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    <p>Using the example, where rectangles are perpendicular to each other and can therefore be presented by four values (two x coordinates and two y coordinates):</p> <pre> 1 2 3 4 5 6 1 +---+---+ | | 2 + A +---+---+ | | B | 3 + + +---+---+ | | | | | 4 +---+---+---+---+ + | | 5 + C + | | 6 +---+---+ </pre> <p>1) collect all the x coordinates (both left and right) into a list, then sort it and remove duplicates</p> <pre>1 3 4 5 6</pre> <p>2) collect all the y coordinates (both top and bottom) into a list, then sort it and remove duplicates</p> <pre>1 2 3 4 6</pre> <p>3) create a 2D array by number of gaps between the unique x coordinates * number of gaps between the unique y coordinates. It only needs to be one bit per cell, so in c++ a vector&lt;bool&gt; with likely give you a very memory-efficient version of this</p> <pre>4 * 4</pre> <p>4) paint all the rectangles into this grid</p> <pre> 1 3 4 5 6 1 +---+ | 1 | 0 0 0 2 +---+---+---+ | 1 | 1 | 1 | 0 3 +---+---+---+---+ | 1 | 1 | 1 | 1 | 4 +---+---+---+---+ 0 0 | 1 | 1 | 6 +---+---+ </pre> <p>5) for each cell in the grid, for each edge, if the cell beside it in that cardinal direction is not painted, draw the boundary line for that edge</p> <hr> <p>In the question, the rectangles are described as being four vectors where each represents a corner. If each rectangle can be at arbitrary and different rotation from others, then the approach I've outlined above won't work. The problem of finding the path around a complex polygon is regularly solved by vector graphics rasterizers, and a good approach to solving the problem is using a library such as Cairo to do the work for you!</p>
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    1. COMy co-worker agreed that this was the best approach for solving my problem.
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