A d-dimensional point.

Point representing the origin in d dimensions

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

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]

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

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]

Constructs a point from a list of coordinates

>>> pointFromList [1,2,3] :: Maybe (Point 3 Int)
Just Point3 [1,2,3]

Project a point down into a lower dimension.

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.

Similarly, we can write:

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

Construct a 2 dimensional point

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

Destruct a 2 dimensional point

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

Construct a 3 dimensional point

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

Destruct a 3 dimensional point

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

Shorthand to access the first coordinate C 1

>>> point3 1 2 3 ^. xCoord
1
>>> point2 1 2 & xCoord .~ 10
Point2 [10,2]

Shorthand to access the second coordinate C 2

>>> point2 1 2 ^. yCoord
2
>>> point3 1 2 3 & yCoord %~ (+1)
Point3 [1,3,3]

Shorthand to access the third coordinate C 3

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

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

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

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

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)

Quadrants of two dimensional points. in CCW order

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

Quadrants with respect to the origin

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.

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.

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.

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)

Squared Euclidean distance between two points

Euclidean distance between two points