Documentation

A d-dimensional point.

There are convenience pattern synonyms for 1, 2 and 3 dimensional points.

>>> let f (Point1 x) = x in f (Point1 1)
1
>>> let f (Point2 x y) = x in f (Point2 1 2)
1
>>> let f (Point3 x y z) = z in f (Point3 1 2 3)
3
>>> let f (Point3 x y z) = z in f (Point $ Vector3 1 2 3)
3

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

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

Project a point down into a lower dimension.

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

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

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

Be vary of numerical instability: >>> ccw (Point2 0 0.3) (Point2 1 0.6) (Point2 2 (0.9::Double)) CCW

>>> ccw (Point2 0 0.3) (Point2 1 0.6) (Point2 2 (0.9::Rational))
CoLinear

If you can't use Rational, try SafeDouble instead of Double: >>> ccw (Point2 0 0.3) (Point2 1 0.6) (Point2 2 (0.9::SafeDouble)) CoLinear

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 if the line from p to r via q is straight/colinear.

This is identical to `ccw p q r == CoLinear` but doesn't have the Ord constraint.

CounterClockwise orientation. Also called a left-turn.

Clockwise orientation. Also called a right-turn.

CoLinear orientation. Also called a straight line.

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

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

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

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

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

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

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

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

\( O(n log n) \) 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.

\( O(n log n) \) 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.

\( O(n) \) 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.

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.

Compare by distance to the first argument

Compare by distance to the first argument

Squared Euclidean distance between two points

Euclidean distance between two points

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

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