Whether a point lies within a rectangle (Fast solution)

I have a large list of points and a large list of rectangles.I want to find the number of points inside each rectangle.I have a working solution which is very TPT heavy.

Is there a faster way of implementing this.

What I am doing now : Assume point P’s coordinate is (xp,yp), and the rectangle’s lower left point is (x1,y1) and upper right point is (x2,y2):if (xp is between x1 and x2) AND (yp is between y1 and y2) then the point(xp,yp) is inside the rectangle.The issue is i have a large set of points (> 20000) and a larger set of rectangles(lets say also > 2000)

Now i can loop over each rectangle to caluclate the the number of points in each

    for ii=1:20000
          ind = Xcord>Rects(ii,1) & Xcord<Rects(ii,3) & Ycord>Rects(ii,2) & Ycord<Rects(ii,4);
          count = sum(ind);
      end

[Guillaume]

Do the rectangles overlap?

Are the coordinates integer or floating point?

[vivek]

The rectangles can overlap and the coordinates are floating point.

Answer 1

[Star Strider]

The inpolygon (and possibly rectint depending on what you want to do) functions will likely make your task easier, although they would not eliminate the loops over the rectangles.

[vivek]

I have already tries inpolygon. I found that it is slower than simple inequality checks like i have shown on the loop above.

[Adam Danz]

* Just FYI, I edited Star Strider's answer to update the links to the two functions. They were from r2014a documentation which no longer exists.

+1

[Star Strider]

Adam — Thank you!

Answer 2

[Guillaume]

I don't think you'll find a faster way to do it in matlab, short of performing the search in a mex file.

In my limited understanding of this domain , a spatially indexed R-tree would be the way to go. Implementing this in matlab is bound to be difficult with the limited data structures available and probably not that efficient in the end.

Answer 3

[Matt J]

You should partition your field into an NxN chequerboard of 2D bins, say with N=10. Use sort or histc to bin your Rect and XY coordinate data into each square of the chequerboard . Then you don't have to compare all XY coordinates with all Rectangles. You can loop over the chequerboard squares and just compare XY data lying in a given square with rectangle data lying in that square.

[vivek]

A simple example code would be very helpful for the idea mentioned.

Answer 4

[Leonardo Souto Ferreira]

U can accelerate your search using a quadtree for example.

Answer 5

[Hary]

Using index would much faster than row to row comparison if you have less rectangle in comparison to the points you are checking in. Although loop is still needed. For example

For ii.....

index=the whole matrix >=xmin(ii) &...

end