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Integrate lots image

hello and i've been busy for the last couple of weeks with the olc code jam 2020 but i thought i would find the time to squeeze in a quick video and this video is about a rather niche data structure called an integral image conventionally there aren't a lot of uses for integral images but when the circumstances are just right it's a very powerful structure indeed and can significantly reduce the computational complexity of various spatial algorithms now this is a coding quickie video so we'll be going through things at some pace and just because it's been the focus of my week if you stick around to the end there's a little demonstration of my submission to the code jam so let's get started fundamentally integral images or sometimes called summed area tables are a way of calculating the sum of a sub region within a space here i have a 2d space split up into a grid it's a 2d array and for example we could set some of the cells in this grid to be on so let's set these ones shade them in means that these cells are active two together there in total i've shaded in seven cells and so assuming that my cells can only have the values zero or one if i were to sum this entire region the result would be seven and calculating the sum of this region is as trivial as it sounds we would start at the top and we would just iterate through all of the cells counting whenever we hit a cell that's equal to one and if we were interested in some sub-region we would define where that sub-region starts and we would do the same thing we'd start here and we'd iterate through all of the cells in that region and count how many are set to one in a small example such as this that might not seem like much of a problem but let's say our grid was very large indeed suddenly counting through cells individually is quite a time-consuming task and even worse the time that it takes depends on the size of the sub-region you're trying to find the sum of if however we first generated an integral image we could calculate the sum of a region with just four additions and it doesn't matter how large that region is one of the drawbacks to using an integral image is that that computational cost exists when we create the integral image in the first place so they are useful for data sets such as this that don't change very often for example our space here could represent a tile map in a game and the tiles that are shaded are the solid platforms we might want to do some sort of collision check against them i.e fundamentally they don't change thus we can create the integral image map potentially even offline but we only need to create it once...