圆形中矩形的最大堆积 [英] Maximum packing of rectangles in a circle

问题描述

我在纳米技术实验室工作，在那里我进行硅片切割. (晶圆锯只能切割平行线)，当然，我们正在努力使切割出的芯片的成品率最大化.所有裸片的大小均相等，可以是矩形或正方形，并且所有裸片都是从圆形晶圆上切割下来的.本质上，我试图将最大的矩形压缩成一个圆形.

I work at a nanotech lab where I do silicon wafer dicing. (The wafer saw cuts only parallel lines) We are, of course, trying to maximize the yield of the die we cut. All the of die will be equal size, either rectangular or square, and the die are all cut from a circular wafer. Essentially, I am trying to pack maximum rectangles into a circle.

我对MATLAB仅有一个非常基本的了解，而对微积分没有一个中等的了解.有什么(相对)简单的方法可以做到这一点，还是我不知所措?

I have only a pretty basic understanding of MATLAB and an intermediate understanding of calculus. Is there any (relatively) simple way to do this, or am I way over my head?

推荐答案

我很着迷于阅读您的问题，因为我为此进行了一个项目以进行数学老师的培训.我也很高兴得知它被认为是一个NP问题，因为我的项目使我得出了相同的结论.

I was fascinated to read your question because I did a project on this for my training as a Mathematics Teacher. I'm also quite pleased to know that it's thought to be an NP-problem, because my project was leading me to the same conclusion.

通过使用基本演算，我计算出最大尺寸的矩形的前几代"，但是它很快变得复杂.

By use of basic calculus, I calculated the first few 'generations' of rectangles of maximum size, but it gets complex quite quickly.

您可以在这里阅读我的项目:

You can read my project here:

Beckett，R. Pi地块:曲线堆积问题.巴斯温泉MEC. 2009年.

Beckett, R. Parcels of Pi: A curve-packing problem. Bath Spa MEC. 2009.

• Pages 1 - 15
• Pages 16 - 30

我希望我的一些发现对您有用或至少有趣.我以为这个想法很可能会应用在计算机纳米技术中.

I hope that some of my findings are useful to you or at least interesting. I thought that the application of this idea would most likely be in computer nano technology.

亲切的问候.

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