Safe Haskell | Safe-Infered |
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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

- type Distance = Double
- type Heading = Double
- type Speed = Double
- type Vector = (Distance, Heading)
- type Trail a = [a]
- type Circle a = (a, Distance)
- type Arc a = (Circle a, Heading, Heading)
- data Point = Point {}
- pt :: Latitude -> Longitude -> Maybe Double -> Maybe UTCTime -> Point
- north :: Heading
- south :: Heading
- east :: Heading
- west :: Heading
- radiusOfEarth :: Double
- circumferenceOfEarth :: Double
- heading :: Point -> Point -> Heading
- distance :: Point -> Point -> Distance
- speed :: Point -> Point -> Maybe Speed
- getVector :: Point -> Point -> Vector
- addVector :: Vector -> Point -> Point
- interpolate :: Point -> Point -> Double -> Point
- circleIntersectionPoints :: (Point, Distance) -> (Point, Distance) -> Maybe (Point, Point)
- intersectionArcsOf :: [Circle Point] -> [Arc Point]
- maximumDistanceOfArc :: Point -> Arc Point -> Distance
- readGPXFile :: FilePath -> IO (Maybe GPX)
- data AvgMethod c
- = AvgMean
- | AvgHarmonicMean
- | AvgGeometricMean
- | AvgMedian
- | AvgEndPoints
- | AvgMinOf [AvgMethod c]
- | AvgWith ([c] -> Speed)

- data Selected a
- type PointGrouping c = Trail c -> [Selected (Trail c)]
- type TransformGrouping c = [Selected (Trail c)] -> [Selected (Trail c)]
- isSelected :: Selected a -> Bool
- isNotSelected :: Selected a -> Bool
- onSelected :: (a -> b) -> (a -> b) -> Selected a -> b
- selLength :: Selected [a] -> Int
- totalDistance :: [Point] -> Distance
- totalTime :: Trail Point -> NominalDiffTime
- avgSpeeds :: NominalDiffTime -> Trail Point -> [(UTCTime, Speed)]
- slidingAverageSpeed :: AvgMethod Point -> NominalDiffTime -> Trail Point -> [(UTCTime, Speed)]
- closestDistance :: Trail Point -> Trail Point -> Maybe Distance
- convexHull :: [Point] -> [Point]
- bezierCurveAt :: [UTCTime] -> Trail Point -> Trail Point
- bezierCurve :: [Selected (Trail Point)] -> Trail Point
- linearTime :: [Point] -> [Point]
- filterPoints :: PointGrouping a -> Trail a -> Trail a
- betweenSpeeds :: Double -> Double -> PointGrouping Point
- restLocations :: Distance -> NominalDiffTime -> PointGrouping Point
- spansTime :: NominalDiffTime -> PointGrouping Point
- everyNPoints :: Int -> PointGrouping a
- intersectionOf :: [PointGrouping Point] -> PointGrouping Point
- invertSelection :: TransformGrouping a
- firstGrouping :: TransformGrouping a
- lastGrouping :: TransformGrouping a
- unionOf :: [PointGrouping Point] -> PointGrouping Point
- refineGrouping :: PointGrouping a -> TransformGrouping a
- (/\) :: [Selected (Trail a)] -> TransformGrouping a
- (\/) :: [Selected (Trail a)] -> TransformGrouping a
- smoothRests :: Trail Point -> Trail Point
- smoothTrail :: Trail Point -> Trail Point
- bezierPoint :: [Point] -> Double -> Point

# Types

Angles are expressed in radians from North.
0 == North
pi/2 == West
pi == South
(3*2)pi == East == - (pi * 2)

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)

type Arc a = (Circle a, Heading, Heading)Source

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.

# Constants

radius of the earth in meters

circumferenceOfEarth :: DoubleSource

Circumference of earth (meters)

# Coordinate Functions

heading :: Point -> Point -> HeadingSource

Direction two points aim toward (0 = North, pi*2 = West, pi = South, 3pi*2 = East)

speed :: Point -> Point -> Maybe SpeedSource

Speed in meters per second, only if a `Time`

was recorded for each waypoint.

addVector :: Vector -> Point -> PointSource

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 :: Point -> Point -> Double -> PointSource

`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.

# IO helpers

readGPXFile :: FilePath -> IO (Maybe GPX)

# Types

AvgMean | Obtain the |

AvgHarmonicMean | Obtain the |

AvgGeometricMean | Obtain the |

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) |

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

isSelected :: Selected a -> BoolSource

isNotSelected :: Selected a -> BoolSource

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

# Trail Functions

## Queries

totalDistance :: [Point] -> DistanceSource

Find the total distance traveled

avgSpeeds :: NominalDiffTime -> Trail Point -> [(UTCTime, Speed)]Source

`avgSpeeds n points`

Average speed using a window of up to `n`

seconds and averaging by taking the
Median (`AvgMedian`

).

slidingAverageSpeed :: AvgMethod Point -> NominalDiffTime -> Trail Point -> [(UTCTime, Speed)]Source

`slidingAverageSpeed m n`

Average speed using a moving window of up to `n`

seconds
and an `AvgMethod`

of `m`

.

closestDistance :: Trail Point -> Trail Point -> Maybe DistanceSource

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

bezierCurveAt :: [UTCTime] -> Trail Point -> Trail PointSource

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!

bezierCurve :: [Selected (Trail Point)] -> Trail PointSource

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

betweenSpeeds :: Double -> Double -> PointGrouping PointSource

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)

restLocations :: Distance -> NominalDiffTime -> PointGrouping PointSource

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

spansTime :: NominalDiffTime -> PointGrouping PointSource

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

everyNPoints :: Int -> PointGrouping aSource

chunk the trail into groups of N points

## Group Transformations

intersectionOf :: [PointGrouping Point] -> PointGrouping PointSource

intersects the given groupings

invertSelection :: TransformGrouping aSource

Inverts the selected/nonselected segments

firstGrouping :: TransformGrouping aSource

`firstGrouping f ps`

only the first segment remains `Select`

ed, and only
if it was already selected by `f`

.

lastGrouping :: TransformGrouping aSource

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

)

unionOf :: [PointGrouping Point] -> PointGrouping PointSource

Union all the groupings

refineGrouping :: PointGrouping a -> TransformGrouping aSource

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)

smoothRests :: Trail Point -> Trail PointSource

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.

# Misc

bezierPoint :: [Point] -> Double -> PointSource