Distances are expressed in meters

Angles are expressed in radians from North. 0 == North pi/2 == West pi == South (32)pi == East == - (pi 2)

Speed is hard coded as meters per second

Genearlly a circle indicates a known area in which we are searching (so a center point and maximum possible distance from that point)

An arc is represented as a circle, starting heading and ending heading

Track point is a full-fledged representation of all the data available in most GPS loggers. It is possible you don't want all this data and can just made do with coordinates (via Pnt) or a custom derivative.

North is 0 radians

South, being 180 degrees from North, is pi.

East is 270 degrees (3 pi / 2)

West is 90 degrees (pi/2)

radius of the earth in meters

Circumference of earth (meters)

Direction two points aim toward (0 = North, pi2 = West, pi = South, 3pi2 = East)

Speed in meters per second, only if a Time was recorded for each waypoint.

Given a vector and coordinate, computes a new coordinate. Within some epsilon it should hold that if

dest = addVector (dist,heading) start

then

heading == heading start dest

dist    == distance start dest

interpolate c1 c2 w where 0 <= w <= 1 Gives a point on the line between c1 and c2 equal to c1 when w == 0 (weighted linearly toward c2).

Compute the points at which two circles intersect (assumes a flat plain). If the circles do not intersect or are identical then the result is Nothing.

Find the area in which all given circles intersect. The resulting area is described in terms of the bounding arcs. All cirlces must intersect at two points.

When grouping points, lists of points are either marked as Select or NotSelect.

A PointGrouping is a function that selects segments of a trail.

Grouping point _does not_ result in deleted points. It is always true that:

forall g :: PointGrouping c --> concatMap unSelect (g ts) == ts

The purpose of grouping is usually for later processing. Any desire to drop points that didn't meet a particular grouping criteria can be filled with a composition with filter (or directly via filterPoints).

Given a selection of coordinates, transform the selected coordinates in some way (while leaving the non-selected coordinates unaffected).

Find the total distance traveled

avgSpeeds n points Average speed using a window of up to n seconds and averaging by taking the Median (AvgMedian).

slidingAverageSpeed m n Average speed using a moving window of up to n seconds and an AvgMethod of m.

Returns the closest distance between two trails (or Nothing if a trail is empty). Inefficient implementation: O( (n * m) * log (n * m) )

Uses Grahams scan to compute the convex hull of the given points. This operation requires sorting of the points, so don't try it unless you have notably more memory than the list of points will consume.

Construct a bezier curve using the provided trail. Construct a new trail by sampling the given bezier curve at the given times. The current implementation assumes the times of the input coordinates are available and all equal (Ex: all points are 5 seconds apart), the results will be poor if this is not the case!

Interpolate selected points onto a bezier curve. Note this gets exponentially more expensive with the length of the segement being transformed - it is not advisable to perform this operation on trail segements with more than ten points!

Filters out any points that go backward in time (thus must not be valid if this is a trail)

Remove all points that remain NotSelected by the given grouping algorithm.

Groups trail segments into contiguous points within the speed and all others outside of the speed. The "speed" from point p(i) to p(i+1) is associated with p(i) (execpt for the first speed value, which is associated with both the first and second point)

A "rest point" means the coordinates remain within a given distance for at least a particular amount of time.

chunking points into groups spanning at most the given time interval.

chunk the trail into groups of N points

intersects the given groupings

Inverts the selected/nonselected segments

firstGrouping f ps only the first segment remains Selected, and only if it was already selected by f.

Only the last segment, if any, is selected (note: the current implementation is inefficient, using reverse)

Union all the groupings

For every selected group, refine the selection using the second grouping method. This differs from IntersectionOf by restarting the second grouping algorithm at the beginning each group selected by the first algorithm.

Intersection binary operator

Union binary operator

Smooth points with rest areas using a bezierCurve.

Parameters: rest for 1 minute within 30 meters get smoothed in a bezier curve over every 8 points.

Smooth every 7 points using a bezier curve