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    <p>Yes, as mentioned before, the Douglas-Peucker algorithm is a straightforward way to simplify 2D connected paths. But as you have pointed out, you will need to extend it to the 3D case to properly simplify a GPS track with an inherent time dimension associated with every point. I have done so for a web application of my own using a PHP implementation of Douglas-Peucker.</p> <p>It's easy to extend the algorithm to the 3D case with a little understanding of how the algorithm works. Say you have input path consisting of 26 points labeled A to Z. The simplest version of this path has two points, A and Z, so we start there. Imagine a line segment between A and Z. Now scan through all remaining points B through Y to find the point furthest away from the line segment AZ. Say that point furthest away is J. Then, you scan the points between B and I to find the furthest point from line segment AJ and scan points K through Y to find the point furthest from segment JZ, and so on, until the remaining points all lie within some desired distance threshold. </p> <p>This will require some simple vector operations. Logically, it's the same process in 3D as in 2D. If you find a Douglas-Peucker algorithm implemented in your language, it might have some 2D vector math implemented, and you'll need to extend those to use 3 dimensions.</p> <p>You can find a 3D C++ implementation here: <a href="http://softsurfer.com/Archive/algorithm_0205/algorithm_0205.htm" rel="noreferrer" title="3D Douglas-Peucker in C++">3D Douglas-Peucker in C++</a></p> <p>Your x and y coordinates will probably be in degrees of latitude/longitude, and the z (time) coordinate might be in seconds since the unix epoch. You can resolve this discrepancy by deciding on an appropriate spatial-temporal relationship; let's say you want to view one day of activity over a map area of 1 square mile. Imagining this relationship as a cube of 1 mile by 1 mile by 1 day, you must prescale the time variable. Conversion from degrees to surface distance is non-trivial, but for this case we simplify and say one degree is 60 miles; then one mile is .0167 degrees. One day is 86400 seconds; then to make the units equivalent, our prescale factor for your timestamp is .0167/86400, or about 1/5,000,000.</p> <p>If, say, you want to view the GPS activity within the same 1 square mile map area over 2 days instead, time resolution becomes half as important, so scale it down twice further, to 1/10,000,000. Have fun.</p>
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