이것이 왜 필요할까요?
어떤 분이 질문하셨던 문제입니다.
if you want to have this excel file...
https://drive.google.com/file/d/0B0ETb2rCxDW2a2hsQWdYR21zRlU/view?usp=sharing
it's free for your study.
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let me think a ball(unit sphere, r=1)
if you choose random latitudes and random longitudes
it will result in an uneven distribution,
with the density increasing as we get closer to the poles.
So I want make a map.
this will be easy for even a student to understand.
if there is a ball. which r=1
, the circle is as long as 2π
if you choose a point on surface, which has θ in latitudes
the horizontal diameter will be cosθ
and the new circle which the the point will have a length 2πcosθ
if you spread the surface of the ball flat, while maintain the area.
you will get this picture,
this is a identical to cosθ curve actually.
Now choose several points randomly
Point
A is in red which means out of the Ball
Point
B is in blue which means on the surface of the Ball
we will take Point B
and ignore Point A
let me thick, Point
X
if Point X =(x,
y)
you will get this picture.
Can you get latitudes and random longitudes?
it is easy enough, a school test.
x:2πcosy=x’:2π
then
x’=x/cosy
shortly
YOU can get