2016/07/21 21:32

# 把立方体映射为球体

• 全程机器翻译, 看看效果如何

After the last post, I got to thinking about how to come up with a mapping from the cube

img1

to the points in the unit sphere. In the last post I used the mapping

img2

Taking the length of the new point gives

img3

So you can see that if x or y are either -1 or +1, this yeilds a vector with unit length. So, beginning with this, I decided that I'd work backward from the guess that if I had a mapping from the cube to the unit sphere, the length of a generated point would need to be

img4

Which leads to the mapping

img5

Trying this out yields some pretty nice results. This is the cube and its mapping onto the unit sphere. The thick lines are lines where at least two of the components are -1 or +1.

cubesphere

And here's another view from inside the sphere

sphereInside

Sorry this post is a little light on justification. I might try to explain this by looking at the level curves defined by constant x, y and z, but I'll save that for another day (maybe).

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codea编辑器为什么不搞了

Codea编辑器?
2016/07/22 17:18

codea编辑器为什么不搞了
2016/07/22 16:30

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