I have a bunch of polygons and a coarse uniform grid. I want to implement two different range queries, for a rectangle aligned with the uniform grid: Does the rectangle intersect with any polygon at all? Give me all the polygons which intersect the rectangle. A simple data-structure would be ...

Question: I have problems with sidelobes when computing the convolution of two radially symmetric functions. I wonder whether I should just switch from second order to fourth order and refine the grid aggressively, or whether there are more appropriate methods for computing this convolution. ...