Say, I have 9 circles, each containing a few thousands discrete points (coordinates).
I want to write a matrix where circle 1 points belong to the first row, circle 2 points belong to the second row, etc.
How do I find all possible combinations of such matrix rows, such that:
- all rows still only contain coordinates from their corresponding circles;
- each row only uses one point from its circle at a time (no different point combinations within a row).
Is there a better way to do it rather than having 9 nested loops and appending matrices into a list in which every matrix is a list and each row within a matrix is a list, too?
Thank you!
update: I'll try to make myself clearer.
Say, I have a list, each element of each is a list containing the coordinates in its corresponding circle.
[[x1,y1],[x2,y2],[x3,y3]] = [ [[1,2],[3,4]], [[5,6],[7,8]], [[9,10],[11,12]] ]
where x1, y1 are the coordinates of the points in circle 1. In this case there are only 3 circles and each of them contains only 2 points.
Now I want to make a matrix where rows correspond to circles, and columns correspond to coordinates (column 1 is x, column 2 is y).
I want all possible combinations of points, so that I get matrices like these:
possibility 1: [[1,2], [5,6], [9,10]]
possibility 2: [[3,4], [7,8], [11,12]]
possibility 3: [[1,2], [7,8], [9,10]]
possibility 4: [[3,4], [5,6], [11,12]]
etc.
Note that row n always corresponds to circle n. How do I find all possible matrix combinations of this form?
(In reality I need to solve a linear programming problem in spherical coordinates, but I hope I simplified the problem well enough. I could draw a picture if you'd like)
