Safe Haskell | None |
---|---|

Language | Haskell2010 |

- newtype Point d r = Point {}
- origin :: (Arity d, Num r) => Point d r
- vector :: Lens' (Point d r) (Vector d r)
- unsafeCoord :: Arity d => Int -> Lens' (Point d r) r
- coord :: forall proxy i d r. (Index' (i - 1) d, Arity d) => proxy i -> Lens' (Point d r) r
- pattern Point2 :: r -> r -> Point 2 r
- pattern Point3 :: r -> r -> r -> Point 3 r
- point2 :: r -> r -> Point 2 r
- _point2 :: Point 2 r -> (r, r)
- point3 :: r -> r -> r -> Point 3 r
- _point3 :: Point 3 r -> (r, r, r)
- type (<=.) i d = (Index' (i - 1) d, Arity d)
- xCoord :: 1 <=. d => Lens' (Point d r) r
- yCoord :: 2 <=. d => Lens' (Point d r) r
- zCoord :: 3 <=. d => Lens' (Point d r) r
- class PointFunctor g where
- data CCW
- ccw :: (Ord r, Num r) => Point 2 r -> Point 2 r -> Point 2 r -> CCW
- sortArround :: (Ord r, Num r) => (Point 2 r :+ p) -> [Point 2 r :+ p] -> [Point 2 r :+ p]
- data Quadrant
- quadrantWith :: (Arity d, Ord r, 1 <=. d, 2 <=. d) => (Point d r :+ q) -> (Point d r :+ p) -> Quadrant
- quadrant :: (Arity d, Ord r, Num r, 1 <=. d, 2 <=. d) => (Point d r :+ p) -> Quadrant
- 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])
- ccwCmpAround :: (Num r, Ord r) => (Point 2 r :+ qc) -> (Point 2 r :+ p) -> (Point 2 r :+ q) -> Ordering
- cwCmpAround :: (Num r, Ord r) => (Point 2 r :+ qc) -> (Point 2 r :+ p) -> (Point 2 r :+ q) -> Ordering
- insertIntoCyclicOrder :: (Ord r, Num r) => (Point 2 r :+ q) -> (Point 2 r :+ p) -> CList (Point 2 r :+ p) -> CList (Point 2 r :+ p)
- squaredEuclideanDist :: (Num r, Arity d) => Point d r -> Point d r -> r
- euclideanDist :: (Floating r, Arity d) => Point d r -> Point d r -> r

# Documentation

`>>>`

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

# A d-dimensional Point

A d-dimensional point.

Arity d => Functor (Point d) Source | |

Arity d => Foldable (Point d) Source | |

Arity d => Traversable (Point d) Source | |

Arity d => Affine (Point d) Source | |

PointFunctor (Point d) Source | |

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

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

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

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

IsBoxable (Point d r) Source | |

IpeWriteText r => IpeWriteText (Point 2 r) Source | |

Coordinate r => IpeReadText (Point 2 r) Source | |

HasDefaultIpeOut (Point 2 r) Source | |

type Diff (Point d) = Vector d Source | |

type NumType (Point d r) = r Source | |

type Dimension (Point d r) = d Source | |

type DefaultIpeOut (Point 2 r) = IpeSymbol Source |

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

Point representing the origin in d dimensions

`>>>`

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

## Accessing points

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

Lens to access the vector corresponding to this point.

`>>>`

Vector3 [1,2,3]`(point3 1 2 3) ^. vector`

`>>>`

Point3 [1,2,3]`origin & vector .~ v3 1 2 3`

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

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

instead.

`>>>`

2`point3 1 2 3 ^. unsafeCoord 2`

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

Get the coordinate in a given dimension

`>>>`

2`point3 1 2 3 ^. coord (C :: C 2)`

`>>>`

Point3 [10,2,3]`point3 1 2 3 & coord (C :: C 1) .~ 10`

`>>>`

Point3 [1,2,4]`point3 1 2 3 & coord (C :: C 3) %~ (+1)`

# Convenience functions to construct 2 and 3 dimensional points

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

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 Source

Similarly, we can write:

`>>>`

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

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

Construct a 3 dimensional point

`>>>`

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

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

Destruct a 3 dimensional point

`>>>`

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

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

Shorthand to access the first coordinate C 1

`>>>`

1`point3 1 2 3 ^. xCoord`

`>>>`

Point2 [10,2]`point2 1 2 & xCoord .~ 10`

yCoord :: 2 <=. d => Lens' (Point d r) r Source

Shorthand to access the second coordinate C 2

`>>>`

2`point2 1 2 ^. yCoord`

`>>>`

Point3 [1,3,3]`point3 1 2 3 & yCoord %~ (+1)`

zCoord :: 3 <=. d => Lens' (Point d r) r Source

Shorthand to access the third coordinate C 3

`>>>`

3`point3 1 2 3 ^. zCoord`

`>>>`

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

# Point Functors

class PointFunctor g where Source

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

PointFunctor (Point d) Source | |

PointFunctor (Triangle p) Source | |

PointFunctor (Box d p) Source | |

PointFunctor (LineSegment d p) Source | |

PointFunctor (PolyLine d p) Source | |

PointFunctor (Polygon t p) Source |

# Functions specific to Two Dimensional points

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.

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

Quadrants of two dimensional points. in CCW order

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

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]) 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.

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. 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 Source

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) 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)