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Move rectangles so they don't overlap

由 南笙酒味 提交于 2019-12-04 04:01:45

You could use a greedy algorithm. It will be far from optimal, but may be "good enough". Here is a sketch:

 1 Sort the rectangles by the x-axis, topmost first. (n log n)
 2 for each rectangle r1, top to bottom
       //check for intersections with the rectangles below it.
       // you only have to check the first few b/c they are sorted 
 3     for every other rectangle r2 that might intersect with it 
 4         if r1 and r2 intersect //this part is easy, see @Jose's answer
 5             left = the amount needed to resolve the collision by moving r2 left
 6             right = the amount needed to resolve the collision by moving r2 right
 7             down = the amount needed to resolve the collision by moving r2 down

 8             move r2 according to the minimum value of (left, right down)
               // (this may create new collisions, they will be resolved in later steps)
 9         end if

10     end
11 end

Note step 8 could create a new collision with a prior rectangle, which wouldn't be resolved properly. Hm. You may need to carry around some metadata about previous rectangles to avoid this. Thinking...

Keep in mind the box model, given any two rectangles you have to calculate the two boxes width and height, adding their respective margins, paddings, and borders (add the left/right of them to detect collision on the x axis, and top/bottom to detect collision on the y axis), then you can calculate the distance between element 1 and 2 adding the result to their respective coordinate position, for example ((positionX2+totalWidth2) - (positionX1+totalWidth1)) to calculate collision along the X axis. If it is negative, they are overlapping. Once you know this, if they won't overlap by moving them, you can move them normally, otherwise you have to subtract the amount of space they are overlapping from the value you want to move them.

Since the environment is a 2D plane, this should be pretty straightforward. With a library such as jQuery would be a joke, but even in plain js is just basic addiction and subtraction.

Assuming the boxes are aligned to the x and y axis as in your comment, first I'd change the representation of each rectangle to 4 points: top, right, bottom, left and store them as points on the rectangle. Second, let's simplify the problem to "Given n rectangles, where is the nearest point where rectangle r can move to so that it doesn't overlap any other rectangles"? That simplifies the problem a great deal, but also should provide a decent solution. Thus, we have our function:

function deOverlapTheHonkOuttaTheRectangle(rectangle, otherRectangles){
    ..
}

Now, each other rectangle will disallow a certain range of motion for the original rectangle. Thus, you calculate all of these disallowed moves. From these, you can calculate the disallow shape that overlaps the origin and each other. For example, lets say rect1 disallows a shift of -3px to 5px right and 4px to 10px up, and rect2 disallows -4px to 1px right and -2px to 5px up. rect1 was not considered until rect2 came along, since that one overlaps the origin and rect1. Starting with rect2, you'd have [[-4, -2],[1,-2],[1,5],[-4,5]]. Figuring in rect1 gives [[-4, -2],[1,-2],[1,4],[5,4],[5,10],[-3,10],[-3,5],[-4,5]] (see image below for clarification). You keep building these up for each overlapping disallowed rectangle. Once you have considered all the rectangles, then you can use a distance formula from the origin to get the smallest distance you can move your rectangle and move it.

Finally, you repeat this process for all remaining rectangles.

标签
javascript
performance
geometry
collision-detection
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