3D向量的哈希值 [英] Hash Value for 3D Vector

问题描述

有没有一种方法可以将3D矢量表示为定数?我的意思是两个具有不同值的向量永远不会具有相同的哈希值.我敢肯定已经有一个问题了，但不幸的是我没有找到它.感谢您的帮助.

Is there a way to represent a 3D Vector as a definite number? I mean that two vectors with different values can't ever have the same hash value. I'm sure there already is a question about this but I haven't found it unfortunately. Thanks for your help.

我知道这种用于2D向量的算法非常好(我认为):(x + y) * (x + y + 1) / 2 + y

I know this algorithm for 2D vectors which is pretty good (I think): (x + y) * (x + y + 1) / 2 + y

推荐答案

请参见鸽子洞原理-用同样的方法，您无法容纳100羽鸽子进入10洞，也无法将3个值唯一地转换为1个值(所有值均相同).必须有重复项.

See the pigeon-hole principle - in the same way you can't fit you can't 100 pigeons into 10 holes, you can't uniquely convert 3 values into 1 value (with all values of the same size). There will have to be duplicates.

现在，如果您的数字位数可以是向量值的3倍，那么问题就变得很简单了:

Now, if you could have a number with 3x as many bits as the vector values, the problem becomes fairly easy:

// convert x, y and z to the range 0-...
x -= minimum possible value
y -= minimum possible value
z -= minimum possible value

mult = maximum possible value + 1
hash = x * mult * mult + y * mult + z

如果您在理解上述内容时遇到困难，请以数值范围为0-99的示例为例.我们将x乘以100*100 = 10000，将y乘以100，因此哈希将是一个十进制值，最多包含6个数字，其中x，y和z都紧随其后彼此，保证不会重叠:

If you're having trouble understanding the above, just take the example of the range of the values being 0-99. We'd multiple x by 100*100 = 10000 and y by 100, so the hash would be a decimal value with (at most) 6 digits with x, y and z all next to each other, guaranteed to not overlap:

x = 12
y = 34
z = 56
hash = 123456

现在，只需更改基数/基数，该想法就可以保持任何最大值.

Now this same idea will hold for any maximum value by just changing the base / radix.

如果某个基数中没有任何重叠，则x，y和z值的每个唯一组合将导致唯一的哈希.

If there isn't any overlap in some base, each unique combination of values of x, y and z will result in a unique hash.

这是迄今为止最简单的方法，尽管它不会产生特别好的 哈希，因此这取决于您要使用的哈希值-可能有一种方法可以唯一地转换此数字到另一个数字，这将是一个很好的哈希值.

This is by far the simplest approach, although it doesn't produce a particularly good hash, so it depends what you want to use it for - there might be a way to uniquely convert this number to another number which will be a good hash.

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