2D array manipulation
I would like to do array manipulation like the following example.
Rotation 90 degree
a b
c d
becomes
c a
d b
Mathematically, just swap the x and y coordinate and put a - sign with x coordinate like 1,1--> -1,1.
But in terms of array, there is no negative index and starts from 0 so how can i deal with this operation?
Also the operation is accumulated like if i rotate it 4 times then the output is the same as the initial one.
Any hints or help would be appreciated.
Rotation 90 degree
a b
c d
becomes
c a
d b
Mathematically, just swap the x and y coordinate and put a - sign with x coordinate like 1,1--> -1,1.
But in terms of array, there is no negative index and starts from 0 so how can i deal with this operation?
Also the operation is accumulated like if i rotate it 4 times then the output is the same as the initial one.
Any hints or help would be appreciated.
Last edited on
Mathematically, just swap the x and y coordinate |
"Swap x and y" is not "mathematically". Mathematically it is multiplication by rotation matrix. And I am not sure this helps you in rotating big rectangular matrix.
However for arrays things are simpler. Imagine array of size 100*100. Write down coordinates of its corner elements. Then write which coordinates these elements will have after rotation.
This should give you satisfactory clue.
Last edited on
Umm.....i still cannot get what you mean
The corner x and y coordinate originally and after clockwise rotation are
0,0-->0,99
0,99-->99,99
up to this part, swapping and the y coordinate+99
99,99-->99,0
99,0-->0,0
but here swapping and the y coordinate -99
Also in the inner part like array[20][60], follow those equation will output a value which is over 99 or under 0
Can i do in this way?
1.swapping
2.x coordinate - 99
3.x coordinate* -1
The corner x and y coordinate originally and after clockwise rotation are
0,0-->0,99
0,99-->99,99
up to this part, swapping and the y coordinate+99
99,99-->99,0
99,0-->0,0
but here swapping and the y coordinate -99
Also in the inner part like array[20][60], follow those equation will output a value which is over 99 or under 0
Can i do in this way?
1.swapping
2.x coordinate - 99
3.x coordinate* -1
Last edited on
Notice that column { a, c, e, g } converts into row { g, e, c, a }. 'c' is the second character. In the result 'c' is second from end.
Does i convert to "ith from end" by adding or subtracting 99?
Does i convert to "ith from end" by adding or subtracting 99?
Can i do in this way? |
You can simply flip array around horizontal axis and then around main diagonal. But this takes two operations.
0,0-->0,99 0,99-->99,99 up to this part, swapping and the y coordinate+99 99,99-->99,0 99,0-->0,0 but here swapping and the y coordinate -99 |
You are close, though you misscalculate something.
Try represent this as:
xNew = A*xOld + B*yOld + U
yNew = C*xOld + D*yOld + V
where A, B, C, D should be chosen among 1, 0 or -1. Make your numbers fill these formulas correctly. You should get something really simple.
http://en.wikipedia.org/wiki/Rotation_matrix
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