把立方体映射为球体

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2016/07/21 21:32
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把立方体映射为球体

翻译自Mapping a Cube to a Sphere

  • 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

上一篇文章: Mapping a Square to a Circle 中, 我开始思考如何从该多维数据集来一个映射

img1

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

在单位球面点。在最后一篇文章中,我使用映射

img2

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Taking the length of the new point gives

以新点的长度了

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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

所以你可以看到,如果 x 或 y 是-1 或 + 1,这个产量与单位长度的向量。所以,从这开始,决定我会从我要是从多维数据集映射到生成长度单位球面点需要能够猜测工作落后

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Which leads to the mapping

这就导致映射

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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.

这尝试收益率一些相当不错的结果。这是该多维数据集和其映射到单位球面上。粗粗的线是的线在那里至少两个组件都是 + 1 或-1。

cubesphere

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And here's another view from inside the sphere

这里是从球体内的另一种视角

sphereInside

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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).

抱歉这篇文章是一个小灯上的理由。我会试着解释这看水平曲线定义的常数 x、 y 和 z,但我会保存,另一天 (也许)。

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引用来自“风吹草不动”的评论

codea编辑器为什么不搞了

Codea编辑器?
2016/07/22 17:18
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codea编辑器为什么不搞了
2016/07/22 16:30
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