StackOverflow2013

Note that there are some explanatory texts on larger screens.

plurals

PO
text
Body
copied!<p>The <a href="http://en.wikipedia.org/wiki/Integral" rel="nofollow">integral</a> of a function is the area bound by the limits, the curve of the function, and the x-axis. Define one side of the rectangle as the x-axis, then find the boundaries for the others. There are plenty of numerical integration libraries around in the language of your choice. </p> <p>EDIT: some difficulties in trying to illustrate in words...</p> <p>Assuming, at least, that the containing rectangle has an area larger than the sum of the areas of the sub-regions; and there is no requirement of a certain order of containment:</p> <ol> <li>Contain the largest sub-region first with edges on the axes.</li> <li>Pick the next smaller sub-region.</li> <li>Create the function (integral) to calculate the free area as seen from each axes.</li> <li>With windows/limits equal to the length on the sub-region's sides (facing the axes), slide these windows along the axes away from the origin.</li> <li>Create the function for finding the free space bounded by the outside arms of the cross formed by the windows as they slide along the axes. Efficiency in the use of space is found in the region where free space is minimal (differentiation).</li> <li>Rotate the sub-region by 90 degrees and repeat from step 3.</li> <li>Place the sub-region in the orientation and location where most efficient.</li> <li>Repeat step 2. Stop when sliding windows report negative </li> </ol> <p>free space for the entire domain (allocated space overlaps the placeholder made by the windows).</p> <p>In theory, this will systematically try to squeeze in sub-regions. Sketch and pseudocode to follow if time permits.</p>

Querying!

Guidance

An individual column

Larger individual text columns get their own page to allow for proper reading.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload