查找矩形的大小以填充区域 [英] Find size of rectangles to fill area

问题描述

我遇到麻烦需要您的帮助:

I got trouble need your help:

我正在开发一个程序，该程序以平铺模式显示n视频(又名视频墙，c列和r行). n是任意的，视频具有相同的大小(W x H)，并且我们具有W / H的比例，墙的大小是固定的，我该如何最好地设置c，r，W和H当n更改时?最佳定义为W和H是最大值，视频会填满墙壁的最大面积.

I'm working on a program that shows n videos in tiling mode (aka, videos wall, c columns and r rows). The n is arbitrary, the videos have same size (W x H) and we have W / H ratio, the size of wall is fixed, how can I get best set of c, r, W and H when n changes? The best set defined as: W and H is maximum values and videos fill maximum area of the wall.

我看过包装问题，但仍然不能解决上面的问题，有人可以帮我吗?非常感谢你！

I have taken a look at Packing Problem but still can't solve my problem above, can someone help me this? Thank you very much!

推荐答案

据我所知，您要在给定Width和Height

As far as I understand, you want to place n rectangles with fixed C=W/H ratio on the wall with given Width and Height

让矩形的高度为h(未知)，宽度为w = C * h

Let rectangle height is h (unknown yet), width is w = C * h

网格的每一行都包含

 nr =  Floor(Width / (C * h))   // rounding down

每个列都包含

nc = Floor(Height / h)

写不等式

n <= nc * nr
n <=  Floor(Width / (C * h)) * Floor(Height / h)

并求解(找到最大可能的h值)以获取未知的h

and solve it (find maximal possible h value) for unknown h

对于参数h的实际值，可能会得到初始近似值:

For real values of parameters h might be found getting initial approximate value:

 h0 = Ceil(Sqrt(Width * Height / (n * C)))

并递减h值，直到不等式变为真

and decrementing h value until inequality becomes true

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