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Minkowski Sum

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Minkowski sum of two arrays

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S=MINKSUM(A,B) produces the Minkowski sum of two sets A and B in Euclidean space, the result being the addition of every element of A to every element of B.
 
[S,D]=MINKSUM(A,B) returns the Minkowski sum S, and also the multiplicity of each element in S.
 
The number of columns represent the dimensionality. An array of M points in N-D space is an MxN array. A vector of 1D values is a column vector.
 
If the sizes of A and B are MAxN and MBxN respectively, then the size of S will be at most (MA*MB)xN
  
    Example:
      A=[1 1; 2 1; 2 2; 1 2]; B=[3 3; 4 3; 4 4; 3 4];
      [S,D]=minksum(A,B);
      plot(A(:,1),A(:,2),'*',B(:,1),B(:,2),'s',S(:,1),S(:,2),'d')
      axis([0 7 0 7])
 

Comments and Ratings (5)

I follow the instruction exactly but I received an error which states that the minksum function is undefined, whats the problem?

Samuel Cole

Alex,
Columns add dimensions, rows add cardinality. You want:

minksum([1;2],[6;7])

ans =

     7
     8
     9

Alex Dytso

Alex Dytso (view profile)

I don't think that your code works.
Try this:

X2=[1 2]
X2 = 1 2
>> X1=[ 6 7]
X1 = 6 7
>> minksum(X1,X2)
ans =7 9

the answer should be 7 8 9

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