uunet!stanford.edu!sun-barr!sh.wide!cawgw!canongw!cau1!lalaReferences:
<MURATA.93Mar26122610@is19e1s08.jaist-east.ac.jp>Show Full Headers
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X-Google-Language: Japanese,JIS X-Google-Thread: f4956,25620c72d78e4b89 X-Google-Attributes: gidf4956,public X-Google-ArrivalTime: 1993-03-26 16:55:48 PST Path: arc1-ca.pugleaf.net!sparky!uunet!stanford.edu!sun-barr!sh.wide!cawgw!canongw!cau1!lala From: lala@cau1.crc.canon.co.jp (Hiroshi Matsuoka) Newsgroups: fj.sci.math Subject: Re: 2 curves between 2 point Message-ID: <1993Mar26.065338.27108@cau1.crc.canon.co.jp> Date: 26 Mar 93 06:53:38 GMT References: <MURATA.93Mar26122610@is19e1s08.jaist-east.ac.jp> Distribution: fj Organization: Imaging Research Center Atsugi-branch-office, Canon Inc., JAPAN Lines: 79