boostorg/geometry — pull request #89 by awulkiew (2014-07-04 17:13:28+00:00)
Title: feature/projected_point

The initial commits of this PR adds a distance::detail::projected_point_ax strategy returning 2-component Point/Segment distance.

The intention is to use it as a parameter of the Douglas-Peucked simplify() strategy in order to remove unneeded Points based on the parallel and perpendicular distances of the projected Point instead of the default Point/Segment distance.

The ATD (along track distance) is parallel to the Segment and is a distance between Point projected into a line defined by a Segment and the nearest Segment's endpoint. If the projected Point intersects the Segment the ATD is equal to 0.

The XTD (cross track distance) is perpendicular to the Segment and is a distance between input Point and its projection.