Question

How to get the co-ordinates of the outline shape formed using smaller grid blocks.

For example, If I used 32×32 unit blocks for construct a shape (any shape).
Then how can I get overall co-ordinates of the shape, including the negative spaces.

For example:
One could arrange the blocks like this:
(each block is 32×32 and coordinates refer to bottom left corner of the block)

Block 1 - (0,0)
BLock 2 - (32,0)
Block 3 - 64,0)
Block 4 - (64,32)
Block 5 - (64, 64)
BLock 6 - (32, 64)
BLock 6 - (0 64)
Block 7 - (0, 32)

Now you can see this will create an empty space in the middle.

So what I would like to know is, how to get the coordinates of the above shape such that I get:

Main Block = (0,0), (96,0), (0,96)
Empty space = (32,32), (64,32), (64,64), (32,64)

Is there any mathematical solution to this?

Eventually I will be doing complex shapes.

thanks

******** edit ****
Hi,

How to deal with this condition?

<------------------^<----^
|                  ||    |
V------------------>|    |
<------^          /^|    |
|      |<------^ / ||    |
|      ||      |/  ||    |
V------>V------>V-->V---->

i would like the result to be like this

<-------------------<----^
|                        |
V      ^----------->     |
|      |          /      |
|      <-------^ /       |
|              |/        |
V------>------->--->----->

Answer 1

Think of each square as an outline comprised of four vectors going in a counter-clockwise chain.

<-----^
|     |
|     |
V----->

So for all the squares in your shape, take the union of their outline vectors. If two outline vectors in the union are identical but go in opposite directions, they cancel each other out and are removed from the union.

For example, for two squares that are side by side the union is 8 vectors

<-----^<-----^
|     ||     |
|     ||     |
V----->V----->

which reduces to 6 vectors because the two vertical vectors in the middle cancel:

<-----<-----^
|           |
|           |
V----->----->

For the example you gave, the result of this will be (after cancellations):

<-----<-----<-----^
|                 |
|                 |
V     ^----->     ^
|     |     |     |
|     |     |     |
V     <-----V     ^
|                 |
|                 |
V----->----->----->

You just have to connect up the vectors in the final reduced union to read off the outline paths. Note that the inner outline (“the hole”) runs clockwise.