Geom2D

Basic 2 dimensional geometry functions.

Documentation

data Point a

Constructors

Point

Fields

pointX :: !a

pointY :: !a

Instances

Functor Point

Unbox a => Vector Vector (Point a)

Unbox a => MVector MVector (Point a)

Eq a => Eq (Point a)

Show a => Show (Point a)

Unbox a => Unbox (Point a)

Num a => AffineTransform (Point a) a

data MVector s (Point a) = MV_Point (MVector s (a, a))

data Vector (Point a) = V_Point (Vector (a, a))

type DPoint = Point Double

data Transform a

A transformation (x, y) -> (ax + by + c, dx + ey + d)

Constructors

Transform

Fields

xformA :: !a

xformB :: !a

xformC :: !a

xformD :: !a

xformE :: !a

xformF :: !a

Instances

Functor Transform

Eq a => Eq (Transform a)

Show a => Show (Transform a)

Num a => AffineTransform (Transform a) a

data Line a

Constructors

Line (Point a) (Point a)

Instances

Functor Line

Eq a => Eq (Line a)

Show a => Show (Line a)

data Polygon a

Constructors

Polygon [Point a]

Instances

Functor Polygon

Eq a => Eq (Polygon a)

Show a => Show (Polygon a)

Num a => AffineTransform (Polygon a) a

class AffineTransform a b | a -> b where

Methods

transform :: Transform b -> a -> a

Instances

Num a => AffineTransform (Polygon a) a

Num a => AffineTransform (Transform a) a

Num a => AffineTransform (Point a) a

Num a => AffineTransform (CubicBezier a) a

($*) :: AffineTransform a b => Transform b -> a -> a infixr 5

Operator for applying a transformation.

inverse :: (Eq a, Num a, Fractional a) => Transform a -> Maybe (Transform a)

Calculate the inverse of a transformation.

lineEquation :: Floating t => Line t -> (t, t, t)

Return the parameters (a, b, c) for the normalised equation of the line: a*x + b*y + c = 0.

lineDistance :: Floating a => Line a -> Point a -> a

Return the signed distance from a point to the line. If the distance is negative, the point lies to the right of the line

closestPoint :: Fractional a => Line a -> Point a -> Point a

Return the point on the line closest to the given point.

vectorMag :: Floating a => Point a -> a

The lenght of the vector.

vectorAngle :: RealFloat a => Point a -> a

The angle of the vector, in the range (-pi, pi].

dirVector :: Floating a => a -> Point a

The unitvector with the given angle.

normVector :: Floating a => Point a -> Point a

The unit vector with the same direction.

(*^) :: Num a => a -> Point a -> Point a infixl 7

Scale vector by constant.

(^/) :: Fractional a => Point a -> a -> Point a infixl 7

Scale vector by reciprocal of constant.

(^*) :: Num a => Point a -> a -> Point a infixl 7

Scale vector by constant, with the arguments swapped.

(^+^) :: Num a => Point a -> Point a -> Point a infixl 6

Add two vectors.

(^-^) :: Num a => Point a -> Point a -> Point a infixl 6

Subtract two vectors.

(^.^) :: Num a => Point a -> Point a -> a

Dot product of two vectors.

vectorCross :: Num a => Point a -> Point a -> a

Cross product of two vectors.

vectorDistance :: Floating a => Point a -> Point a -> a

Distance between two vectors.

interpolateVector :: Num a => Point a -> Point a -> a -> Point a

Interpolate between two vectors.

rotateScaleVec :: Num a => Point a -> Transform a

Create a transform that rotates by the angle of the given vector and multiplies with the magnitude of the vector.

flipVector :: Num a => Point a -> Point a

reflect the vector over the X-axis.

rotateVec :: Floating a => Point a -> Transform a

Create a transform that rotates by the angle of the given vector with the x-axis

rotate :: Floating s => s -> Transform s

Create a transform that rotates by the given angle (radians).

rotate90L :: Floating s => Transform s

Rotate vector 90 degrees left.

rotate90R :: Floating s => Transform s

Rotate vector 90 degrees right.

translate :: Num a => Point a -> Transform a

Create a transform that translates by the given vector.