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 (32)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, pi2 = West, pi = South, 3pi2 = 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