How to compute the two closest points between two geometries and how this differs from distance computation? What happens when some points are on opposite/antipodal sides of the globe? How can one create equidistant points along a line composed of one or more line segments?

We discuss solutions to those questions highlighting some of the latest developments in Boost Geometry, the library that is currently being used to provide GIS support to MySQL. The implemented algorithms are parameterized by strategies that control the accuracy-efficiency trade-off. The proposed solutions work for 3 different coordinate systems (namely, cartesian, spherical and ellipsoidal) each of which comes with its own advantages and limitations.

We sum up by briefing the plan of future development and a short discussion.