, , . , . . , , , , . , , . . , . , . 5.1. ( 0 45 ), = , . = 0 . = 0 . . 5.1 .
. 5.1. .
. , = 0, = R, (. 5.2). , = 0, == R, . = 0, = R. , .
, : , , . . 5.3 mH, mD, mV. , , . .
mH = |(xi + 1)2 + (yi)2 -R2|
mD = |(xi + 1)2 + (yi -1)2 -R2|
mV = |(xi)2 + (yi -1)2 -R2|
. 5.2. . | .5.3. . |
, , (xi,yi,) , . 5.4.
. 5.4. .
(xi, + 1, i - 1) R2
i = (xi + 1)2 + (yi -1)2 -R2
, , .
i < 0 (xi, + 1, i - 1) , . . 1 2 . 5.4. , (xi, + 1, i), . . mH, (xi, + 1, i - 1), . . mD. 1 :
|
|
= |(xi + 1)2 + (yi)2 -R2| - |(xi + 1)2 + (yi -1)2 -R2|
< 0 , . , > 0, . ,
<= 0 mH (xi, + 1, i - 1)
> 0 mD (xi, + 1, i - 1)
= 0, , .
, , , , 1
(xi + 1)2 + (yi)2 -R2 >= 0
(xi + 1)2 + (yi -1)2 -R2 < 0
(xi, + 1, i - 1) , (xi, + 1, i) - . ,
= (xi + 1)2 + (yi)2 -R2 + (xi + 1)2 + (yi -1)2 -R2
(yi)2 - 2yi + 1
= 2[(xi + 1)2 + (yi -1)2 -R2] + 2yi - 1
i
= 2(i + yi) - 1
.
2 . 5.4 , (xi, + 1, i), . . ,
(xi + 1)2 + (yi)2 -R2 < 0
(xi + 1)2 + (yi -1)2 -R2 < 0
2 (xi, + 1, i) (xi, + 1, i -1) . , < 0, , 1, (xi, + 1, i).
i > 0, (xi, + 1, i -1) , . . 3 4 . 5.4. , (xi, + 1, i -1), (xi,, i -1). , 3 mD mV ,
. . ' = |(xi + 1)2 + (yi -1)2 -R2| - |(xi)2 + (yi -1)2 -R2 |
' < 0 (xi,, i -1) (xi, + 1, i -1). , '> 0 (xi,, i -1). ,
' <= 0 mD (xi +1,, i -1)
'> 0 mV (xi,, i -1)
' = 0, . . , .
' ,
(xi)2 + (yi -1)2 -R2 >= 0
(xi + 1)2 + (yi -1)2 -R2 < 0
3 (xi +1, i -1) , (xi,, i -1) . '
' = (xi +1)2 + (yi -1)2 -R2 + (xi)2 + (yi -1)2 -R2
|
|
(xi)2 2xi + 1
' = 2[(xi +1)2 + (yi -1)2 -R2] - 2xi - 1
i
' = 2(i - xi )- 1
, 4, , (xi, i -1), .
' 4 ,
(xi +1)2 + (yi -1)2 -R2 > 0
(xi)2 + (yi -1)2 -R2 > 0
. , ' > 0 , 3, mV.
5 . 5.4, , (xi,, i -1) , . . i = 0. ,
(xi +1)2 + (yi)2 -R2 > 0
(xi +1)2 + (yi -1)2 -R2 = 0
, > 0 (xi +1, i -1). ':
(xi +1)2 + (yi -1)2 -R2 = 0
(xi +1)2 + (yi -1)2 -R2 < 0
' < 0, (xi +1, i -1). , i = 0 , i < 0 i > 0. :
i < 0
<= 0 (xi +1, i) - mH
> 0 (xi +1, i -1) - mD
i > 0
' <= 0 (xi +1, i -1) - mD
' > 0 (xi, i -1)- mV
i = 0 (xi +1, i -1) - mD
. mH (xi + 1, i). (i + 1). i
xi+1 = xi +1
yi+1 = yi
i+1 = (xi+1 +1)2 + (yi+1 -1)2 -R2 i + 2xi+1+ 1
i mD (xi + 1, i -1) :
xi+1 = xi +1
yi+1 = yi -1
i+1 = i + 2xi+1 - 2yi+1 +2
mV (xi, i -1)
xi+1 = xi
yi+1 = yi -1
i+1 = i - 2yi+1 +1
.
-
xi = 0
yi = R
i =2(1 - R)
= 0
1 Plot (xi, yi
if yi <= then 4
1 2, 4 5, 3
if i < 0 then 2
ifi > 0 then 3
if i= 0 then 20
1 2
2 = 2i+ 2i - 1
if <= 0 then 10
if > 0 then 20
4 5
3 = 2i+ 2i - 1
if <= 0 then 20
if > 0 then 30
mH
10 i = i + 1
i = i+ 2i + 1