Data.Geometry.Point

Documentation

>>> :{
let myVector :: Vector 3 Int
    myVector = v3 1 2 3
    myPoint = Point myVector
:}

A d-dimensional Point

newtype Point d r

A d-dimensional point.

Constructors

Point

Fields

toVec :: Vector d r

Instances

Arity d => Functor (Point d)

Arity d => Foldable (Point d)

Arity d => Traversable (Point d)

Arity d => Affine (Point d)

PointFunctor (Point d)

(Eq r, Arity d) => Eq (Point d r)

(Ord r, Arity d) => Ord (Point d r)

(Show r, Arity d) => Show (Point d r)

(Num r, Arity d, AlwaysTrueDestruct d ((+) 1 d)) => IsTransformable (Point d r)

IsBoxable (Point d r)

IpeWriteText r => IpeWriteText (Point 2 r)

Coordinate r => IpeReadText (Point 2 r)

HasDefaultIpeOut (Point 2 r)

type Diff (Point d) = Vector d

type NumType (Point d r) = r

type Dimension (Point d r) = d

type DefaultIpeOut (Point 2 r) = IpeSymbol

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

Point representing the origin in d dimensions

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

Accessing points

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

Lens to access the vector corresponding to this point.

>>> (point3 1 2 3) ^. vector
Vector3 [1,2,3]
>>> origin & vector .~ v3 1 2 3
Point3 [1,2,3]

unsafeCoord :: Arity d => Int -> Lens' (Point d r) r

Get the coordinate in a given dimension. This operation is unsafe in the sense that no bounds are checked. Consider using coord instead.

>>> point3 1 2 3 ^. unsafeCoord 2
2

coord :: forall proxy i d r. (Index' (i - 1) d, Arity d) => proxy i -> Lens' (Point d r) r

Get the coordinate in a given dimension

>>> point3 1 2 3 ^. coord (C :: C 2)
2
>>> point3 1 2 3 & coord (C :: C 1) .~ 10
Point3 [10,2,3]
>>> point3 1 2 3 & coord (C :: C 3) %~ (+1)
Point3 [1,2,4]

Convenience functions to construct 2 and 3 dimensional points

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

We provide pattern synonyms Point2 and Point3 for 2 and 3 dimensional points. i.e. we can write:

>>> :{
  let
    f              :: Point 2 r -> r
    f (Point2 x y) = x
  in f (point2 1 2)
:}
1

if we want.

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

Similarly, we can write:

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

point2 :: r -> r -> Point 2 r

Construct a 2 dimensional point

>>> point2 1 2
Point2 [1,2]

_point2 :: Point 2 r -> (r, r)

Destruct a 2 dimensional point

>>> _point2 $ point2 1 2
(1,2)

point3 :: r -> r -> r -> Point 3 r

Construct a 3 dimensional point

>>> point3 1 2 3
Point3 [1,2,3]

_point3 :: Point 3 r -> (r, r, r)

Destruct a 3 dimensional point

>>> _point3 $ point3 1 2 3
(1,2,3)

type (<=.) i d = (Index' (i - 1) d, Arity d)

xCoord :: 1 <=. d => Lens' (Point d r) r

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 => Lens' (Point d r) r

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 => Lens' (Point d r) r

Shorthand to access the third coordinate C 3

>>> point3 1 2 3 ^. zCoord
3
>>> point3 1 2 3 & zCoord %~ (+1)
Point3 [1,2,4]

Point Functors

class PointFunctor g where

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

Instances

PointFunctor (Point d)

PointFunctor (Triangle p)

PointFunctor (Box d p)

PointFunctor (LineSegment d p)

PointFunctor (PolyLine d p)

PointFunctor (Polygon t p)

Functions specific to Two Dimensional points

data CCW

Constructors

CCW

CoLinear

CW

Instances

Eq CCW

Show CCW

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

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

sortArround :: (Ord r, Num r) => (Point 2 r :+ p) -> [Point 2 r :+ p] -> [Point 2 r :+ p]

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)

data Quadrant

Quadrants of two dimensional points. in CCW order

Constructors

TopRight

TopLeft

BottomLeft

BottomRight

Instances

Bounded Quadrant

Enum Quadrant

Eq Quadrant

Ord Quadrant

Read Quadrant

Show Quadrant

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

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

Quadrants with respect to the origin

partitionIntoQuadrants :: (Ord r, Arity d, 1 <=. d, 2 <=. 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])

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.

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

Counter clockwise ordering of the points around c. Points are ordered with respect to the positive x-axis. Points nearer to the center come before points further away.

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

Clockwise ordering of the points around c. Points are ordered with respect to the positive x-axis. Points nearer to the center come before points further away.

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

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)

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

Squared Euclidean distance between two points

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

Euclidean distance between two points