hgeometry-0.11.0.0: Geometric Algorithms, Data structures, and Data types.

Data.Geometry.Point

Description

$$d$$-dimensional points.

Synopsis

# Documentation

newtype Point d r Source #

A d-dimensional point.

Constructors

 Point FieldstoVec :: Vector d r
Instances

origin :: (Arity d, Num r) => Point d r Source #

Point representing the origin in d dimensions

>>> origin :: Point 4 Int
Point4 [0,0,0,0]


vector :: Lens' (Point d r) (Vector d r) Source #

Lens to access the vector corresponding to this point.

>>> (Point3 1 2 3) ^. vector
Vector3 [1,2,3]
>>> origin & vector .~ Vector3 1 2 3
Point3 [1,2,3]


pointFromList :: Arity d => [r] -> Maybe (Point d r) Source #

Constructs a point from a list of coordinates. The length of the list has to match the dimension exactly.

>>> pointFromList [1,2,3] :: Maybe (Point 3 Int)
Just Point3 [1,2,3]
>>> pointFromList  :: Maybe (Point 3 Int)
Nothing
>>> pointFromList [1,2,3,4] :: Maybe (Point 3 Int)
Nothing


projectPoint :: (Arity i, Arity d, i <= d) => Point d r -> Point i r Source #

Project a point down into a lower dimension.

pattern Point1 :: r -> Point 1 r Source #

We provide pattern synonyms for 1, 2 and 3 dimensional points. i.e. we can write:

>>> :{
  let
f            :: Num r => Point 1 r -> r
f (Point1 x) = x + 1
in f (Point1 1)
:}
2


pattern Point2 :: r -> r -> Point 2 r Source #

Pattern synonym for 2 dimensional points

>>> :{
  let
f              :: Point 2 r -> r
f (Point2 x y) = x
in f (Point2 1 2)
:}
1


pattern Point3 :: r -> r -> r -> Point 3 r Source #

Similarly, we can write:

>>> :{
  let
g                :: Point 3 r -> r
g (Point3 x y z) = z
in g myPoint
:}
3


xCoord :: (1 <= d, Arity d, AsAPoint point) => Lens' (point d r) r Source #

Shorthand to access the first coordinate C 1

>>> Point3 1 2 3 ^. xCoord
1
>>> Point2 1 2 & xCoord .~ 10
Point2 [10,2]


yCoord :: (2 <= d, Arity d, AsAPoint point) => Lens' (point d r) r Source #

Shorthand to access the second coordinate C 2

>>> Point2 1 2 ^. yCoord
2
>>> Point3 1 2 3 & yCoord %~ (+1)
Point3 [1,3,3]


zCoord :: (3 <= d, Arity d, AsAPoint point) => Lens' (point d r) r Source #

Shorthand to access the third coordinate C 3

>>> Point3 1 2 3 ^. zCoord
3
>>> Point3 1 2 3 & zCoord %~ (+1)
Point3 [1,2,4]


class PointFunctor g where Source #

Types that we can transform by mapping a function on each point in the structure

Methods

pmap :: (Point (Dimension (g r)) r -> Point (Dimension (g s)) s) -> g r -> g s Source #

Instances
 Source # Instance detailsDefined in Data.Geometry.Point.Internal Methodspmap :: (Point (Dimension (Point d r)) r -> Point (Dimension (Point d s)) s) -> Point d r -> Point d s Source # Source # Instance detailsDefined in Data.Geometry.Polygon.Convex Methodspmap :: (Point (Dimension (ConvexPolygon p r)) r -> Point (Dimension (ConvexPolygon p s)) s) -> ConvexPolygon p r -> ConvexPolygon p s Source # PointFunctor (Box d p) Source # Instance detailsDefined in Data.Geometry.Box.Internal Methodspmap :: (Point (Dimension (Box d p r)) r -> Point (Dimension (Box d p s)) s) -> Box d p r -> Box d p s Source # Source # Instance detailsDefined in Data.Geometry.LineSegment Methodspmap :: (Point (Dimension (LineSegment d p r)) r -> Point (Dimension (LineSegment d p s)) s) -> LineSegment d p r -> LineSegment d p s Source # PointFunctor (PolyLine d p) Source # Instance detailsDefined in Data.Geometry.PolyLine Methodspmap :: (Point (Dimension (PolyLine d p r)) r -> Point (Dimension (PolyLine d p s)) s) -> PolyLine d p r -> PolyLine d p s Source # Source # Instance detailsDefined in Data.Geometry.BezierSpline Methodspmap :: (Point (Dimension (BezierSpline n d r)) r -> Point (Dimension (BezierSpline n d s)) s) -> BezierSpline n d r -> BezierSpline n d s Source # PointFunctor (Triangle d p) Source # Instance detailsDefined in Data.Geometry.Triangle Methodspmap :: (Point (Dimension (Triangle d p r)) r -> Point (Dimension (Triangle d p s)) s) -> Triangle d p r -> Triangle d p s Source # PointFunctor (Polygon t p) Source # Instance detailsDefined in Data.Geometry.Polygon.Core Methodspmap :: (Point (Dimension (Polygon t p r)) r -> Point (Dimension (Polygon t p s)) s) -> Polygon t p r -> Polygon t p s Source #

data CCW Source #

Data type for expressing the orientation of three points, with the option of allowing Colinearities.

Instances
 Source # Instance details Methods(==) :: CCW -> CCW -> Bool #(/=) :: CCW -> CCW -> Bool # Source # Instance details MethodsshowsPrec :: Int -> CCW -> ShowS #show :: CCW -> String #showList :: [CCW] -> ShowS #

ccw :: (Ord r, Num r) => Point 2 r -> Point 2 r -> Point 2 r -> CCW Source #

Given three points p q and r determine the orientation when going from p to r via q.

ccw' :: (Ord r, Num r) => (Point 2 r :+ a) -> (Point 2 r :+ b) -> (Point 2 r :+ c) -> CCW Source #

Given three points p q and r determine the orientation when going from p to r via q.

pattern CCW :: CCW Source #

pattern CW :: CCW Source #

pattern CoLinear :: CCW Source #

ccwCmpAround :: (Num r, Ord r) => (Point 2 r :+ qc) -> (Point 2 r :+ p) -> (Point 2 r :+ q) -> Ordering Source #

Counter clockwise ordering of the points around c. Points are ordered with respect to the positive x-axis.

cwCmpAround :: (Num r, Ord r) => (Point 2 r :+ qc) -> (Point 2 r :+ p) -> (Point 2 r :+ q) -> Ordering Source #

Clockwise ordering of the points around c. Points are ordered with respect to the positive x-axis.

ccwCmpAroundWith :: (Ord r, Num r) => Vector 2 r -> (Point 2 r :+ c) -> (Point 2 r :+ a) -> (Point 2 r :+ b) -> Ordering Source #

Given a zero vector z, a center c, and two points p and q, compute the ccw ordering of p and q around c with this vector as zero direction.

pre: the points p,q /= c

cwCmpAroundWith :: (Ord r, Num r) => Vector 2 r -> (Point 2 r :+ a) -> (Point 2 r :+ b) -> (Point 2 r :+ c) -> Ordering Source #

Given a zero vector z, a center c, and two points p and q, compute the cw ordering of p and q around c with this vector as zero direction.

pre: the points p,q /= c

sortAround :: (Ord r, Num r) => (Point 2 r :+ q) -> [Point 2 r :+ p] -> [Point 2 r :+ p] Source #

Sort the points arround the given point p in counter clockwise order with respect to the rightward horizontal ray starting from p. If two points q and r are colinear with p, the closest one to p is reported first. running time: O(n log n)

insertIntoCyclicOrder :: (Ord r, Num r) => (Point 2 r :+ q) -> (Point 2 r :+ p) -> CList (Point 2 r :+ p) -> CList (Point 2 r :+ p) Source #

Given a center c, a new point p, and a list of points ps, sorted in counter clockwise order around c. Insert p into the cyclic order. The focus of the returned cyclic list is the new point p.

running time: O(n)

Quadrants of two dimensional points. in CCW order

Constructors

 TopRight TopLeft BottomLeft BottomRight
Instances

quadrantWith :: (Ord r, 1 <= d, 2 <= d, Arity d) => (Point d r :+ q) -> (Point d r :+ p) -> Quadrant Source #

Quadrants around point c; quadrants are closed on their "previous" boundary (i..e the boundary with the previous quadrant in the CCW order), open on next boundary. The origin itself is assigned the topRight quadrant

quadrant :: (Ord r, Num r, 1 <= d, 2 <= d, Arity d) => (Point d r :+ p) -> Quadrant Source #

Quadrants with respect to the origin

partitionIntoQuadrants :: (Ord r, 1 <= d, 2 <= d, Arity d) => (Point d r :+ q) -> [Point d r :+ p] -> ([Point d r :+ p], [Point d r :+ p], [Point d r :+ p], [Point d r :+ p]) Source #

Given a center point c, and a set of points, partition the points into quadrants around c (based on their x and y coordinates). The quadrants are reported in the order topLeft, topRight, bottomLeft, bottomRight. The points are in the same order as they were in the original input lists. Points with the same x-or y coordinate as p, are "rounded" to above.

cmpByDistanceTo :: (Ord r, Num r, Arity d) => (Point d r :+ c) -> (Point d r :+ p) -> (Point d r :+ q) -> Ordering Source #

Compare by distance to the first argument

squaredEuclideanDist :: (Num r, Arity d) => Point d r -> Point d r -> r Source #

Squared Euclidean distance between two points

euclideanDist :: (Floating r, Arity d) => Point d r -> Point d r -> r Source #

Euclidean distance between two points

class AsAPoint p where Source #

Methods

asAPoint :: Lens (p d r) (p d' r') (Point d r) (Point d' r') Source #

Instances
 Source # Instance detailsDefined in Data.Geometry.Point.Class MethodsasAPoint :: Lens (Point d r) (Point d' r') (Point d r) (Point d' r') Source #

coord :: (1 <= i, i <= d, KnownNat i, Arity d, AsAPoint p) => proxy i -> Lens' (p d r) r Source #

unsafeCoord :: (Arity d, AsAPoint p) => Int -> Lens' (p d r) r Source #

vector' :: AsAPoint p => Lens (p d r) (p d r') (Vector d r) (Vector d r') Source #