It would probably help a lot if you provide a sample data set (data pairs I guees to provide the position and quality values) and an indication of a "good" set of result points.

On the face of it one approach may be to bin the points then select a point for each bin based on a "distance from bin centre" weight and the quality for each point in the bin. That would get the distribution about right by selecting lower quality points as needed to maintain a reasonable distribution.