gps-1.1: For manipulating GPS coordinates and trails.

Geo.Computations

Description

A basic GPS library with calculations for distance and speed along with helper functions for filtering/smoothing trails. All distances are in meters and time is in seconds. Speed is thus meters/second

Synopsis

# Types

type Distance = DoubleSource

Distances are expressed in meters

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

type Speed = DoubleSource

Speed is hard coded as meters per second

type Trail a = [a]Source

type Circle a = (a, Distance)Source

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

data Point

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.

Constructors

 Point FieldspntLat :: Latitude pntLon :: Longitude pntEle :: Maybe DoubleIn meters pntTime :: Maybe UTCTime

Instances

 Eq Point Ord Point Read Point Show Point

pt :: Latitude -> Longitude -> Maybe Double -> Maybe UTCTime -> Point

# Constants

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)

# Coordinate Functions

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).

circleIntersectionPoints :: (Point, Distance) -> (Point, Distance) -> Maybe (Point, Point)Source

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`.

intersectionArcsOf :: [Circle Point] -> [Arc Point]Source

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.

# Types

data AvgMethod c Source

Constructors

 AvgMean Obtain the `mean` of the considered points AvgHarmonicMean Obtain the `harmonicMean` AvgGeometricMean Obtain the `geometricMean` AvgMedian Obtain the median of the considered points AvgEndPoints Compute the speed considering only the given endpoints AvgMinOf [AvgMethod c] Take the minimum of the speeds from the given methods AvgWith ([c] -> Speed)

data Selected a Source

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

Constructors

 Select FieldsunSelect :: a NotSelect FieldsunSelect :: a

Instances

 Functor Selected Eq a => Eq (Selected a) Ord a => Ord (Selected a) Show a => Show (Selected a)

type PointGrouping c = Trail c -> [Selected (Trail c)]Source

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`).

type TransformGrouping c = [Selected (Trail c)] -> [Selected (Trail c)]Source

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

# Utility Functions

onSelected :: (a -> b) -> (a -> b) -> Selected a -> bSource

# Trail Functions

## Queries

totalDistance :: [Point] -> DistanceSource

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) )

convexHull :: [Point] -> [Point]Source

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.

## Transformations

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!

linearTime :: [Point] -> [Point]Source

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

filterPoints :: PointGrouping a -> Trail a -> Trail aSource

Remove all points that remain `NotSelect`ed by the given grouping algorithm.

## Grouping Methods

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

## Group Transformations

intersects the given groupings

Inverts the selected/nonselected segments

`firstGrouping f ps` only the first segment remains `Select`ed, 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.

(/\) :: [Selected (Trail a)] -> TransformGrouping aSource

Intersection binary operator

(\/) :: [Selected (Trail a)] -> TransformGrouping aSource

Union binary operator

## Composite Operations (Higher Level)

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