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.
EDIT:
I know this algorithm for 2D vectors which is pretty good (I think): (x + y) * (x + y + 1) / 2 + y
The best approach to get a hash for a vector of floats is to convert it to a string of bytes or characters and calculate a hash on it. An example of this is given using numpy and python in the following answer: Most efficient property to hash for numpy array.
This will work efficiently for large numbers of vectors, but you cannot guarantee that you will not get collisions due to the simple fact of mapping three floats onto an integer. However there are a number of hashing algorithms available in the python hashlib library to choose from, you might need to experiment. An option in C++ is Boost::Hash.
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.
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
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
Now this same idea will hold for any maximum value by just changing the base / radix.
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.
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.
