具有给定纵横比的树形图
我想创建一个 TreeMap，使用图片来填写树状图矩形。我可以假设所有图片都具有相同的宽度和高度（即长宽比）。因此，我需要一个树形映射算法来创建具有给定比例的矩形，我是否能够将图片放在那里（如果需要，也许可以缩放图片）。
你能推荐一个吗？
I would like to create a TreeMap, using pictures to fill out the treemap rectangles. I can assume that all the pictures have the same width and height (i.e. the aspect ratio). Thus, I need a treemapping algorithm to create the rectangles with a given ratio, do I will be able to put the pictures there (and perhaps scale the pictures if I need).
Could you recommend one ?
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一般来说，解决方案是不可能的 - Albin Sunnanbo 提供了反例证明。假设您的边界矩形与目标矩形具有相同的纵横比，您可以通过将边界矩形缩放为正方形并运行 方形树状图[pdf]算法对其进行处理，然后缩放回矩形。由于方形树状图不能保证完美的正方形，因此您的最终矩形不会具有完美的纵横比，但实际上它可能不会使您的图片扭曲太多。
一个很好的改进是对图片进行接缝雕刻，使它们正确地适应稍微偏离的纵横比矩形；例如，如果您使用它来组装拼贴画，您应该从中获得视觉上令人愉悦的结果。
In general, a solution is not possible - Albin Sunnanbo has provided a proof by counterexample. Assuming your bounding rectangle has the same aspect ratio as your target rectangles, you might be able to get a good-enough solution by scaling the bounding rectangle to be a square, running the squarified treemap[pdf] algorithm over it, and then scaling back to a rectangle. Since the squarified treemap doesn't guarantee perfect squares, your final rectangles will not have a perfect aspect ratio, but in practice it might not distort your pictures too much.
A nice refinement would be to run a seam carving pass over your pictures to fit them properly into the slightly-off aspect-ratio rectangles; if you're using this to assemble a collage, for instance, you should get visually pleasing results out of this.