DeleteCases vs. DeleteDuplicates for removing points within a critical Euclidean distance

Question

I'm attempting to remove all points in an array which are within a Euclidean distance "ThresDist" of one-another. Using the command:

DeleteDuplicates[List, EuclideanDistance[#1, #2] <= ThresDist &];

I can remove one point in a pair of points that fall within a distance "ThresDist" of one-another. However:

DeleteCases[List, EuclideanDistance[#1, #2] <= ThresDist  &];

Fails to work similarly. Is there something wrong with my approach?

Note : I made a typo earlier in writing DeleteCases, and also used a poor variable name. This was sloppy of me.

As for the actual question - how might I best accomplish my goal? I've searched through Mathematica's function directory, and I can't seem to find an appropriate way to prune not just a duplicate point, but all points that fall within a threshold distance of one-another?

Answer 1

You seem to be new around here so I am going to answer this, but others may close it as "a simple mistake."

• D is a reserved (System) Symbol; use d or dist etc. instead.

• DeleteDCases should be DeleteCases.

• DeleteCases looks at each element independently, not pairs of elements as does DeleteDuplicates (when using a custom equivalence function).

• DeleteCases requires a pattern, not a function, for the second argument.

Since you are making a number of mistakes I shall direct you to this massive omnibus collection of instructional resources:

Where can I find examples of good Mathematica programming practice?

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In response to your updated question, specifically:

As for the actual question - how might I best accomplish my goal?

Please see:

• DeleteDuplicates[] does not work as expected on floating point values

• How to remove duplicates from set of machine precision 2D points?

• Intersection for lists of numeric data

Also related:

• Fastest way to calculate matrix of pairwise distances