Move #09 02 августа 1997

Программирование

algorithm - One useful trick with ^ (an algorithm for the circle).

(C) Tom_HIAL / Ascendancy Cr.L. Grodno


          One useful trick c


    I wonder you ever tried
draw a circle in the codes? Even if so,
agree with me that you have left
feeling that it is, well, if not the trash
(Pre-made sprites), it is still
something wrong ... Namely, in any
more or less decent calculations as air
need a table of squares. And how to do it
each has its own methods ...

    I offer you the following method, and
accurate method: first, it is important to understand that
As, and then apply where deem
necessary. Take a sheet of paper, draw
sign a three-line and At least ten
column (for ease of communication we agree
that line is - s1, s2, s3 ,..., and columns -
t0, t1, t2, t3, t4, t5 ...), then fill
upper (s1) line numbers in ascending order
starting from one end of the line
(1,2,3,4,5 ,...), second (s2) line
fill odd numbers in
ascending order (1,3,5,7,9,11,13 and
etc.). Now we will fill the last
string (s3): to put it in position
(S3, t0) unit, and then for each
subsequent column, run the following
operation: take the number from the third row
previous column, add up the number of
the second row of the current column, the result
written in the third row in the current column
go to the next column, do
such actions for each column ...
Well, why do it? And if you carefully
look at the first and third row of
columns, then do not even need to have seven spans
Balde in to see: in the first row
numbers and their squares in the third ...


        t0 t1 t2 t3 t4

    s1 1 2 3 4 5 ...

    s2 1 3 5 7 9 ...

            / / / /

    s3 April 1 September 16, 1925 ...

I would say more, the second line -
auxiliary, and in the process of settlement
can be generated from the first: take
number from the first row the desired column
multiply it by two (shift left) and
yedinichku defraud. Circles, for example,
such vykruntasah obtained becpodobno.
Even easier to explain I can not. But who
something in my head is, he will find and
better use.

    Well, here today and all. Next
time will tell something more ...

p.s. That you do not @ throw to repay
SH-shke ;-)