| Copyright | (C) Frank Staals |
|---|---|
| License | see the LICENSE file |
| Maintainer | Frank Staals |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.Geometry.Point
Description
\(d\)-dimensional points.
Synopsis
- newtype Point d r = Point {}
- origin :: (Arity d, Num r) => Point d r
- vector :: Lens' (Point d r) (Vector d r)
- pointFromList :: Arity d => [r] -> Maybe (Point d r)
- projectPoint :: (Arity i, Arity d, i <= d) => Point d r -> Point i r
- pattern Point1 :: r -> Point 1 r
- pattern Point2 :: r -> r -> Point 2 r
- pattern Point3 :: r -> r -> r -> Point 3 r
- xCoord :: (1 <= d, Arity d, AsAPoint point) => Lens' (point d r) r
- yCoord :: (2 <= d, Arity d, AsAPoint point) => Lens' (point d r) r
- zCoord :: (3 <= d, Arity d, AsAPoint point) => 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
- ccw' :: (Ord r, Num r) => (Point 2 r :+ a) -> (Point 2 r :+ b) -> (Point 2 r :+ c) -> CCW
- pattern CCW :: CCW
- pattern CW :: CCW
- pattern CoLinear :: CCW
- 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
- ccwCmpAroundWith :: (Ord r, Num r) => Vector 2 r -> (Point 2 r :+ c) -> (Point 2 r :+ a) -> (Point 2 r :+ b) -> Ordering
- cwCmpAroundWith :: (Ord r, Num r) => Vector 2 r -> (Point 2 r :+ a) -> (Point 2 r :+ b) -> (Point 2 r :+ c) -> Ordering
- sortAround :: (Ord r, Num r) => (Point 2 r :+ q) -> [Point 2 r :+ p] -> [Point 2 r :+ p]
- insertIntoCyclicOrder :: (Ord r, Num r) => (Point 2 r :+ q) -> (Point 2 r :+ p) -> CList (Point 2 r :+ p) -> CList (Point 2 r :+ p)
- data Quadrant
- quadrantWith :: (Ord r, 1 <= d, 2 <= d, Arity d) => (Point d r :+ q) -> (Point d r :+ p) -> Quadrant
- quadrant :: (Ord r, Num r, 1 <= d, 2 <= d, Arity d) => (Point d r :+ p) -> Quadrant
- 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])
- cmpByDistanceTo :: (Ord r, Num r, Arity d) => (Point d r :+ c) -> (Point d r :+ p) -> (Point d r :+ q) -> Ordering
- squaredEuclideanDist :: (Num r, Arity d) => Point d r -> Point d r -> r
- euclideanDist :: (Floating r, Arity d) => Point d r -> Point d r -> r
- class AsAPoint p where
- coord :: (1 <= i, i <= d, KnownNat i, Arity d, AsAPoint p) => proxy i -> Lens' (p d r) r
- unsafeCoord :: (Arity d, AsAPoint p) => Int -> Lens' (p d r) r
- vector' :: AsAPoint p => Lens (p d r) (p d r') (Vector d r) (Vector d r')
Documentation
A d-dimensional point.
Instances
origin :: (Arity d, Num r) => Point d r Source #
Point representing the origin in d dimensions
>>>origin :: Point 4 IntPoint4 [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) ^. vectorVector3 [1,2,3]>>>origin & vector .~ Vector3 1 2 3Point3 [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 [1] :: 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 ^. xCoord1>>>Point2 1 2 & xCoord .~ 10Point2 [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 ^. yCoord2>>>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 ^. zCoord3>>>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
Instances
| PointFunctor (Point d) Source # | |
| PointFunctor (ConvexPolygon p) Source # | |
Defined in Data.Geometry.Polygon.Convex Methods pmap :: (Point (Dimension (ConvexPolygon p r)) r -> Point (Dimension (ConvexPolygon p s)) s) -> ConvexPolygon p r -> ConvexPolygon p s Source # | |
| PointFunctor (Box d p) Source # | |
| PointFunctor (LineSegment d p) Source # | |
Defined in Data.Geometry.LineSegment Methods pmap :: (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 # | |
| PointFunctor (BezierSpline n d) Source # | |
Defined in Data.Geometry.BezierSpline Methods pmap :: (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 # | |
| PointFunctor (Polygon t p) Source # | |
Data type for expressing the orientation of three points, with the option of allowing Colinearities.
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.
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
| Bounded Quadrant Source # | |
| Enum Quadrant Source # | |
Defined in Data.Geometry.Point.Quadrants | |
| Eq Quadrant Source # | |
| Ord Quadrant Source # | |
Defined in Data.Geometry.Point.Quadrants | |
| Read Quadrant Source # | |
| Show Quadrant Source # | |
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