How to do Subtraction on sets?

I have a continuous set (A=[0 , 2pi]) and want to subtract the following sets from it:

B= [0, pi/2];

C=[pi/4, pi];

D=[3pi/2, 7pi/4];

...

In general, I could just build the union of "B, C, ..." and then do the subtraction BUT I have to do this process a lot of times. In other words, the whole process is in a "for loop" and each time some sets need to be subtracted from A (each time the number of sets and their length is not necessarily might change). The initial interval (A) is the same for all the iterations (after each iteration I would get an interval corresponding to that iteration: Answer(i) = A - B(i) - C(i) -...).

I found a function in MATLAB called "setdiff" but it seems to only work on discrete intervals or images (I mean a 2D matrix)!

Is there a similar function for continuous intervals/sets?

Any help would be appreciated,

[Image Analyst]

What's a continuous set? There is no continuous set of numbers in computers. If A is an array, then A has a certain, fixed and finite number of elements with certain definite values, so A must be discrete/digitized, not continuous.

Answer 1

[Image Analyst]

Try this:

A = 0:360;
B = 0 : 60;
C = 45 : 60;
D = 270 : 360;
foundIndexesB = find(ismember(B, A))
foundIndexesC = find(ismember(C, A))
foundIndexesD = find(ismember(D, A))
allFoundIndexes = [foundIndexesB, foundIndexesC, foundIndexesD]
% Get rid of those numbers from A
A(allFoundIndexes) = [];

Note, it only works for integers. Why? See the FAQ: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

[ramin bba]

tnx a lot, it works but with a minor change:

foundIndexesB = find(ismember(A,B))
foundIndexesC = find(ismember(A,C))
foundIndexesD = find(ismember(A,D))

[ramin bba]

I used the method you outlined and it works. However, I am getting this suggestion from MATLAB and was wondering if you could elaborate on it a bit:

"if "A" is an indexed variable, performance can be improved using logical indexing instead of FIND.".

I know what is Logical indexing in general but I do not know how it can be used instead of "find".

tnx in advance

Answer 2

[Roger Stafford]

You might consult these sites:

http://www.mathworks.com/matlabcentral/fileexchange/31753-range-intersection
http://www.mathworks.com/matlabcentral/fileexchange/24254-interval-merging

[ramin bba]

tnx for the answer Roger but the codes do not work. for example, if I have the following:

A=[0 360];

B=[0 60], C=[45 60], D=[270 360];

A-B-C-D=[60 27]

I even tried going one at a time (like below), but no success:

A-B=[60 360];

A-C=[0 45]+[60 360];

A-D=[0 270];

union{(A-B),(A-C),(A-D)}=[60 270];

They gave me though a rough idea of how to approach the problem.

tnx again,